Selection of the Approximating Function for Isobologram Modeling

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Applied Researches in Technics, Technologies and Education Faculty of Technics and Technologies, Trakia University Vol. 3, No. 1, 2015 ISSN 1314-8788 (print), 1314-8796 (online)

ARTTE

Applied Researches in Technics, Technologies and Education Journal of the Faculty of Technics and Technologies, Trakia University https://sites.google.com/a/trakia-uni.bg/artte/

ARTTE Vol. 3, No. 1, 2015 ISSN 1314-8788 (print), ISSN 1314-8796 (online)

ARTTE Applied Researches in Technics, Technologies and Education ISSN 1314-8788 (print), ISSN 1314-8796 (online)

The Scientific Journal of the Faculty of Technics and Technologies of Yambol, Trakia University of Stara Zagora, Bulgaria

The Journal is available online at: https://sites.google.com/a/trakia-uni.bg/artte/ Address of the Editorial Office: Graf Ignatiev 38, 8600 Yambol, Bulgaria Phone/fax: +359 46 669183, E-mail: [email protected], [email protected]

EDITORS

Editor-in-Chief Krasimira Georgieva, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Co-Editors-in-Chief Georgi Tassev, DSc, Faculty of Technics and Technologies, Trakia University, Bulgaria Zlatina Kazlacheva, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Editorial Board Nikolai Ganev, PhD, Czech Technical University of Prague, Czech Republic Iliya Ginkov, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Savvas Vassiliadis, PhD, Technological Educational Institute of Piraeus, Greece Mariana Ursache, PhD, “Gheorghe Asachi” Technical University of Iasi, Romania Elsayed Elnashar, PhD, Kafrelsheikh University, Egypt Nuno Belino, PhD, University of Beira Interior, Covilha, Portugal Plamen Daskalov, PhD, University of Ruse "Angel Kanchev", Bulgaria Marin Vlada, PhD, University of Bucharest, Romania Penka Martincova, PhD, University of Zilina, Slovakia Veselina Nedeva, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Tania Pehlivanova, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Nely Georgieva, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Albena Stoyanova, DSc, University of Food Technologies of Plovdiv, Bulgaria Krasimira Dobreva, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria Larisa Tarasenko, DSc, Southern Federal University, Rostov-on-Don, Russia Bianka Tornyova, PhD, Medical University of Plovdiv, Bulgaria Margarita Pehlivanova, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria English Editor Emilia Dimova, PhD, Faculty of Technics and Technologies, Trakia University, Bulgaria

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ARTTE Vol. 3, No. 1, 2015 ISSN 1314-8788 (print), ISSN 1314-8796 (online)

CONTENTS

ICTTE 2014, https://sites.google.com/a/trakia-uni.bg/ictte-2014/

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1 Georgi Tassev, Krasimira Georgieva. INVESTIGATION OF THE PREVENTIVE REPLACEMENTS PERIODICITY IMPACT ON THE MACHINES RESOURCE AT USING OF ELEMENTS WITH DECREASED RELIABILITY LEVEL

7 ElSayed A. ElNashar, Hanaa H. Sidhom, and Zlatina Kazlacheva. NEW APPROACH OF TECHNICAL CRITICISM OF EGYPTIAN ANCIENT CLOTHES WITH VITRUVIUS AESTHETICS THEORY FOR FASHION DESIGN

11 Arafa A. Nasef & ElSayed A. ElNashar. SOFT SET THEORY AND ITS APPLICATION IN DECISION MAKING FOR TEXTILES AND APPAREL MARKETING

32

ElSayed A. ElNashar. SMART SUPPORT SYSTEM FOR FASHION TRENDS OF KNITWEAR

40

Kaloyan Yankov. ASSESSMENT OF PROCESSES USING IDENTIFICATION MODELS

52

Gabriela Kiryakova. INFORMATION SUPPORT OF E-LEARNING 61 Nadezhda Angelova. PEDAGOGICAL SUPPORT OF E-LEARNING USING CONDITIONAL ACTIVITIES IN LMS

67

Aneta Popova, Dasha Mihaylova & Jordanka Alexieva. IMPACT OF DECOCTION DURATION ON THE ANTIOXIDANT CAPACITY OF BULGARIAN ALLIUM URSINUM LEAVES

75 Lidya Georgieva, Nadezhda Petkova & Dasha Mihaylova. BULGARIAN PLANTS – A

POTENTIAL SOURCE OF VALUABLE COMPOUNDS WITH ANTIOXIDANT CAPACITY – A REVIEW

80

Ivan Ivanov, Nina Dencheva, Nadezhda Petkova, Panteley Denev. DETERMINATION OF TOTAL POLYPHENOLS AND ANTIOXIDANT ACTIVITY OF DIFFERENT EXTRACTS FROM FICUS CARICA L. LEAVES

87 Snejana Dineva. SAFETYNESS OF CONSUMING IRRADIATED FOOD 93 Snejana Dineva, Kremena Andreeva. HEALTHY RISK OF DIOXINS IN FOOD 101 Snezhana Dragusheva, Diana Paskaleva. MOTIVATING HEALTH CARE SPECIALISTS TO EMBRACE LIFELONG LEARNING

109

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ARTTE Vol. 3, No. 1, 2015 ISSN 1314-8788 (print), ISSN 1314-8796 (online), doi: 10.15547/artte.2015.01.006

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ASSESSMENT OF PROCESSES USING IDENTIFICATION MODELS

Kaloyan Yankov

Trakia University of Stara Zagora Faculty of Technics and Technologies

Graf Ignatiev 38, 8600 Yambol, Bulgaria e-mail: [email protected]

Abstract. This work formulates specific parameters of processes described by differential equations of first order. These classes of equations are models of quantitative changes in biology, physiology, pharmacology. Computational algorithms are proposed for parameters calculation, based on the identified mathematical model. The parameters can be used to make a comparative analysis of the process behavior under different conditions. With the implemented algorithms the possibilities of the computer program Korelia-Ident are expanded and the process of simulating the modeled process is facilitated. Keywords: system identification, data modeling, mathematical model, simulation.

“However, I assume that every natural concept contains as much real science as it contains mathematics."

Immanuel Kant 1. INTRODUCTION The purpose of scientific experiment is to obtain data, which after evaluation and analysis provide new knowledge about the investigated object or process. Primary data quality is that they are discreet. If the sampling interval is too long, it does not always satisfy the Nyquist-Shannon sampling theorem. The discretization of experimental data raises a number of problems. Necessity of large amount of storage medium for data - from several tens to hundreds of

thousands of items. This requires preprocessing [6] and is a prerequisite of velocity reduction of the software.

Necessity of choosing an appropriate approximation of the data, for example with cubic spline [1]. This is disadvantage because an interpolation algorithm can not be used to model the process - the dependent variable is expressed as a function of the abscissa variable and not as a function of the parameters that characterize the nature of the process.

Data differentiation is limited by the sampling interval. The algorithms are generally unstable. It is possible that integration and differentiation operations are realized on the analytic expression of the approximate function [2]. Thus the positive effect is that a stable algorithm is obtained, but it is difficult to examine the accuracy of the approach.

Calculation of the parameters of the research process is done by the application of numerical methods [7, 8].

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The data identification is a process that leads to replacing them with analytic expression [4]. That is the way to obtain the mathematical model of the process.A mathematical model is a description of a system in terms of equations. It is a generalization, abstraction of the studied processes. Additional characteristics can be obtained from it, not by specific experimental data. The mathematical model has several advantages: Less computing resources - the mathematical description in compact form can be stored

in computer memory. An interpolation to find intermediate points is not required. The mathematical model allows to obtain a general result, correct for all numerical

conversions, including areas outside the experimental data. Mathematical model allows devoting the most important properties of the object,

abstracting from the non-essentials in accordance with the accepted level of significance.

The most important is the ability to simulate the process - with a change the parametersof the model to examine the change of the observed characteristics.

The aim of this work is to formulate a set of parameters of aperiodic processes described by first order differential equations and offer algorithms for their calculation using the analytic models of the processes. With interactive modification of the model characteristics are simulated and explored their influence on calculated parameters.

2. SMULATION MODEL

Quantitative changes in processes and systems with self-regulation are described by first order differential equation:

)(.)(.)(

tUKtyrdt

tdy

0)0( Cy

(1)

The solution of Eq.(1) is:

CeCCty tr .

0 .)(

r

UKtyC

t

.)(lim

- infinite asymptote of y(x)

(2)

The identification vector [4] is Q=[C0 , C∞ , r]. Parameters that can be the subject of simulation are r – the rate constant of the process; K – the proportionality coefficient; U(t) – the input step force; C∞ is a theoretical value, which in practice is not used. Close to its is steady state value YS. Steady state value depends on the pre-selected tolerance band ε related to the range of the process |С∞ - С0|:

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1,0 CC

St

s tttyCYS

,)(min

CCYC s 0)(

For Ys the following expression is obtained:

CCCYs 0.)( (3)

Thus, an exponential model is a function of the four independent parameters. This arranged five-element set (Figure 1) defines the simulation model SM:

,,,,0 UKrCSM (4)

Their change realized the simulation process, yielding computational parameters that characterize it.

Figure 1. Simulation parameters of aperiodic process

3. CALCULATION ALGORITHM

Based on the simulation model SM (4) and the graph of the process (Fig.1) a number of parameters will defined. They provide a quantitative evaluation of the modeled processes and may be a criterion to compare them. 3.1. Inverse function It gives the time to reach level yc of function y(t):

C

CyC

CC

ryt 0ln.

1)( (5)

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In control systems is important to know what is the time to reach a predetermined level of the observed process. This formula gives several special cases that follow. 3.2. Settling time ts The settling time is the time required for the unit step response to reach and stay within the tolerance band δ, i.e. steady state level YS is reached. By substituting the Ys in Eq.(5) an expression for the settling time is obtained:

1ln

1)(

rts (6)

The point (tS, YS) is important for the processes described by Eq.(2), but it depends on the selected value for δ. 3.3. Half-time t½ The time when the process reaches half of steady state level. This is an important parameter used to evaluate the absorption of drugs, the half life of radioactive materials, etc.

)2ln(.1

21

rt (7)

3.4. Process area SR This is the rectangle envelope of the process:

SSR tCYS .0 (8)

It is used as a normalized value in assessing and comparing the parameters representing areas of the simulated process. 3.5. Quality factor of regulation Sp It determines how much the system reaction is optimal and it is estimated using integral criteria. It is measured with the area determined by the actual curve of the transient process and the ideal transient process:

S

S

tr

S

t

SP eCYr

dttyCYS.

0

0

0 1..1

)(

(9)

3.6. Area under curve (AUC) It seems to reason that a good measurement of the strength of a signal would be the area under the curve. This feature in recent years has been the subject of interest in medical and biological sciences. The AUC is interpreted as the total systemic exposure and is used as a

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criterion for evaluation of drug absorption, drug bio-availability and drug concentrations over time, integral muscle force and so on. The AUC in interval [0,tS] is:

S

SS

tr

SSS

t

trtr

S

t

eCYr

tYdteCeYdttyAUC.

0

0

.

0

.

0

11

.1).(

PR SSAUC (10)

Both parameters Sp and AUC (Fig.2) cannot be used to compare processes that have different steady state levels or different values of δ. Such processes are typical for chemical and biological sciences, where it can be expected that the processes have wide statistical dispersion.

Figure 2. Interpretation of the areas for decreasing and increasing processes

3.7. Signal energy EY

The terms signal energy and signal power are used to characterize a signal, in our case that is the observed process. They are not actually measures of energy and power. The definition of the signal energy in the signal y(t) is:

St

Y dttyE0

2)(

After integration and algebraic transformations the algorithm is:

0

.0

.

2 4.2

. CYeYr

CYetYE S

tr

S

S

tr

SYS

S

S

(11)

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3.8. Process power PY Power is a time average of energy in a period ts is:

S

YY

t

EP (12)

The above listed parameters can be used to compare aperiodic processes described by first order differential equation. For each concrete experiment some of them will be informative. Who they are, must be established in the processing of experimental data. This will be these data, which prove a statistically significant difference in the pre-selected level of significance between selected null hypothesis and alternative hypothesis. 4. DERIVATIVES ON MODELS In assessing the studied processes is important to know the derivatives at least to the second order. The first derivative of the process Eq (2) is:

treCCrdt

tdy .

0 .)(

(13)

The velocity graph gives an idea about the quantitative process changes, as it coincides with the sign of the velocity. Positive first derivative characterized quantitative accumulation. The negative part of the graph is an indicator to reduce the amount The second derivative of the process is:

treCCrdt

tyd .

0

2

2

2

.)(

(14)

Acceleration graph reflects the intensity of the action of the main factors influencing the studied process. When the acceleration is positive, the positive influence on the process factors and speed also rises. Accelerations less than zero indicate a prevailing negative factors. Important in this case are extreme points and zero points. The process has the high / low intensity at the time of the global maximum / minimum of the acceleration. To be able to apply algorithms 3.1-3.10 for calculating the parameters of derivatives, recursive formulas for identification vector Q=[C0 , C∞ , r]. should be formulated. Let the identification velocity vector is:

'''

0

' ,, rCCQ

(15)

Applying the method of undetermined coefficients and comparing Eq (14) and Eq (17) gives the identification vector for first derivative:

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re

eCrCrQ

tr

tr

,1

..,.

.

.

0

'

(16)

Recurrent formula for acceleration received from Eq (16) is:

re

erCerCQ

tr

trtr ,

1

..,

.

.2.2

0

''

(17)

5. GRAPHICAL VIZUALIZATION AND OPERATIONS

Program Korelia-Ident allows visualization of experimental data as discrete points and graphical class KPoint is used [3]. Classes KLine, KSpline realize linear and spline interpolation of data. Graphs of the first and second derivative may be in the same screen of the main process or in different, situated in cascade or horizontally. Upon the images the next operations can be applied: SET-operations

• Changing the screen coordinates. • Changing the world coordinates. • Set a color of the graphics element.

GET-operations • Coordinates of the nearest point indicated by the locator. • Copy an image in MS Clipboard.

File operations Experimental data are saved in a file format (.SSP), specific for the Korelia software. The trivial file operations are realized for SSP files:

• Save model in a file. • Read model from a file. • Save an image as „BMP„ file.

Another file format that reads the program is comma-separated values (CSV files). That is a file format common on all computer platforms. To facilitate the user when transfer data from other programs to Korelia-Ident, means for reading data stored in CSV file format and transform them into SSP are created [5]. For the same reason the numerical results obtained with the program can be transferred to MS Excel. 6. EXAMPLE

In [9] are studied the color changes in bread crust during baking (with permission from Mr Zl. Zlatev). The Z-component of the XYZ-color model identification is made using Korelia-Ident. The model is:

382.0202.1)( 207.0

06.0

t

ety

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The graphics of the process and the calculated parameters according to algorithms 3.1-3.10 are on figure 3.

Figure 3. Z-component changes in bread crust

7. CONCLUSIONS

In the present work the term simulation model of aperiodic process is defined. Specific parameters for numerical evaluation of processes as a function of the simulation model are formulated. These parameters can be used to make a comparative analysis of the process behavior under different conditions. Computational algorithms are proposed for parameters calculation, based on the identified mathematical model. Recursive formulas for calculating the derivatives of the process are proposed. The graph of the derivatives is a characteristic of the distribution of the intensity of the modeled process. The approach is implemented with the software Korelia-Ident. It gives extensive information about the processes under different conditions without the need of new experiments. Thus it is a useful tool for teaching, simulation, scientific hypotheses and demonstration purposes.

8. ACKNOWLEDGMENTS

This study was supported by Grant 04.ФТТ/ 18.07.2014 from the Faculty of Technics and Technologies of Yambol, Trakia University of Stara Zagora, Bulgaria.

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9. REFERENCES [1] Yankov K. (1998). Evaluation of Some Dynamics Characteristics of Transient Processes.

12-th Int.Conf.SAER'98. , sept.19-20, 1998, Varna, Bulgaria. pp. 113-117. [2] Yankov K.(1998). Software Utilities for Investigation of Regulating Systems, Proc. Ninth

Nat. Conf. "Modern Tendencies in the Development of Fundamental and Applied Sciences". June, 5-6, 1998, Stara Zagora, Bulgaria, pp.401-408.

[3] Yankov K. (1999). Object Oriented Two-Dimensional Graphics in a Borland Delphi Environment. Proc. 13-th Int.Conf. SAER'99, sept.18-19, 1999, st.Konstantin resort, Varna, Bulgaria, ISBN 954-438-248-8, pp. 169-173.

[4] Yankov K. (2006). System Identification оf Biological Processes. Proc. 20-th Int.Conf. "Systems for Automation of Engineering and Research (SAER-2006). St.St. Constantine and Elena resort, sept.23-24, 2006, Varna, Bulgaria, pp 144-149. ISBN 954-438-575-4.

[5] Yankov K. (2007). Interactive Generation оf Data Transmission Protocol Between External Device аnd Computer. Proc. of the Int. Conference on Information Technologies (InfoTech-2007). St. Constantine and Elena resort, Varna, Bulgaria, sept.21-23, 2007, ,vol.2, pp 231-238.

[6] Yankov K. (2010). Preprocessing of Experimental Data in Korelia Software. Trakia Journal of Sciences, Vol. 8, Suppl. 3, pp. 41-48, 2010. ISSN 1313-7069.

[7] Yankov K. (2011). Evaluation of Characteristic Parameters of Dynamic Models. Proc. Int. Conference on Information Technologies (InfoTech-2011). St. Constantine and Elena resort, Bulgaria,sept.15-17, 2011, pp.225-234. ISSN 1314-1023.

[8] Yankov K. (2012). Assessment of Characteristic Parameters of Oscillating Models. Proc. Int. Conference on Information Technologies (InfoTech-2012). St.Constantine and Elena resort, Bulgaria, sept.20-21, 2012, pp.114-123. ISSN 1314-1023.

[9] Zlatev Z. (2014). Modeling of Color Changes in Bread Crust During Baking. Proc. Int. Conf. on Technics, Technologies and Education “ICTTE 2014”, oct. 30-31, 2014, Yambol, Bulgaria. pp. 680-685.

Selection of the Approximating Function for Isobologram Modeling

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