Studies in Engineering and Technology, Vol. 1, No. 1, February 2014

Editorial Team

Editorial Assistant

Andrew Walter, Redfame Publishing, United States

Editorial Board Members

Abdulrahman F Almarshoud, College of Engineering, Qassim University, Saudi Arabia

Ahmet Can ALTUNIŞIK, Karadeniz Technical University, Civil Engineering Department, Turkey

Alexander Medvedev, Transport and Telecommunication Institute, Latvia

Alexander Pisarevskiy, Bauman Moscow State Technical University, Russian Federation

Alexander Russell, Otto von Guericke University of Magdeburg, Germany

Andrea Amicarelli, RSE, Italy

Giovanni Angrisani, Università degli Studi del Sannio, Italy

Girish Upreti, University of Tennessee, United States

Haiming Wen, University of California, Davis Northwestern University, United States

Hala Abd El Megeed, National Institute for Standards, Egypt

Halil KARAHAN, Civil Engineering Department, Pamukkale University, Turkey

Hassan Ibrahim Shaaban, Prof of Metallurgy, Atomic Energy Authority of Egypt, Egypt

Hossam Adel Zaqoot, Visiting assistant professor at Al-Azhar University-Gaza, Palestinian Territory, Occupied

Hossein Lavvafi, Case Western Reserve University, United States

Isaac Atuahene, University of Tennessee, United States

Kaan Yetilmezsoy, Yildiz Technical University, Turkey

KaiLong Hsiao, Taiwan Shoufu University, Taiwan, Province of China

Kalyanmoy Michigan State University, United States

Lei Kang, University of California at Berkeley, United States

Mahsa Seyyedian Choobi, University of Applied Science and Technology, Iran, Islamic Republic Of

Maibritt Pedersen Zari, Victoria University, New Zealand

Marco A Ruano, Economics Department Universidad Carlos III de Madrid, Spain

Martin Jaeger, Australian College of Kuwait, Kuwait

Pau Redon, Fundación Hospital General de Valencia, Spain

Paul Steskens, Belgian Building Research Institute, Belgium

Quamrul H. Mazumder, University of Michigan-Flint, United States

Roohollah Kalatehjari, Universiti Teknologi Malaysia 81310 Johor, Malaysia

Shahab Bahrami, University of British Columbia, Canada

Simona Rainis, Cirmont-International Research Center for Mountain, Italy

Sivasubramanian V, National Institute of Technology Calicut, India

Sonia Maria Gomez Puente, Eindhoven University of Technology (TU/e) the Netherlands, Netherlands

Sudip Chakraborty, Department of Chemical Engineering and Materials, University of Calabria, Italy

Tangming Yuan, University of York, United Kingdom

Wael A. Salah, Faculty of Engineering, Multimedia University Jalan Multimedia, Selangor, Malaysia

Xiuyu Gao, Wood Group Kenny, United States

Yao Liu, University Malaysia Pahang, Malaysia

Studies in Engineering and Technology

Vol. 1, No. 1; February 2014

ISSN 2330-2038 E-ISSN 2330-2046

Published by Redfame Publishing

URL: http://set.redfame.com

i

Contents

Sewer Networks Optimization Using Cellular Automata

Maryam Rohani, Mohammad Hadi Afshar 1-12

Finding a Common Weight Vector of Data Envelopment Analysis Based upon Bargaining Game

Manabu Sugiyama, Toshiyuki Sueyoshi 13-21

Examples of Mental Mistakes Made by Systems Engineers While Creating Tradeoff Studies

James Bohlman, A. Terry Bahill 22-43

The Valve Timing Optimization of the Diesel Engine Based on Response Surface Methodology

Jun Li, Lei Ji, Yangjiao Xu, Jinli Xie 44-49

Network-based Management on Repairing Tool Kits of Civil Aviation Engineering Maintenance

Xiaoxu Tian, Xinlei Zheng, Ting Wang, Na Li, Haifeng Wang, Fuqing Huang 50-55

Times Semi-Passive RFID Tags with Double Loop Antennas Arranged as a Shifted Gate Stability

Optimization

Ofer Aluf 56-73

Reviewer Acknowledgements

Andrew Walter 74



ISSN 2330-2038 E-ISSN 2330-2046



1

Sewer Networks Optimization Using Cellular Automata

Maryam Rohani1, Mohammad Hadi Afshar

1

1School of Civil Engineering, Iran Univ. of Science and Tech., Tehran, Iran

Correspondence: Maryam Rohani, PhD Student, School of Civil Engineering, Iran Univ. of Science and Tech., Tehran,

Iran. Tel: 98-9123162480. E-mail: [email protected]

Received: October 15, 2013 Accepted: October 27, 2013 Available online: November 7, 2013

doi:10.11114/set.v1i1.237 URL: http://dx.doi.org/10.11114/set.v1i1.237

Abstract

The Hybrid Cellular Automata (HCA) method is used in this paper for the optimal design of sewer network problems

with the fixed layout. The HCA method decomposes the problem into two sub-problems with considering the pipe

diameters and nodal cover depths as decision variables. Two stages are solved iteratively for determining the decision

variables in a manner to minimize the total cost of the sewer network subject to the operational constraints. The HCA

method is used to optimally solve three benchmark examples with different sizes and the results are presented and

compared to those of the existing methods. The results indicate that the HCA method is more efficient and effective

than the alternative methods.

Keywords: Sewer Network, Optimization methods, Cellular Automata, design problem.

1. Introduction

Sewer network systems as a necessary urban infrastructure play an important role in the urban areas. The main objective

of optimal sewer network design problem is minimization of the capital investment on infrastructure whereas ensuring

good performance under specified design criteria. This topic has received considerable attention and different numerical

optimization approaches have been introduced and applied to the optimal design of sewer networks (Afshar, Shahidi,

Rohani, & Sargolzaei, 2011, Afshar & Rohani, 2012). These include the Linear Programming (LP), Non-Linear

Programming (NLP), Dynamic Programming (DP), and Evolutionary Algorithms.

There have been some attempts using the Linear Programming method to solve the problem of sewer network design,

such as Deininger (1970), Dajani and Gemmell (1971), Froise and Burges (1978), and Walters and Templeman (1979).

Gupta, Agarwal, & Khanna (1976), Lemieux, Zech, & Delarue (1976), and Price (1978) applied NLP and Swamee

(2001) used the Lagrange multiplier method to yield optimal sewer network design.

Among these methods, DP is the mostly used method for the optimal design of the sewer networks due to serial features

of these networks. Merrit and Bogan (1973), Mays and Wenzel (1976), Robinson and Labadie (1981), Yen, Cheng, Jun,

Voohees, & Wenzel (1984), and Kulkarni and Khanna (1985) applied DP for the optimal design of wastewater and/or

storm water networks. Although, DP methods are theoretically capable of finding the global optimum solution, but they

suffer from the curse of dimensionality limitation and therefore are not appropriate method for the large scale real-world

sewer networks.

Recently, Evolutionary approaches are being used for the problem due to their simplicity and flexibility for both

continuous and discrete problems without any assumption about the optimization objectives and good results have been

reported using these methods. Heaney, Wright, Sample, Field, & Fan (1999) had used Genetic Algorithm (GA) on

spreadsheet templates to get near-optimal solutions for the optimal design of sewer networks. Liang, Thompson, &

Young (2004) applied GA and Tabu Search (TS) algorithm for the optimal design of sewer networks. Afshar (2007)

proposed the sequential feature of solution construction in the Ant Colony Optimization Algorithm (ACOA) to develop

two partially constrained ACO algorithms for the solution of storm sewer network design problems. Pan and Kao (2009)

had integrated Quadratic Programming (QP) with GA to solve the sewer network optimization problem. The

applicability and efficiency of the GA-QP model were tested and the results indicated that the GA-QP model could

obtain various near optimum design alternatives within an acceptable computational time. Wang and Zhou (2009)

analyzed and compared the performances of GA, Particle Swarm Optimization (PSO) and Ant Colony Algorithms

(ACA) from three aspects of convergence, speed and complexity. It was shown that ACA is superior to other methods

Studies in Engineering and Technology Vol. 1, No. 1; 2014

2

for better convergence and satisfactory speed. Afshar (2010) applied the Continuous Ant Colony Optimization

Algorithm (CACOA) for the optimal design of sewer networks. Yeh, Chu, Chang, & Lin (2011) applied TS and

Simulated Annealing (SA) for the optimization of sewer network problems.

Since the basic theories of Evolutionary Algorithms, emulating the natural optimization process of evolution, are similar

to the natural evolutionary process, they need a big search space in spite of intelligent process, and so they involve high

computational costs and need a large number of iteration and computational efforts to achieve the optimum solutions.

Moreover, they require some free parameters that should be sensitive analyzed for obtaining the optimal solution.

Cellular Automata (CA), a novel optimization algorithm, has recently introduced and attracted much attention and has

been widely applied to some engineering problems.

In this paper, Hybrid CA (HCA) methods are used for the design of sewer network with the fixed layout. In the HCA

methods, the problem is decomposed in two stages solved iteratively to get the results. In the first stage, nodal cover

depths of the network are determined with the fixed values for pipe diameters using a CA method with the nodes

considered as the CA cells and nodal cover depths as cell states. In the second stage, the obtained nodal cover depths in

the first stage are used to calculate the pipe diameters with another CA method. In this stage, the pipes considered as the

CA cells and their diameters as the cell states. Two different updating rules, Continuous and Discrete approaches, are

used for CA updating rule of the second stage depending on the treatment of the pipe diameters. The CA updating rule is

derived by requiring that the network cost is minimized in the neighborhood of each cell. The HCA methods are used to

design three benchmark examples and comparison the results with the existing ones show the efficiency and

effectiveness of the methods to solve the sewer design optimization problems.

2. Cellular Automata

Cellular Automata (CA), a model of self-reproducing system, was conceived by Ulam (1960) and Von Neumann (1966)

and later completed and improved with the work of other researchers like Thatcher (1964), Codd (1968), and Burks

(1972).

CA has a set of identical elements, called cells with finite possible value called cell state. The new states of all cells are

defined simultaneously using an updating rule, which is a function of the previous state of the cell itself and its

neighborhoods.

CA had been used as a simulator in various fields such as computer science, (Wolfram 1988), chemistry (Packard, 1986),

and medical profession (Sentos & Coutinho, 2001). Recently, some research showed that CA can be used as a practical

and efficient optimization engine, which relies on the key properties of: locality of the neighborhoods interactions,

homogeneity of the evolving mechanism, parallelism of the computation, and simplicity of the model structure. CA has

been extensively used as a viable and efficient optimization algorithm for the structural design (Kita & Toyoda, 2000,

Missoum, Gürdal, & Setoodeh, 2005, and Setoodeh, Gürdalb, & Watson, 2006), estimating shortest path (Adamatzky

1996) or trip distribution problems (El Dessouki, Fathi, & Rouphail, 2001), and computer networks (Shuai & Zhao,

2004).

In the early applications in water resource problems, CA was used to produce good initial populations for a GA leading

to improved performance of the GA (Keedwell & khu, 2005, Guo, Keedwell, Walters, & Khu, 2007a). The first use of

CA as a stand-alone optimizer was demonstrated by Guo, Walters, Khu, & Keedwell (2007b) for optimal design of

storm sewer networks based on the simplifying assumption of known slopes. Afshar and Shahidi (2009) were the first to

propose CA with mathematically derived transition rules for the optimal water supply and hydropower operation of a

single reservoir. Later, Afshar et al. (2011) proposed a single stage CA for the optimal design of sewer networks with

fixed layout using the nodal excavation depth as the decision variables of the problem. Afshar and Rohani (2012)

extended the single stage CA method of Afshar et al. (2011) to two stage CA and proposed Hybrid CA, in which nodal

cover depths and pipes diameter were considered as decision variables.

3. Sewer Network Size Optimization

Sewer network system is one of the urban infrastructure systems with huge construction and operation cost and any

attempt to reduce these costs result in considerable saving. A sewer network is an underground system built to convey

waste water to one or more collection points (outfalls).

Optimal sewer network design with a fixed layout aims to find a cost-effective solution by determining the pipes

diameters and slopes which minimizes the capital investment whilst ensuring a good system performance under specific

design criteria. The problem of sewer network design for a fixed network layout, in the absence of pumps and drops,

can be formulated as:

Min Cnetwork =∑Cpl+∑Cmi=∑LlKp(Dl,Xi,Xj)+∑Km(hmk) (1)


3

Subject to:

Vmin≤ Vl≤ Vmax l=1,...,NL (2)

βmin≤ βl≤ βmax l=1,...,NL (3)

Smin≤ Sl≤ Smax l=1,...,NL (4)

Xmin≤ Xk≤ Xmax k=1,...,NN (5)

Dlє D l=1,...,NL (6)

Dl≤ Dl' l=1,...,NL (7)

Where, Cnetwork is the total cost of the network, Cpl is the installation cost of lth

pipe, Cmi is the cost of ith

manhole, NL is

the number of pipes in the network, NN is the number of nodes in the network, Ll is the length of lth

pipe, Kp is the unit

cost of lth

pipe defined as a function of its diameter (Dl) and upstream and downstream nodal cover depth (Xi,Xj), and

Km is the cost of manhole construction as a function of manhole depth (hm).

Equations (2) to (7) represents the constraints of velocity, water-depth ratio, pipe slope, nodal cover depth,

commercially available pipe diameter, and progressive diameter for the sewer network problem, respectively, where, Vl

is the velocity of lth

pipe, βl = yl/Dl, yl is the flow depth of lth

pipe, Sl is the slope of lth

pipe, Xk is the cover depth of kth

node, D is the set of commercially available pipe diameters, l' refers to the set of pipe located downstream of pipe l, and

min, max are the allowable minimum and maximum parameters, respectively.

4. Hybrid Cellular Automata (HCA)

Application of CA to any problem requires that four basic components of the CA method, cell, cell state, neighborhood,

and updating rule, are properly defined. In this paper, pipe diameters and nodal cover depths are chosen as the decision

variables.

The Hybrid Cellular Automata (HCA) formulation requires decomposing the problem into two sub-optimization

problems which are solved iteratively in two stage manners. In the first stage, each node of the sewer network is

regarded as a cell and nodal cover depths are considered as the cell states, which are determined with the fixed values of

pipe diameters. In the second stage, the pipe diameters are calculated by solving a second nonlinear sub-optimization

problem with considering the calculated nodal cover depths from the first stage as fixed values. Two different updating

rules, continuous and discrete, are derived and used depending on the treatment of pipe diameters. In the continuous

approach, the pipe diameters are considered as continuous variables and the corresponding updating rule is derived

mathematically from the original objective function of the problem and followed by a rounding process in which the

continuous pipe diameters calculated are rounded, if required, to find the discrete optimal pipe diameters, while in the

discrete approach, an ad-hoc updating rule is derived based on the discrete nature of pipe diameters. The described two

stage process is iterated until convergence is achieved.

Considering the nodal cover depths, Xk;k=1,…,NN, and pipe diameters, Dl;l=1,…,NL, as the decision variables, these

constraints can be easily applied as box constraints. Using a penalty method for satisfaction of remaining constraints,

the total penalized objective function of the sewer network optimization problem can be defined as follows:

Min C=∑Cpl+∑Cmi+∑(αCSVvl+ αCSVsl+ αCSVβl) (8)

Where, α is the penalty parameters with large enough positive value, and CSVv, CSVs, CSVβ represent the violation

from the constraints of velocity, slope, and water-depth ratio for each pipe, respectively, CSVvl=(1-Vl/Vmin)2+(Vl/Vmax-1)

2,

CSVβl=(1-βl/βmin)2+(βl/βmax-1)

2, CSVsl=(1-sl/smin)

2+(sl/smax-1)

2.

Subject to:

Xmin≤ Xk≤ Xmax k=1,...,NN (9)

Dlє D l=1,...,NL (10)

The process is started with arbitrary sets of pipe diameters and nodal cover depths satisfying the constraints of (9) and

(10).

4.1 First Stage

In the first stage, the nodal cover depths are calculated with the minimization of the following local objective function

over the cell neighborhood (k ) considering the fixed values for the pipe diameters:

Ck=∑(Cpl+αCSVvl+ αCSVsl+ αCSVβl)+Cmk (11)


4

Subject to the box constraints of Xmin≤ Xk≤ Xmax.

Minimization of the local objective function of Equation (11) with respect to the nodal cover depth (Xk) leads to the

nonlinear equations to be solved with the Newton-Raphson method which results in the updated nodal cover depths

defined as:

F(Xk)=∂Ck/∂Xk=0 ∆Xk=-Fk/(∂F/∂X)k│kk

∆Xk=∆Xkkk+1

-∆Xkkk

(12)

Where, Fkkk

=F(Xkkk

), kk is the nonlinear iteration index, and ∆Xk is the change in the value of the cell state. Fk and

(∂F/∂X)k are both implicit functions of the Xk which can be calculated using the chain rule of differentiation and

Manning equation. This procedure is repeated for the cell under consideration until the convergence is met and the

process of updating is repeated for all cells of the network at the end of which the first stage is terminated.

4.2 Second Stage

In the second stage, the values of nodal cover depths obtained in the first stage are used to get the optimal pipe

diameters. Two CA approaches are applied to solve this problem, in which the pipes and corresponding diameters are

considered as the CA cell and cell state, respectively. The neighborhood of the CA is simply considered as the cell itself

without any neighboring cells.

4.2.1 Discrete Approach

In discrete method, the pipe diameters are treated as discrete values leading to an ad-hoc CA updating rule derived

based on engineering judgment. The diameter of each pipe is changed such that the pipe cost is minimized in a manner

to satisfy the constraints of velocity and water depth ratio. The following three engineering based ad-hoc updating rule

is used to update the cell state:

1) If constraints of velocity and water-depth ratio are all satisfied, pipe diameter is decreased to the lower diameter

available to minimize the objective function.

2) If one or both of the maximum velocity and water-depth ratio constraints are violated, the pipe diameter is increased

to the upper diameter available.

3) If one or both of the minimum velocity and water-depth ratio constraints are violated, the pipe diameter is decreased

to the lower diameter available.

4.2.2 Continuous Approach

In continuous method, the updating rule is derived mathematically assuming pipe diameter as continuous variable

followed by a rounding procedure to convert the continuous solutions to discrete available diameters such that the

following localized objective function is minimized:

Minimize Cl=Cpl+αCSVvl+αCSVβl+Cmi+Cmj (13)

Subject to the box constraints of:

Dmin≤ Dl≤ Dmax (14)

Where i and j refer to the upstream and downstream node of lth

pipe, Dmin and Dmax represent the minimum and

maximum components of available commercial diameters, respectively. The updating rule is derived mathematically by

requiring that the objective function of Equation (13) is stationary with respect to the cell state with applying the

Newton-Raphson linearization:

Gl=∂Cl/∂Dl=0 ∆Dl=-Gl/(∂G/∂D)l ∆Dl=∆Dlkk+1

-∆Dlkk

(15)

This procedure is repeated for the cell under consideration until the convergence is met. Once the process of updating of

all cell states are completed, the continuous diameters so calculated are rounded to the upper discrete diameters

available before returning to the first stage. More details of the method can be found in the work of Afshar and Rohani

(2012).


5

Figure 1. Schematic description of the HCA method.

A schematic description of the HCA method is illustrated in Figure 1 for both discrete and continuous versions in which

the cells, cell states, neighborhood and the updating rules are briefly described for more clarification.

5. Test Examples

The performance of the HCA method is investigated in this section by applying the model to three design problems with

different sizes in the literature. These hypothetical test examples were previously proposed and used by Moeini and

Afshar (2012 a,b) for the simultaneous layout and size optimization of sewer network using ACOA based methods.

First Stage:

Cells: Network nodes

Cell state: nodal cover depths

Neighborhood: Neighboring pipes

i=1

kk=1 kk=kk+1

i=i+1

If k=NN

Yes

Update the nodal cover

depths, Xk, using Eq. 12

∆Xk<ε No

Yes

No

Second Stage

Cells: Network pipes

Cell state: Diameter

Neighborhood: Null

l=1 l=l+1

Update the pipe diameter,

Dl, using steps 1-3 in

section 4.2.1

Discrete CA Continuous CA

Update the pipe diameter, Dl

∆Dl<ε

Finish

Convergence is met?

Yes

If l=NL

kk=kk+1

Yes

No

Yes

kk=1

No

No

Start with random nodal cover depths, Xk;k=1,…,NN,

and pipe diameters, Dl;l=1,…,NL


6

Figure 2. Network layouts for three examples: a) small scale sewer network, b) medium scale sewer network, c) large

scale sewer network.

The optimal layouts obtained by Moeini and Afshar (2012 b), shown in Figure 2, is used here to assess the efficiency

and effectiveness of the CA and HCA method. The small scale sewer network consists of 9 nodes and 12 pipes, the

medium scale sewer network has 25 nodes and 40 pipes and the large scale sewer network includes 81 nodes and 144

pipes. All the networks have two treatment plants with fixed elevation located at the bottom corner of the sewer network.

(c)

[144] [143] [142]

67

[33]

17

[16] [9] [10] [11] [12] [15] [17]

[32]

[49]

24

[136]

[137] 73 74 [138] 75 [139] 76 [140] [141]

[132]

77

[133]

78 79

[134] [135]

80 81

72 71 [127] [126] 70

[128] [129] [130] [131]

69 [125] 68 [124] [123] 66 [122] 65 [121] 64 [120]

[117] [118] [119] [116] [115] [114] [113] [112] [111]

[103] 55

0

56 [104] 57 [105] 58 [106] 59 [107] 60 [108] 61 [109] 62 [110] 63

[102]

54 [93] 53

[101] [100]

[92] 52

[94] [95] [96] [97] [98] [99]

46 [86] 47 [87] 48 [88] 49 [89] 50 [90] 51 [91]

[85]

[76]

[84] [83] [82] [81] [80] [79] [78] [77]

37 [69] 38 [70] 39 [71] 40 [72] 41 [73] 42 [74] 43 [75] 44 45

[68] [67] [66]

W.T.P

8 [8] 9 7 [7] 6

[23] [24]

[65] [64] [60]

28 [52]

[61] [62] [63]

29 [53] 30 [54] 31

[55] 32 [56] 33

[57] 34 [58] 35 [59] 36

26

[50]

[42] 27

[51] [47] [48]

25 [41] [40] 23 [39]

[43] [44] [45] [46]

[38] 22 [37] 21 19 [35] 20 [36]

[26]

10 [18]

[27] [28] [29] [30]

[25] 18

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16 15

[31]

14 [22] 12 [20] 11 [19]

[6]

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13 [21]

1 2 3 [2] [1] [3] [5] 5 4 [4]

(a)

W.T.P W.T.P

[2] [1]

[3] [4] [5]

[7] [6]

[12] [11]

[8] [9] [10]

1

2

3

4 6 5

7 9 8

(b) W.T.P W.T.P

[2] [1] [4] [3]

[5] [6] [7] [8] [9]

[11] [10] [13] [12]

[20] [19] [22] [21]

[29] [28] [31] [30]

[14] [15] [16] [17] [18]

[23] [24] [25] [26] [27]

[32] [33] [34] [35] [36]

1 3 2 4 5

6 8 7 9 10

11 13 12 14 15

16 18 19 20

21 23 22 24 25

17

[40] [39] [38] [37]

W.T.P


7

The ground elevation of a reference point located at the middle of the upper edge of the area denoted by node 8, 23 and

77 in small, medium and large scale networks, respectively, is considered 1000 metres. The area is considered to have a

constant slope of 2% from the reference point to the left and right and toward the bottom edge. The lengths of pipes in

three networks are considered as 100 meters and the set of commercially available pipe diameters for all the pipes is

included in the range of 100 mm to 1500 mm with an interval of 50 mm from 100 mm to 1000 mm and an interval of

100 mm from 1000 mm to 1500 mm. The Manning coefficient is considered as 0.015 and the problem is constrained to

a maximum and minimum velocity of 6 m/s and 0.75 m/s, maximum and minimum cover depth of 10 m and 2.5 m, and

maximum and minimum relative flow depth of 0.83 and 0.1, respectively.

The terms of pipe and manhole construction costs are defined as (Moeini and Afshar, 2012 a,b):

Kp=10.93e3.43D

+0.012X1.53

+0.437X1.47

D (16)

Kh=41.46hm

Where, D is the pipe diameter (m), X is the buried depth (m), and hm is the depth of manhole (m).

These test problems are here solved using CA method of Afshar et al. (2011) and HCA methods and the results are

presented and compared with other existing methods.

Table 1. Optimal network cost obtained by different methods

Test Example Model Cost Time (milli second)

small scale network

ACOA-TGA

(Moeini and Afshar, 2012 a) 23467 -

CACOA-TGA

(Moeini and Afshar, 2012 b) 23467 -

CA 23811 1.6

HCA-Discrete 23460 4.7

HCA-Continuous 23513 3.1

medium scale network

ACOA-TGA


CACOA-TGA


CA 88096 14.1


HCA- Continuous 86678 15.6

large scale network

ACOA-TGA


CACOA-TGA


CA 370486 103.1


HCA- Continuous 367436 54.6

Table 1 compares the optimal network costs and the CPU time required by the CA methods introduced here and those of

ACOA-TGA (Moeini and Afshar, 2012 a) and CACOA-TGA (Moeini and Afshar, 2012 b) methods using a 2 MHz

Pentium 4. It can be seen that both HCA methods produce better solutions than CA method in three sewer networks.

Moreover, the HCA methods result in comparable solutions to the ACOA in small scale network, while with increasing

the scale of the problem, the HCA methods produce superior solutions than ACOA. Furthermore, the HCA-discrete

method results in better solution than the existing methods while requiring less than one second CPU time to achieve

the solutions. It should be noted that ACOA needs much more time than CA methods, because of its mechanism and it is

one the population based methods. Since the HCA method requires an initial guess for the decision variables of the

problem, pipe diameters and the nodal cover depths, to start off the solution procedure, a sensitivity analysis is carried

out here to assess the sensitivity of the final solution to the initial guess.


8

Table 2. Maximum, Minimum and Average solution costs over 10 runs

Cost

Test Example Model Minimum Maximum Average Scaled Standard

Deviation

small scale network

ACOA-TGA

(Moeini and Afshar, 2012 a) 23467 23467 23467 0.0000

CACOA-TGA

(Moeini and Afshar, 2012 b) 23467 23467 23467 0.0000

CA 23811 23811 23811 0.0000

HCA-Discrete 23460 23747 23546 0.0059

HCA-Continuous 23513 34064 25798 0.1683

medium scale network

ACOA-TGA


CACOA-TGA


CA 88096 88096 88096 0.0000

HCA-Discrete 85873 86953 86410 0.0052

HCA- Continuous 86678 87786 87397 0.0038

large scale network

ACOA-TGA


CACOA-TGA


CA 370486 370489 370488 0.0000

HCA-Discrete 361685 367131 363894 0.0040

HCA- Continuous 367436 371350 369661 0.0031

Table 2 represents the maximum, minimum and average solution costs over 10 runs using different initial designs along

with the scaled standard deviation of the solutions defined as the ratio of the standard deviation to the average solution.

This table emphasizes on the insensitivity of the CA methods to the initial population.

Table 3. Results obtained from HCA method (discrete) for the small scale sewer network

Cover Depth (m)

Pipe D (mm) Upstream Downstream V (m/s) y/d

1 100 2.50 4.50 1.39 0.57

2 150 2.50 4.50 1.83 0.58

3 200 3.40 4.50 2.04 0.67

4 150 2.50 2.50 1.27 0.56

5 200 2.50 4.50 2.08 0.50

6 150 2.50 3.40 1.67 0.82

7 150 2.50 2.50 1.27 0.56

8 150 2.50 3.40 1.47 0.50

9 150 2.50 2.50 1.27 0.56

10 150 2.50 2.50 1.27 0.56

11 100 2.50 2.50 1.05 0.73

12 100 2.50 2.50 1.05 0.73


9

Table 4. Results obtained from HCA method (discrete) for the medium scale sewer network

Cover Depth (m)

Cover Depth (m)

Pipe D(mm) Upstream Downstream V (m/s) y/d Pipe D(mm) Upstream Downstream V (m/s) y/d

1 200 2.50 4.50 2.18 0.55 21 150 2.50 2.50 1.27 0.56

2 150 2.50 2.50 1.38 0.74 22 150 2.50 2.50 1.27 0.56

3 100 2.50 2.50 1.05 0.73 23 200 2.50 2.50 1.60 0.62

4 150 2.50 4.50 1.94 0.71 24 200 2.50 2.80 1.79 0.75

5 350 3.45 4.50 2.92 0.65 25 150 2.50 3.40 1.67 0.82

6 150 2.50 2.50 1.27 0.56 26 200 2.50 2.50 1.68 0.80

7 150 2.50 2.50 1.27 0.56 27 200 2.50 2.50 1.60 0.62

8 150 2.50 2.50 1.27 0.56 28 150 2.50 2.50 1.27 0.56

9 300 3.17 4.50 2.82 0.73 29 150 2.50 2.50 1.27 0.56

10 300 3.47 3.45 2.19 0.82 30 150 2.50 2.50 1.27 0.56

11 150 2.50 3.47 1.69 0.81 31 150 2.50 2.50 1.27 0.56

12 150 2.50 2.50 1.27 0.56 32 150 2.50 2.50 1.27 0.56

13 250 2.50 3.17 2.26 0.82 33 150 2.50 2.50 1.38 0.74

14 200 2.50 3.45 2.03 0.76 34 150 2.50 2.50 1.27 0.56

15 250 2.80 3.47 2.26 0.82 35 150 2.50 2.50 1.38 0.74

16 150 2.50 2.50 1.27 0.56 36 150 2.50 2.50 1.27 0.56

17 250 2.50 2.50 1.92 0.71 37 100 2.50 2.50 1.05 0.73

18 200 2.50 3.17 1.94 0.79 38 100 2.50 2.50 1.05 0.73

19 150 2.50 2.50 1.27 0.56 39 100 2.50 2.50 1.05 0.73

20 200 3.40 2.80 1.41 0.82 40 100 2.50 2.50 1.05 0.73

Table 5. Results obtained from HCA method (discrete) for the large scale sewer network

Cover Depth (m)

Cover Depth (m)

Pipe D(mm) Upstream Downstream V (m/s) y/d Pipe D(mm) Upstream Downstream V (m/s) y/d

1 350 4.14 4.50 2.59 0.68 73 200 2.50 2.50 1.52 0.53

2 300 3.34 4.14 2.61 0.82

74 200 2.50 3.00 1.88 0.82

3 200 2.50 3.34 1.90 0.62 75 400 3.00 3.17 2.77 0.76

4 150 2.50 2.50 1.38 0.74 76 150 2.50 2.50 1.27 0.56

5 100 2.50 2.50 1.05 0.73

77 250 3.00 2.50 1.69 0.80

6 200 2.50 2.50 1.52 0.53 78 400 4.02 4.37 2.84 0.70

7 200 2.50 2.50 1.68 0.80 79 150 2.50 2.50 1.27 0.56

8 200 2.50 4.50 2.38 0.81 80 150 2.50 2.50 1.27 0.56

9 500 3.93 4.50 3.52 0.82 81 150 2.50 2.50 1.27 0.56

10 150 2.50 4.14 1.60 0.47 82 150 2.50 2.50 1.27 0.56

11 300 3.88 3.34 1.88 0.82 83 350 2.71 3.00 2.62 0.82

12 150 2.50 2.50 1.27 0.56 84 250 2.50 3.17 2.26 0.82

13 150 2.50 2.50 1.27 0.56 85 250 3.00 2.50 1.69 0.80

14 150 2.50 2.50 1.27 0.56 86 150 2.50 3.00 1.39 0.52

15 150 2.50 2.50 1.27 0.56 87 300 2.50 4.02 2.93 0.82

16 150 2.50 2.50 1.27 0.56 88 200 2.50 2.50 1.65 0.70

17 550 3.78 4.50 3.86 0.82 89 150 2.50 2.50 1.27 0.56

18 200 2.50 3.93 2.05 0.58 90 200 2.50 3.00 1.88 0.82

19 150 2.50 2.50 1.27 0.56 91 250 3.00 2.71 1.81 0.82

20 200 2.50 3.88 2.04 0.58 92 150 2.50 2.50 1.27 0.56

21 150 2.50 2.50 1.27 0.56 93 150 2.50 3.00 1.39 0.52

22 150 2.50 3.40 1.67 0.82 94 200 2.50 3.00 1.88 0.82

23 200 3.40 3.89 1.88 0.82 95 250 2.50 4.02 2.41 0.58

24 250 3.89 3.60 1.81 0.82 96 300 2.50 2.50 2.20 0.78

25 550 3.60 3.78 3.43 0.76 97 150 2.50 2.50 1.27 0.56

26 500 3.71 3.93 3.26 0.82 98 200 2.50 2.50 1.65 0.70

27 150 2.50 2.50 1.27 0.56 99 150 2.50 3.00 1.39 0.52

28 200 2.50 3.88 1.77 0.78 100 300 2.5 2.71 2.30 0.74

29 150 2.50 2.50 1.27 0.56 101 250 2.50 2.50 1.92 0.71


10

30 150 2.50 2.50 1.27 0.56 102 200 2.50 3.00 1.88 0.82

31 150 2.50 3.40 1.47 0.50 103 150 2.50 2.50 1.27 0.56

32 150 2.50 3.89 1.56 0.48 104 150 2.50 2.50 1.27 0.56

33 550 4.00 3.60 2.95 0.77 105 200 2.50 2.50 1.65 0.70

34 300 2.50 3.78 2.71 0.64 106 150 2.50 2.50 1.27 0.56

35 500 4.32 3.71 2.59 0.82 107 150 2.50 2.50 1.27 0.56

36 150 2.50 4.32 1.63 0.46 108 250 2.50 2.50 1.92 0.71

37 200 2.50 2.50 1.65 0.70 109 150 2.50 2.50 1.27 0.56

38 150 2.50 2.50 1.27 0.56 110 150 2.50 2.50 1.27 0.56

39 200 2.50 2.50 1.52 0.53 111 200 2.50 2.50 1.60 0.62

40 200 2.50 3.00 1.88 0.82 112 200 2.50 2.50 1.68 0.80

41 250 3.00 4.00 2.31 0.65 113 250 2.50 2.50 1.94 0.76

42 150 2.50 2.50 1.27 0.56 114 150 2.50 2.50 1.27 0.56

43 300 2.50 3.71 2.60 0.58 115 200 2.50 2.50 1.52 0.53

44 500 5.08 4.32 2.44 0.82 116 200 2.50 2.50 1.68 0.80

45 150 2.50 2.50 1.27 0.56 117 200 2.50 2.50 1.68 0.80

46 150 2.50 2.50 1.27 0.56 118 200 2.50 2.50 1.68 0.80

47 150 2.50 2.50 1.27 0.56

119 200 2.50 2.50 1.60 0.62

48 150 2.50 2.50 1.27 0.56 120 150 2.50 2.50 1.27 0.56

49 150 2.50 3.00 1.39 0.52 121 150 2.50 2.50 1.27 0.56

50 450 3.09 4.00 3.48 0.82 122 200 2.50 2.50 1.68 0.80

51 300 2.83 2.50 2.00 0.73 123 150 2.50 2.50 1.27 0.56

52 150 2.50 2.50 1.27 0.56 124 150 2.50 2.50 1.27 0.56

53 200 2.50 5.08 2.54 0.76 125 150 2.50 2.50 1.27 0.56

54 200 2.50 2.50 1.65 0.70 126 150 2.50 2.50 1.27 0.56

55 150 2.50 2.50 1.27 0.56 127 150 2.50 2.50 1.27 0.56

56 150 2.50 3.40 1.67 0.82

128 150 2.50 2.50 1.27 0.56

57 250 3.40 2.50 1.42 0.70 129 150 2.50 2.50 1.38 0.74

58 250 2.50 3.09 2.17 0.68 130 150 2.50 2.50 1.38 0.74

59 150 2.50 2.83 1.35 0.53 131 150 2.50 2.50 1.38 0.74

60 300 2.50 2.50 2.07 0.60 132 150 2.50 2.50 1.27 0.56

61 400 4.37 5.08 3.11 0.82 133 150 2.50 2.50 1.38 0.74

62 150 2.50 2.50 1.27 0.56 134 150 2.50 2.50 1.38 0.74

63 150 2.50 2.50 1.27 0.56 135 150 2.50 2.50 1.38 0.74

64 150 2.50 2.50 1.27 0.56 136 150 2.50 2.50 1.27 0.56

65 150 2.50 3.40 1.47 0.50 137 100 2.50 2.50 1.05 0.73

66 150 2.50 2.50 1.27 0.56 138 100 2.50 2.50 1.05 0.73

67 450 3.17 3.09 2.83 0.82 139 100 2.50 2.50 1.05 0.73

68 250 2.50 2.83 2.11 0.82 140 100 2.50 2.50 1.05 0.73

69 150 2.50 2.50 1.27 0.56 141 100 2.50 2.50 1.05 0.73

70 200 2.50 4.37 2.34 0.82 142 100 2.50 2.50 1.05 0.73

71 200 2.50 2.50 1.65 0.70 143 100 2.50 2.50 1.05 0.73

72 150 2.50 2.50 1.27 0.56 144 100 2.50 2.50 1.05 0.73

Details of the optimal solution obtained by the HCA-discrete method for three sewer networks are also shown in Table

3, 4, and 5, respectively.

6. Concluding Remarks

In this paper, Hybrid Cellular Automata approach was used for the optimal solution of sewer network design problems.

The problem was decomposed to two stages with considering the nodal cover depths and pipe diameters as decision

variables. In the first stage, nodal cover depths were calculated assuming fixed values for the pipe diameters, while in

the second stage, the pipe diameters were determined in two approaches of continuous and discrete with nodal cover

depths of the first stage. Two stages were solved iteratively until the convergence was achieved. The HCA methods

were used to solve three benchmark examples in the literature and the comparison of results with two versions of Ant

Colony Optimization Algorithm indicated the ability and efficiency of the HCA methods to produce better results

comparable to those of heuristic search methods with much higher efficiency.


11

References

Adamatzky, A. I. (1996). Computation of shortest path in cellular automata. Mathematical and Computer Modelling,

23(4), 105-113.

Afshar, M. H. (2007). Partially Constrained Ant Colony Optimization Algorithm for the solution of constrained

optimization problems: application to storm water network design. Adv Water Resour, 30, 954–965.

Afshar, M. H., & Shahidi, M. (2009). Optimal solution of large scale reservoir operation problems: Cellular Automata

versus heuristic-search methods. Engineering Optimization, 41(3), 275-293.

Afshar, M. H. (2010). A parameter free Continuous Ant Colony Optimization Algorithm for the optimal design of storm

sewer networks: Constrained and unconstrained approach. Advances in Engineering Software, 41(2), 188–195.

Afshar, M. H., Shahidi, M., Rohani, M., & Sargolzaei, M. (2011). Application of cellular automata to sewer network

optimization problems. Scientia Iranica A, 18(3), 304–312.

Afshar, M. H., & Rohani, M. (2012). Optimal design of sewer networks using cellular automata-based hybrid methods:

Discrete and continuous approaches. Engineering Optimization, 44(1), 1-22.

Burks, E. (1972). Essays on Cellular Automat, University of Illinois Press, Champaign, IL.

Codd, E F. (1968). Cellular Automata, Academic Press, New York.

Dajani, J. S., & Gemmel, R. S. (1971). Economics of wastewater collection networks, Civil Eng. Res. Rep. 43, Water

Resour. Center, Univ. of Ill. At Urbana-Champaign, Urbana.

Deininger, R. A. (1970). Systems analysis for water supply and pollution control. Natural Resource Systems Models in

decision Making, edited by G.H. Toebes, Water Resources Center, Purdue Univ. Lafayette, Ind., 45-65.

El Dessouki, W. M., Fathi, Y., & Rouphail, N. (2001). Meta-optimization using cellular automata with application to the

combined trip distribution and assignment system optimal problem. Computer-Aided Civil and Infrastructure

Engineering, 16(6), 384-396.

Froise, S., & Burges, S. J. (1978). Least-cost design of urban drainage networks. Water Resources Planning and

Management Division, ASCE, 104(1), 75-92.

Guo, Y., Walters, G. A., Khu, S. T., & Keedwell, E. (2007a). A novel cellular automata based approach to storm sewer

design. Engineering Optimization, 39(3), 345-364.

Guo, Y., Keedwell, E. C., Walters, G. A., & Khu, S. T. (2007b). Hybridizing Cellular Automata Principles and NSGAII

for Multi-objective Design of Urban Water Networks. Evolutionary Multi-Criterion Optimization, 546-559.

Gupta, J. M., Agarwal, S. K., & Khanna, P. (1976). Optimal design of wastewater collection systems. The

Environmental Engineering Division, 102(EE5), 1029–1041.

Heaney, J. P., Wright, L. T., Sample, D., Field, R., & Fan, C. Y. (1999). Innovative methods for the optimization of

gravity storm sewer design. Proceedings the 8th international conference on urban storm drainage, Sydney,

Australia, 1896–1903.

Keedwell, E., & Khu, S. T. (2005). Using cellular automata to seed genetic algorithms for water distribution network

design problems. Engineering Applications of Artificial Intelligence, 18(4), 461-472.

Kita, E., & Toyoda, T. (2000). Structural design using cellular automata. Structural and Multidisciplinary Optimization,

19, 64–73.

Kulkarni, V. S., & Khanna, P. (1985). Pumped wastewater collection systems optimization. Environ Eng, ASCE, 111(5),

589–601.

Lemieux, P. F., Zech, Y., & Delarue, R. (1976). Design of a stormwater sewer by nonlinear programming. Canadian

Journal of Civil Engineering, 3(1), 83-89.

Liang, L.Y., Thompson, R. G., & Young, D.M. (2004). Optimizing the design of sewer networks using genetic

algorithms and tabu search. Engineering, Construction and Architectural Management, 11(2), 101-112.

Mays, L. W., & Wenzel, H. G. (1976). Optimal design of multi-level branching sewer systems. Water Resources

Research, 12(5), 913-917.

Merrit, L. B., & Bogan, R. H. (1973). Computerbase Optimal Design of Sewer System. The Environmental Engineering

Division, ASCE, 99(EE1), 35-53.

Missoum, S., Gürdal, Z., & Setoodeh, S. (2005). Study of a new local update scheme for cellular automata in structural

design. Struct. Multidisciplinary Optimization, 29, 103–112.


12

Moeini, R., & Afshar, M. H. (2012a). Layout and size optimization of sanitary sewer network using intelligent ants.

Advances in Engineering Software, 51, 49–61.

Moeini, R., & Afshar, M. H. (2012b). Constrained Ant Colony Optimisation Algorithm for the layout and size

optimisation of sanitary sewer networks. Urban Water Journal, 1–20.

Packard, N. H. (1986). Lattice Models for Solidification and Aggregation. In First International Symosium for Science

on Form.

Pan, T. C., & Kao, J. J. (2009). GA-QP model to optimize sewer system design. Environmental Engineering, 135(1),

17–24.

Price, R. K. (1978). Design of storm water sewers for minimum construction cost. In Proc. 1st International Conference

on Urban Strom Drainage, Southampton, United Kingdom, 636-647.

Robinson, D. K., & Labadie, J. W. (1981). Optimal design of urban storm water drainage system. International

symposium on urban hydrology, hydraulics, and sediment control, University of Kentucky Lexington, 145–56.

Sentos, R. M. Z. D., & Coutinho S. (2001). Dynamics of HIV Approach: A Cellular Automata Approach. Phys. Rev.

Lett., 87(16), 102-104.

Setoodeh, S., Gürdalb, Z., & Watson, L. T. (2006). Design of variable-stiffness composite layers using cellular automata.

Computer Methods in Applied Mechanics and Engineering, 195(9-12), 836-851.

Shuai, D., & Zhao, H. (2004). A new generalized cellular automata approach to optimization of fast packet switching.

Computer Networks, 45, 399-419.

Swamee, P. K. (2001). Design of sewer line. Environmental Engineering, 127(9), 776–781.

Thatcher, J. (1964). Universality in the von Neumann cellular model. Technical Report 03105-30-T, University of

Michigan.

Ulam, S. (1960). A collection of mathematical problems. NewYork, Interscience publishers.

Von Neumann, J. (1966). Theory of self-reproducing automata. Champaign, IL, University of Illinois Press.

Walters, G. A., & Templeman, A. B. (1979). Non-optimal dynamic programming algorithms in the design of minimum

cost drainage systems. Engineering Optimization, 4, 139-148.

Wang, L., Zhou, Y. (2009). Comparative Study on Bionic Optimization Algorithms for Sewer Optimal Design. 2009

Fifth International Conference on Natural Computation, 24-29.

Wolfram, S. (1988). High Speed Computing: Scientific Application and Algorithm Design. University of Illinois Press.

Yeh, S. F., Chu, C. W., Chang, Y. J., & Lin, M. D. (2011). Applying tabu search and simulated annealing to the optimal

design of sewer networks. Engineering Optimization, 43(2), 159–174.

Yen, B. C., Cheng, S. T., Jun, B. H., Voohees, M. L., & Wenzel, H. G. (1984). Illinois least cost sewer system design

model. User’s guide, Department of Civil Engineering, University of Texas at Austin.

This work is licensed under a Creative Commons Attribution 3.0 License.

http://creativecommons.org/licenses/by/3.0/




ISSN 2330-2038 E-ISSN 2330-2046



13

Finding a Common Weight Vector of Data Envelopment Analysis Based

upon Bargaining Game

Manabu Sugiyama1 & Toshiyuki Sueyoshi

2

1Faculty of Social and Information Studies, Gunma University, Maebashi-City, Gunma, Japan

2Department of Management, New Mexico Institute of Mining & Technology, Socorro, NM, USA

Correspondence: Manabu Sugiyama, Faculty of Social and Information Studies, Gunma University, 4-2 Aramaki-machi,

Maebashi-City, Gunma 371-8510, Japan. Tel: 81-27-220-7522. E-mail: [email protected]

Received: October 20, 2013 Accepted: November 6, 2013 Available online: November 11, 2013


Abstract

Data Envelopment Analysis (DEA) is a mathematical programming method for measuring the relative efficiency of

Decision Making Units (DMUs) by evaluating their outputs and inputs. In the history of DEA, the cross-efficiency of

jth DMU is widely used as an efficiency measure of a given DMUo among researchers. The approach always utilizes

weights related to inputs and outputs in the assessment. Unfortunately, the weights are not always uniquely determined

in the cross-efficiency measurement because DEA always suffers from an occurrence of multiple solutions, so

indicating an occurrence of multiple weights. To overcome such a difficulty, this paper proposes a new approach for

determining a common weight vector of DEA based on bargaining game.

Keywords: Bargaining Game, Kalai-Smorodinsky Bargaining Solution, Data Envelopment Analysis, Common Weight

Vector

1. Introduction

A large number of studies on Data Envelopment Analysis (DEA) have developed after DEA was first proposed by

Charnes, Cooper and Rhodes (1978), as confirmed by Glover and Sueyoshi (2009). DEA is a mathematical

programming approach to assess relative efficiencies within a group of Decision Making Units (DMUs). An important

result of such an analysis is a set of virtual multipliers, or weights, accorded to production factors (i.e., inputs or

outputs). The set of weights are often different for each of the participating DMUs.

Sexton, Silkman and Hogan (1986) have defined the cross-efficiency of jth DMU (DMUj) as a measure of DMUo that is

the ratio of weighted outputs to weighted inputs obtained when we use both input and output levels of DMU j. There

were several research efforts (e.g. Kao & Hung, 2005, Sugiyama & Yamada, 2001) that applied the cross-efficiency.

Moreover, there were other articles (e.g. Kao & Hung, 2005, Boussofiane & Dyson, 1991, Cook, Kress & Seiford, 1992,

and Roll, Cook & Golany, 1991) that discussed about a use of common weights. However, it is widely known that the

weights are not always uniquely determined. Therefore, the cross-efficiency method is not uniquely determined in DEA.

The DEA measurement process regarding efficiency of each DMU can be considered as playing a bargaining game

(Peters, 1992, and Thomson, 1994). In some cases, the measurement of relative efficiency by using a scheme of the

bargaining game is useful for group decision making. Thus, this study proposes a new approach for determining a

common weight vector based on the bargaining game. Furthermore, this research uses an example on Japanese electric

power industries in order to document the practicality of the proposed approach.

The remainder of this paper is organized as follows: Section 2 introduces a basic DEA model for making the proposed

analysis that incorporates cross-efficiency and its related total efficiency measures. Section 3 defines a feasible set from

the bargaining game for DEA. The section also proposes the calculation on Kalai-Smorodinsky bargaining solution by a

feasible set. Section 4 applies the proposed approach to measure the productivity analysis of Japanese electric power

industry. Section 5 summarizes conclusions and future extensions.

2. DEA Model and the Cross-efficiency

There are various descriptions about DEA. To uniform symbols and expressions, this study follows a description of

Cooper, Seiford and Tone (2006).


14

2.1 DEA Model

DEA presupposes total “n” DMUs as research objects of its analysis. It is also assumed that each DMUj (j=1,2,…,n) has

common inputs and outputs which contain m inputs xij>0 (i=1,2,…,m) and s outputs yrj>0 (r=1,2,…,s). Input-oriented

radial model under constant Returns to Scale (RTS), which is a basic DEA model on DMUo (o=1,2,…,n) to be

examined, has the following mathematical formulation:

.,...,2,1 0

,,...,2,1 0

,,...,2,1 0

,,...,2,1

,,...,2,1 0 subject to

, min.

1

1

11

mis

srs

nj

srysy

misxx

ss

io

ro

jo

roro

n

jjorj

io

n

jjoijioo

s

rro

m

iioo

(1)

The dual form of Model (1) are expressed by

.,...,2,1

,,...,2,1

,,...,2,1 0

,1 subject to

, max.

11

1

1

miv

sru

njyuxv

xv

yu

io

ro

s

rrjro

m

iijio

m

iioio

s

rroroo

(2)

The DMUo has an efficiency measure o that is obtained by a relative comparison with total n of DMUs’ production

activities. The optimal value *o obtained from Model (1) is often called “technical efficiency” in production

economics. The status of DEA-efficiency needs both 1* o and all slack variables are zero, i.e., 0* ros for all

,...,s,r 21 and 0* ios for all mi ,...,2,1 . If 1* o and at least one or more slack variables are 0*

ros for some

sr ,...,2,1 and 0* ios for some mi ,...,2,1 or 1* o , DMUo is defined as inefficient. Hence, Model (1) can be

usually solved by two steps of optimization without providing a specific value to ε, which is a non-Archimedean

infinitesimal (Cooper et al., 2006). This study extends the discussion by using this radial model under constant RTS.

The radial model is expressed as:

.,...,2,1

,,...,2,1

,,...,2,1 1 subject to

, max.

1

1

1

1

miv

sru

nj

xv

yu

xv

yu

io

ro

m

iijio

s

rrjro

m

iioio

s

rroro

o

(3)

Here, let *rou be an optimal value of rou , and, let *

iov be an optimal value of iov in the Model (2). This study refers

to these *rou and *

iov as DEA-solutions.

2.2 The Cross-efficiency and the Accommodated Total Efficiency

The cross-efficiency was first proposed by Sexton et al. (1986). They have defined the cross-efficiency of DMUj as

measured by DMUo as the ratio of weighted outputs to weighted inputs obtained when we use the input and output

levels of DMUj along with these weights derived for DMUo, as discussed previously. Mathematically, the


15

cross-efficiency is the ratio of the sums on the left side of constraint j in Model (3) for DMUo:

.,...,2,1 ; ,...,2,1

1

*

1

*

njno

xv

yu

Em

iijio

s

rrjro

oj

(4)

The cross-efficiencies are simply the ratios in the constraints of Model (3). The cross-efficiencies are easily summarized

by an nn matrix, whose (o,j) component is ojE . Sexton et al. (1986) called it as cross-efficiency matrix. The

conventional efficiency measures exist on the diagonal of the cross-efficiency matrix.

By examining the row o of the cross-efficiency matrix, this study can identify how DMUo rates each of the other DMUs,

that is, how efficient each of the other DMUs is when an optimal weights generated by DMUo are used for its

measurement. The mean efficiency in the row o (including the diagonal) is called EROW(o)

nj ojn

E1

1 . The measure

indicates the average efficiency of all DMUs according to DMUo. In a similar manner, this study can examine the

column j of the cross-efficiency matrix to identify how DMUj is rated by each of the other DMUs when it is evaluated

by means of the optimal weights that they are generated. The mean efficiency in the column j (including the diagonal) is

referred to as ECOL(j)

no ojn

E1

1 . The measure indicates the average efficiency of DMUj according to all other

DMUs. They can compute the average of all the cross-efficiency values, or EBAR. However, there may be no common

weights of the cross-efficiency because DEA always suffers from an occurrence of multiple solutions.

The accommodated total efficiency was proposed by Sugiyama and Yamada (2001). They showed that the

accommodated total efficiency is a general form for the cross-efficiency. The accommodated total efficiencies of DMUs

are calculated from the following three steps. (a) In the first step, they evaluate the relative efficiencies of DMUs as

group members. (b) In the second step, the mutual evaluation information of DMUs can be defined and calculated by

using their weights. They indicate the mutual evaluation information by a form of matrix which they called it as

“Accommodation Efficiency Matrix.” It is widely known that the weights are not always uniquely determined. The

mutual evaluation information is not uniquely determined. Here, they have proposed a method for determining the

weights uniquely by minimizing square of the weights differences. (c) In the third step, they calculate the

accommodated total efficiency which is the group efficiencies of DMUs by using the maximum eigenvalue of

“Accommodation Efficiency Matrix.”

3. A Common Weight Vector by the Bargaining Game Approach

This section defines some feasible sets of bargaining game on DEA and proposes the Kalai-Smorodinsky bargaining

solution by using those feasible sets. There are various descriptions about the bargaining game, and many articles. See,

for example, Peters (1992) and Thomson (1994). The study of DEA with the Game theory can be found in Banker,

Charnes, Cooper and Clarke (1989), Semple (1996), Hao, Wei and Yan (2000), Nakabayashi and Tone (2006), and etc.

On the other hand, Du, Liang, Chen, Cook and Zhu (2011) described DEA on the bargaining game. A Nash bargaining

game has also been proposed for measuring the performance of a two-stage network DEA system.

3.1 The Bargaining Game

By nN ,...,2,1 , this study denotes the set of players. The bargaining game (Peters, 1992, and Thomson, 1994) is

defined by a pair of d,S . The players in N try to reach a unanimous agreement on some outcome Sη , yielding

utility k for player k. If they fail, the disagreement outcome or disagreement point d occurs in the game. The set S is

referred to as a feasible set of the bargaining game. The set S needs to be convex, bounded and closed. There is at least

one point of S strictly dominating d.

This study chooses one of the bargaining solutions by applying an axiomatic approach. In the axiomatic approach, the

typical solution on the bargaining game is the Nash bargaining solution (Thomson, 1994). The Nash bargaining solution

is a single solution on the feasible set S satisfying Pareto-optimality, symmetry, scale invariance and independence of

irrelevant alternatives (IIA). Here, a solution of the proposed bargaining game on DEA satisfies Pareto-optimality,

symmetry and scale invariance. However, the solution of the bargaining game on DEA may not satisfy independence of

irrelevant alternatives (IIA). Therefore, the Nash bargaining solution is not appropriate. The rationale is because a

DEA-efficiency score is a relative evaluation score.

Meanwhile, a DEA solution of the proposed bargaining game fully satisfies individual monotonicity. The

Kalai-Smorodinsky bargaining solution (Thomson, 1994) is the only solution on a feasible set S satisfying

Pareto-optimality, symmetry, scale invariance and individual monotonicity. Consequently, this study selects the

Kalai-Smorodinsky bargaining solution.

These axioms are described in research efforts (i.e., Peters, 1992, and Thomson, 1994). The definition of the

Kalai-Smorodinsky bargaining solution (Thomson, 1994) is specified as follows.


16

[The Kalai-Smorodinsky bargaining solution] SK :

SK

is the maximal point of S on a segment connecting the origin to Sa , the ideal point of S, defined by

SSa kk ηmax for all k.

[In another definition, d,SK is the maximal point of S on a segment connecting d to d,Sa where

dηηd ,max, SSa kk for all k.]

3.2 The Feasible Set S of the Bargaining Game on DEA

Let the players be DMUs. Consequently, the number of the players is n. In addition, game situations assume the

bargaining game. Then, this study generalizes a feasible set of bargaining game on DEA. The feasible set in a correlated

pure strategy is expressed as follows:

,...,m,iv

,...,s,ru

Nj

xv

yu

Nj

xv

yu

S

i

r

m

iiji

s

rrjr

m

iiji

s

rrjr

j

n

21 0

,21 0

, 1

,

R

1

1

1

1

P

η . (5)

The feasible set in correlated pure strategy PS is the feasible set of a common weight vector of DEA. Moreover, the

comprehensive hull of PS is expressed as follows:

,...,m,iv

,...,s,ru

Nj

xv

yu

Nj

xv

yu

S

i

r

m

iiji

s

rrjr

m

iiji

s

rrjr

j

n

21 0

,21 0

, 1

,

Rcom

1

1

1

1

P

η. (6)

Here, it is expected that the feasible set in correlated pure strategy PS is a convex set. However, it is difficult to prove

whether PS is a convex set because PS includes the fractional equations. Let the input and output data for DMUj be

T21 ,...,, mjjjj xxxx and T21 ,...,, mjjjj yyyy , respectively. The symbol “T” denotes vector transpose. In addition, let

the weight vector be suuu ,...,, 21u and mvvv ,...,, 21v . Therefore, this study sets Model (6) by relaxing the equality

constraints jjj vxuy into inequality ones. This relaxation of Pcom S is naturally accepted in the bargaining

game. Then, this study calculates the Kalai-Smorodinsky bargaining solution by these feasible sets in the proceeding

section. By comparing results obtained by the Kalai-Smorodinsky bargaining solution that obtains from the two feasible

sets, it is possible to confirm that these feasible solutions are convex sets near the Kalai-Smorodinsky bargaining

solution.

3.3 The Computational Mode for Bargaining Solution

Let the ideal point of S be each DMU's efficiency score *j . The proposed bargaining game can establish various

kinds of points as the disagreement point d. Therefore, this study sets the disagreement point d as the origin. However,

this study cannot accept the bargaining solution from the origin. Because the DEA-solutions become 0u * or 0v * .

The weight of the DEA problem (3) is a non-zero vector. Since PS η0 and 0u are equivalent, a

Kalai-Smorodinsky bargaining solution η such as a common weight vector of DEA is a non-zero vector. In addition,

since 0y j for all Nj , 0u and 0u , and 0η are equivalent. Therefore, this study refers to as a

Kalai-Smorodinsky bargaining solution 0η as a positive Kalai-Smorodinsky bargaining solution. A

Kalai-Smorodinsky bargaining solution corresponds to a desirable common DEA weights is a positive

Kalai-Smorodinsky bargaining solution.


17

Since **2

*1

P ,...,, nSa and a line segment between the origin 0 and PSa is NjηSa j ,10Pη , finding a positive

Kalai-Smorodinsky bargaining solution PSK of 0,PS is the same of solving the positive optimal value *j of

.21 0

,21 0

, 01

, 1

, subject to

, max.

1

1

1

1

1

*

,...,m,iv

,...,s,ru

Nj

Nj

xv

yu

Nj

xv

yu

i

r

j

m

iiji

s

rrjr

jm

iiji

s

rrjr

n

jjj

　

(7)

The maximization of Model (7) is an unbounded problem. Thus, the maximization problem form, modified by adding

the equation 1jvx , becomes:

.21 0

,21 0

, 0

, 1 subject to

, max.

11

1

1

1

1*

,...,m,iv

,...,s,ru

Njyuxv

Njxv

xv

yu

i

r

s

rrjr

m

iiji

m

iiji

n

jm

iiji

s

rrjr

j

　

(8)

If Pcom S is a feasible set of the bargaining game, then finding a Kalai-Smorodinsky bargaining solution Pcom SK

of 0,com PS is the same of solving the positive optimal value *j of

.21 0

,21 0

, ,01

, 1

, subject to

, max.

1

1

1

1

1

*

,...,m,iv

,...,s,ru

Nj

Nj

xv

yu

Nj

xv

yu

i

r

j

m

iiji

s

rrjr

jm

iiji

s

rrjr

n

jjj

(9)

The maximization of Model (9) is an unbounded problem, as well. Thus, the maximization problem by adding the

equation 1jvx becomes as follows:


18

.21 0

,21 0

, ,01

, 0

, 0

, 1 subject to

, max.

11

11

1

1

*

,...,m,iv

,...,s,ru

Nj

Njyuxv

Njyuxv

Njxv

i

r

j

s

rrjr

m

iiji

s

rrjr

m

iijij

m

iiji

n

jjj

(10)

That is, P*P comcom SaSK η . Here, this study can set the ideal point of S be an each DMU's efficiency score.

Furthermore, it is possible to set the disagreement point d as the origin.

4. Numerical Example

This section documents the productivity analysis of Japanese electric power industry by applying the proposed approach.

This example was given in Sugiyama and Yamada (2001).

4.1 Data

The subjects of analysis are nine electric power companies in Japan. This study utilizes the management indexes, given

below, as input/output data of each company in the fiscal year 1991. The data source is “Hand Book of Electric Power

Industry '91” (Statistics Committee of Electric Utilities Association (Ed.), 1992), in the form of Table 1.

[Input/Output Items]

Inputs: x1j “Number of Employees”, x2j “Maximum Generation Capacity” and x3j “Total Assets”.

Outputs : y1j “Electricity Sales” and y2j “Number of Customers”.

Table 1. Observed Inputs and Outputs

Number of

Employees

Maximum

Gen. Cap.

Total

Assets

Electricity

Sales

Number of

Customers

x1j x2j x3j y1j y2j

Hokkaido 6,457 5,315 1,320,938 21,389 3,256

Tohoku 13,557 10,150 2,657,112 55,227 6,445

Tokyo 40,063 46,905 11,627,131 227,631 23,221

Chubu 20,285 22,799 4,896,313 103,140 8,711

Hokuriku 5,338 4,453 1,252,893 21,711 1,712

Kansai 25,166 33,158 5,931,094 122,749 11,331

Chugoku 10,898 9,433 2,148,717 44,498 4,578

Shikoku 6,603 5,423 1,214,685 20,548 2,490

Kyushu 13,669 14,063 3,305,687 57,272 7,007

Scale 100 103(kW) 106(YEN) 106(kWh) 103

Table 2. Modified Input/Output Data by Average

Number of

Employees

Maximum

Gen. Cap.

Total

Assets

Electricity

Sales

Number of

Customers

x1j x2j x3j y1j y2j

Hokkaido 0.4091 0.3153 0.3461 0.2855 0.4262

Tohoku 0.8590 0.6022 0.6961 0.7373 0.8437

Tokyo 2.5386 2.7828 3.0460 3.0388 3.0398

Chubu 1.2853 1.3526 1.2827 1.3769 1.1403

Hokuriku 0.3382 0.2642 0.3282 0.2898 0.2241

Kansai 1.5946 1.9672 1.5538 1.6387 1.4833

Chugoku 0.6905 0.5596 0.5629 0.5940 0.5993

Shikoku 0.4184 0.3217 0.3182 0.2743 0.3260

Kyushu 0.8661 0.8343 0.8660 0.7646 0.9173


19

4.2 Analysis and Evaluation

First, DEA is appiled on the nine electric power companies as DMUs. Table 3 summarizes the computational results

obtained from the proposed analysis, i.e., DEA-efficiency scores * and its reference set, for each DMU. As a result,

Hokkaido, Tohoku, Tokyo and Chubu are determined DEA-efficient. In contrast, Hokuriku, Kansai, Chugoku, Shikoku

and Kyushu are determined DEA-inefficient.

Table 3. DEA-efficiency of Electric Power Companies

DEA-efficiency reference set

*o

Hokkaido 1.0000 ---

Tohoku 1.0000 ---

Tokyo 1.0000 ---

Chubu 1.0000 ---

Hokuriku 0.9245 Tohoku, Tokyo

Kansai 0.9928 Tohoku, Tokyo, Chubu

Chugoku 0.9906 Tohoku, Chubu

Shikoku 0.8430 Hokkaido, Tohoku

Kyushu 0.9560 Hokkaido, Tohoku, Tokyo

Second, the study calculates the efficiency of each electric power company from a DEA common weight vector based

on the Kalai-Smorodinsky bargaining solution. As discussed in Section 3.3, let the ideal point of S be an each DMU's

efficiency score. The proposed bargaining game can establish various kinds of points as the disagreement point d. This

study sets the disagreement point d as the origin. To calculate the Kalai-Smorodinsky bargaining solution, this study

uses the maximization problems (8) and (10), modeled by each feasible set: Sa and d. Tables 4 and 5 indicate the

results on efficiencies for each DMU and a common weight vector obtained from the Kalai-Smorodinsky bargaining

solution.

Table 4. The Kalai-Smorodinsky Bargaining Solution of Electric Power Companies

The Kalai-Smorodinsky Bargaining Solution DEA-efficiency

the feasible set PS the feasible set Pcom S *o

Hokkaido 0.8411 0.8411 1.0000

Tohoku 1.0000 1.0000 1.0000

Tokyo 1.0000 1.0000 1.0000

Chubu 1.0000 1.0000 1.0000

Hokuriku 0.8082 0.8082 0.9245

Kansai 0.9928 0.9928 0.9928

Chugoku 0.9716 0.9716 0.9906

Shikoku 0.8071 0.8071 0.8430

Kyushu 0.8863 0.8863 0.9560

Table 5. A Common Weight Vector

1v 2v 1u 2u 3u

the feasible set PS 0.6779 0.0000 2.3778 2.3584 0.5912

the feasible set Pcom S 0.6779 0.0000 2.3778 2.3584 0.5912

In Tables 4 and 5, the results based on the feasible set PS and the feasible set Pcom S are same in each company.

Consequently, this study assumes that the Kalai-Smorodinsky bargaining solution, the feasible set PS and Pcom S are

a convex set. Therefore, this study determines that Tohoku, Tokyo and Chubu are efficient. Hokkaido, Hokuriku, Kansai,

Chugoku, Shikoku and Kyushu are inefficient. Thus, this study is able to identify that Tohoku, Tokyo and Chubu attain

a desirable performance level. On the other hand, Hokkaido, Hokuriku, Kansai, Chugoku, Shikoku and Kyushu do not

attain the desirable performance level. In this study, the calculated common weight 2v score is 0000.02 v . In other

words, the input item jx2 “Maximum Generation Capacity” may not be necessary for measuring the relative

efficiencies of DMUs. The details of this analysis will become very important information at selecting the input/output

items on DEA.


20

Table 6. Efficiency of Nine Electric Power Companies

The Kalai-Smorodinsky

Bargaining Solution

The Accommodated

Total Efficiency

The Cross-Efficiency

(by the weights

determined uniquely)

Hokkaido 0.8411 0.9155 0.8884

Tohoku 1.0000 1.0000 0.9757

Tokyo 1.0000 0.9658 0.9419

Chubu 1.0000 0.8643 0.8476

Hokuriku 0.8082 0.7244 0.7120

Kansai 0.9928 0.8500 0.8321

Chugoku 0.9716 0.9018 0.8824

Shikoku 0.8071 0.7879 0.7689

Kyushu 0.8863 0.8893 0.8655

Third, Table 6 indicates the results obtained from the Kalai-Smorodinsky bargaining solution and conventional

approaches. The accommodated total efficiencies of each DMU were given in Sugiyama and Yamada (2001), as well.

Furthermore, the cross-efficiencies (ECOL(j)) of each DMU were calculated by using the weights determined uniquely

in Sugiyama and Yamada (2001). The Kalai-Smorodinsky bargaining solution satisfies Pareto-optimality, symmetry,

scale invariance and individual monotonicity, thus the result obtained from the Kalai-Smorodinsky bargaining solution

may be more useful for a group decision making than other efficiencies. Therefore, each DMU may be able to accept

the solution more easily.

Fourth, Table 7 indicates a common weight vector obtained from each approach. Here, the weights of the accommodated

total efficiency were given in Sugiyama and Yamada (2001), as well. There were not the weights satisfying the

cross-efficiency in the feasible set of DEA-solutions. Hence, these weights were not calculated in this study.

Table 7. A Common Weight Vector of Each Approach

1v 2v 1u 2u 3u

The Kalai-Smorodinsky Bargaining Solution 0.6779 0.0000 2.3778 2.3584 0.5912

The Accommodated Total Efficiency 0.3739 0.3199 0.6984 0.5755 0.6824

The Cross-Efficiency --- --- --- --- ---

5. Conclusions and Future Extensions

This research discussed a methodology for determining a common weight vector of DEA based on the

Kalai-Smorodinsky bargaining solution. The calculated common weight vector was uniquely determined. This study

applied the proposed approach to examine the productivity analysis of Japanese electric power industry. The application

indicates the practicality of the proposed approach.

This research is the first effort for applying a scheme of bargaining game to determine a common weight vector of DEA.

Furthermore, this paper contributed to the progress of the study of DEA with the Game theory.

In conclusion, it is hoped that this study makes a contribution in DEA. We would like to anxiously wait for future

extensions that are originated from this research effort.

Acknowledgement

This work is supported by JSPS Grant-in-Aid for Scientific Research (C) 23510159.

References

Banker, R. D., Charnes, A., Cooper, W. W., & Clarke, R. (1989). Constrained Game Formulations and Interpretations

for Data Envelopment Analysis, European Journal of Operational Research, 40, 299-308.

http://dx.doi.org/10.1016/0377-2217(89)90422-0

Boussofiane, A., Dyson, R. G., & Thanassoulis, E. (1991). Applied Data Envelopment Analysis, European Journal of

Operational Research, 52, 1-15. http://dx.doi.org/10.1016/0377-2217(91)90331-O

Charnes, A., Cooper, W.W., & Rhodes, E. (1978). Measuring the Efficiency of Decision Making Units, European

Journal of Operational Research, 2, 429-444. http://dx.doi.org/10.1016/0377-2217(78)90138-8

Cook, W. D., Kress, M., & Seiford, L. M. (1992). Prioritization Models for Frontier Decision Making Units in DEA,

European Journal of Operational Research, 59, 319-323. http://dx.doi.org/10.1016/0377-2217(92)90148-3

Cooper, W. W., Seiford, L.M., & Tone, K. (2006). Data Envelopment Analysis : A Comprehensive Text with Models,

Applications, References and DEA-Solver Software (2nd ed.), New York, Springer Science.


21

Du, J., Liang, L., Chen, Y., Cook, W. D., & Zhu, J. (2011). A bargaining game model for measuring performance of

two-stage network structures, European Journal of Operational Research, 210, 390-397.

http://dx.doi.org/10.1016/j.ejor.2010.08.025

Glover, F., & Sueyoshi, T. (2009). Contributions of Professor William W. Cooper in Operations Research and Management

Science, European Journal of Operational Research, 197, 1-16. http://dx.doi.org/10.1016/j.ejor.2008.08.011

Hao, G., Wei, Q., & Yan, H. (2000). The Generalized DEA Model and the Convex Cone Constrained Game, European

Journal of Operational Research, 126, 515-525. http://dx.doi.org/10.1016/S0377-2217(99)00306-9

Kao, C., & Hung, H. T. (2005). Data envelopment analysis with common weights: the compromise solution approach,

Journal of the Operational Research Society, 56, 1196–1203. http://dx.doi.org/10.1057/palgrave.jors.2601924

Nakabayashi, K., & Tone, K. (2006). Egoist's Dilemma: a DEA Game, Omega, 34, 135-148.

http://dx.doi.org/10.1016/j.omega.2004.08.003

Peters, H. J. M. (1992). Axiomatic Bargaining Game Theory, Kluwer Academic Publishers.

http://dx.doi.org/10.1007/978-94-015-8022-9

Roll, Y., Cook, W. D., & Golany, B. (1991). Controlling Factor Weights in Data Envelopment Analysis, IIE

Transactions, 23, 2-9. http://dx.doi.org/10.1080/07408179108963835

Semple, J. (1996). Constrained Games for Evaluating Organizational Performance, European Journal of Operational

Research, 96, 103-112. http://dx.doi.org/10.1016/S0377-2217(96)00068-9

Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data Envelopment Analysis: Critique and Extensions, Silkman, R.

H. (Ed.), Measuring Efficiency: Assessment of Data Envelopment Analysis (pp. 73-105), San Francisco, Jossey Bass.

Statistics Committee of Electric Utilities Association (Ed.). (1992). Hand Book of Electric Power Industry '91 (in

Japanese), Tokyo, Japan Electric Association.

Sugiyama, M., & Yamada, Y. (2000). Data Envelopment Analysis Using Virtual DMU as Intermediates: An Application

to Business Analysis of Japan's Automobile Manufatures, Journal of Japan Industrial Management Association, 50,

341-354. http://ci.nii.ac.jp/naid/110003945554/en

Sugiyama, M., & Yamada, Y. (2001). Group-Consensus Biilding on DEA (in Japanese), Communications of the

Operations Research Society of Japan, 46, 284-289. http://ci.nii.ac.jp/naid/110001184921/en

Thomson, W. (1994). Cooperative Models of Bargaining, Aumann, R. J. & Hart, S. (Eds.), Handbook of Game Theory

with Economic Applications (pp. 1237-1284), Elsevier Science B.V..

von Neumann, J., & Morgenstern, O. (1953). Theory of Games and Economic Behavior (3rd ed.), New Jersey, Princeton

University Press.

Yamada, Y., Matsui, T., & Sugiyama, M. (1994). An Inefficiency Measurement Method for Management Systems (in

Japanese), Journal of the Operations Research Society of Japan, 37, 158-168.

http://ci.nii.ac.jp/naid/110001184395/en






ISSN 2330-2038 E-ISSN 2330-2046



22

Examples of Mental Mistakes Made by Systems Engineers While Creating Tradeoff Studies

James Bohlman1 & A. Terry Bahill

1

1Systems and Industrial Engineering, University of Arizona, USA

Correspondence: Terry Bahill, Systems and Industrial Engineering, University of Arizona, 1622 W. Montenegro, Tucson

AZ 85704-1822, USA. E-mail: [email protected]

Received: October 21, 2013 Accepted: November 4, 2013 Available online: November 21, 2013


Abstract

Problem statement: Humans often make poor decisions. To help them make better decisions, engineers are taught to

create tradeoff studies. However, these engineers are usually unaware of mental mistakes that they make while creating

their tradeoff studies. We need to increase awareness of a dozen specific mental mistakes that engineers commonly

make while creating tradeoff studies.

Aims of the research: To prove that engineers actually do make mental mistakes while creating tradeoff studies. To

identify which mental mistakes can be detected in tradeoff study documentation.

Methodology: Over the past two decades, teams of students and practicing engineers in Bahill’s Systems Engineering

courses wrote the system design documents for an assigned system. On average, each of these document sets took 100

man-hours to create and comprised 75 pages. We used 110 of these projects, two dozen government contractor tradeoff

studies and three publicly accessible tradeoff studies. We scoured these document sets looking for examples of 28

specific mental mistakes that might affect a tradeoff study. We found instances of a dozen of these mental mistakes.

Results: Often evidence of some of these mistakes cannot be found in the final documentation. To find evidence for

such mistakes, the experimenters would have had to be a part of the data collection and decision making process. That

is why, in this paper, we present only 12 of the original 28 mental mistakes. We found hundreds of examples of such

mistakes. We provide suggestions to help people avoid making these mental mistakes while doing tradeoff studies.

Conclusions: This paper shows evidence of a dozen common mental mistakes that are continually being repeated by

engineers while creating tradeoff studies. When engineers are taught about these mistakes, they can minimize their

occurrence in the future.

Keywords: validation, decision making, mistakes, design documentation

1. Introduction

Humans often make poor decisions. To help them be better decision-makers, engineering professors teach their students

to create tradeoff studies. Tradeoff studies are broadly recognized as the method for simultaneously considering

multiple alternatives with many criteria, and as such are recommended and mandated in the Capability Maturity Model

Integration (CMMI®) (CMMI, 2010; Chrissis, Konrad and Shrum, 2003) Decision Analysis and Resolution (DAR)

process. The decision-making fields of Judgment and Decision Making, Cognitive Science and Experimental

Economics have built up a large body of research on human biases and errors in considering numerical and

criteria-based choices. Relationships between experiments in these fields and the elements of tradeoff studies show that

tradeoff studies are susceptible to human mental mistakes. Smith, Son, Piattelli-Palmarini and Bahill (2007) postulated

28 specific mental mistakes that could affect the ten specific components of a tradeoff study.

However, Smith et al. (2007) did not have examples from the system engineering literature. So we sought to validate

their model by finding and documenting specific instances of these mental mistakes in tradeoff studies. This present

paper validates the proposals of the Smith, et al. (2007). It presents real-world examples of a dozen of these mistakes. It

would have been a daunting challenge to find examples of such mistakes in the open systems engineering literature,

because the literature just does not publish mistakes.


23

1.1 What Are Tradeoff Studies?

Tradeoff studies are broadly recognized and mandated as the method for simultaneously considering multiple

alternatives with many criteria (Daniels, Werner & Bahill, 2001; Smith et al., 2007). Tradeoff studies provide an ideal,

rational method for choosing among alternatives. Tradeoff studies involve a mathematical consideration of many

evaluation criteria for many alternatives simultaneously, in parallel.

Tradeoff studies are performed at the beginning of a project to help state the problem, select the desired system

architecture and make major purchases. However, throughout a project tradeoffs are continually being made: creating

team communication methods, selecting tools and vendors, selecting components, choosing implementation techniques,

designing test programs, and maintaining schedule. Many of these tradeoffs should be formally documented.

The components of a tradeoff study are the (1) problem statement, (2) evaluation criteria, (3) weights of importance, (4)

alternate solutions, (5) evaluation data, (6) scoring functions, (7) normalized scores, (8) combining functions, (9)

preferred alternatives and (10) sensitivity analysis.

The following is a cartoon of a simple tradeoff study. The analyst is designing a system to help a baseball umpire to call

balls and strikes. He is trying to select the preferred alternative. His two alternatives are a complex instrument named

the Umpire’s Assistant and a Seeing Eye dog. His evaluation criteria are Accuracy of the Call and Silence of

Communication between the alternative systems and the umpire. (We do not want it to intrude on the classic game.) The

very bottom row shows that the Umpire’s Assistant was the recommended alternative.

Table 1. A Generic Tradeoff Study

Criteria

Weights of

Importance of the

Criteria

Alternative-1 Scores Alternative-2 Scores

Criterion-1 wt1 s11 s12

Criterion-2 wt2 s21 s22

Alternative

Rating 1 1 11 2 21sum wt s wt s

2 1 12 2 22sum wt s wt s

Table 2. Tradeoff Study Numerical Example

Alternatives

Evaluation Criteria Weights of

Importance

Umpire’s

Assistant

Seeing

Eye Dog

Accuracy of the Call 0.75 0.67 0.33

Silence of Communication 0.25 0.83 0.17

Sum of weight times score 0.71

The winner 0.29

The numerical values go from 0 to 1, with 1 being the best.

2. Research Methodology

Over the last quarter of a century, Bahill has sought out and collected examples of tradeoff studies. He collected 110

university projects, two dozen government contractor tradeoff studies (these reports are proprietary and cannot be

published) and three publicly accessible tradeoff studies such as the San Diego Airport site selection study.

Then the authors read these reports looking for evidence of the 28 specific mental mistakes postulated by Smith et al

(2007). Bohlman read all 8000 pages of the university projects and filled a database with over 800 examples of such

mistakes. These examples were put into categories according to the 28 specific mental mistakes that we were looking

for. After several iterations, we decided that our examples fit into only 12 of these categories. Bahill then rated each

example for the perceived heuristic value, meaning the goodness of illustrating each type of mental mistake. The

examples with the least perceived value were set aside. The remaining examples were compared with the original

documents checking for context and accuracy. They were then re-rated based on the perceived heuristic value, uniform

coverage of the dozen mental mistakes and reducing the number of different projects that would have to be explained.

We created the 20 development cases that are in this paper, and another 50 cases that were used for testing. Finally,


24

Bahill read the government contractor tradeoff studies and the three identified publicly accessible tradeoff studies and

similarly created case studies.

Often evidence of some of these mental mistakes cannot be found in the final documentation. To find evidence for such

mistakes, the experimenters would have to have been a part of the data collection and decision making process. That is

why, in this paper, we present only 12 of the original 28 mental mistakes. This paper presents examples of the following

mental mistakes.

1. Using Dependent Criteria

2. Not Stating the Problem in Terms of Stakeholder Needs

3. Vague Problem Statement

4. Substituting a Related Attribute

5. Sensitivity Analysis Mistakes

6. Forer Effect

7. Weight of Importance Mistakes

8. Anchoring and the Status Quo

9. Treating Gains and Losses Equally

10. Not Using Scoring Functions

11. Implying False Precision

12. Obviating Expert Opinion

This paper is organized as follows: for each of the above (1) the section heading announces the type of mental mistake,

(2) Smith et al’s (2007) explanation of the mistake is given, (3) Smith et al’s (2007) recommendations for avoiding that

mistake are stated, (4) the problem that the teams were modeling is explained (if it is the first time the problem has been

presented), (5) an excerpt of this type of mistake is presented in the Garamond font, (6) it is explained why the

particular example contains a mental mistake in the Times New Roman font, (7) a suggested rewrite is given in the

Arial font. The mistake excerpts have not been edited: they are direct quotes: however, they might have been

reformatted. The sections from Smith, et al. (2007) have been edited.

In the decision making literature there are hundreds of names for such mistakes, names such as attribute substitution,

dominated criteria, cognitive illusions, emotions, fallacies, simplifying heuristics, fear of regret, paradoxes, herding,

group think, psychological traps (Marquard & Robinson, 2008) and cognitive biases (Sage, 1981: Smith,

Piattelli-Palmarini & Bahill, 2008; Smith & Bahill, 2010). However, in this paper we will simply call them mental

mistakes.

The purpose of this paper is to explain and give examples of certain types of mental mistakes that humans often make

while doing tradeoff studies. Many of these mistakes are subtle and it is hard to avoid making them. However, it is

hoped that systems analysts who read this paper will be able to recognize these mistakes in tradeoff studies created by

others and to avoid these mistakes in their own tradeoff studies.

3. Examples of Mental Mistakes in Tradeoff Studies

This section shows examples of a dozen types of common mental mistakes that were made while doing tradeoff studies.

We believe these mistakes are continually being repeated by systems engineers worldwide. We hope that reading this

paper will help systems engineers to avoid such mental mistakes in the future.

3.1 Using Dependent Criteria

Evaluation criteria should be independent. In a tradeoff study, alternatives should be evaluated based on independent

evaluation criteria. However, analysts often choose dependent criteria. When scoring these criteria for the different

alternatives, having multiple dependent criteria can magnify or diminish the final scores of the alternatives, thus

recommending the wrong alternative. Here are some simple examples of evaluation criteria. For evaluating humans,

Height and Weight are not independent: Sex (male versus female) and Intelligence Quotient are independent. In

selecting a car, the following criteria are dependent: Maximum Horse Power, Peak Torque, Top Speed, Time for the

Standing Quarter Mile, Engine Size (in liters), Number of Cylinders and Time to Accelerate 0 to 60 mph (Smith et al.,

2007).

Recommendation: Dependent criteria should be grouped together as subcriteria. The seven subcriteria for the car given

in the previous paragraph could all be grouped into the criteria Power.


25

For each year, the class project was designed to be unprecedented, with no possible optimal solution, realistic, solved

by teams of three or four engineers who would have to analyze, synthesize and evaluate alternative designs. The

following example does not depend on the particular project: it could have occurred in any project.

Team Excerpt

The maximum current drawn by the system shall not exceed 15 amperes.

The system shall operate on 120 volt, 60 hertz electricity.

The system shall not consume more than 1.8 kilowatts.

Why is this a mental mistake?

If you know the voltage and the current, then you know the power; Power = Voltage x Current.

Suggested rewrite

The system shall operate on 120 volt, 60 hertz AC electricity.

The system shall draw a maximum of 15 amperes.

3.2 Not Stating the Problem in Terms of Stakeholder Needs

Committing to a class of preconceived solutions (instead of stating the true stakeholder needs) causes a lack of

flexibility. Identifying the true stakeholder needs can be difficult because stakeholders often refer to both problem

domains and solution domains – whichever comes most naturally. In systems engineering, the initial problem statement

must be written before looking for solutions (Wymore, 1993; Smith et al., 2007).

Recommendation: Communicate with and question the stakeholders in order to determine their values and needs. State

the problem in terms of customer requirements (Bahill & Dean, 1999, 2009; Hooks & Farry, 2001; Daniels & Bahill,

2004; Hull, Jackson & Dick, 2005). Later, after a better understanding of evaluation criteria and weights of importance

has been gained, one must find alternative solutions that provide a good match to the requirements.

The project for 2006 was the SpinCoach™. When a spinning object (like a baseball) is put in a moving fluid (like air),

it will experience a force that pushes it sideways (Bahill, Baldwin, & Venkateswaran, 2005; Baldwin, Bahill & Nathan,

2007; Bahill & Baldwin, 2008; Bahill, Baldwin & Ramberg, 2009.) Some highly successful baseball players have said

and written that they see this spin of the ball and use it to track the ball with saccadic and smooth pursuit eye

movements (Bahill & Stark, 1975; Bahill & Stark, 1977; Bahill & LaRitz, 1984). But at present, there is no system that

can teach high school and college baseball and softball players to predict this spin-induced deflection of the pitch.

Therefore, this project was to design and document the design of a system that would help train baseball and softball

players to pick up the spin on the ball and predict the spin's effect on the ball's deflection. The system would be capable

of displaying images of spinning balls, allowing the subject to predict the spin induced deflection and providing

feedback to facilitate learning. The key architectural decision in this project is whether to design the first version for

baseball or softball.

Team Excerpt

The batter believes he can predict the trajectory until the ball and bat connect and therefore swing accordingly.

Because of the deflection in the last milliseconds of the balls flight however, the batter is not able to adjust his swing

in time to compensate and therefore the likelihood for there to be a strike called is increased because of the batter

swing. In essence the pitcher is trying to fake out the batter and get him to swing at the ball or not swing at the ball

based on a seemingly predictable trajectory. It appears to the batters, however that the ball seems to change direction

in the last moments of its trajectory and is cause for batters to swing without connecting with the ball.


This problem statement does not mention the batter’s needs. It is certainly stating correct things about

what the batter and the pitcher are doing. But it fails to describe the batter’s needs in terms of the

system being designed. If they were designing a different system, then the excerpt might be useful.

But they were supposed to be designing a system to help the batter learn the spin-induced deflection

of the ball.

Suggested rewrite

Baseball and softball players need to learn how to recognize the spin of a pitched ball

and use that information to predict the spin-induced deflection of the ball.

Second Team Excerpt

A video game trainer could also be used, in which a batter tries to gauge the spin on a video ball and predict where it

would end up. This option could be implemented with a CD-ROM. The CD would go through the process of how to

see the spin based on video taken from a laboratory. Dr. Terry Bahill, a professor in the Systems and Industrial

Engineering (SIE) department at the University of Arizona, has set up a laboratory with equipment to simulate


26

pitches with different types of spins. This laboratory would be a valuable resource in designing experiments to train a

player to pick up the spin on a ball.


This problem statement does not mention the batter’s needs.

Suggested rewrite

The top-level system function is to teach batters to recognize the spin of a pitched

ball and then use this information to predict the spin-induced movement of the ball.

3.3 Vague Problem Statement

If a problem statement is vague, proposed solutions could vary greatly, and derive support for very different reasons

and in different ways. If a problem statement is poorly written or ambiguous, dissimilar alternative solutions could

remain in the solution pool, obfuscating their rational consideration, especially if the rationale for the different

psychologically attractive values of the alternative solutions are not well understood (Keeney, 1992). Failing to mention

customer needs makes the problem statement seem vague (Smith et al., 2007).

Recommendation: Stating the problem is the most important and possibly the most difficult aspect of a tradeoff study.

The problem should be stated in terms of the stakeholder’s needs. But be sure to state the problem so that it is

independent of preconceived solutions. State the problem so that it can be satisfied by a large number of alternative

solutions.

The project for 2007 was the PopupCoach™. Even professional baseball players occasionally find it difficult to

gracefully approach seemingly routine pop-ups. McBeath, Nathan, Bahill & Baldwin (2008) describe a set of towering

pop-ups with trajectories that exhibit cusps and loops near the apex. For a normal fly ball, the horizontal velocity is

continuously decreasing due to drag caused by air resistance. But for pop-ups, the Magnus force (the force due to the

ball spinning in a moving airflow) is larger than the drag force: therefore, the horizontal velocity decreases in the

beginning, like a normal fly ball, but after the apex, the Magnus force accelerates the horizontal motion (Bahill &

Baldwin, 2007). We refer to this class of pop-ups as paradoxical because they appear to misinform the typically robust

optical control strategies used by fielders and lead to systematic vacillation in running paths, especially when a

trajectory terminates near the fielder. In short, some of the dancing around when infielders pursue pop-ups can be

explained as a combination of bizarre trajectories and misguidance by the normally reliable optical control strategy,

rather than apparent fielder error. Former major league infielders confirm that our model agrees with their experiences.

But at present, there is no methodological system that can teach high school and college baseball and softball players

(more specifically catchers and infielders) to track pop-ups. Batting practice and ball games offer few opportunities for

a player to learn this skill. Our customer needs a system that will provide frequent convenient opportunities to learn to

field pop-ups. The goal of this project is to design and document the design of such a system.

Team Excerpt for the PopupCoach

The occurrence of pop-ups in major league games is an average of five times per game. This frequency provides

reason for effective practice to be devoted to train players in order to hone their ability to catch these routine

pop-ups.


This problem statement is vague.

Suggested rewrite

For baseball and softball fielders who need to catch pop-ups, the PopupCoach is a

training system that teaches fielders to track and catch pop-ups: unlike present

coaches and books, the PopupCoach explains the trajectory, offers convenient

practice opportunities and complements players’ improvement.

Team Excerpt for the SpinCoach

The differences in (baseball) spin result in visually detectable differences in the appearance of the spinning ball as it

approaches the batter. Currently, players practice the assessment of spin and trajectory prediction during actual game

play and team practice sessions. This process requires coordination between multiple players, and the use of a pitcher

capable of delivering a repeatable baseball pitch to the batter.


This problem statement is vague.

Suggested rewrite

For the baseball batter who needs to predict the trajectory of the pitch, the

SpinCoach is a training system that helps him to recognize the spin on the pitch and

predict the ball’s spin-induced movement; unlike present coaches and books, the

SpinCoach shows the batter how each pitch spins and helps him to recognize this

spin.


27

3.4 Substituting a Related Attribute

Attribute substitution occurs when a subject is assessing an attribute and substitutes a related attribute that comes

more readily to mind. In effect, people who are confronted with a difficult question sometimes answer an easier one

instead (Kahneman, 2003). In a similar vein, when confronted with a choice among alternatives that should properly be

decided by a full tradeoff study, there is a strong tendency to substitute a seemingly equivalent yet much simpler

decision question in place of the tradeoff study process (Smith et al., 2007).

Recommendation: Sponsors of tradeoff studies should realize that a premature reduction of a tradeoff study process to

a simpler decision question is a common heuristic that prevents consideration of the original multi-objective decision.

Team Excerpt for the SpinCoach

Use Case 2.

Name: Learn Spin-induced Deflections

Iteration: 2.3

Derived from: Concept of operations

Brief description: Player uses the SpinCoach and learns to predict the spin-induced deflection of a ball.

Added value: Player will be better able to predict the trajectory of the ball and consequently should have a higher

batting average.

Second Team Excerpt for the SpinCoach

5.2.1.2 Effectiveness

The measurement of effectiveness determines the percent increase on the user’s batting average over time.

The purpose of the SpinCoach is to teach batters to predict the spin-induced deflection of the baseball, but as a

measure of success, these teams proposed to record the player’s batting average.


What we really want to know is “Does training with the SpinCoach teach batters to predict the

spin-induced deflection of the baseball?” But this is too hard to measure; therefore, our engineers

substituted the player’s batting average as a measure of success.

Suggested rewrite

We want to teach baseball batters to predict the spin-induced deflection of the

baseball. Therefore, we want to know how well they predict the spin-induced

deflection, but that is hard to measure, therefore we substitute the player’s batting

average as a measure of success.

In this particular design what we really want to know is “Does training with the SpinCoach teach batters to predict the

spin-induced deflection of the baseball?” But this is too hard to measure; therefore, we substitute the player’s batting

average as a measure of success. But we do tell our readers that we are doing this.

After he received the Nobel Prize for developing Prospect Theory (RSAS, 2002; Kahneman, 2002), Kahneman spent

most of his time trying to unify mental mistakes. He suggested that many or most could be explained by attribute

substitution. This is a very difficult mistake to avoid. People do it all the time. The point of this section is that analysts

should understand what attribute substitution is and avoid making it as a mistake. However, if the analyst really wants

to use a substitute attribute, then he or she should go ahead and use it. But be sure to tell that reader that he or she is

using attribute substitution.

Team Excerpt for the PopupCoach

The ability of a defending baseball team to catch pop-up balls can provide a key advantage needed to win a baseball

game. That pop-ups occurs in major league games an average of five times underscores the need for players to

improve their ability to catch them. Pop-ups are difficult to catch because their trajectories are irregular and it is not

readily predictable where players should stand and catch them. There is no existing training system to improve

players’ catching percentage.

Second Team Excerpt for the PopupCoach

Thus, the need for a system to teach fielders about and offer practice scenarios involving trajectory and spin is

necessary if it can help increase fielding percentages and improve the win percentages for players and teams.


What we really want to know is “Does training with the PopupCoach teach fielders to use the optimal

running path and running speed while fielding fly balls. But this is too hard to measure; therefore, our

engineers substituted the player’s catching percentage and fielding percentages.

Suggested rewrite for the PopupCoach


28

For each pop-up, we will compute the player’s optimal running path and then

compare it to the player’s actual running path. We will also compute the optimal

running speed at the time of the catch and compare this to the player’s actual running

speed. These two metrics will be combined to indicate how well the fielder tracked

the pop-up.

Attribute substitution is a tricky mistake, because everyone does it. In this design what we really want to know is “Does

training with the PopupCoach teach fielders to use the Optical Acceleration Cancellation algorithm (McBeath, Nathan,

Bahill, & Baldwin, 2008) to catch Pop-ups?” But we cannot use as a metric the probability of catching a pop-up,

because 9 of our 12 alternative designs do not use real pop-ups. For these 9 designs we think it would be too expensive

(if not impossible) to gather enough data for every player to make valid inferences. Furthermore we have no method of

measuring the spin of pop-us. Therefore, we think variability in the speed and spin rate of real pop-ups would obscure

any evidence that the fielder used the Optical Acceleration Cancellation algorithm to catch pop-ups. Because we could

not measure the desired attribute, we substituted a simpler attribute, the running speed and path. Attribute substitution is

not always a mistake: often it is deliberate and stated.

3.5 Sensitivity Analysis Mistakes

Most people are not well trained in the machinery and methods of sensitivity analysis. They often fail to compute

second- and higher-order partial derivatives. When estimating partial derivatives, they often use too large a step size.

When estimating partial derivatives of functions of two parameters, they often use the wrong formula; they use a

formula with two instead of four numerator terms. Smith, Szidarovszky, Karnavas and Bahill (2008) has shown that

interactions among parameters in tradeoff studies can be important, step sizes for the approximation of effects should be

small, and second-order derivatives should be calculated accurately. It is expected that only the best-trained personnel

will know of such results, illustrating the gap between truth and training (Smith et al., 2007).

Recommendation: Investments in sensitivity analysis training must be made. Perhaps enabling software can substitute

for much sensitivity analysis knowledge. (Hsu, Bahill & Stark, (1976); Karnavas, Sanchez & Bahill, (1993); Smith,

Szidarovszky, Karnavas & Bahill, (2008) describe the development and use of sensitivity analyses.

First Team Excerpt

Since the training methods are independent of any resources and a tradeoff analysis was not required, no sensitivity

analysis will be done for it.

Second Team Excerpt

The I/O performance weights more than the utilization of resources in the trade-off analysis. TW1P0 and TW2P0

values will be switched to determine the sensitivity of the design concepts to weighting and the results are shown

below:

Third Team Excerpt

The current trade study has an emphasis placed on the performance requirements of the SlugMaster to determine

the sensitivity of results to the weighting of the requirements, a plot was constructed as a function of the two

weights: I/O Performance and utilization of resources.


These Teams considered at most one parameter, the relative tradeoff weight between performance and

cost.

Suggested rewrite, derived from Smith, Szidarovszky, Karnavas & Bahill, (2008).

Concept

Weights are Weights are

0.70/0.30 0.30/0.70

Score Score

1 0.3811 0.7347

2 0.5172 0.3665

3 0.5191 0.3061

4 0.568 0.3416

5 0.563 0.3249

6 0.6275 0.3362

7 0.5739 0.3132


29

Table 1. A Generic Tradeoff Study

Criteria Weights of

Importance Alternative 1 Alternative 2

Criterion-1 Wt1 S11 S12

Criterion-2 Wt2 S21 S22

Alternative

Rating

1

1 11

2 21

Sum

Wt S

Wt S

2

1 12

2 22

Sum

Wt S

Wt S

Table 2 gives numerical values for one particular tradeoff study, The Umpire’s

Assistant (http://www.sie.arizona.edu/sysengr/sie577/UmpiresAssistant.doc).

Table 2. Tradeoff Study Numerical Example

Alternatives

Criteria Weights of

Importance

Umpire’s

Assistant

Seeing

Eye

Dog

Accuracy

of the call 0.75 0.67 0.33

Silence of

Signaling 0.25 0.83 0.17

Sum of

weight

times

score

0.71

The

winner

0.29

Definition of the semirelative sensitivity function:

0

NOP

F FS

%

These are the semirelative sensitivity functions for Tables 1 and 2.

1

1

1

2

1

11

1

21

1

12

1

22

11 12 1

21 22 2

1 11

2 21

1 12

2 22

0.26

0.16

0.50

0.21

-0.25

-0.04

PI

Wt

PI

Wt

PI

S

PI

S

PI

S

PI

S

S S S Wt

S S S Wt

S Wt S

S Wt S

S Wt S

S Wt S

%

%

%

%

%

%

These functions show that the most important parameter is the score for alternative-1

on criteria-1. Sensitivity analyses need mathematical detail. Failure to do the

mathematics right produces erroneous results. Smith, Szidarovszky, Karnavas and

Bahill, (2008) present the correct mathematical equations.

For more comments about sensitivity analyses, see these online documents:

http://www.sie.arizona.edu/sysengr/sie554/SpinCoach/JA2/index.html

http://www.sie.arizona.edu/sysengr/sie554/PopUpCoach/index.html


30

3.6 Forer Effect

According to the Forer Effect, previously existing criteria will be adopted if (1) the analyst believes that the criteria

apply to the present problem, (2) the criteria are well presented and (3) the analyst believes in the authority of the

previous criteria writer. For example, the analyst might fail to question or re-write criteria from a legacy tradeoff study

that originated from a perceived authority and is now seemingly adaptable to the tradeoff at hand. This is called the

Forer effect. Forer (1949) gave a personality test to his students. He then asked them to evaluate his personality analyses

of them, supposedly based on their test's results. Students rated their analyses on a scale of 0 (very poor) to 5 (excellent)

as to how well it applied to them. The average score was 4.26. Actually, Forer had given the same analysis to all the

students. He had assembled this analysis of a generally likeable person from horoscopes. Variables that contribute to

this fallacy in judgment are that the subject believes the analysis only applies to them, the subject believes in the

authority of the evaluator, and the analysis contains mainly positive traits (Smith et al., 2007).

Recommendation: Spend time considering and formulating criteria from scratch, before consulting and possibly

reusing previously written criteria.

The textbook for the course (Chapman, Bahill & Wymore, 1992) had a primitive sensitivity analysis that only

considered one parameter, the tradeoff weight between cost and performance. In Section 5.5.4 it states, “The system is

sensitive to tradeoff weightings. For example changing the weights of the Trade-Off Requirement can easily sway the

answer. The current trade-off puts heavy emphasis on the I/O performance of the system (0.90) and not on the

utilization of resources (0.10). Changing the degree of emphasis can change the results…” In the course, we had a

lecture and a homework that described how to take partial derivatives and form the semirelative sensitivity functions for

each parameter in the tradeoff study (Smith, Szidarovszky, Karnavas & Bahill, 2008). However, the students repeatedly

copied the method of conducting a sensitivity analysis from a legacy tradeoff study published in the course textbook.

Despite warnings about the inadequacy of that sensitivity analysis, the students conducted their analyses in that very

same way. This was an example of the Forer effect (Forer, 1949) Students failed to question a sensitivity analysis that

was presented by a perceived authority and was seemingly adaptable to their own tradeoff study.

Team Excerpt

Figure 1. Team summary of a sensitivity analysis. It shows how the overall tradeoff scores vary for a dozen

alternatives as the cost becomes less important and the performance becomes more important.

cost performance 1wt wt



31

The only parameter being varied here is the relative weight of performance versus cost. In this figure,

the team just put their new data into a figure from their textbook (Chapman, Bahill & Wymore, 1992).

They ignored all sensitivity analyses that we developed later. Students failed to question a sensitivity

analysis that was presented by a perceived authority and was seemingly adaptable to their own

tradeoff study.

3.7 Weight of Importance Mistakes

When a group of people is asked to assign a weight of importance for an evaluation criterion, each person might

produce a different value. Different weights arise not only from different preferences, but also from irrational severity

amplifiers (Bahill & Karnavas, 2000; Bahill & Smith, 2009). These include the factors of lack of control, lack of choice,

lack of trust, lack of warning, lack of understanding, manmade, newness, dreadfulness, personalization, recallability and

immediacy. Excessive disparities occur when a person assesses a weight of importance after framing the problem

differently. An evaluation may depend on how the criterion affects that person, how well that person understands the

alternative technologies, the dreadfulness of the results, etc. As a result, each person might assign a different weight of

importance to any criterion. The decision analyst should assign weights to the criteria so that the more important ones

will have more effect on the outcome. Weights are often given as numbers between 0 and 10, but are usually

normalized so that in each category they sum to 1.0. These methods can be used by individuals or teams. If pair-wise

comparisons of preferences between the criteria can be elicited from experts, then the weights of importance can be

determined through the Analytic Hierarchy Process (AHP). However, performing pair-wise comparisons can lead to

intransitive preferences: Therefore, the AHP computes an inconsistency index to warn if the domain expert is giving

intransitive responses (Smith et al., 2007).

Recommendation: Interpersonal variability can be reduced with education, peer review of the assigned weights, and

group discussions. But be aware that people are like lemmings: if you reveal how other people are voting, then they are

likely to respond with the most popular answers. It is also important to keep a broad view of the whole organization, so

that criteria in one area are considered in light of all other areas. A sensitivity analysis can show how important each

weight is. For unimportant weights, move on. For important weights, spend more time and money trying to get

consensus: this might include showing the recommended alternatives for several different sets of weights.

The project for 2005 was the Umpire’s Assistant. For the baseball umpire who needs to call balls and strikes, the

Umpire’s Assistant is an intelligent decision aiding system that helps him or her to call balls and strikes accurately,

consistently and in real-time. Unlike unassisted human umpires, the Umpire’s Assistant uses the same strike-zone

standards for all leagues, parks, umpires, batters and pitchers.

Table 3. Umpire’s Assistant Team Excerpt

Utilization of Resources Figures

of Merit Requirements

Weight

Value

Normalized

weight

1. Available Money 2 0.02326

2. Available Time 2 0.02326

2.1 System design &

prototyping by 12/31/05

2 0.02326

2.2 System verification testing

by 2/06

2 0.02326

3. Technological Restrictions 10 0.11628

3.1 to not significantly alter

the dynamics of baseball

9 0.10465

3.2 to comply with local,

regional, state, federal laws

10 0.11628

3.3 to comply with FCC rules 10 0.11628

4. Adaptability 8 0.09302

4.1 to comply with Standards

& Specifications of MLB

8 0.09302

4.2 to comply with Standards

& Specifications of NCAA

8 0.09302


The normalized weights add up to 0.826. They should add up to 1.0 in each category and each

subcategory.

Table 4. Suggested rewrite for the Umpire’s Assistant


32

Utilization of Resources Evaluation Criteria

We

ights

of

Import

ance

Crite

ria

Norm

aliz

ed

We

ights

Subcrite

ria

Norm

aliz

ed

We

ights

1. Available Money 2 0.09

2. Available Time 2 0.09

2.1 System design & prototyping by

12/31/05

2 0.5

2.2 System verification testing by 2/14/06 2 0.5

3. Technological Restrictions 10 0.45

3.1 to not significantly alter baseball

dynamics

9 0.31

3.2 to comply with local, state & federal laws 10 0.35

3.3 to comply with FCC rules 10 0.35

4. Adaptability 8 0.36

4.1 to comply with MLB rules 8 0.5

4.2 to comply with NCAA rules 8 0.5

Of course, there would be a paragraph explaining each of these short evaluation

criteria tags. The abbreviations would be explained in these paragraphs.

3.8 Anchoring and the Status Quo

The order in which the alternatives are listed has a big effect on the values that humans give for the evaluation data

(Piattelli-Palmarini, 1994; Tversky & Shafir, 1992). Therefore, tradeoff study matrix should be filled out row by row

and the status quo should be the alternative in the first column. This will make the evaluation data for the status quo the

anchors for estimating the evaluation data for the other alternatives. This is good because the anchoring alternative is

known, is consistent, and you have control over it (Smith et al., 2007).

Note: The status quo will probably have low evaluation data values (inputs for scoring functions) for performance, cost,

schedule and risk. If the status quo had high performance values, then you probably would not be trying to replace it.

The status quo already exists, so (1) it will not be expensive, which gives it a low (good) value for cost, (2) it should not

have schedule problems, which gives it a low (good) value for schedule and (3) it should also be low risk.

Recommendation: Put the status quo alternative in the first column. In the first iteration, evaluate the scores left to

right and in the next iteration evaluate them right to left. The more alternatives that exist and the more complicated the

decision, the more the status quo will be favored. Do not needlessly increase the number of alternatives in a tradeoff

study. More alternatives increase the difficulty of the decision. However, in the very beginning of a project it is good to

have many alternatives in order to better understand the problem and the requirements. View the problem from different

perspectives. Use different starting points. When estimating values for parameters of scoring functions, think about the

whole range of expected values for the parameters.

Table 5. Team Excerpt for ranking process alternatives

Criterion 1 2 3 4 5 6 7 Max

Score

Metric

Value 1.8 0.7 2.3 1.5 0.7 1 2 100

Raw Wtd Raw Wtd Raw Wtd Raw Wtd Raw Wtd Raw Wtd Raw Wtd Solution

Alternative Scr Scr Scr Scr Scr Scr Scr Scr Scr Scr Scr Scr Scr Scr Score

Solution 1 2 7.2 10 6.3 9 14 3 9 3 2.1 8 2 2 4 41.8

Solution 2 9 3.6 7 7 9 21 9 4.5 2 1.4 2 8 10 20 76.6

Solution 3 3 16 2 4.9 4 9.2 8 14 3 2.1 8 9 1 2 67.3

Solution 4 9 5.4 10 1.4 5 12 9 12 9 6.3 9 8 10 20 76.6

Solution 5 3 16 3 7 5 12 8 14 8 5.6 7 9 2 4 67.3

Solution 6 9 16 3 2.1 5 12 9 11 9 6.3 5 7 10 20 76.6

Solution 7 3 5.4 8 5.6 9 21 7 11 3 2.1 5 5 9 18 67.3


33

Do

Nothing 10 18 10 7 10 23 10 15 10 7 10 10 10 20 100


In a tradeoff study matrix the alternatives should be in columns, not rows, because humans find it

easier to compare across rather than down. The alternatives and evaluation criteria should be

identified by names, not numbers. The alternatives and evaluation criteria should be explained with

sentences and paragraphs. Finally, the do nothing alternative should be in the first column.


Table 5 also shows a mistake at the implementation level: the engineers intended each weighted score

to be its raw score times the metric value, and the solution score to be the summation of the weighted

scores in that row. But their Excel worksheet had mistakes: only the Do Nothing row was correct.

Table 6. Suggested rewrite of the Tradeoff matrix

for alternative architectures of the SpinCoach

Alternatives

Criteria

Do N

oth

ing

Com

pute

r

Sim

ula

tion

CD

RO

M

DV

D

Web

Pa

ge

Vid

eo G

am

e

Fidelity of Images

Feedback Time

Product Production Cost

Shipping Cost

Updatability

Each evaluation criterion and each alternative architecture must have a paragraph of

explanation, as in the following paragraphs.

Previously, we have written that the tables and figures of a tradeoff study do not contain the evaluation criteria and the

design alternatives: they merely contain tags. The actual criteria and alternatives must be explained elsewhere using

sentences and paragraphs. The following is an example for the SpinCoach.

Alternative architectures for the SpinCoach

1. The Status Quo. Some batters can recognize the spin on the ball and predict its spin induced movement. But they

have difficulty verbalizing this capability and teaching it to others. In batting practice, we can have the pitcher announce

to the batter “curve” and then throw a curveball: announce “slider” and then throw a slider. Etc. This could be done with

a human pitcher or a pitching machine.

2. Computer Simulations. Images of spinning balls can be simulated and presented on a computer monitor. This system

is described in SpinTeacherGray.doc.

4. Spinning Balls. Holes are drilled into baseballs or softballs and the balls are skewered on bolts. These bolts are

chucked into drills. The drills are spun at controlled speeds. Videos of this setup are on my web site.

http://www.sie.arizona.edu/sysengr/baseball/index.html. Do not let someone’s tie or scarf get tangled in the drills.

4. CD-ROM or DVD. Balls spinning on drills can be photographed and their images stored on CD-ROM or DVD disks.

Such videos are on my web site. http://www.sie.arizona.edu/sysengr/baseball/index.html. These images along with the

software program will be transferred from the CD-ROM to the user’s hard disk using a license key provided by BICS.

There after the user runs the SpinCoach from his or her hard disk. The user must login for each session. The information

gathered at login is used to track user performance history. System upgrades will be provided with new CD-ROMs.

5. Web-based Application. Balls spinning on drills can be photographed and their images stored on the BICS web

server. Such videos are on my web site. http://www.sie.arizona.edu/sysengr/baseball/index.html. These images along

with the software program will be on an Internet accessible web site. This system will be based on the Apache web

server with web pages written in PHP or HTML and video clips in AVI format. Access to the system will be granted by

monthly subscription and login based authentication control. The user will have a profile in the system and can access

this profile from any terminal connected to the Internet. The system will store user information in a database. This


34

information is used to track user performance history. System upgrades can be made on the web site at any time and

will be transparent to the user.

6. Make it into a video game and sell it to Nintendo, Sony or Microsoft.

Evaluation criteria for the SpinCoach

Fidelity of Images. How realistic are the images? Are they two or three-dimensional? What is the resolution? What is

the color depth? What is the update rate? Will the presentation vary depending on the processor speed or the

communications bandwidth? For example, would the system degrade with a dialup telephone connection to the

Internet? This criterion traces to the Operational Concept Description (OCD). Importance weight is 6.

Feedback Promptness. The system shall provide positive or negative feedback to the player after each prediction. The

system shall provide this feedback to the player within 500 milliseconds of the player's response. This will be a Boolean

(yes or no) function. This traces to customer requirement 10. Importance weight is 10.

Product Production Cost is a measure of how much it will cost in U. S. dollars for BICS to produce one unit of the

product. A monotonic decreasing scoring function shall be used (L=0, B=10, S=-0.1, U=500). Input range is 0 to 500

dollars, baseline is 10 dollars and slope is -0.1. This traces to customer requirement 1. Importance weight is 6.

Figure 2. A scoring function for the Product Production Cost evaluation criteria

The Shipping Cost evaluation criterion is composed of Shipping Weight, Shipping Expenses, Shipping Effort and

Billing Cost per unit. A scoring function is not necessary if the subcriteria have scoring functions and normalized

weights. Our target value is ten dollars. This traces to customer requirement 1. Importance weight is 5.

Updatability. This criterion evaluates how easy and convenient updates are expected to be. The system shall be

continually improved and updated throughout the system life cycle. Corrective maintenance such as bug fixes should be

performed within weeks. Adaptive maintenance, which includes revisions necessary to allow the system to run on new

or improved hardware and software, should be accomplished in a monthly time frame. Performance and functional

updates will be performed yearly. This should trace to the business plan. Importance weight is 5.

3.9 Treating Gains and Losses Equally

People do not treat gains and losses equally. Kahneman earned the Nobel Prize for explaining the fact that people

prefer to avoid losses rather than to acquire gains. Prospect Theory (Kahneman & Tversky, 1979) suggests that

psychologically losses are twice as powerful as gains. Would you rather get a 5% discount, or avoid a 5% penalty?

Most people would rather avoid the penalty. In a tradeoff study, you will get a different result if the scoring function

expresses losses rather than gains (Abdellaaoui, 2000) (Smith et al., 2007).

Recommendation: Human unequal treatment of gains and losses suggests that scoring functions in a tradeoff study

should uniformly express either gains or losses. Principles of linguistic comprehensibility suggest that criteria should be

worded in a positive manner, so that more is better. For example, use Uptime rather than Downtime, Mean Time

Between Failures rather than Failure Rate, and Probability of Success rather than Probability of Failure. Finally, when

using scoring functions, make sure that more output is better.

Team Excerpt

2.2 Number of Complaints

2.3 Number of Problems with the System

3.1 Number of Accidents per visit.

2.5.3. Number of Curses per day

5.2.6. Injury -- Is it possible for the design to inflict bodily injury on the batter? This rated by the players on a scale of

1 – 10 (1 being no bodily harm, 10 being serious injury requiring hospitalization).


These criteria are phrased negatively.

Suggested rewrite


35

2.2 Customer Approval Rating (%)

2.3 Mean Time to Failure (MTTF)

3.1 Number of accident-free visits

2.5.3 Time without cursing

5.2.6. Safety – Mean time between injuries.

Second Team Excerpt

3.5.2.6 Availability of system

This figure of merit measures the availability of the system, in terms of the number of hours per year for which the

system is unavailable during working hours due to failure or unscheduled maintenance.

3.5.2.7 Safety of system

This figure of merit measures the safety of the system in terms of injuries caused by the system.


Evaluation criteria should be phrased so that more is better. Availability of System and Safety of

System contradict themselves. The titles are phrased positively, but the descriptions contain the

negative words unavailable and injuries.

Suggested rewrite

3.5.2.6 System Availability

This criterion is the percent of time that the system is available during working hours,

average per week.

3.5.2.7 System Safety

The units for this criterion are the number of days that the system has operated

without an injury.

3.10 Not Using Scoring Functions

Evaluation data are transformed into normalized scores by scoring functions (utility curves) or qualitative scales (fuzzy

sets). The shape of scoring functions should ideally be determined objectively, but often, subjective expert opinion is

involved in their preparation. Creating scoring function packages takes time and effort (Bahill, 2008). A scoring

function package should be created by a team of analysts, and be reevaluated with the stakeholders with each use. Most

tradeoff studies that we have observed in industry did not use scoring functions. In some cases, scoring functions were

explained in the company process, but they were not convenient, hence they were not used (Smith et al., 2007).

Recommendation: Wymorian standard scoring functions (or similar scoring functions, fuzzy sets or utility functions)

should be used in tradeoff studies. Easy-to-use scoring functions should be referenced in company processes.

Team excerpt:

Many teams just did not use scoring functions.

Evaluation data are transformed into normalized scores by scoring functions (Wymore, 1993, pp. 385-398; Daniels,

Werner & Bahill, 2001). The shape of scoring functions should ideally be determined objectively, but often, subjective

expert opinion is involved in their preparation. Scoring functions are also called utility functions, utility curves, value

functions, normalization functions and mappings. Evaluation criteria should always have scoring functions so that the

preferred alternatives do not depend on the units used. For example, see what would happen if you were to add values

for something that cost about one hundred dollars and lasted about a millisecond.

Alt-1 cost a hundred dollars and lasts one millisecond, Sum = 100.001.

Alt-2 only cost ninety-nine dollars but it lasts two millisecond, Sum = 99.002.

The duration does not have any effect on the decision. A simple program that creates scoring functions is available free

at http://www.sie.arizona.edu/sysengr/slides. It is called the Wymorian Scoring Function tool. An example of a scoring

function was given in Figure 2 for the Product Production Cost.

Scoring functions must state the units for the input: for example, actual dollar values will be used as input to a cost

scoring function. Without scoring functions, the preferred alternative would depend on the units used, for example,

whether the costs were given in U. S. Dollars or British pounds. With scoring functions, this will not happen.

3.11 Implying False Precision

The most common mistake that we have seen in tradeoff studies is implying false precision. For example, a tradeoff

analyst might ask a subject matter expert to estimate values for two criteria. The expert might say something like, “The

first criterion is about 2 and the second is around 3.” The analyst puts these numbers into a calculator and computes the

ratio as 0.666666667. This is nonsense, but nine digits might be used throughout the tradeoff study. The Forer Effect

might explain this. The analyst believes that the calculator is an impeccable authority in calculating numbers. Therefore,

what the calculator says must be true (Smith et al., 2007).

http://www.sie.arizona.edu/sysengr/slides


36

Recommendation: Use significant figures methodology. Furthermore, in numerical tables, print only a sufficient

number of digits after the decimal place as is necessary to show a difference between the preferred alternatives.

Team Excerpt

5.3.1.1 Trade-off scores

Concept 1: Customer chooses the bat 0.6 * 0.22500 + 0.4 * 0.41435 = 0.30074

Concept 2: Store owner chooses the bat 0.6 * 0.25125 + 0.4 * 0.41435 = 0.31649

Concept 3: BatChooser chooses the bat 0.6 * 0.67500 + 0.4 * 0.96840 = 0.79236

Concept 4: BatSelect Chooses with the help of the BatChooser 0.6 * 0.84280 + 0.4 * 0.96840 = 0.89304

Presenting five digits after the decimal point obfuscates the equations and does not help to

differentiate between the alternatives.

Suggested rewrite

5.3.1.1 Trade-off scores

Concept 1: Customer chooses the bat 0.6 * 0.23 + 0.4 * 0.41 = 0.30

Concept 2: Storeowner chooses the bat 0.6 * 0.25 + 0.4 * 0.41 = 0.32

Concept 3: BatChooser chooses the bat 0.6 * 0.68 + 0.4 * 0.97 = 0.79

Concept 4: BatSelect chooses the bat with the help of the BatChooser

0.6 * 0.84 + 0.4 * 0.97 = 0.89

Table 7. Second Team Excerpt for Bat

Chooser

Concept Weighted

Score Ranking

Concept 1 Score 0.4414 7








Table 8. Suggested rewrite for the Bat Chooser

Alternative Weighted

Score Ranking

Concept 1 0.44 7

Concept 2 0.54 4

Concept 3 0.21 8

Concept 4 0.67 2

Concept 5 0.65 3

Concept 6 0.46 6

Concept 7 0.68 1

Concept 8 0.48 5

Table 9. Team Excerpt for the SpinCoach

Performance

Requirements Value

Normalized

weight


37

1. Accuracy 8 0.235294

1.1 Spin Rate 10 0.384615

1.2 Launch Angle 8 0.307692

1.3 Launch Speed 8 0.307692

2. Consistency 7 0.205882

3. Ease of Use 6 0.176471

3.1 Portability 6 0.260870

3.2 Location 7 0.304348

3.3 # of Operators 10 0.434783

4. Opportunity 8 0.235294

5. Feedback 5 0.147059


The original Value data have one significant digit. Therefore, the normalized weights certainly should

not have six digits after the decimal point.

Table 10. Suggested rewrite for the SpinCoach

Evaluation Criteria

We

ights

of

Import

ance

Crite

ria

Norm

aliz

ed

We

ights

*

Subcrite

ria

Norm

aliz

ed

We

ights

*

1. Accuracy 8 0.24

1.1 Spin Rate 10 0.38

1.2 Launch Angle 8 0.31

1.3 Launch Speed 8 0.31

2. Consistency 7 0.21

3. Ease of Use 6 0.18

3.1 Portability 6 0.26

3.2 Location 7 0.30

3.3 Number of

Operators

10 0.43

4. Opportunities per Hour 8 0.24

5. Feedback Response Time 5 0.15

*Significant figures methodology suggests that the

normalized weights should only have one significant

digit. But here we have used two to make the

calculations obvious.

Table 10 has also put the criteria and subcriteria weights in separate columns. All of

the subcriteria weights for a particular criteria sum to 1.0. All of the criteria weights

sum to 1.0.

On the other hand, Table 5 shows an example not of false precision, but of inconsistent precision. In some columns,

Excel is set to display integers while in others it is set to one decimal place.

When determining how many digits should be printed consider (1) how many digits are necessary to differentiate

between the preferred alternatives, (2) the sensitivity of the final recommendations to the parameters, the most sensitive

parameters should be given extra resources and therefore perhaps more significant digits (Karnavas, Sanchez & Bahill,

1993; Smith, Szidarovszky, Karnavas & Bahill, 2008) and (3) no parameters need to be more exact than the least

accurate parameter (presuming of course that the tradeoff matrix is as described in this paper and it does not have a

multi-step process for estimating any parameters).

As an example, when humans state preferences between risky prospects, their judgments are not linear in probability.

Humans overweight small probabilities and underweight high probabilities. This has been modeled with several

different equations (Abdellaoui, 2000; Bleichrodt & Pinto, 2000).


38

1( )

(1 )

pw p

p p

( )(1 )

pw p

p p

and

( ) exp( ( ln ) )w p p .

In these equations w is the probability weighting function, p is the probability of a particular prospect, , , and are parameters fit to experimental data of individual humans. Now the question becomes, Should a tradeoff analyst use

equations like these when eliciting information for a tradeoff study? The answer depends on the accuracy of the other

parameters. In all of the design documents that we examined, the weights of importance had only one significant digit.

Therefore correcting for each human’s incorrect estimation and use of probabilities is not warranted. In a tradeoff study,

the number of significant figures should be determined for each parameter. Then resources should not be committed to

increasing the number of significant figures for any except the most important and the least precise parameters.

3.12 Obviating Expert Opinion

An analyst could hold a circular belief that expert opinion or review is not necessary, because no evidence for the need

of expert opinion is present. This is especially true if no expert has ever been asked to comment on the tradeoff study

(Smith et al., 2007).

Recommendation: Experts should be sought, formally or informally, to evaluate the results of tradeoff studies.

The most common mistake that we have found in design projects over the last 35 years is failing to talk with

stakeholders and failing to consult experts and experienced advisors. The university and local industry is full of experts

in the fields of every project that we have done. In this time, very few teams have sought advice from domain experts.

Why do people fail to seek out the advice of experts and experienced advisors? The students rated the following

possible reasons. In each category, the reasons are arranged from the most frequent to the least.

It was common for our teams to not seek outside advice or guidance in the course of performing their tradeoff studies. If

they had sought this guidance, expert review or opinion, they might have avoided the errors we detected in their tradeoff

studies. This would most likely be the case if the guidance concerned the tradeoff study itself (not just the technical

matters) and elicited high-quality examination of all tradeoff study components.

Table 11. Possible reasons for failing to talk with stakeholders, experts and advisors.

Timidity

Perhaps they do not want to inconvenience the wise men or waste their time. However, people are not reluctant

to seek the advice of physicians, tax accountants and lawyers. To overcome timidity, before you talk to an

expert, you should formulate your questions and explain your problem in a way that the expert can quickly

understand. Tailoring a message and formulating the right questions is hard and must be done iteratively.

Before you leave your meeting, you should state what you think the expert said, to make sure that you

understood and to prevent having to go back later for clarification.

Perhaps they are shy or intimidated by experts.

Perhaps they fear that the incompleteness of their project will be interpreted as incompetence.

Perhaps they think that a face-to-face meeting would display their naïveté. This is not a problem with e-mails,

because most people do not expect e-mails to be thoughtful, coherent and grammatically correct: most

students do not edit their e-mails or use a spelling and grammar checker on them.

Perhaps they think that seeking advice reveals their ignorance, and that ignorance is shameful.

Perhaps they think that consulting experts shows weakness, whereas going it alone shows strength.

Perhaps they feel that, because they do not have a charge number, they cannot ask experts in their company for

advice.

Perceived Value


39

Perhaps they do not realize the usefulness of face-to-face meetings with experts.

Perhaps it is a matter of return on investment. Consulting experts takes time and effort. Perhaps these teams

thought the improvement in their tradeoff studies would not be worth the effort of consulting experts.

Perhaps the smart people thought, “We can get an A without wasting our time talking to our advisor.”

Perhaps the new technology generation thinks that they can just Google the web and get all the information that

experts might provide.

Perhaps they noticed that other courses at the university do not provide world-class experts to meet with them, so

it must not be important.

Perhaps they do not see a direct correlation between their grade and meetings with their advisor.

Perhaps they do not perceive added value.

Time (obviously time and perceived value will be traded off)

Perhaps they thought that they were too busy; meeting with their advisor would take time and effort; it would be

hard to schedule meetings with their advisor. Maybe they were just lazy.

Communication

Perhaps they have had no experience initiating a meaningful conversation with a stranger and are therefore

reluctant to do so.

Most of our students communicate with cell phones, twitter, the internet or e-mail. So they are multitaskers,

jumping from task to task. Therefore, they are good at multitasking, but their attention spans are perhaps

short. So they do not know how to talk face-to-face with an expert.

Other

Perhaps they have been taught that engineers work alone: after all, cooperating on exams is frowned upon.

However, in the modern industrial environment, engineering is done by teams and when success is

important consultants are also hired.

Perhaps they are reluctant to change or they don’t want to do it someone else’s way. If you ask for advice, then

you should use the advice you are given.

Foreign students said, “It’s embarrassing to show weakness in the English language” and “Our culture teaches us

to not approach an advisor or mentor.”

Similarly, the medical profession does not practice extensive consultation with experts. In one study of over 300 breast

cancer surgeons (Katz et al., 2010), only one-fourth typically consulted medical oncologists, radiation oncologists or

plastic surgeons prior to surgery. About two-thirds of the surgeons reported that almost none of their patients

participated in patient decision-support activities, such as attending a practice-based presentation, viewing web-based

materials or participating in peer-support programs.

“He who trusts in himself is a fool, but he who walks in wisdom is kept safe” (Proverbs 28; 26)

4. Statistical Summary of Mental Mistakes

We examined 110 project reports composed of over 8000 pages of text that had been submitted over the last two

decades and we compiled the following statistics.

Type of Mental Mistake Number of

mistakes found

Using Dependent Criteria 75

Not Stating the Problem in Terms of

Stakeholder Needs 62

Vague Problem Statement 65

Substituting a Related Attribute 24

Sensitivity Analysis Mistakes 91

Forer Effect 61


40

Weight of Importance Mistakes 11

Anchoring and the Status Quo 69

Treating Gains and Losses Equally 46

Not Using Scoring Functions 32

Implying False Precision 59

Obviating Expert Opinion 85

Other Mental Mistakes 128

In these 110 tradeoff study reports, we found 808 mental mistakes. We put these in a spreadsheet. Then for 100 of these

mental mistakes, we made example cases using (1) direct quotes from the original reports, (2) an explanation of the

mistake, (3) related paragraphs from Smith et al. (2007) and (4) recommended revisions. We used a format similar to

that used in this paper. Based on the perceived heuristic value, uniform coverage of the 12 mental mistakes and

minimization of the number of projects that would have to be explained, we selected the two dozen development cases

(team excerpts) that are in this paper, and another 50 cases that were used for testing. Then 20 Raytheon engineers and

50 University of Arizona students tried to identify the mental mistakes in the 50 excerpts of the test set. The average

agreement was about 80%.

In general, we found no correlation between the number of mistakes we detected and the students’ grades on the reports.

There are several reasons for this. First, the reports with the highest grades were usually written better and they were

therefore easier to understand. The better we understand something the easier it is to find and identify mental mistakes

in it. Second, the better reports tended to be longer and more complete, and thus there was more opportunity for mental

mistakes. On the other hand, the poor reports showed more instances of mistakes of omission, such as failure to use

scoring functions, incomplete sensitivity analyses and failure to get advice from experts.

5. Who Cares?

Who cares about mistakes in doing tradeoff studies? Perhaps everyone should. If a tradeoff study is not performed or is

done badly it could cost a company a lot of money. As an example will now consider the San Diego Airport Site

Selection Tradeoff Study. This is a large, expensive, publicly accessible tradeoff study that contains mental mistakes

like those we present in this paper. This tradeoff study took six years and cost 17 million dollars. When its results were

presented to the voters in November of 2006, the voters turned the proposal down and the $17M was wasted. Some

mistakes might have been made in conducting this tradeoff study.

They did a tradeoff study, but only four of the ten tradeoff study components were utilized: Problem Statement,

Alternate Solutions, Evaluation Criteria and Preferred Alternatives.

They used five evaluation criteria: Aeronautical, Environmental, Market, Military and Financial. The criteria were

arranged hierarchally with subcriteria and subsubcriteria. However, the criteria did not have weights of importance or

scoring functions.

They had a dozen alternative sites, including the Do Nothing alternative. They often added and deleted alternatives. For

example, the floating platform in the Pacific Ocean was dismissed early. The Campo and Borrego Springs sites were

added late, so these sites had greater visibility in the public mind. However, the Campo and Borrego Springs sites were

similar so, because of distinctiveness by addition of alternatives, they faded away.

They did a rudimentary sensitivity analysis looking at changes in their planning parameters at two different demand

levels. They also did a small sensitivity analysis showing changes in total cost as a function of available funding

(without issuing bonds or increasing taxes).

The interim results of the study were continually being reported in the press. So they certainly received a lot of expert

opinions. However, in the end, the voters did not trust the study. The objectivity of the Regional Airport Authority that

conducted the study was questioned. It appeared over time that the Authority was more interested in supporting a

particular airport site than in explaining the various options for the voters. The Authority was perceived as being

pro-business and anti-military. The difficulties of military and civilian joint use were not ameliorated. San Diegans were

happy with the status quo: Lindberg Field was good for its community and the Marine Corps Air Station was good for

its community. The Authority did not show a burning platform or a compelling reason for change. It seemed that they

only considered future business growth.

The ballot proposal asked, “Should Airport Authority and government officials work toward obtaining 3,000 acres at

MCAS Miramar by 2020 for a commercial airport, providing certain conditions are met?” It was turned down 38% to


41

62%. We are not saying that if they had done a more thorough tradeoff study, then the ballot proposal would have

passed. We are only saying that they could have done a better tradeoff study.

6. Summary

Good industry practices for improving the probability of success of tradeoff studies include having teams evaluate the

data, evaluating the data in many iterations and expert review of the results and recommendations. It is important that

the review teams have a substantial number of reviewers that are external to the project and that the reviewers consider

design decisions as well as simple checking to ensure that tasks were done. Reviews are often hampered by failure to

allow external reviewers access to proprietary or classified data. To improve your tradeoff study process you should

inform your decision makers about how mental mistakes affect tradeoff studies (forewarned is forearmed), encourage a

long-term institutional decision horizon, use a team approach with frequent iterations and institute both expert and

public reviews. Finally try to reduce mental mistakes by using the recommendations of this paper.

The literature on Decision Making, Cognitive Science and Experimental Economics contains hundreds of experiments

showing persistent human mistakes of judgment. Smith et al. (2007) postulated 28 specific types of mental mistakes that

could affect the ten specific components of a tradeoff study. This paper has shown examples in a dozen categories of

mental mistakes that systems engineers have actually made while creating tradeoff studies. The research found over

eight hundred examples of such mistakes: these examples prove that systems engineers really do make such mistakes.

References

Abdellaaoui, M. (2000). Parameter-free elicitation of utility and probability weighting functions, Management Science,

46(11), 1497-1512. http://dx.doi.org/10.1287/mnsc.46.11.1497.12080

Bahill, A. T. (2008). Decision Making and Tradeoff Studies,

http://www.sie.arizona.edu/sysengr/slides/decisionMaking.ppt, last accessed March 2010.

Bahill, A. T., & Baldwin, D. G., (2007). Describing baseball pitch movement with right-hand rules, Computers in

Biology and Medicine, 37, 1001-1008. http://dx.doi.org/10.1016/j.compbiomed.2006.06.007

Bahill, A. T., & Baldwin, D. G. (2008). Mechanics of baseball pitching and batting, Chapter 16 Applied Biomedical

Engineering Mechanics, Dhanjoo Ghista, CRC Press and Taylor & Francis Asia Pacific, pp. 445-488.

Bahill, A. T., Baldwin, D. G., & Ramberg, J. S. (2009). Effects of altitude and atmospheric conditions on the flight of a

baseball, International Journal of Sports Science and Engineering, 3(2), 109-128. ISSN 1750-9823 (print).

http://www.worldacademicunion.com/journal/SSCI/online.htm

Bahill, A. T., Baldwin, D. G., & Venkateswaran, J. (2005). Predicting a baseball's path, American Scientist, 93(3),

218-225.

Bahill, A. T., & Dean, F. F. (1999, 2009). Discovering system requirements, Chapter 4 in Handbook of Systems

Engineering and Management, A.P. Sage & W.B. Rouse (Eds), John Wiley & Sons, first edition 175-220, 1999,

second edition, 205-266.

Bahill, A. T., & Karnavas, W. J. (2000). Risk analysis of a pinewood derby: A case study, Systems Engineering, 3(3),

143-155. http://dx.doi.org/10.1002/1520-6858(200033)3:3<143::AID-SYS3>3.0.CO;2-0

Bahill, A. T., & LaRitz, T. (1984). Why can't batters keep their eyes on the ball, American Scientist, 72, 249-253.

Bahill, A. T., & Smith, E. (2009). An industry standard risk analysis technique, Engineering Management Journal,

21(4), 16-29.

Bahill, A. T., & Stark, L. (1975). Neurological control of horizontal and vertical components of oblique saccadic eye

movements, Mathematical Biosciences, 27, 287-298. http://dx.doi.org/10.1016/0025-5564(75)90107-8

Bahill, A. T., & Stark, L. (1977). Oblique saccadic eye movements: Independence of horizontal and vertical channels,

Archives of Ophthalmology, 95, 1258-1261. http://dx.doi.org/10.1001/archopht.1977.04450070156016

Baldwin, D. G., Bahill, A. T., & Nathan, A. (2007). Nickel and dime pitches, Baseball Research Journal, 35, 25-29.

Bleichrodt, H., & Pinto, J. L. (2000). A parameter-free elicitation of the probability weighting function in medical

decision analysis, Management Science, 46(11), 1485-1496. http://dx.doi.org/10.1287/mnsc.46.11.1485.12086

Chapman, W. L., Bahill, A. T., & Wymore, A. W. (1992). Engineering modeling and design, CRC Press Inc., Boca

Raton, FL.

Chrissis, M. B., Konrad, M., & Shrum, S. (2003). CMMI: Guidelines for Process Integration and Product Improvement,

Pearson Education Inc., Boston.

http://www.sie.arizona.edu/sysengr/slides/decisionMaking.ppt

http://www.sie.arizona.edu/sysengr/publishedPapers/GhistaChapt16.pdf

http://www.sie.arizona.edu/sysengr/publishedPapers/airDensity.pdf



http://www.sie.arizona.edu/sysengr/publishedPapers/baseballPath.pdf

http://www.sie.arizona.edu/sysengr/publishedPapers/NickelDime_BRJ35.pdf


42

CMMI for Development, ver. 1.3, (2010). Software Engineering Institute, Pittsburgh, PA,

http://cmmiinstitute.com/resource/cmmi-for-development-version-1-3-microsoft-word/

Retrieved November 2013

Daniels, J. P., & Bahill, A. T. (2004). Hybrid process combines traditional requirements and use cases, Systems

Engineering, 7(4), 303-319. http://dx.doi.org/10.1002/sys.20013

Daniels, J., Werner, P., & Bahill, A. T. (2001). Quantitative methods for tradeoff analyses, Systems Engineering, 4(3)

190-212. http://dx.doi.org/10.1002/sys.1016

Forer, B. R. (1949). The fallacy of personal validation: A classroom demonstration of gullibility, Journal of Abnormal

Psychology, 44, 118-121. http://dx.doi.org/10.1037/h0059240

Hanselmann, M., & Tanner, C. (2008). Taboos and conflicts in decision making: sacred values, decision difficulty, and

emotions, Judgment and Decision Making, 3(1), 51-63.

Hooks, F., & Farry, K. A. (2001). Customer-centered products: Creating successful products through smart

requirements management, AMACOM, New York.

Hsu, F. K., Bahill, A. T., & Stark, L. (1976). Parametric sensitivity of a homeomorphic model for saccadic and

vergence eye movements, Computer Programs in Biomedicine, 6, 108-116.

http://dx.doi.org/10.1016/0010-468X(76)90032-5

Hull, E., Jackson, K., & Dick, J. (2005). Requirements engineering, Springer, London.

INCOSE Systems Engineering Handbook v3.2.2, (2011). Retrieved November 2013

http://www.incose.org/ProductsPubs/incosestore.aspx

Kahneman, D. (2002). Maps of bounded rationality: a perspective on intuitive judgment and choice, Nobel Prize

Lecture, December 8, 2002, this site also has a video of the speech,

http://nobelprize.org/nobel_prizes/economics/laureates/2002/kahneman-lecture.html

Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality, American Psychologist,

58(9), 697-720. http://dx.doi.org/10.1037/0003-066X.58.9.697

Kahneman, D., & Tversky, A. (1979).Prospect theory: An analysis of decision under risk, Econometrica, 46(2),

171-185.

Karnavas, W. J., Sanchez, P. J., & Bahill, A. T., (1993). Sensitivity analyses of continuous and discrete systems in the

time and frequency domains, IEEE Transactions on Systems, Man and Cybernetics, SMC-23, 488-501.

http://dx.doi.org/10.1109/21.229461

Katz, S. J., Hawley, S. T., Morrow, M., Griggs, J. J., Jagsi, R.., Hamilton, A. S., Graff, J. J., Friese, C. R., & Hofer, T. P.

(2010). Coordinating cancer care: patient and practice management processes among surgeons who treat breast

cancer, Medical Care, 48(1), 45-51. http://dx.doi.org/10.1097/MLR.0b013e3181bd49ca

Keeney, R. L. (1992). Value-focused thinking: A path to creative decision making, Harvard University Press,

Cambridge, MA.

Marquard, L., & Robinson, S. M. (2008). Reducing perceptual and cognitive challenges in making decisions with

models, in Decision Modeling and Behavior in Complex and Uncertain Environments, Eds. T. Kugler, J. C. Smith,

T. Connolly & Y. J. Son., Springer, Science+Business Media, NY, NY, pp. 33-55.

McBeath, M. K., Nathan, A. M., Bahill, A. T., & Baldwin, D. G. (2008). Paradoxical pop-ups: Why are they hard to

catch? American Journal of Physics, 76(8), 723-729. http://dx.doi.org/10.1119/1.2937899

Piattelli-Palmarini, M. (1994). Inevitable illusions: How mistakes of reason rule our minds, John Wiley & Sons, New

York.

RSAS, Press release: Nobel Prize in Economics 2002, Retrieved September 2008 from The Royal Swedish Academy of

Sciences: http://nobelprize.org/nobel_prizes/economics/laureates/2002/press.html.

San Diego Airport Site Selection,

http://www.san.org/documents/sdcraa/archives/Airport%20Site%20Selection%20Program/Technical%20Analysis/

Financial%20Comparative%20Analysis%20Presentation.pdf Accessed November 2013.

Sage, A. P. (1981). Behavioral and organizational considerations in the design of information systems and processes for

planning and decision support, IEEE Transactions on Systems, Man and Cybernetics, SMC-11(9) 640-680.

http://dx.doi.org/10.1109/TSMC.1981.4308761

http://cmmiinstitute.com/resource/cmmi-for-development-version-1-3-microsoft-word/

http://www.incose.org/ProductsPubs/incosestore.aspx

http://nobelprize.org/nobel_prizes/economics/laureates/2002/press.html

http://www.san.org/documents/sdcraa/archives/Airport%20Site%20Selection%20Program/Technical%20Analysis/Financial%20Comparative%20Analysis%20Presentation.pdf

http://www.san.org/documents/sdcraa/archives/Airport%20Site%20Selection%20Program/Technical%20Analysis/Financial%20Comparative%20Analysis%20Presentation.pdf


43

Smith, E. D., Piattelli-Palmarini, M., & Bahill, A. T., (2008). Cognitive biases affect the acceptance of tradeoff studies,

in Decision Modeling and Behavior in Complex and Uncertain Environments, Eds. T. Kugler, J. C. Smith, T.

Connolly & Y. J. Son., Springer, Science+Business Media, NY, NY, pp. 227-249.

Smith, E. D., Son, Y. J., Piattelli-Palmarini, M., & Bahill, A. T., (2007). Ameliorating the effects of cognitive biases on

tradeoff studies, Systems Engineering, 10(3), 222-240. http://dx.doi.org/10.1002/sys.20072

Smith, E. D., Szidarovszky, F., Karnavas , W. J., & Bahill, A. T. (2008). Sensitivity analysis, a powerful system

validation technique, The Open Cybernetics and Systemics Journal, 2, 39-56.

http://dx.doi.org/10.2174/1874110X00802010039.

Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty, Psychological Science, 3(5),

305-309. http://dx.doi.org/10.1111/j.1467-9280.1992.tb00678.x

Wymore, A. W. (1993). Model-based systems engineering, CRC Press Inc., Boca Raton, FL.

Zhu, A., Aurum, I., Gorton. & Jeffery, R. (2005). Tradeoff and sensitivity analysis in software architecture evaluation

using analytic hierarchy process, Software Quality Journal, 13(4), 357-375.

http://dx.doi.org/10.1007/s11219-005-4251-0

Biographical Sketches

James Bohlman works for Intex, a small startup making HF IR emitters for gas detection technology. He is working to

specify and obtain equipment for testing and burn-in. He joined STRC a small startup in May 2008 as the senior

engineer and has been involved almost from the beginning in the construction of the lab space. STRC is a research

group dedicated to the purification of metallurgical-grade silicon into solar-cell useable silicon by metallurgical

refination and hydrometallurgy. He attended University of Wisconsin at Madison where receiving a BS in Metallurgical

and Mining Engineering. He worked at Texas Instruments in Dallas Texas in the pilot line wafer fab metallization area

running sputter deposition PVD equipment. He then worked in a production wafer fab called DMOS IV processing 6"

silicon wafers into one megabit DRAM memory circuits later working on application specific integrated circuits (ASICs)

as the memory business went to Japan. James also worked at Analog Devices in Norwood, Massachusetts as a process

engineer in metallization and implant primarily on high-end bipolar circuits customizable with a trimable SiCr (Silicon

Chrome) resistor. Then at Burr Brown Corp., (which subsequently became Texas Instruments in 2000) he was a CVD

and PECVD process engineer producing high-performance bipolar A-to-D circuits. He also worked on implementation

of a special resistor process to make the parts more reliable, reducing quality issues and customer concerns. He has an

MBA from the University of Phoenix and a Masters of Engineering in Systems Engineering from the University of

Arizona; two degrees which complement each other in their approach to projects, systems and business.

Terry Bahill is an Emeritus Professor of Systems Engineering and of Biomedical Engineering at the University of

Arizona in Tucson. He received his Ph.D. in electrical engineering and computer science from the University of

California, Berkeley, in 1975. Bahill has worked with dozens of high-tech companies presenting seminars on Systems

Engineering, working on system development teams and helping them to describe their Systems Engineering processes.

He holds a U.S. patent for the Bat Chooser, a system that computes the Ideal Bat Weight for individual baseball and

softball batters. He was elected to the Omega Alpha Association: the Systems Engineering Honor Society. He received

the Sandia National Laboratories Gold President's Quality Award. He is a Fellow of the Institute of Electrical and

Electronics Engineers (IEEE), of Raytheon Missile Systems, of the International Council on Systems Engineering

(INCOSE) and of the American Association for the Advancement of Science (AAAS). He is the Founding Chair

Emeritus of the INCOSE Fellows Selection Committee. His picture is in the Baseball Hall of Fame's exhibition

"Baseball as America." You can view this picture at http://www.sie.arizona.edu/sysengr/.






ISSN 2330-2038 E-ISSN 2330-2046



44

The Valve Timing Optimization of the Diesel Engine Based on Response

Surface Methodology

Jun Li, Lei Ji, Yangjiao Xu & Jinli Xie

Chongqing Jiaotong University, Chongqing, China

Correspondence: Jun Li, Mechantronics and Automotive Engineering, Chongqing Jiaotong University, 400074,

Chongqing, China. Tel: 86-138-8390-1379. E-mail: [email protected]

Received: October 30, 2013 Accepted: November 11, 2013 Available online: December 5, 2013


Abstract

To study the effect of valve timing on the diesel engine performance, the simulation model of diesel engine was

established with AVL BOOST and its accuracy was proved. The volumetric efficiency is one of the important indicators

to evaluate engine performance. The volumetric efficiency as optimization objective and valve timing were optimized

and discussed by using Box-Behnken test method and the response surface methodology. Optimization result shows that

volumetric efficiency of the diesel engine can been increased by 6.42% under rated speed.

Keywords: response surface methodology, valve timing, volumetric Efficiency

1. Introduction

The simulation of the engine’s working process has become an important method to the research and development (Lei

et al., 2011; Rakopoulos et al., 2004; Razmjooei et al., 2010). It is established the one-dimensional simulation model of

the working process of diesel engine by AVL BOOST. And the simulation model is validated by speed characteristic.

Then the influence of valve timing on the volumetric efficiency of diesel engine is analyzed and optimized in using the

response surface methodology to obtain the optimal valve timing and the volumetric efficiency of engine. The

volumetric efficiency can be increased 6.42% under the rated speed.

2. Model Establishment

2.1 The Model Establishment

The 4-cylinder, 4-stroke and turbocharged diesel engine was used in bench test. The basic parameter of the diesel engine

is shown in Tab.1. The simulation model was established, shown in Fig.1. The Vibe 2 Zone heat release model and

Woschni1978 heat transfer model was used (Liu, 2011).

Table 1. The main parameters of diesel engine

Basic parameters Parameter values

Compression Ratio 18

Bore×Stoke ( mm ) 75×80

Rated Power( kW ) 65

Rated Speed( min/r ) 4500

Intake Valve Close(IVO)(ºCA) 63

Intake Valve Open(IVC)(ºCA) 101

Exhaust Valve Open(EVO)(ºCA) 105

Exhaust Valve Close(EVC)(ºCA) 63

2.2 Validation of the Simulation Model

The simulation model of diesel engine was verified from calculated results and experimental results, shown in Fig.2.


45

Figure 1. Simulation model of diesel engine

Figure 2. The calculated results compared with the experimental results

The comparative result shows that the relative deviation between simulation and experiment are both below

5%.Therefor the simulation model of diesel engine established in this paper is accurate and reliable.

3. Valve Timing Optimization Based on Response Surface Methodology

3.1 Response Surface Methodology

Response Surface Methodology is a product with the development of statistics, mathematics and computer science.

Experimenting, modeling, analyzing data, using graphics technology are used in order to show up the relationship of

response system and we can know and select the optimized response of experiment design directly (Montgomery, 2007;

Chen et al, 2009; Simate et al., 2009; Li et al., 2007; Liu, S. S. et al., 2012; Liu, C. et al., 2012). Response surface

analysis of experiment includes Central Composite Design, Box-Behnken Design, Quadratic saturation D-optimal

Design, Uniform Design, etc. Box-Behnken Design which can be called the efficiency design method, can be estimated

in the Linear and Quadratic polynomial with the Linear interaction of polynomial model by fewer tests (Chen et al,

2009). The influence of valve timing on the volumetric efficiency of diesel engine under the rated speed is discussed

and the response surface experiment is designed by using Box-Behnken Design. The test points and test data are

showed in Tab.2.


46

Table 2. Testing and test data of Box-Behnken design

Std IVO IVC EVO EVC volumetric efficiency

1 73 101 105 73 0.8231

2 63 91 105 73 0.8066

3 63 111 105 53 0.8466

4 63 101 105 63 0.8400

5 63 91 105 53 0.7903

6 63 91 105 63 0.8400

7 53 101 105 73 0.8496

8 73 91 105 63 0.7896

9 73 101 115 63 0.8264

10 53 101 105 53 0.8268

11 63 101 105 63 0.8400

12 63 91 95 63 0.8034

13 63 111 105 73 0.8606

14 63 101 115 53 0.8216

15 63 101 105 63 0.8400

16 53 101 115 63 0.8481

17 73 101 95 63 0.8252

18 63 101 115 73 0.8441

19 63 101 105 63 0.8400

20 63 91 115 63 0.8090

21 63 101 95 73 0.8432

22 73 111 105 63 0.8469

23 53 101 95 63 0.8444

24 63 101 95 53 0.8258

25 63 111 95 63 0.8576

26 63 111 115 63 0.8628

27 53 91 105 63 0.8120

28 53 111 105 63 0.8632

29 73 101 105 53 0.8115

3.2 The Analysis of Response Surface

Design-Expert is a software which is used in optimized experiment by response surface widely. The equation of test

response surface is some supposed. The hypothesis is: H0:β1=β2=β3=…=βi=0， H1:β1, β2, β3, …, βi

Where: at least, one parameter is not equal to zero, and the significance level is α=0.05.The "P value" is a concept

which is the judgment instead of rejection region in statistics. The Box-Behnken Design of optimized analysis is used in

this paper. The Tab.3 shows that the P values of AC, BC, BD, CD and C2 are more than 0.05, which indicates the terms

in model are not notable, and need to be re-optimized.

Table 3. ANOVA for response surface quadratic model

Source Sun of Squares df Mean Square F value P-value

Prob>F

Model 0.012 14 0.00083 344.14 <0.0001

A-IVO 0.00122 1 0.00122 504.82 <0.0001

B-IVC 0.00878 1 0.00878 3609.10 <0.0001

C-EVO 0.000012 1 0.000012 5.10 0.0038

D-EVC 0.000945 1 0.000945 389.24 <0.0001

AB 0.000009 1 0.000009 3.82 0.0453

AC 0.000001 1 0.000001 0.64 0.4363

AD 0.000036 1 0.000036 2.44 0.00140

BC 0.000001 1 0.000001 0.037 0.8502

BD 0.000001 1 0.000001 0.0092 0.9247

CD 0.000009 1 0.000009 2.67 0.1244

A2 0.000151 1 0.000151 62.07 <0.0001

B2 0.000352 1 0.000352 145.02 <0.0001

C2 0.000002 1 0.000002 1.50 0.2409

D2 0.000336 1 0.000336 138.22 <0.0001

Residual 0.000034 14 0.000002

Lack of Fit 0.000034 10 0.000002

Pure Error 0.000 4 0.000003

Cor Total 0.012 28 R2=0.9971


47

The Tab.4 shows that the P values of all are less than 0.05, which indicates the terms in model are significant; then the

response surface equation can be used. The response surface model equation is:

22

2

007342.0*007517.0

004967.0**0028.0**001525.0*008883.0

*001017.0*027.0*010.0814.0efficiencyvolumetric

DB

ADABAD

CBA

(1)

Table 4. ANOVA for the optimized response surface quadratic model

Source Sum of Squares df Mean Square F Value p-value Prob>F

Model 0.012 9 0.00130 538.74 <0.0001

A-IVO 0.00122 1 0.00122 508.82 <0.0001

B-IVC 0.00878 1 0.00878 3635.70 <0.0001

C-EVO 0.000012 1 0.000012 5.14 0.0038

D-EVC 0.000945 1 0.000945 392.11 <0.0001

AB 0.000009 1 0.000009 3.85 0.0453

AD 0.000031 1 0.000031 12.99 0.0019

A2 0.000166 1 0.000166 68.72 <0.0001

B2 0.000380 1 0.000380 157.39 <0.0001

D2 0.000362 1 0.000362 150.15 <0.0001

Residual 0.000034 19 0.000002

Lack of Fit 0.000034 15 0.000002

Pure Error 0.000 4 0.000

Cor Total 0.012 28 R2=0.9971

Figure 5(a). Contour plot of response surface methodology

Figure 5(b). Contour plot of response surface methodology


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Figure 6(a). 3D surface of response surface methodology

Figure 6(b). 3D surface of response surface methodology

The Fig.5 and Fig.6 shows that: IVO is 53ºCA, IVC is 111ºCA, EVO is 115ºCA, EVC is 71ºCA.

3.3 Verifying the Optimized Results of the Response Surface

The optimal valve timing which is got from the response surface methodology is used to verify the simulation model.

The Tab.5 shows that the volumetric efficiency is increased by 6.42% after optimized.

Table 5. Volumetric efficiency contrast of before and after optimization

Type IVO ºCA IVC ºCA EVO ºCA EVC ºCA volumetric efficiency

Original 63 101 105 63 0.841

Optimization 53 111 115 71 0.895

4. Conclusions

1) Based on the response surface methodology, we can optimize the volumetric efficiency and valve timing of diesel

engine, establish the response surface quadratic model, draw the 3D surface of response surface methodology and then

can carry out the optimization and interaction between volumetric efficiency and valve timing.

2) Getting the valve timing of the diesel engine from the response surface methodology, analyzed the simulation model

of the diesel engine. The results show that the volumetric efficiency can be optimal value under the rated speed.


49

Acknowledgements

This project is supported by National Natural Science Foundation of China (No. 51305472) and Education and

Teaching Reform Project of Chongqing CSTC, China (KJ090408; No.0903070)

References

Chen, X. K., Li, B. G., & Lin, Y. (2009). Application of Improved RSM in the Optimization Design of Automotive

Frontal Crashworthiness. Transaction of Beijing Institute of Technology, 1076-1077.

http://lib.cqvip.com/read/detail.aspx?ID=32654508

Lei, J. L., Huang, Z. P., Shen, L. H., et al. (2011). Working Process Simulation and Performance Optimization of

High-pressure Common Rail Diesel Engine. Vehicle Engine, 53-57.

http://202.202.244.3/kns50/detail.aspx?QueryID=27&CurRec=1

Li, J., & Liang, X. G. (2007). Scramjet Inlet Multi-Objective Optimization Based on response surface methodology.

Transactions of Nanjing University of Aeronautics & Astronautics, 205-209.

http://en.cnki.com.cn/Article_en/CJFDTOTAL-NJHY200703006.htm

Liu, C., Pan, X., Yan, Q. D., et al. (2012). Effect of Blade Number on Performance of Torque Converter and Its

Optimization Based on DOE and Response Surface Methodology. Transaction of Beijing Institute of Technology,

689-693. http://lib.cqvip.com/qk/95548X/201207/43098212.html

Liu, F. F., Jiang, C. H., & Xia, X. L. (2011). Effect on Performance of Gasoline Engine about Intake Valve Closing

Angle. Journal of Nanchang University (Engineering & Technology), 66-68.

http://lib.cqvip.com/read/detail.aspx?ID=37154422

Liu, S. S., Gu, Z. Q., Wu, W. G., et al. (2012). Multi-objective Collaborative Optimization of Vehicle Based on

Response Surface Methodology. Journal of Central South University (Science and Technology), 2586-2591.

http://lib.cqvip.com/qk/90745B/201207/42974900.html

Montgomery, D. C. (2007). Design and Analysis of Experiments, 6th Ed. New York: 404-406.

Rakopoulos, C. D., Giakoumis, E. G., Hountalas, D. T., et al. (2004). The Effect of Various Dynamic, Thermodynamic

and Design Parameters on the Performance of a Turbocharged Diesel Engine Operating under Transient Load

Conditions. SAE Paper. http://papers.sae.org/2004-01-0926/

Razmjooei, K., & Nagarajan, G. (2010). Optimization of DI Diesel Engine Operating Parameters Using a Response

Surface Method. SAE Paper. http://papers.sae.org/2010-01-1262/

Simate, G. S., Ndlovu, S., & Gericke, M. (2009). Bacterial leaching of nickel laterite using chemolithotrophic

microorganisms: Process optimization using response surface methodology and central composite rotatable design.

Hydrometallurgy, 4(3), 241-243. http://www.sciencedirect.com/science/article/pii/S0304386X09001236






ISSN 2330-2038 E-ISSN 2330-2046



50

Network-based Management on Repairing Tool Kits of Civil Aviation

Engineering Maintenance

Xiaoxu Tian1, Xinlei Zheng

2, Ting Wang

2, Na Li

2, Haifeng Wang

2, Fuqing Huang

3

1Person-in-charge of project, Civil Aviation University of China, Tianjin, China

2Members of project, Civil Aviation University of China, Tianjin, China

3Instructor, Civil Aviation University of China, Tianjin, China

Correspondence: Xiaoxu Tian, Person-in-charge of project, Civil Aviation University of China, Tianjin 300300, China.

E-mail: [email protected]. Fuqing Huang, Instructor, Civil Aviation University of China, Tianjin 300300, China.

E-mail: [email protected]

Received: December 5, 2013 Accepted: December 23, 2013 Available online: January 16, 2014


Abstract

Based on features of high speed of network transmission and easy operations, this thesis covers two aspects to realize

network-based management on repairing tool kits of civil aviation engineering maintenance. Firstly, develop a network

inquiry system, which can help employees and administrators inquire tool borrowing information. Secondly, a module

is designed that has functions to transmit text messages to tool kits borrowers prompting them to return tools at times

when the returning date approaches.

Keywords: network, management, inquiry system, text messages

1. Introduction

As the civil aviation industry is developing very fast in China, working loads of engineering maintenance is increasing

with each passing day. The traditional registration method for repairing tool kits can no longer meet requirement by

modern management and hence. It is extremely urgent to develop a highly efficient management platform for

engineering maintenance tool kits. This thesis solves the problem from two aspects. Firstly, using ASP (Active Server

Page) technology and network database theory, we design a network inquiry system for repairing tool kits based on the

B/S (Browser/Server) mode. This system contains two parts, which are employee inquiry and administrator inquiry. For

employees, they can inquire their own real-time tool borrowing information and submit tool booking requests on line

according to their needs. For administrators, they are able to remotely inquire tool borrowing information of all the

employees and approve or reject applications by employees. Secondly, design a module that has text message

transmission functions based on GSM (Global System For Mobile Communication) network to tool borrowers

prompting them to return tools at times when the returning date is approaching.

2. Methodology

This system using the B/S model , the Dreamweaver homepage manufacture software, the ASP dynamic homepage

technology and the SQL Server(Structured Query Language Server) backstage data server, realizes network-based

management on repairing tool kits of civil aviation engineering maintenance.

In the mode of B/S, the client does not need any special software except the browser. The browser exchanging

information with database through the web (World Wide Web) server, can work in different platforms expediently. This

system achieves the function that employees and administrators inquire their borrowing information through the

browser based on the B/S model. Dreamweaver MX 2004 is used to design or develop web pages and web applications.

It is a strong software, which contains the visual layout tools, application development function and code editor support

and it has a strong function of multimedia webpage design.

ASP (Yue, et al., 2002) is a server-side scripting environment and it can create and run dynamic web pages or web

applications. When the browser of client sends a request to server, the ASP interpretive program of server carries out

the ASP program at the server-side and delivers the result to the browser in HTML (Hyper Text Markup Language)

format. In the production of web pages, the name of the object which saves and takes database is ADO (ActiveX Data


51

Objects). The main target of ADO is saving, taking or altering the data of source or adding data to the specified data

source.

This system uses SQL Server2000 (Shaosong, et al., 2006) as the data server. SQL Server2000 has many advantages,

such as convenient operation, good scalability and high related software integration degree and it can be used in many

platforms. In this system, the name of database is SCHOOL and many tabulations in the SCHOOL have been used,

such as EMP (tabulation of employee), ADM (tabulation of administrator), BOR (tabulation of borrowing tools),

ABOR (tabulation of available borrowing tools), BOO (tabulation of booking tools) and APP (tabulation of approval).

Furthermore, this system uses a lot of scripting language, which is an explanatory language. Not only can scripting

language be executed by browser directly, but also it can access to the various objects in the browser. With the help of

scripting language, this system completes the task of data validation before the tabulation is submitted and achieves the

function of opening or closing the window.

The above methodology is for the network inquiry system, the methodology of text message prompt modules will be

introduced in the fourth part of the thesis.

3. Network Inquiry System

3.1 Employee Inquiry

The network inquiry system (Chenzhi, et al., 2013; Iahad, et al., 2012) offers employee a platform, where they can

inquire their real-time tool borrowing information in order to avoid forgetting owing to too long a time. Figure 1

illustrates flowchart of the employee inquiry. Employees only input their account number in the log-in page to enter

their own tool borrowing information interface, where information about tool kits they have borrowed and tools that can

be borrowed can be searched. Based on the above two basic functions, we have perfected the network platform so as to

realize tool online booking functions. If employees apply online, tool kits can be borrowed, thus simplifying borrowing

procedures and increasing efficiency. Figure 2 shows the interface of employee inquiry.

Figure.1 Flowchart of employee inquiry

Figure 2. Interface of employee inquiry

Figure 1. Flowchart of employee inquiry


52

3.2 Administrator Inquiry

How to manage tools in an overall and unified way is hard to administrators in maintenance practices and in order to

solve this problem, we have developed the administrator inquiry, flowchart of which is shown in Figure 3. In the

flowchart, you can find four functions of the administrator inquiry.

There is no difference in appearances between employee and administrator inquiry interface. However, there is essential

difference in power and permission of them. First, for employee inquiry, only tool borrowing information of the

employee himself can be inquired. While for administrator inquiry, tool borrowing information of all employees can be

inquired. Second, employees only have right to apply for tool borrowing, while administrators have right to approve or

reject applications by employees.

4. Text Message Prompt Modules

4.1 Basic Targets of the Modules

In maintenance practices of employees, it is hard to avoid forgetting tool borrowing owing to too long a time, thus

decreasing tool utilization rates. We have developed text message transmission modules based on GSM network to deal

with this problem. When tool returning date is approaching, the module will transmit text messages to borrowers

prompting them to return the tools they have borrowed on time.

4.2 Fundamental Principles of the Text Message Transmission Modules

Flowchart of the module is shown in Figure 4.The upper computer transmits instructions to a single-chip

microcontroller for processing and AT (Attention) instructions are then transmitted to the GSM modules through a

serial port, completing control on the GSM modules and transmitting text messages.

4.3 Hardware Development of the Text Message Modules

The system hardware comprises two modules, i.e. controller and communication. As the communication module will

generate strong current during starting and text message transmission and reception . In order to enhance resistance to

interferences and expandability, we made the two modules in two separate boards. Figure 5 is a picture of the text

message transmission module.

Figure 3. Flowchart of administrator inquiry

Figure 4. Flowchart of text message transmission module


53

The controller mainly controls and protects the single-chip microcontroller, and C8051F020 (Ling, et al., 2006) is used

in this design as the MCU (Micro Control Unit), where pipeline architecture is used in its internal core at a speed as

high as 25MIPS (Million Instructions Per Second), ten times faster than common ones. The controller circuits comprise

eight sub-modules. They are C8051F020 minimum system, NOKIA5110 liquid crystal display, keyboard, SD card,

power, RS232 (Recommend Standard 232) communication interfaces, MC52 control interface and external memory

interface, totaling eight. Two modules, i.e. SD card and RS232 are described in detail as the following.

The reason for designing a SD memory module in the controller circuits is mainly for real-time records of messages

transmitted for future access. There are two bus modes, one being SD and one being SPI(Single Program Initiation), the

more popular SPI mode is used in this system. Figure 6 shows actual SD card driving circuit, where R31 - R35 are

pull-up resistors. The RS232 interface circuits are mainly for realization of data transmission between the single-chip

microcontroller and GSM module. Because the main controlling board is supplied with power 3.3V, so, the level

translation chip used is MAX3232, actual circuit of which is shown in Figure 7.

Core of the communication module is a GSM module (Wei, et al., 2008), which is a communication module similar to

the cell phone, having functions of sending text messages, voice communications and so on. Although being small, this

module has been utilized widely in many fields. The GSM module makes control by means of AT instructions and can

be connected to computer RS232 serial ports. Furthermore, it can be controlled by single-chip microcontrollers.

Compared with other kinds of remote transmission networks, GSM has higher security and confidentiality features,

which makes it suitable for applications in sensitive industrial sites. Besides, GSM networks covers wide areas and is

basically not limited by transmission distances and there is no need to establish special network and maintenance

Figure 5. A picture of text message transmission module

Figure 7. RS232 Interface circuits Figure 6. SD card driving circuits


54

networks, enjoying great superiority in communication costs. Hence, GSM modules are selected for this text message

prompting module.

4.4 Software Development of the Text Message Transmission Modules

The software developed this time is based on the platform Keil uVision 4, using language C as shown in Figure 8

program flowchart. After the device is powered, all the modules will be initialized and text messages can be sent after

success. Information transmitted can be stored in the SD card.

The AT instructions general apply in the connection and communication between PC and terminal equipment. As

mentioned in the previous paragraphs, the GSM (Biancucci, et al., 2013) modules perform control through AT

instructions. In other words, control processes on the GSM modules are, in reality, processes of sending AT instructions.

Sending a piece of text message is completed through the following steps:

1) Sending AT+CMGF, setting text message format;

2) Sending AT+CSCA, setting text message center number;

3) Sending AT+CMGS, setting user’s cell phone number;

4) Inputting characters to be sent.

The SD card memory (Huan, 2009) is another highlight in this design. In order to read text messages on different

platforms, FAT32 (File Allocation Table) file system is transplanted into the SD card read-write operations so as to

write all communication messages into SD card in format TXT, realizing data records.

5. Conclusions

We complete the network inquiry system and the text message prompt modules through intensive research and

development, realizing network management and efficient management on civil aviation engineering maintenance tool

kits. This system solves practically the hard-to-solve problem facing the civil aviation engineering maintenance sector

and it meets the modern requirement of the development. We believe that once this project is promoted and used widely,

efficient management on civil aviation engineering maintenance tool kits is expected.

Based on the system, we will continue to develop the management of tool kits to improve the speed of borrowing and

returning tools. We will establish a POS (Point Of Sales) machine terminal, which can replace the way of manual input

with scan mode. If the terminal is complete, the whole system will be a powerful tool management system.

Acknowledgement

This work was supported by National Training Programs of Innovation and Entrepreneurship for Undergraduates.

Figure 8. Flowchart of programs


55

References

Anonymous. Record management system based on the B/S model. Retrieved from

http://wenku.baidu.com/view/d307220c6c85ec3a87c2c53d.html

Biancucci, G., Claudi, A., & Dragoni, A. F. (2013). Secure data and voice transmission over GSM voice channel:

Applications for secure communications. Proceedings - 4th International Conference on Intelligent Systems,

Modelling and Simulation, ISMS 2013, 230-233. http://dx.doi.org/ 10.1109/ISMS.2013.10

Chenzhi, G., & Zhenya, L. (2013). An inquiry-based blended learning system for computer network curriculum.

Proceedings of the 8th International Conference on Computer Science and Education, ICCSE 2013, 1340-1345.

http://dx.doi.org/10.1109/ICCSE.2013.6554130

Huan, H. (2009). Development of network monitoring system based on the CAN buses. Retrieved from

http://d.wanfangdata.com.cn/Thesis_D066827.aspx

Iahad, N. A, Mirabolghasemi, M., & Huspi, S. H. (2012). A blended community of inquiry approach: The usage of

social network as a support for Course Management System. 2012 International Conference on Computer and

Information Science, ICCIS 2012 - A Conference of World Engineering, Science and Technology Congress,

ESTCON 2012 - Conference Proceedings,180-183. http://dx.doi.org/ 10.1109/ICCISci.2012.6297235

Ling, X., & Xiaoyan, C. (2006). Single-chip microcontroller C8051F020, its features and applications in

telecommunication systems. Journal of Henan Mechanical and Electrical Engineering College, 14(6), 15-16.

http://dx.doi.org/10.3969/j.issn.1008-2093.2006.06.007

Shaosong, Y., Xiangfa, R., & Yan, Z. (2006). Design and research of storehouse manage system based on SQL Server

2000 database. MACHINERY DESIGN & MANUFACTURE. http://dx.doi.org/

10.3969/j.issn.1001-3997.2006.02.078

Wei, X., & Jianqing, Z. (2008). GSM modules – A New prominent in realization of remote control. Radio, 10, 54-56.

http://lib.cqvip.com/qk/94496X/200810/28294784.html

Yue, Z., & Yushun, F. (2002). The Design and Implementation of Workfiow Management System Based on COM and

ASP. COMPUTER ENGINEERING AND APPLICATIONS, 38(1),

http://dx.doi.org/10.3321/j.issn:1002-8331.2002.01.080


http://wenku.baidu.com/view/d307220c6c85ec3a87c2c53d.html

http://d.wanfangdata.com.cn/Thesis_D066827.aspx





ISSN 2330-2038 E-ISSN 2330-2046



56

Times Semi-Passive RFID Tags with Double Loop Antennas Arranged as

a Shifted Gate Stability Optimization

Ofer Aluf

Correspondence: Physical Electronics Dept., Tel-Aviv University, Ramat-Aviv, 69978, Israel

Received: December 13, 2013 Accepted: December 29, 2013 Available online: January 17, 2014


Abstract

In this article, Very Crucial subject discussed in Semi-Passive RFID TAGs system stability. Semi-Passive TAGs with

double loop antennas arranged as a shifted gate system stability optimization under delayed electromagnetic

interferences. The double loop antenna is employed due to the fact that this antenna consists of two parallel loops; i.e.,

primary and secondary loops. We define Vi1(t) and Vi2(t) as the voltages in time on double loop antennas. Vi1(t) is the

voltage in time on the primary loop and Vi2(t) is the voltage in time on the secondary loop. The index (i) stand for the

first gate (i=1) and second gate (i=2). Due to electromagnetic interferences there are different in time delays respect to

gate antenna's first and second loop voltages and voltages derivatives. The delayed voltages are Vi1(t-τ1) and Vi2(t-τ2)

respectively (τ1≠ τ2) and delayed voltages derivatives are dVi1(t-Δ1)/dt, dVi2(t-Δ2)/dt respectively

1 2 1 2 1 2( ; 0 ; 0 ; , 0) .

Keywords:Double loop antenna, Shifted Gate antennas, Delay Differential Equations (DDEs), Bifurcation, Stability

1. Introduction

In this article, Very Critical and useful subject is discussed: Semi-Passive RFID TAGs system stability.A semi-passive

tags operate similarly to passive RFID tags. However, they contain a battery that enables longer reading distance and also

enables the tag to operate independently of the reader.Semi-Passive TAGs with double loop antennas arranged as a shifted

gate system influence by electromagnetic interferences which effect there stability behavior. The below figure describes

the double loop antennas as a shifted gate in x-direction.

Figure 1. Double loop antennas arranged as a shifted gate in x-direction.

The Semi-Passive RFID TAG with double loop antennas equivalent circuit can be represent as a delayed differential

equations which depending on variable parameters and delays.

2. Semi-passive RFID Tag with Double Loop Gate Antenna Equivalent Circuit and Represent Delay Differential

Equations

Semi-Passive RFID TAG with double loop antenna can be representing as a two inductors in series (L11 and L12 for the

first double loop gate antenna) with parasitic resistance rP1. The double loop antennas in series are connected in parallel to

Semi-Passive RFID TAG. The Equivalent Circuit of Semi-Passive RFID TAG is Capacitor (C1) and Resistor (R1) in

parallel with voltage generator Vs1(t) and parasitic resistance rS1. In case we have Passive RFID TAG switch S1 is OFF

otherwise is ON (Reader/Active RFID system) and long distance is achievable. The second double loop gate antenna is

D

d1


57

defined as two inductors in series L21 and L22 with series parasitic resistor rP2. Vs2(t) and parasitic resistance rS2 are belong

to the second gate antenna system with another Semi-Passive RFID TAG (Supakit, et al.) .

Figure 2.Double loop antennas in series with parasitic resistance and Semi-Passive RFID TAG.

Figure 3. Equivalent circuit of Double loop antennas in series with Semi-Passive RFID TAG.

L11 and L12 are mostly formed by traces on planar PCB. 2∙Lm element represents the mutual inductance between L11 and

L12. We consider that the double loop antennas parameters values (La1, La2, Lb1, Lb2, a1, a2) are the same in the first and

second gates. Since two inductors (L11, L12) are in series and there is a mutual inductance between L11 and L12, the total

antennainductance LT: LT=L11+L12+2∙Lmand . Lm is the mutual inductance between L11 and L12. K is

the coupling coefficient of two inductors . We start with the case of passive RFID TAG which switch S1 is

OFF. I(t) is the current that flow through double loop antenna. V11 and V12 are the voltages on L11 and L12 respectively. Vm

is the voltage on double loop antenna mutual inductance element.

111 11 12 12 1 1 1 11 12 1 1 ; ; ; 2 ; ; C

CD p m m AB R C CD m C

dVdI dI dIV L V L V I r V L V V V V V V V I C

dt dt dt dt (1)

1 1 1 11 121 1 1 11 12 11 12

1 11 12

1 10 0 ; ; ; C C C CD m

C R

dV V dV dV dVdV dVI I I C I L L I V dt V dt

dt R dt dt dt dt dt L L

(2)

1 11 11 1211 12 1 11 12

11 12 11 12

1 1 ; ;

p pC CD mCD p

r rdV dV dVdV dVI V dt V dt V I r V dt V dt

dt dt dt dt dt L L L L (3)

11 12mL K L L

0 1K


58

1 1 11 1211 12 11 12 12 11 11 12 11 12

11 12 12 11 11 12 11 12

1 1 1 1 ; ; ;

p pCDr rdV L L dI

V V V V V V I V dt V dt V Vdt L L L L L L dt L L

(4)

12 12 1111 12 11 11

11 11 11

12 2 2 ; 2m

m m

dVL L dVdIV L K L L V K V K

dt L L dt L dt (5)

We get the following differential equation respect to V11(t) variable, are global parameters.

(6)

(7)

' 2' 11 11 11

1 1 1 12 11 2 2 1 1 12 11 1 3 3 11 1 1 11 2( , , , ) ; ( , , , , , ) ; ( , , ) ; ; p p

dV dV d VC L L K C r L L K R L r R V

dt dt dt (8)

(9)

In the same manner we find our V12 differential equation. We get the following differential equation respect to V12(t)

variable, are global parameters.

21 1 112 12 11 11 11 11

1 2 12 3 1 1 2 32

12 12 12 1 12 12 12 1

1 10 ; (1 2 ) ; (1 2 ) ; (1 )

p pC r rd V dV L L L LV C K K

dt dt L L L R L L L R

(10)

(11)

'' '312 2 12

1 1 1 12 11 2 2 1 1 12 11 1 3 3 12 1 1 12 12 12

1 1

( , , , ) ; ( , , , , , ) ; ( , , ) ; ; p p

dV dVC L L K C r L L K R L r R V V V

dt dt

(12)

Summary: We get our RFID double loop antennas system's four differential equations.

' '' ' ' '3 311 2 11 12 2 12

11 11 11 12 12 12

1 1 1 1

; ; ; dV dV dV dV

V V V V V Vdt dt dt dt

(13)

'

11

'

1111

11 14

11 3 32 211 12 33 34 21 43' '

1 1 1 112 1241 44

12

12

; ; ; ; ; 1

dV

dtVdV

Vdt

dV V

dt V

dV

dt

(14)

(15)

The RFID double loop antennas system's primary and secondary loops are composed of a thin wire or a thin plate element

(Figure 2). Units are all in cm, and a1, a2 are radiuses of the primary and secondary wires in cm. There inductances can be

calculated by the following formulas:

1 2 3, ,

21 111 11 12 12 12 12

1 2 11 3 1 1 22

11 11 11 1 11 11

10 ; (1 2 ) ; (1 2 )

pC rd V dV L L L LV C K K

dt dt L L L R L L

1 1 112 3

11 1 1 11 1

1 1 ; (1 )

p pC r r

L R C L R

'' '311 2 11

11 11 11

1 1

; dV dV

V V Vdt dt

1 2 3, ,

' 21 1 '1 12 12 12

2 12 2

12 1 1

1 ; ;

pC r dV dV d VV

L R C dt dt dt

13 14 22 23 24 31 32 41 42 44 0


59

1 111 1 1 1 1 1 1

1 1 1 1 1 1

2 24 { ln[ ] ln[ ] 2 [ ( )]}

( ) ( )b a c a b

b c b c

A AL L L a l L L

a L l a L l

(16)

2 2 2 22 212 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2

2 2 2 2 2 2

2 24 { ln[ ] ln[ ] 2 [ ( )]} ; ; ; ;

( ) ( )b a c a b c a b a b c a b a b

b c b c

A AL L L a l L L l L L A L L l L L A L L

a L l a L l

(17)

Due to electromagnetic interferences we get a shifted gate RFID system's primary and secondary antennas loops voltages

with delays and respectively. Additionally we get antennas loops voltages derivatives with delays Δ1 and Δ2

respectively.

; ' ' ' '

12 12 2 11 11 1 12 12 2( ) ( ) ; ( ) ( ) ; ( ) ( )V t V t V t V t V t V t (18)

. We consider no delay effect on . (19)

The RFID shifted gate system differential equations under electromagnetic interferences (delays terms) influence only

RFID double loop voltages V11(t), V12(t) and voltages derivatives and respect to time, there is no

influence on

'

11

'

11 111

11 14' '11 111 12 11 12

' '

12 12 241 44

12 2

12

( )

( )( ) ( ) ( ) ( ) ; ; ; ;

( )

( )

dV

dtV tdV

V tdV t dV t dV t dV t dt

dt dt dt dt dV V t

dt V t

dV

dt

. (20)

To find equilibrium points (fixed points) of the RFID shifted gate system is by

, , , (21)

. ' '

11 12 11 121 2 1 2

( ) ( ) ( ) ( )=0 ; =0 ; =0 ; =0. t ; t ; t ; t

dV t dV t dV t dV t

dt dt dt dt (22)

(23)

We get four equations and the only fixed point is Since (24)

. Stability analysis: The standard local stability analysis about

any one of the equilibrium points of RFID shifted gate system consists in adding to coordinates

arbitrarily small increments of exponential form , and retaining the first order terms in

. The system of four homogeneous equations leads to a polynomial characteristics equation in the

eigenvalues . The polynomial characteristics equations accept by set the below voltages and voltages derivative respect

to time into two RFID shifted gate system equations.

RFID shifted gate system fixed values with arbitrarily small increments of exponential form are:

i=0 (first fixed point), i=1 (second fixed point), i=2 (third fixed point), etc.,

1 2

11 11 1( ) ( )V t V t

' '

12 12 2( ) ( )V t V t ' '

11 12 11 12 ; ; ; dV dV dV dV

dt dt dt dt

'

11( )V t'

12 ( )V t

11 1 11lim ( ) ( )t

V t V t

12 2 12lim ( ) ( )t

V t V t

' '

11 1 11lim ( ) ( )t

V t V t

' '

12 2 12lim ( ) ( )t

V t V t

1 2 1 2 ( ) ; ( ) ; ( ) ; ( ) , tt t t t t t t t

(0) ' (0) (0) ' (0) (0)

11 11 12 12( , , , ) (0,0,0,0)E V V V V

3 1 12 3 1 340 & 0 0 ; 0 & 0 0

' '

11 11 12 12[ ]V V V V

' '

11 11 12 12[ ] tv v v v e

' '

11 11 12 12 V V V V

' '

11 11 12 12[ ] tv v v v e


60

' '( ) ' ( ) ' '( ) ' ( )

11 11 11 11 11 11 12 12 12 12 12 12( ) ; ( ) ; ( ) ; ( )i t i t i t i tV t V v e V t V v e V t V v e V t V v e (25)

We choose the above expressions for our and as small displacement from the

system fixed points at time t=0.

' '( ) ' ( ) ' '( ) ' ( )

11 11 11 11 11 11 12 12 12 12 12 12( 0) ; ( 0) ; ( 0) ; ( 0)i i i iV t V v V t V v V t V v V t V v (26)

For the selected fixed point is stable otherwise is Unstable. Our system tends to the

selected fixed point exponentially for otherwise go away from the selected fixed point exponentially.

is the eigenvalue parameter which establish if the fixed point is stable or Unstable, additionally his absolute value (

)establish the speed of flow toward or away from the selected fixed point (Yuri&Jack).

Table 1. Semi-passive RFID TAGs with double loop antennas, variables function of λ eigenvalue and time.

λ<0 λ>0

t=0

;

;

t>0 ;

;

t>0

t→∞

;

;

The speeds of flow toward or away from the selected fixed point for RFID shifted gate system voltages and voltages

derivatives respect to time are

' ' ' '( ) ' ( ) '( ) ' '1 '11 11 11 11 11 11 11 11

110 0 0

( ) ( ) ( ) [ ] [ 1]lim lim lim

ti t t i t t t

e t t

t t t

dV t V t t V t V v e V v e v e ev e

dt t t t

(27)

1 1

' '' '11 12 12 11 1 11 1

11 12 12 11 11

( ) ( ) ( ) ( ) ( ) ; ; ; ; t t t t tdV t dV t dV t dV t dV t

v e v e v e v e e v e edt dt dt dt dt

(28)

(29)

'

11 11( ), ( )V t V t '

12 12( ), ( )V t V t' '

11 11 12 12[ ]v v v v

0, t > 0 0, t > 0

0, t > 0

| |

' '( ) '

11 11 11

( )

11 11 11

( 0)

( 0)

i

i

V t V v

V t V v

' '( ) '

12 12 12

( )

12 12 12

( 0)

( 0)

i

i

V t V v

V t V v

' '( ) '

11 11 11

( )

11 11 11

( 0)

( 0)

i

i

V t V v

V t V v

' '( ) '

12 12 12

( )

12 12 12

( 0)

( 0)

i

i

V t V v

V t V v

' '( ) ' | |

11 11 11

( ) | |

11 11 11

( )

( )

i t

i t

V t V v e

V t V v e

' '( ) ' | |

12 12 12

( ) | |

12 12 12

( )

( )

i t

i t

V t V v e

V t V v e

' '( ) ' | |

11 11 11

( ) | |

11 11 11

( )

( )

i t

i t

V t V v e

V t V v e

' '( ) ' | |

12 12 12

( ) | |

12 12 12

( )

( )

i t

i t

V t V v e

V t V v e

' '( )

11 11

( )

11 11

( )

( )

i

i

V t V

V t V

' '( )

12 12

( )

12 12

( )

( )

i

i

V t V

V t V

' ' | |

11 11

| |

11 11

( , 0)

( , 0)

t

t

V t v e

V t v e

' ' | |

12 12

| |

12 11

( , 0)

( , 0)

t

t

V t v e

V t v e

2 2

''12 2 12 2

12 12

( ) ( ) ; t tdV t dV t

v e e v e edt dt


61

First we take the RFID shifted gate's voltages V11, V12 differential equations: and adding

coordinates arbitrarily small increments of exponential terms and retaining the

first order terms in .

' ''( ) ' '( 0) '( ) ' '( 0)11 12

11 11 11 11 1 12 12 12 12 2

11 12

; =0 = 1>0 ; ; 0 1 0t i t i t i t iv vv e V v e V v e V v e V

v v

(30)

Second we take the RFID shifted gate's voltages derivatives differential equations:

(31)

and adding coordinates arbitrarily small increments of exponential terms and

retaining the first order terms in .

' '( ) ' ( ) '( 0) ( 0) 11 1111 11 11 11 12 11 11 11 11 3 11 12 3 11 12' '

11 11

[ ] [ ] ; 0 ; 0 ; 1t i t i t i i v vv e V v e V v e V V

v v

(32)

'( 0) ( 0) ' '( ) ' ( )11 1111 11 3 11 12 3 11 12 12 33 12 12 34 12 12' '

11 11

0 ; 0 ; 1 ; [ ] [ ]i i t i t i tv vV V v e V v e V v e

v v

(33)

(34)

If λ3>0 and λ4>0 then our fixed point is unstable node. If (λ3>0 and λ4<0) or (λ3<0 and λ4>0) or (λ3<0 and λ4<0)

Then our fixed point is saddle point. We define

(35)

(36)

Then we get four delayed differential equations respect to coordinates arbitrarily small increments of

exponential

. (37)

1 2 2( ) ( ) ( )' ' '

11 11 12 33 12 34 12 ; t t tt te v e v e v e v e v

(38)

. In the equilibrium fixed point (39)

. The small increments Jacobian of our RFID shifted gate system is as bellow:

1 1 1

11 11 12 12 13 14 21 22 23 24 31 32 ; ; 0 ; 0 ; ; ; 0 ; 0 ; 0 ; 0e e e

(40)

2 2 2

'

11

11 14

11

33 33 34 34 41 42 43 44'

1241 44

12

; ; 0 ; 0 ; 0 ; ;

v

ve e e

v

v

(41)

' '11 1211 12 ;

dV dVV V

dt dt

' '

11 11 12 12[ ]V V V V' '

11 11 12 12[ ] tv v v v e

' '

11 11 12 12 v v v v

' '

11 12, V V

' '' '11 12

11 11 12 11 33 12 34 12 ; dV dV

V V V Vdt dt

' '

11 11 12 12[ ]V V V V' '

11 11 12 12[ ] tv v v v e

' '

11 11 12 12 v v v v

'( 0) ( 0) 12 1212 12 33 34 4 33 34' '

12 12

0 ; 0 ; 1i i v vV V

v v

1 1( ) ( )' '( ) ' ( )

11 1 11 11 11 1 11 11( ) ; ( )t ti iV t V v e V t V v e

2 2( ) ( )' '( ) ' ( )

12 2 12 12 12 2 12 12( ) ; ( )t ti iV t V v e V t V v e

' '

11 11 12 12[ ]V V V V

' '

11 11 12 12[ ] tv v v v e 1 1( ) ( )' '

11 11 11 12 11

t tte v e v e v

2( ) '

12 12

tte v e v ' ( 0) ( 0)

11 110, 0i iV V

' ( 0) ( 0)

12 120, 0i iV V


62

(42)

2 2 2 2

2 1

1 1 1 1

2

12 2 1 1 2 1

[ ] [ ] [ ]4

1 2 1 2 12 34 11 34 33 12

( ) ( )2 3

34 12 11 33 33 11

( , , , , ) { }

{ } { }

i j j j

i j j j

j

j

D e e e

e e e e e

(43)

We have three stability cases:

Or or (44)

Otherwise and they are positive parameters. There are other possible simple stability cases:

or ; or (45)

We need to get characteristics equations for all above stability analysis cases. We study the occurrence of any possible

stability switching resulting from the increase of value of the time delays for the general characteristic equation

. If we choose parameter then . The expression for :

2 3

0 1 2 30

( , ) ( ) ( ) ( ) ( ) ( ) ........n

k

n kk

P P P P P P

(46)

The expression for

: (47)

3. RFID Shifted Gate System Fourth Order Characteristic Equation

The second case we analyze is when there is delay in RFID gate's primary and secondary loop antennas voltages (

) and no delay in in gate's primary and secondary loop antennas voltages derivatives (Kuang, 1993; Beretta,

et al., 2002). The general characteristic equation D(λ, τ) is ad follow: 4 3 2 2

33 11 11 33 12 34 11 34 12 33 34 12( , ) ( ) { ( ) ( )}D e e (48)

Under Taylor series approximation: . The Maclaurin series is a Taylor series expansion of a

function about zero (0). We get the following general characteristic equation D(λ, τ) under Taylor series approximation:

. (49)

4 3 2 2 2

33 11 11 33 12 34 11 34 12 33 12 34 12 34 34 12

1( , ) [ ] { [ ] [ ]}

2D e (50)

. The expression for is

2 3 4 4 3 2

33 11 11 330 1 2 3 40

( , ) ( ) ( ) ( ) ( ) ( ) ( ) [ ]n

k

n kk

P P P P P P P

(51)

11 14

41 44

; det | | 0A I A I

1 2 1 2 & 0 1 2 1 20 & 1 2 1 2

1 2 1 2 &

1 2 1 2 ; 0 ; 0 1 2 1 20 ; ; 0 1 2 1 20 ; ; 0 1 2 1 20 ; 0 ;

, ,

( , / / )D ( , ) ( , ) ( , )n m

D eQP ( , )

nP

( , )m

Q 2

0 1 20

( , ) ( ) ( ) ( ) ( ) ........m

k

m kk

Q q q q q

1 2 1 2 & 0

1 2

2 211

2e e

2 211

2e

( , ) ( , ) ( , ) ; 4 ; 2 ; n m

D e n m n mQP ( , )

nP


63

11 33 33 110 1 2 3 4( ) 0 ; ( ) 0 ; ( ) ; ( ) [ ] ; ( ) 1P P P P P (52)

The expression for

is (53)

2 2

12 34 11 34 12 33 12 34 12 34 34 12 12 340

0

2

11 34 12 33 12 34 12 34 34 121 2

1( , ) ( ) [ ] [ ] ; ( )

2

1( ) ; ( )

2

mk

m kk

Q q q

q q

(54)

The homogeneous system for leads to a characteristic equation for the eigenvalue λ having the form

and the coefficients

Depend on and delay . are any two shifted gate system's parameters, other parameters keep as a constant

.

0 1 2 11 33 3 33 11 40 ; 0 ; ; [ ] ; 1a a a a a (55)

2

0 12 34 1 11 34 12 33 12 34 2 12 34 34 12

1 ; ;

2c c c (56)

Unless strictly necessary, the designation of the variation arguments will subsequently be omitted from P, Q, aj,

cj. The coefficients aj, cj are continuous, and differentiable functions of their arguments, and direct substitution shows that

a0+c0≠0 for , i.e. λ=0 is not a of . We assume that and

can't have common imaginary roots. That is for any real number : 4 3 2

33 11 11 33( , ) ( , ) 0 ; ( , ) ( )n m np i Q i p i i (57)

2 2

12 34 11 34 12 33 12 34 12 34 34 12

1( , ) [ ] [ ]

2mQ i i (58)

4 2 2 3

12 34 34 12 11 33 12 34 33 11

11 34 12 33 12 34

1( , ) ( , ) [ ] ( )

2

[ ] 0

n mp i Q i i

i

(59)

2 8 6 2 4 2 2

33 11 11 33 11 33| ( , ) | {( ) 2 }P i (60)

2 2 2 2 2 2

12 34 11 34 12 33 12 34 12 34 12 34 34 12

4 2 2

12 34 34 12

1| ( , ) | {[ ] 2 [ ]}

2

1[ ]2

Q i

(61)

We need to find the expression for

(62)

( , )m

Q 2

0 1 20

( , ) ( ) ( ) ( ) ( )m

k

m kk

Q q q q q

' '

11 11 12 12 V V V V

4 2

0 0

( , ) ( , ) 0 ; ( ) ; ( )j j

j j

j j

P Q e P a Q c

{ ( , , ), ( , , )}j i k j i ka q q c q q

,i kq q ,i kq q

( , )i kq q

,i kq q ( , ) ( , ) 0P Q e ( , )nP ( , )mQ

2 2( , ) | ( , ) | | ( , ) |F P i Q i


64

2 2 8 6 2

33 11 11 33

4 2 2 2 2 2 2

11 33 12 34 34 12 11 34 12 33 12 34

2 2 2

12 34 12 34 34 12 12 34

( , ) | ( , ) | | ( , ) | {( ) 2 }

1{ [ ] } {[ ]

2

12 [ ]}

2

F P i Q i

(63)

We define the following parameters for simplicity:

2 2 2 2

0 12 34 2 11 34 12 33 12 34 12 34 12 34 34 12

2 2 2 2 2

4 11 33 12 34 34 12 6 33 11 11 33 8

1 ; [ ] 2 [ ]

2

1[ ] ; ( ) 2 ; 12

(64)

42 2 2 4 6 8 2

0 2 4 6 8 2

0

( , ) | ( , ) | | ( , ) | k

k

k

F P i Q i

(65)

Hence implies and its roots are given by solving the above polynomial. Furthermore

4 2 3

11 33 33 11( , ) ; ( , ) ( )R IP i P i (66)

2 2

12 34 12 34 34 12 11 34 12 33 12 34

1( , ) [ ] ; ( , ) [ ]

2R IQ i Q i (67)

2 2

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )sin ( ) ; cos ( )

| ( , ) | | ( , ) |

R I I R R R I IP i Q i P i Q i P i Q i P i Q i

Q i Q i

(68)

4 2 3 2 2

11 33 11 34 12 33 12 34 33 11 12 34 12 34 34 12

2 2 2 2 2 4 2

12 34 11 34 12 33 12 34 12 34 12 34 34 12 12 34

1{ } [ ] ( ) { [ ]}

2sin ( )1 1

{[ ] 2 [ ]} [2 2

2

34 12 ]

(69)

4 2 2 2 4

11 33 12 34 12 34 34 12 33 11 11 34 12 33 12 34

2 2 2 2 2 4 2

12 34 11 34 12 33 12 34 12 34 12 34 34 12 12 34

1{ } { [ ] } ( ) [ ]

2cos ( )1 1

{[ ] 2 [ ]} [2 2

2

34 12 ]

(70)

That are continuous and differentiable in based on Lema 1.1 (see Appendix A). Hence we use theorem 1.2(see

Appendix B). This prove the theorem 1.3 (see Appendix C).

4. RFID shifted gate system stability analysis under delayed variables in time

Our RFID shifted gate homogeneous system for leads to a characteristic equation for the eigenvalue λ

having the form ; Second case ; .

4 3 2 2

1 2 1 2 33 11 11 33 12 34 11 34 12 33 34 12( , , 0) ( ) { ( ) ( )}D e e (71)

Under Taylor series approximation: . The Maclaurin series is a Taylor series expansion of a

function about zero (0). We get the following general characteristic equation D(λ, τ) under Taylor series approximation:

. (27)

4 3 2 2 2

33 11 11 33 12 34 11 34 12 33 12 34 12 34 34 12

1( , ) [ ] { [ ] [ ]}

2D e (73)

We use different parameters terminology from our last characteristics parameters definition:

( , ) 0F 4

2

2

0

0k

k

k

'

11 11 v v '

12 12 v v

( ) ( ) =0 P Q e 1 2 1 2 0

2 211

2e e

2 211

2e


65

. Additionally

Then

4 24 3 2

33 11 11 33

0 0

( ) ; ( ) ; [ ]j j

j j

j j

P a Q c P

(74)

(75)

and are continuous and differentiable function of such that . In the

following denotes complex and conjugate. Are analytic functions in and differentiable in . The

coefficients and de pend on RFID

shifted gate system's C1, R1, values and antenna parameters.

(76)

2

0 12 34 1 11 34 12 33 12 34 2 12 34 34 12

1 ; ;

2c c c (77)

Unless strictly necessary, the designation of the variation arguments will

subsequently be omitted from P, Q, aj, cj. The coefficients aj, cj are continuous, and differentiable functions of their

arguments, and direct substitution shows that .

1 2

3 3 11 12 1

21 1 12 12 11 111

11 11 12 12

1(1 )

0

(1 2 ) (1 2 )

pr

L L R

L L L LC K K

L L L L

(78)

i.e is not a root of characteristic equation. Furthermore are

analytic function of for which the following requirements of the analysis (see kuang, 1993, section 3.4) can also be

verified in the present case (Kuang, 1993; Beretta et al., 2002).

(a) If , then , i.e P and Q have no common imaginary roots. This

condition was verified numerically in the entire domain of interest.

(b) is bounded for , . No roots bifurcation from . Indeed, in the limit

2 2

12 34 11 34 12 33 12 34 12 34 34 12

4 3 2

33 11 11 33

1{ [ ] [ ]}

Q( ) 2| | | |( ) [ ]P

(79)

(c) (80)

; ( ) ; ( ) ; 4 ; 2 ; k j k jk j p a q c n m n m ( , ) ( ) ; ( , ) ( )n m

P QQP

2 2

12 34 11 34 12 33 12 34 12 34 34 12

1[ ] [ ]

2Q

0, , n m n m 0, : Rj ja c R

0 0 0a c

" " ( ), ( )P Q

1 1{ ( , ,gate antenna parametrs)ja C R 1 1( , , ,gate antenna parametrs)}jc C R

0 1 2 11 33 3 33 11 40 ; 0 ; ; [ ] ; 1a a a a a

1 1( , , ,gate antenna parametrs)R C

0 0 12 340 ; 0a c

1 , gate antenna parametersC 0 ( ), ( )P Q

i ( ) ( ) 0P i Q i

1 1( , ,antenna parametrs)R C

|Q( ) / ( ) |P | | Re 0

2 2( ) | ( ) | | ( ) |F P i Q i


66

2 2 8 6 2 4 2 2 2 2

33 11 11 33 11 33 12 34 34 12

2 2 2 2 2

11 34 12 33 12 34 12 34 12 34 34 12 12 34

1( , ) | ( , ) | | ( , ) | {( ) 2 } { [ ] }

2

1{[ ] 2 [ ]}

2

F P i Q i

(81)

Has at most a finite number of zeros. Indeed, this is a polynomial in (degree in ).

(d) Each positive root of is continuous and differentiable with

respect to . This condition can only be assessed numerically.

In addition, since the coefficients in P and Q are real, we have , and thus ,

may be on eigenvalue of characteristic equation. The analysis consists in identifying the roots of characteristic

equation situated on the imaginary axis of the complex λ – plane, where by increasing the parameters

, Reλ may, at the crossing ,Change its sign from (-) to (+), i.e. from a stable focus

to an unstable one, or vice versa. This feature may be further assessed by

examining the sign of the partial derivatives with respect to and gate antenna parameters.

1 1

1 1 1 1

1 1

Re Re( ) ( ) , R , ,gate antenna parametrs ; (R ) ( ) , , ,gate antenna parametrs

Ri iC const C const

C

(82)

1 1

1 1 11 1 1

1 11

Re Re(R ) ( ) , , ,gate antenna parametrs ; ( ) ( ) , ,R ,

Ri iC const L C const

L

(83)

1 1

11 1 1 12 1 1

11 12

Re Re( ) ( ) , ,R , ; ( ) ( ) , ,R ,i iL C const L C const

L L

(84)

1 1

12 1 1 1 1

12

Re Re( ) ( ) , ,R , ; ( ) ( ) , ,R ,gate antenna parametrs , where .i iL C const C const

L

(85)

1

1 1

Re( ) ( ) , ,R ,gate antenna parametrs , where .i C const

(86)

For the case we get the following results:

(87)

2 2

12 34 12 34 34 12 11 34 12 33 12 34

1( , ) [ ] ; ( , ) [ ]

2R IQ i Q i (88)

2 2 2 2

0 12 34 2 11 34 12 33 12 34 12 34 12 34 34 12

2 2 2 2 2

4 11 33 12 34 34 12 6 33 11 11 33 8

1 ; [ ] 2 [ ]

2

1[ ] ; ( ) 2 ; 12

(89)

42 2 2 4 6 8 2

0 2 4 6 8 2

0

( , ) | ( , ) | | ( , ) | k

k

k

F P i Q i

(90)

Hence

implies (91)

8

1 1( , , ,gate antenna parametrs)R C F( )=0

1 1, , ,gate antenna parametrsR C

( ) ( )P i P i ( ) ( )Q i Q i i

0

1 1, , ,gate antenna parametrsR C

(0) ' (0) (0) ' (0) (0)

11 11 12 12( , , , ) (0,0,0,0)E V V V V

1 1, ,C R

1 2 1 2 & 0

4 2 3

11 33 33 11( , ) ; ( , ) ( )R IP i P i

( , ) 0F 4

2

2

0

0k

k

k


67

When writing and , and inserting

Into RFID Gate system's characteristic equation , must satisfy the following :

2 2

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )sin ( ) ; cos ( )

| ( ) | | ( ) |

R I I R R R I IP i Q i P i Q i P i Q i P i Q ig h

Q i Q i

(92)

Where in view of requirement (a) above, and . Furthermore, it follows above and

equations that, by squaring and adding the sides, must be a positive root of

. Note that is dependent of . Now it is important to notice that if (assume

that is the set where is a positive root of and for , is not define. Then for all τ in I

is satisfies that ). Then there are no positive solutions for , and we cannot have

stability switches. For any where is a positive solution of , we can define the angle

as the solution of

2 2

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )sin ( ) ; cos ( )

| ( ) | | ( ) |

R I I R R R I IP i Q i P i Q i P i Q i P i Q i

Q i Q i

(93)

And the relation between the argument and fo must be

. Hence we can define the maps given by

. Let us introduce the functions ;

That are continuous and differentiable in . In the following, the subscripts and RFID Gate antenna

parameters indicate the corresponding partial derivatives. Let us first concentrate on

,remember in and , and keeping all parameters except one (x)

and . The derivation closely follows that in reference [BK]. Differentiating RFID characteristic equation

with respect to specific parameter (x), and inverting the derivative, for convenience, one

calculates: Remark:

1 ( , ) ( , ) ( , ) ( , ) ( , ) ( , )( )

( , ) ( , ) ( , ) ( , )x x

P x Q x Q x P x P x Q x

x P x Q x Q x P x

(44)

Where etc., Substituting , and bearing i ,

( ) ( ) ( )R IP P i P ( ) ( ) ( )R IQ Q i Q i

2| ( ) | 0Q i ( , )g h R sin

cos

2 2( ) | ( ) | | ( ) | 0F P i Q i ( )F I

0I R ( ) ( )F I ( )

( ) ( , ) 0F ( ) ( , ) 0F

I ( ) ( , ) 0F

( ) [0,2 ]

( ) ( ) I 0( ) ( ) 2 n n

0:n I R

0

( ) 2( ) ; ,

( )n

nn I

I R

0( ) ( ), , n nS I n

1 1, , , R C

1 2 1 2 1 2( , , , , , )a a b bL L L L a a ( )x

1 2 1 2 1 2( , , , , , )a a b bL L L L a a 1 2 1 2 1 2( , , , , , )a a b bL L L L a a

( ) ( ) =0 P Q e

1 1 1 2 1 2 1 2, , , , , , , , .,a a b bx R C L L L L a a etc

,....P

P

i ( ) ( )P i P i ( ) ( )Q i Q i


68

Then and and that on the surface , one obtains

21 ( , ) ( , ) ( , ) ( , ) | ( , ) |

( ) | ( )( , ) ( , ) ( , ) ( , )

i

x x

i P i x P i x i Q i x Q x P i x

x P i x P i x Q i x Q i x

(95)

Upon separating into real and imaginary parts, with

; (96)

; 2 2 2 ; x Rx Ix R IQ Q i Q P P P (97)

When (x) can be any RFID Gate parameters R1, C1, And time delay etc,.Where for convenience, we have dropped the

arguments , and where

(98)

2 [( ) ( )] ; /x Rx R Ix I Rx R Ix I x xF P P P P Q Q Q Q F F . We define U and V:

( ) ( ) ; ( ) ( )R I I R R I I R R Ix I Rx R Ix I RxU P P P P Q Q Q Q V P P P P Q Q Q Q (99)

We choose our specific parameter as time delay

x = τ. (100)

2 3 4 2 2 2

12 34 12 34 11 33 11 330 ; 0 ; ; ; 2 [2 3 ]R I R I R RP P Q Q P P (101)

5 2 2

33 11 12 34 34 12 11 34 12 33 12 34

13 ( ) ; / ; 2 [ ] ;

2I I R IP P F F Q Q (102)

2

12 34 34 12 11 34 12 33 12 34

12 [ ] ;

2R IQ Q (103)

2 2 2

12 34 34 12 12 34 12 34 34 12

1 12 [ ] [ ( )]

2 2R RQ Q (104)

2

11 34 12 33 12 34[ ] ; 2 [( ) ( )]I I R R I I R R I IQ Q F P P P P Q Q Q Q (105)

(106)

2 2 2

12 34 11 34 12 33 12 34 34 12

12 [ ( )]

2F (107)

4 2 4 2

11 33 33 11 33 11 11 333 ( ) ( ) ; 2 ( ) (2 )R I I RP P P P (108)

2 2

12 34 12 34 34 12 11 34 12 33 12 34

1[ ( )] [ ]

2R IQ Q (194)

2 2

11 34 12 33 12 34 12 34 34 12

12 ( ) ( )

2I RQ Q (110)

( ) ( ) ; 0 ; 0R I I R R I I R R I I RV P P P P Q Q Q Q P P P P (111)

2 2 3

12 34 12 34 12 34 34 12 12 34 11 34 12 33 12 34

1[ ( )] ; [ ]

2R I I RQ Q Q Q (112)

( ) ( )i P i P i ( ) ( )i Q i Q i 2 2| ( ) | | ( ) |P i Q i

; R I R IP P i P Q Q i Q R IP P i P

; R I x Rx IxQ Q i Q P P i P

( , )i x

2 [( ) ( )]R R I I R R I IF P P P P Q Q Q Q

2 2

11 33 33 112 [2 ] ; 3 ( )R IP P



69

. Differentiating with respect to and we get

(113)

21 1

2

2 [ | | ]Re( ) ( ) ; ( ) Re{ } ;

2 [ | | ]i

U P i F F

F i V P F

(114)

21 1

2

2 [ | | ] Re( ) Re{ } ; ; { ( )} {( ) }

2 [ | | ]i

U P i F Fsign sign

F i V P F

(115)

(116)

We shall presently examine the possibility of stability transitions (bifurcations) in a shifted gate double loop RFID

system, about the equilibrium point as a result of a variation of delay parameter τ. The

analysis consists in identifying the roots of our system characteristic equation situated on the imaginary axis of the

complex λ-plane Where by increasing the delay parameter τ, Re λ may at the crossing, change its sign from – to +, i.e.

from a stable focus E(*)

to an unstable one, or vice versa. This feature may be further assessed by examining the sign of the

partial derivatives with respect to τ,

(117)

1

1 1

Re( ) ( ) , ,R ,gate antenna parametrs ; where .i C const

(118)

For our stability switching analysis we choose typical RFID shifted gate parameters values: L11=4.5mH, L12=2.5mH,

C1=23pF, R1=100kOhm=105, , K=0.6, 2·Lm=0.004 ( ).

12 5 12 5

1 2 3 1 256.22 10 ; 2.49 10 ; 222.42 ; 101.2 10 ; 4.492 10 (119)

5 12 5 5 12322 3 1 2 3 11 12

1 1

2.49 10 ; 222.42 ; 101.2 10 ; 4.492 10 ; 400.4 ; = 4.42 10 ; 3.95 10

(120)

5 123233 34 21 43 13 14 22 23 24 31 32 41 42 44

1 1

= 4.43 10 ; = 3.95 10 ; 1 ; 0 ; 0

(121)

Then we get the expression for for typical RFID shifted gate parameters values.

2 2 8 6 10 4 20 24 2 12 2

2 17 24 2 24 24 2 12 48

( , ) | ( , ) | | ( , ) | 39.16 10 {383.17 10 [7.8 10 7.9 10 ] }

{[34.94 10 15.6 10 ] 31.2 10 [7.8 10 7.9 10 ]} 243.39 10

F P i Q i

(122)

We find those values which fulfill . We ignore negative, complex, and imaginary values of for

specific values. and we can be express by 3D function . Since it is a very complex

function, we recommend to solve it numerically rather than analytic. We plot the stability switch diagram based on

different delay values of our RFID double gate system. Since it is a very complex function we recommend to solve it

numerically rather than analytic.

2 2 21 1

2 2 2 2

2 [ | | ] 2 { ( ) ( )}Re Re( ) ( ) Re{ } ; ( ) ( )

2 [ | | ] 4 ( )i i

U P i F F V P F U P

F i V P F V P

(123)

( , ) 0F

0 ; F

F F IF

1

2{ ( )} { } { }

| |

U V

sign sign F signP

(0) ' (0) (0) ' (0) (0)

11 11 12 12( , , , )E V V V V

1 Re( ) ( ) i

1 100pr Ohm11 122 2mL K L L

( , )F

, ( , ) 0F

[0.001..10] ( , ) 0F


70

The stability switch occurs only on those delay values ( ) which fit the equation: and is the solution of

when if only is feasible. Additionally when all RFID double gate

system's parameters are known and the stability switch due to various time delay values is describe in the following

expression:

1

2

( ( )) ( ( )) ( ( )){ ( )} { ( ( ), )} { ( ( )) ( ) }

| ( ( )) |

U Vsign sign F sign

P

(124)

Remark: we know implies it roots and finding those delays values which is feasible. There are

values which is complex or imaginary number, then unable to analyse stability (Kuang, 1993; Beretta, et al. 2002).

5. Results of RFID Shifted Gate System Stability Switching under Delayed Variables in Time

We find those ω, τ values which fulfil F(ω, τ)=0. We ignore negative, complex, and imaginary values of ω for specific τ

values. and we can express by 3D function F(ω, τ)=0. We define new MATLAB script parameters:

τ→Tau, Gi(i=1,..,10): G1=39.16e10; G2=383.17e20; G3=7.8e24; G4=7.9e12; G5=34.94e17; G6=15.6e24;

G7=31.2e24;G8=7.8e24;G9=7.9e12;G10=243.39e48, Ξj→Phij ; j=8, 6, 4, 2, 0, Running MATLAB script for τ values

gives the following results:

MATLAB script:

Tau=10;G1=39.16e10;G2=383.17e20;G3=7.8e24;G4=7.9e12;G5=34.94e17;G6=15.6e24;G7=31.2e24;G8=7.8e24;G9=

7.9e12;G10=243.39e48;Phi8=1;Phi6=G1;Phi4=G2-(G3*Tau*Tau+G4).^2;

Phi2=-((G5-G6*Tau).^2-G7*(G8*Tau*Tau+G9)); Phi0=-G10;p=[Phi8 0 Phi6 0 Phi4 0 Phi2 0 Phi0];r=roots(p)

Results: We plot 3D function F(ω, τ)=0. τ:0→10; ω:0→1e13. We define additional MATLAB script parameters: ω→w,

τ→t. We get some possible real values for ω which fulfil F(ω, τ)=0, F(ω=0 or ω=2.1437, ω=2.7928, ω=1.0e+006,

ω=1.0e+009, ω=1.0e+010, ω=1.0e+011, ω=1.0e+012, ω=1.0e+013, τ)=0; . Next is to find those ω, τ

values which fulfil

sinθ(τ)=…. and cosθ(τ)=.. (125)

(126)

Table 2a. Semi-passive RFID TAGs with double loop antennas, ωi(τ).

ωi τ=0 τ=0.001 τ=0.01

ω1 1.0e+006 1.0e+009 1.0e+010

ω2 -0.0000+3.105i -2.7928 -2.7928

ω3 -0.0000-3.105i -0.0000+2.792i -0.0000+2.7928i

ω4 -2.1437 -0.0000-2.792i -0.0000-2.7928i

ω5 -1.528+0.0823i 2.7928 2.7928

ω6 -1.528-0.0823i 0.0000+0.0000i -0.0000+0.0000i

ω7 2.1437 0.0000-0.0000i -0.0000-0.0000i

ω8 1.528+0.0823i -0.0000+0.0000i 0.0000+0.0000i

ω9 1.528-0.0823i -0.0000-0.0000i 0.0000-0.0000i

( )

( )

( )

sin ( ) ... ; cos ( ) ... ( )

( , ) 0F ( )i i

i

[0.001..10]

[0.001..10]

[0.001..10]

2sin( )

| |

R I I RP Q P Q

Q

2 2 2

2

(cos( ) ; | |

| |

R R I IR I

P Q P QQ Q Q

Q


71

Table 2b. Semi-passive RFID TAGs with double loop antennas, ωi(τ).

ωi τ=0.1 τ=1 τ=10

ω1 1.0e+011 1.0e+012 1.0e+013

ω2 -2.7928 -2.7928 -2.7928

ω3 0.0000+2.7928i 0.0000+2.7928i 0.0000+2.7928i

ω4 0.0000-2.7928i 0.0000-2.7928i 0.0000-2.7928i

ω5 2.7928 2.7928 2.7928

ω6 -0.0000+0.0000i -0.0000+0.0000i -0.0000+0.0000i

ω7 -0.0000-0.0000i -0.0000-0.0000i -0.0000-0.0000i

ω8 0.0000+0.0000i 0.0000+0.0000i 0.0000+0.0000i

ω9 0.0000-0.0000i 0.0000-0.0000i 0.0000-0.0000i

Case I: ω=0 then typical RFID shifted gate parameters values: L11=4.5mH,

L12=2.5mH, C1=23pF, R1=100kOhm=105, , K=0.6, 2·Lm=0.004 ( ).

12 12 243 312 34 12 34

1 1

0 ; 0 ; 3.95 10 ; = 3.95 10 ; 15.6 10R R RQ Q Q

(127)

sin(ω∙τ)=… fulfil and cos(ω∙τ)=… can't fulfil since .

Case II: ω≠0 ; ω>0 ; ω=2.1437, 2.7928, 1.0e+006, 1.0e+009, 1.0e+010, 1.0e+011, 1.0e+012, 1.0e+013 which can fulfil

expressions sinθ(τ)=… and cos(ω∙τ)=… Finally we plot the stability switch diagram based on different delay values of our

RFID shifted gate system.

4 2 10 3 5 24 2 24 2 1219.58 10 ; 8.85 10 ; 15.6 10 [7.8 10 7.9 10 ]R I RP P Q . (128)

3 5 24 2 24 2 12 17 24 248.85 10 ; 15.6 10 [7.8 10 7.9 10 ] ; [34.95 10 15.6 10 ] ; 15.6 10I R I IP Q Q Q (129)

2 24 24 24 2 24 2 1215.6 10 ; ( ) ; 15.6 10 {15.6 10 [7.8 10 7.9 10 ]}R R I I R R IQ V Q Q Q Q Q Q (130)

3 24 17 24 2 5 2 1015.6 10 [34.95 10 15.6 10 ] ; 26.55 10 ; 2 (2 19.58 10 )I R I RQ Q P P (131)

12 2 12 17 242 (7.8 10 7.9 10 ) ; Q 34.94 10 15.6 10 ; ( ) ( )R I R I I R R I I RQ U P P P P Q Q Q Q (132)

We plot the function:

2 21 1

2 2 2

2 { ( ) ( )}Re Re( ) ( ) ( ) ; ( ) ( ) ( )

4 ( )i i

F V P F U Pg g

F V P

(133)

2 21

2 2 2

2 { ( ) ( )}Re[ ( )] [ ( )] [( ) ] [ ]

4 ( )i

F V P F U Psign g sign sign sign

F V P

(134)

Since 2 2 2 1 2 24 ( ) 0 [ ( )] { ( ) ( )}F V P sign sign F V P F U P (135)

1 2 2 1 /[ ( )] {[ ] [( ) ( )]} ; ; ( )

/

F F Fsign sign F V P U P

F F F

(136)

1 2 2 1

2 2

1[ ( )] {[ ] [ ]} ; [ ( )] {[ ] [ ] [ ]}

V Usign sign F V U P P sign sign F

P P

(137)

; (138)

; (139)

(Table 3)

(140)

12 340; 0; ; 0R I R IP P Q Q

1 100pr Ohm11 122 2mL K L L

0cos( ) | 0

1

2 2

1[ ( )] {[ ] [ ] [ ]}

V Usign sign F

P P

1

2 2

1[ ] 0 [ ( )] {[ ] [ ]}

V Usign sign sign F

P P

1

2 2

1[ ] 0 [ ( )] {[ ] [ ]}

V Usign sign sign F

P P

1

2[ ( )] [ ] [ ]

V Usign sign F sign

P



72

We check the sign of according the following rule: If sign[Λ-1

(τ)] > 0 then the crossing proceeds from (-) to (+)

respectively (stable to unstable). If sign[Λ-1

(τ)] < 0 then the crossing proceeds from (+) to (-) respectively (unstable to

stable). Anyway the stability switching can occur only for ω≠0; ω>0 ; ω=2.1437, 2.7928, 1.0e+006, 1.0e+009,

1.0e+010, 1.0e+011, 1.0e+012, 1.0e+013 and . Since it is a very complex function we recommend solving

it numerically rather than analytic. We plot the stability switch diagram based on different delay values of our

Semi-passive RFID TAGs with double loop antennas system.

Table 3. Semi-passive RFID TAGs with double loop antennas stability switching criteria.

+/- +/- +

+/- -/+ -

6. Discussion

In this paper we consider Semi-passive RFID TAGs with double loop antennas. Due to electromagnetic interferences

there are delays in time for voltages and voltages derivatives in the first and second loop. These delays cause to stability

switching for our Semi-passive RFID TAGs with double loop antennas. We draw our Semi-passive RFID TAGs with

double loop antennas circuit and get system differential equations. Our variables are first and second loop antennas

voltages and voltages derivative. Our system dynamic behaviour is dependent on circuit overall parameters and parasitic

delays in time. We keep all circuit parameters fix and change parasitic delays over various values . Our

analysis results extend that of in the way that it deals with stability switching for different delay values. This implies that

our system behaviour of the circuit cannot be inspected by short analysis and we must study the full system. Several very

important issues and possibilities were left out of the present paper. One possibility is the stability switching by circuit

parameters. Every circuit's parameter variation can change our system dynamic and stability behaviour. This case can be

solved by the same methods combined with alternative and more technical hypotheses. Moreover, numerical simulations

for the Semi-passive RFID TAGs with double loop antennas model studied in references suggest that this result can be

extended to enhance models with more general functions.

7. Conclusion

Semi-passive RFID TAGs with double loop antennas environment is characterize by electromagnetic interferences which

can influence shifted gate system stability in time. There are four main RFID double loop antenna variables which are

affected by electromagnetic interferences, . Each loop antennas voltages variables under

electromagnetic interferences are characterize by time delay respectively1 2 1 2 1 2( ; 0 ; 0 ; , 0) . The two time

delays are not the same but can be categorized to some subcases due to interferences behavior. The first case we analyze

is when there is delay in RFID first gate's primary loop antenna voltage and no delay in secondary loop antenna

voltage.The second case we analyze is when there is delay in RFID gate's primary and secondary loop antennas voltages (

) and no delay in in gate's primary and secondary loop antennas voltages derivatives (Kuang, 1993; Beretta, et

al., 2002).The third case we analyze is when there is delay in RFID gate's primary and secondary loop antennas voltages (

) and delay in in gate's primary and secondary loop antennas voltages derivatives (Steven; Kuang, 1993).

For simplicity of our analysis we consider in the third case all delays are the same (there is a difference but it is neglected

in our analysis). In each case we derive the related characteristic equation. The characteristic equation is dependent on

double loop antennas overall parameters and interferences time delay. Upon mathematics manipulation and [BK]

theorems and definitions we derive the expression which gives us clear picture on double loop antennas stability map. The

stability map gives all possible options for stability segments, each segment belong to different time delay values

segment. Double loop antennas arranged as a shifted gate's stability analysis can be influence either by system overall

parameters values. We left this analysis and do not discuss it in the current article.

Appendix A: Lemma 1.1

Assume that is a positive and real root of

1( )

[0.001..10]

[ ]sign F 2[ ]V U

signP

1[ ( )]sign

[0.001..10]

'

11 11( ), ( )V t V t'

12 12( ), ( )V t V t

1 2

1 2 1 2

( ) ( , ) 0F


73

Defined for , which is continuous and differentiable. Assume further that if , , then

hold true. Then the functions , are continuous and differentiable on I.

Appendix B: Theorem 1.2

Assume that is a positive real root of defined for , and at some , . For

some then a pair of simple conjugate pure imaginary roots

of (141)

exist at which crosses the imaginary axis from left to right if and cross the imaginary axis from

right to left if where

* *

* * *

( )

( )Re( ) { | } { ( ( ), )} { | }n

i

dSdsign sign F sign

d d

(142)

Appendix C: Theorem 1.3

The characteristic equation has a pair of simple and conjugate pure imaginary roots real at if

for some . If , this pair of simple conjugate pure imaginary roots crosses the

imaginary axis from left to right if and crosses the imaginary axis from right to left if where

(143)

If , this pair of simple conjugate pure imaginary roots cross the imaginary axis from left to right if

and crosses the imaginary axis from right to left If where

(144)

If then and , the same is true when . The

following result can be useful in identifying values of where stability switches happened.

References

Aluf, O. (2008). RFID TAGs COIL’s Dimensional Parameters Optimization As Excitable Linear Bifurcation Systems,

(IEEE COMCAS2008 Conference, May 2008).

Aluf, O. (2011). RFID TAGs Coil's System Stability Optimization Under Delayed Electromagnetic Interferences, (IEEE

COMCAS2011 Conference, November 2011).

Beretta, E., & Kuang, Y. (2002). Geometric stability switch criteria in delay differential systems with delay dependent

parameters. SIAM J. Math. Anal., 33, 1144-1165.

Jack, K. H. (1991)Dynamics and Bifurcations. Texts in Applied Mathematics, 3, 170-484.

Kuang, Y. (1993). Delay Differential Equations with applications in Population Dynamics. Academic Press, Boston.

Steven, H. S. (1994). Nonlinear Dynamics and Chaos(Pp. 123-284). Westview press.

Supakit, K., Chuwong, P., & Danai, T. (2009). Novel design of double loop antennas by Using a shifted Gate for the LF –

RFID system. Faculty of Engineering and Technology, Asian University, Thailand.

Yuri, A. K. Elelments of Applied Bifurcation Theory. Applied Mathematical Sciences. 112.


I i R

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( ) ( , ) 0F 0, I I R * I *( ) 0nS

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* * * *( ) ( ), ( ) ( )i i

( , ) 0D * *( ) 0

*( ) 0

* *( ), ( ) * I

* * *( ) ( ) 0n nS 0n N * *( ) ( )

*( ) 0 *( ) 0

* *

*

( )

( )Re( ) { | } { | }n

i

dSdsign sign

d d

* *( ) ( )

*( ) 0 *( ) 0

* *

*

( )

( )Re( ) { | } { | }n

i

dSdsign sign

d d

* * *( ) ( ) ( ) *( ) 0 *( )

Re{ | } 0

i

dsign

d

' *( ) 0nS





ISSN 2330-2038 E-ISSN 2330-2046



74

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