Multiple sensor fault diagnosis for non-linear and dynamic system by evolving approach

Multiple Sensor Fault Diagnosis for Non-Linear and Dynamic System by Evolving Approach

Mohamed EI-koujok*, Mohieddine Benammar*, Nader Meskin*, Mohamed AI-Naemi*, Reza Langarit

*Department of Electrical Engineering Qatar University

Doha, Qatar [m.elkoujok, mbenammar,nader .meskin,moh97]@qu.edu.qa

-rDepartment of Mechanical Engineering Texas A&M University

Texas, U.S.A [email protected]

Abstract-Reliability of sensor measurement is vital to assure the

performance of complex and nonlinear industrial operation. In

this paper, the problem of designing and development of a data

driven multiple sensor fault detection and isolation (MSFDI)

algorithm for nonlinear processes is investigated. The proposed

scheme is based on an evolving multi-Takagi Sugeno framework

in which each sensor output is estimated using a model derived

from the available input-output measurement. Our proposed

MSFDI algorithm is applied to continuously stirred tank reactor

sensor fault detection and isolation. Simulation results

demonstrate and validate the performance capabilities of our

proposed MSFDI algorithm.

Keywords-Sensor iault, Dynamic and nonlinear system, Data Driven approach

I. INTRODUCTION

In the last decades, the complexity and size of industrial plants has been constantly increasing. A typical industrial processes is combination of sub-processes; most of the time all of these are computer-controlled [ 1]. Industrial plants employ a broad range of sensors as sources of information for control and monitoring purposes. In these facilities, reliability of information provided by these sensors is of paramount importance. This information can translate the state or the condition of the process; monitoring the quality of gathered data from sensors is therefore a critical issue. With time, sensors are affected by various factors such as aging and harsh operating conditions to which sensors are exposed; this can result in drift and even total sensor failure. The lack of sensor integrity can lead to problems in the plant ranging from drift in the operating conditions to complete plant shutdown; in all cases production is affected. Sensor fault detection and isolation (SFDI) can improve the overall reliability of plant operation with the obvious positive implications on production and profit. This calls for continuous monitoring schemes that assess the health or condition of the individual sensors in the plant.

This work was supported by the Qatar Foundation (project: NPRP 09·393·2-145/1/2011)

In general, condition-based maintenance is the solution to maximize equipment up time and to minimize maintenance and operating costs. In this paper, we will apply the conditionbased maintenance on vital equipment in the industrial installation; the sensors. The proposed techniques allow SFDI for the inherently non-linear industrial processes.

II. SENSOR FAULT DIAGNOSIS OF NONLINEAR/DYNAMIC

A. Sensor Fault Diagnosis -a Brief Review

Sensor Fault Diagnosis (SFD) is an active area of research. The SFD is mainly applicable in industrial facilities, such as nuclear plants [2], HV AC systems [3], and aerospace systems where a large number of sensors are used for control and diagnostic purposes. Two methods exist to detect sensor faults: physical redundancy and analytical redundancy methods. Physical redundancy is based on using several sensors to measure the same quantity. However, this approach is not attractive in many industrial applications, because of the incurred high cost of sensor installation and monitoring; this is particularly impossible for existing plants in operation. Analytical redundancy methods use mathematical models to describe the behavior of the process without the need for addional hardware in the plants; this makes analytical redundancy methods acceptable in industry. In the literature, the analytical redundancy methods [4] can be divided into two:

1) Knowledge model-based methods: the mathematical model is based on the fust principles (White Box).

2) Data Driven model-based methods: the mathematical model is usually an Artificial Intelligence model (Black-Box).

In analytical redundancy based methods (Fig. 1), the fust step is to generate a set of residuals where each residual is the difference between the observed behavior (measure value) and that predicted by a model-based method (White-Box or BlackBox).

978-1-4577-1911-0/12/$26.00 ©2012 IEEE MU3258 2012 Prognostics & System Health Management Conference (PHM-2012 Beijing)

j E [I, . . . ,m]

Figure I. Generating the residuals by analytical redundancy.

( 1)

where m is the number of sensors under observation, Yj is the

output of the j'h sensor and the Y j is the estimated value.

The next step is to take decision by choosing a suitable threshold to evaluate all residuals, if the residual overcome the threshold, then a symptom of sensor fault is occurred. There exist several statistical tools that can be utilized to evaluate the residuals [5].

B. To Generate the Residuals

Residual generation can be obtained by several techniques: parity equations, observer-based generation, Neural Networks (NNs) and fuzzy systems [6]. Whatever applied to get the residuals, the challenge is to attain a white noise characteristic for the residuals in the absence of fault. This is challenging to accomplish in the presence of noise and system high nonlinearity/complexity .

In a given industrial process, the data provided by its sensors describe the nonlinear behavior of the process in question. Although, an ideal analytical redundancy model can be the first principal mathematical model, the advantages reside in the high precision in real time application. However, it is very difficult to find good and accurate mathematical models of such complex systems. Moreover, even if this was feasible, the solution would be system-specific that needs to be developed for each process at hand. A more practical solution is to use a Data-Driven approach that makes use of the available process data in order to develop models of the complex plant. The Data-Driven based model is a suitable method to represent complex industrial processes [7]. This technique has been employed to improve the operation and availability of a plant. Data-Driven based models can be described by linear or nonlinear models. However, as industrial processes are nonlinear and dynamic, the nonlinear Data Driven model is better for capturing the behavior of the process. Consequently, the residuals generated by this nonlinear model may have a mean

very close to zero and known variance (white noise) residuals enabling good sensor fault detection capability. In addition, most systems in practice are dynamic, which means that the current output value of a given variable depends not only on the current external stimuli but also on its earlier values. Hence, in order to generate the residuals, we will consider that the assignment is how building a nonlinear mathematical model by observed the input-output of a dynamic system, then the hypothesis in this work no knowledge a priori about the comportment of the process.

C. Nonlinear Data-Driven Model to Describe Dynamic

System

In sensor fault detection, it is very useful to estimate each sensor output with a separate model. In this work a MISO (Multi-Inputs, Single-output) model is used. Let us consider a

system with the input variables vector U = [up ... ,up]T and

output variables vector Y = [y, , ... , Y m { ; the former represent

the plant command signals (known and without fault) and the latter represent the sensors readings (may be affected by faults). For the complex dynamic system, only the inputoutput data sequences is available,

Z (t) = [Y (t), U (t)] t=0,1,2 ... (2)

We assume that every output of the system can be described by

Y j = f; (t, Z ( t), ... , Z (t - tJ.)) (3)

where < is the true function of /h output. In real applications,

we can never find the correct expression for the function f; . However, a relationship for past values of Z (t) can construct

a nominal and nonlinear model of the system. Hence, the role of this model is to predict the actual sensor value. The output of the model is generated by

(4)

where If is the predictor function, r is the vector of

parameters model, and rp is the regression vector

Iy,(t) I. I: I Y", (I) rp=[z(I), ... ,Z(I-s)]=1 () 1",1 I .

l" p (I)

y,(t-s)l I I

Y", (I -s) I ", (I -s) I . I up(t-s)J

(5)

s is the order of the model which s is assumed to be equal for

all elements of Z.


Assuming that we find the best model (jj) , we will never

attain to have an exact value of the sensor without fault, but it is possible to get a close approximation of the real one. Consequently, the residual will not be zero; and it will

converge to a noise distribution (s j) which reflect the

modeling error(s j : N(Ji "" 0, (J J known )) .

rj = Y j - Y j = f/ - jj = £ j (6)

The next section presents a suitable candidate for the Data

Driven based model (model predictor function, j).

III. EVOLVING T AKAGI-SUGENO MODEL

A. Why Evolving Takagi-Sugeno Model

The most popular nonlinear Data-Driven based approach used to detect sensor fault is the Neural Network (NN) ( [8], [9]). NNs have been always viewed like estimators to model complex nonlinear systems due to their approximation and adaptation capabilities. Nevertheless, the concept of NN has the drawback of slow training; the design of an NN is more of an art than a science. On the other hand, first order Tagaki-Sugeno (TS) fuzzy models [ 10] have shown superior performances over NNs and conventional approaches [ 1 1]. Tagaki-Sugeno model provides an efficient and computationally attractive solution to approximate a nonlinear input-output transfer function. For that reason, we will suggest the TS model adjusted by evolving approach [ 12] as a promising concept to detect and isolate sensor fault. The choice of the evolving approach as learning algorithm for the TS is based on the following reasons:

• It does not require the user to defme the structure of the TS model,

• It does not need a complete learning data set to start the identification process of the TS model (i.e., the approach can be started from scratch),

This evolving Takagi-Sugeno (eTS) is expected to remain reliable and computationally efficient in spite of increased system complexity to monitor the input-output information from a set of sensors while considering the entire system as a Black-Box.

B. Takagi-Sugeno Model: principles

A first-order TS model is based on the fuzzy decomposition of the input space. For each part (i E [1, . . . ,R}) of the state space, a fuzzy rule (R,) can be constructed to make a linear approximation of the inputs. TS model can be seen as a multi-model structure consisting of linear models:

Ri: if ZI is A{ and ... and Zn is A� THEN 'i=aiO+ail,ZI+···+ain.zn (7)

z = [ Z I" " ,Z n ] T is the input vector, A � denotes the

antecedent fuzzy sets, b = [I, . . . ,n 1 ,Yi is the output of the

i'h linear subsystem, and aiq are its parameters. Let's assume

Gaussian antecedent fuzzy sets (justified by its generalization capabilities) to define the regions of fuzzy rules in which the local linear sub-models are valid:

i .(41IZj<II/(<7;)') I-Ij=exp j=l, ... ,n;i=l, ... ,R (8)

where a 'i the spread of the membership is function, and Z 'i* is

the focal point (center) of the i'h rule antecedent. The firing

level (T, ) and the normalized firing level Ai of each rule are

obtained as follows:

A = Ti

, R " Tu � v=l

(9)

( 10)

The model output is the weighted averaging of individual rules

contributions. With notations, 7r i = [aiO , ... , am] , the parameters

vector of the i1h sub-model, and Xe = [1,ZT{ the expanded

data vector, this output is expressed as:

2:" 2:R T

Y = ;til i = AiXe 7[; i=l i=l ( 1 1)

A TS model has two types of parameters: the center and the spread deviation of the member functions (referred to as premise or antecedent parameters) and the linear regression parameters of consequent part of each rule. For more clarification about the structure of TS, Fig. 2 shows the TS model with two inputs and two rules.

e. Evolving Takagi-Sugeno Approach

The learning procedure of eTS is composed of two phases: 1) an unsupervised data clustering technique is used to adjust the antecedent parameters; 2) the supervised Recursive Least Squares (RLS) learning method updates consequent parameters.

1) Clustering phase: The eTS clustering phase processes

on the global data space: z = [Z , Y J] Em 11+1 , where n defmes

the dimensionality of the input data space, Y J is the target.

Figure 2. First order TS model.


This clustering algorithm is based on the determination of a potential which is the capability of a data to form a cluster (antecedent of a rule). The procedure starts from scratch and, as more data are available, the model evolves by replacement or upgrade of rules. The coordinates of the fIrst cluster center

are those of the fIrst data point (z; --? z1 )' The potential of the

fIrst data point is set to ideal value (P1 (Z1) +- 1) . Four steps

are then performed for each new data gathered.

Step 1: Starting from k=2, the potential Pk of the data

point Zk is recursively calculated at time k :

( 12)

Step 2: The potential of the cluster/rule centers is recursively updated:

• (k -1)Pk_1 (z;) Pk(z,) = n+1 k - 2 + Pk-I (z;) + Pk (z;) I.1Izt - z :-111 ,

j=l

( 13)

where Pk (z;) is the potential of the cluster at time k , which

is a prototype of the th.

Step 3: The potential of the data point (step 1) is compared to boundaries issued from the potential of the cluster centers (step 2):

( 14)

where (P = max ,R { Pi (= * )} ) is the highest density/potential,

(f... = min ,R { Pi (= * )} ) is the lowest density/potential and given

that the number of clusters is equal to the number of rules, R

represents also the nwnber of centers clusters (z; , [ 1, ... ,R])

formed at time k.

Step 4: If the new data point has a potential within the boundaries no modifIcation of the rules is necessary, otherwise there are two possibilities:

• If the new data point is close to an old center J

(min; Ilzk - z; II < 0"; ), then the new data point (zk ) replaces

this center (Zi* +- zk), • Else, the new data point is added as a new center and

a new rule is formed ( R = R + 1 ).

Note that, the eTS learning algorithm presents an adaptive

calculation of the radius of the clusters (O"!). See [ 13] for

more details.

2) RLS phase, update of consequent parameters: At step k, the equation ( 1 1) can be expressed as follows:

T T T T T · f h ' If! k = [Alxe ' A2xe .... , AnXe h IS a vector 0 t e mputs,

weighted by normalized fIring (A) of the rules, and

Ok =[4, 7r;" n?J; lJ are parameters of the sub-models.

An estimation of the parameters based on k data samples is obtained by applying the following RLS procedure:

rJf= Bk-J + Cklfkek ; k = 2,3, ... T

C _ Ck-J -Ck-Ilfklfk Ck_1 k - T I + If k C k -JIf k T • ek = Yk+I-lfk Bk_1

( 16)

( 17)

( 18)

. h ' .. I d' . T T T T Wit ImtIa con ItlOnsBJ=[JrI, Jr2, ... ,JrRlk =O,CI=fU,

where Q is a large positive number, QJa R(n+ 1)xR(n+ 1) covariance matrix.

By applying this above algorithm in two phases, the nwnber of rules is determined, the centers of the inputs

member functions are found (z; (l x n) E [1, ... , R] ), the spread

deviation of every centers is adjusted and the consequent parameters are estimated. Thus the eTS is built and can be used to approximat nonlinear system.

IV. SENSOR FAULT DIAGNOSIS

In this section, our proposed Multi-Sensor Fault Detection and Isolation (MSFDI) is described. First, the multiple model scheme is described for sensor fault diagnosis. Next, based on the available input/output measurements of a given system, the nonlinear dynamic of the system is approximated using a eTS method described in Section III and a set of residuals is generated in the multiple model framework for fault detection and isolation purpose. A new training method is devised based on the evolving feature of eTS in order to determine when the training should be stopped. Finally, a statistical method is applied for residual evaluation and sensor fault detection and isolation.

A. Mutipie Model Sensor Fault Diagnosis

Two different architectures have been proposed for sensor fault diagnosis in the literature: Single-Model and MultipleModel. In [ 14], [ 15] a single multiple-input, multiple-output auto-associative neural network is proposed for sensor fault diagnosis. On the other hand, some authors have proposed a multiple-model scheme in which each model represents one specifIc output of the system ( [ 16], [ 17] ). In this paper, the multiplemodel scheme is adopted based on the following two reasons:

1- The high performance of prediction by Multi-Model than single Model.


2- It is not necessary to add another concept to isolate, so the detection and isolation included in the MSFDI.

The new key point in our proposed MSFDI is to inject the past estimated values from each model as the inputs without using the sensors output values (Fig. 3). In this proposed scheme, the isolation task is automatically performed by comparing each sensor output with estimated output value from the corresponding model.

B. Training Termination Using Evolving Approach

The objective of this section is to construct the mUltiple models in MSFDI framework. By the eTS approach adopted in this work, these models can be constructed automatically based on the available data. In the eTS approach, if a new data have a higher potential than an existing potential data, the structure of the model will be changed to cover the new data space. In multi-model scheme, every model has different structure

The available data are divided into two sets: the training and test sets. The challenge is how one can exploit the training set to have the best predictive performance for the test data set. In our proposed training scheme, the same training set is used for several epochs to attain a model with best characteristics. However, the problem is when one should stop the training of eTS. In the evolving approach, the evolution of the number of rules begins from scratch (one rule) and grows during the training. When all the space of data is covered by the rules, then no new rule will be added to the structure and the number of the rules becomes constant. Therefore, the training phase of eTS can be stopped whenever the number of rules becomes constant. Moreover, in the evolving approach, the parameters of the models are updated in parallel with the structures and consequently, the models (Modell ... Model m) of the MSDFI is completely obtained after the training phase.

� ______ � ______________________ �Y� (�t) t3

� ____ � __ �Y�l(t� ) �

rill U(t-l)

Z-I

U(t-s) eTSm y", (t)

z-s

Figure 3. New scheme to Multiple Sensor Fault Detection and Isolation.

(number of rules) that reflects the dynamic of each sensor.


C. Reiduals Evaluation

Depending on the condition and working environment, different types of faults can affect the functionality of sensors. In general, sensor faults can be classified as follows [18]:

• Bias fault : a fixed bias is added to the sensor value, • Drifting fault: a slowly changing in the sensor value, • Noise fault: an alteration in sensor noise variance, • Scaling fault: a change in scaling of the sensor value, • Hard fault: sensor reading is stuck at a constant value.

In this paper, only the bias fault is considered. However, our proposed approach can also be extended for other types of sensor fault.

After constructing the residual signals, the last step is to determine the evaluation function and the threshold value for each residual. In this paper, the following evaluation functions are selected

L is the window.

I L r . ( /, L ) = -I r2(t-i)

} L i�O } ( 19)

To take decision, the approach is to observe the scalar value of the window average

if ll rj(t,L) 1 1 >5j => faultinthe/" sensor (20)

where 8 is the threshold. Selecting the threshold depend on the case study. If the value of the threshold decreases then the sensitivity to detect sensor fault increases, it is not the best solution because the fault alarm can be increase. Then, the choice of threshold should be a compromise between assuring the safety of operation and avoid high frequency of false alarm. We suppose that the threshold is dependent of the mean

(flTiUlIlj ) and standard deviation ( (J" Train) ) of the j'h residual in

training phase:

5 = Ilfl . · 1 1 + a * (J" Tralll) Train}

V. CASE STUDY

(2 1)

In this section, the proposed sensor fault diagnosis algorithm is applied to the Continuously Stirred Tank Reactor (CSTR).

A. Description and Simulation of the CSTR Process

The CSTR is a popular system for benchmarking. It is a single first-order exothermic and irreversible reaction A --7 B, [ 19]. Fig. 4 represents the schematic diagram of the reactor wrapped by a cooling jacket. The inlet feed stream of reagent

I�}t) Iltletfeed stream temperature F �=�==il

y,(/) Reactor temperature

I�(/) Concelltratioll of A i"letfeet/ sl,.etlm

Jackel coo/alit (em ')erafure

relK/or F

Figure 4. Schematic representation of the CSTR.

A is fed at a constant rate F. After stirring, the end product is let out of the reactor at the same rate as reagent A is fed into the tank (i.e., the volume V in the reactor tank is thus kept constant). The control strategy requires that the jacket coolant temperature U3(t) is adjusted in order to keep the concentration y,(t) of A in the reactor at a desired level, in spite of disturbances arising from the inlet feed stream concentration and temperature (inputs u,(t) and U2(t), respectively). The temperature in the tank Y2(t) can vary significantly during operation of the reactor, it is desirable to keep it within reasonable limits. This CSTR is a typical chemical process reactor system with nonlinear dynamic characteristics. It can by described by two dynamic and nonlinear differential equations:

dy, (t) F --=-x[u (I)-y (I)]

dt V ' ,

E -k 0 x exp [ - ] x y, (t)

(R x U2 (I»)

dY2(/) F -- =-x[u (t)-y (t)]

dl V 2 2

H E - --- x ko x exp [ - ] x y, (I)

HD (R x Y2(t))

HA - x [Yz (I) -u3 (I)]

HD x V

Where the inputs are:

(22)

(23)

1. u, (t): Concentration of A in inlet feed stream

(kgmol m,3),

2. U2 (t): Inlet feed stream temperature [K],

3. u3(t): Jacket coolant temperature [K].

And the two outputs are: 1. y, (I) : Concentration of A in reactor tank [kgmol

m,3],

2. y 2 (t) : Reactor temperature [K].

In our case study, the used values for the process parameters are shown in Table I.

978-1-4577-1911-0/12/$26.00 ©20121EEE MU3258 2012 Prognostics & System Health Management Conference (PHM-2012 Beijing)

TABLE I. PARAMETERS OF THE CSTR IN CASE STUDY Parameters

values F: Volumetric flow rate [mj h-] 1

V: Volume in reactor [m3] 1

ko : Pre-exponential nonthermal factor [h-/] 3.S6314X 107

E: Activation energy [cal motl] 11854.9 R: Boltzmann's gas constant [cal KI mol I] 1.98589

H: Heat of reaction [cal motl] -5960 HD: Heat capacity times density

500479 [cal m-3 K-/] HA: Overall heat transfer coefficient times tank area

150160 [cal m-3 KI h-/]

In our work, the CSTR system was simulated using Matlab according to the model described by the two highly nonlinear differential equations (22) and (23). The choice of the sampling time depends on the dynamic of the CSTR system and should ensure collection of a set of data that represents well the system. To have an approximate idea about the dynamic of the system, the time constant of the process was determined by investigating the step response of the system. The responses of the outputs (y\(t) and Y2(t)) for step changes in the three inputs (u,(t), U2(t) and U3(t)) as shown in Fig. 5. The step responses of the outputs depends heavily on the input changes scenarios: for

example a step change in the input u, suggests a first order

behavior and time constant of about 1 hour for the output Y1 . On the other hand, the response of y, to changes in U2

indicates a time constant of approximately 7 hours. By investigating the various scenarios, it was found that the smallest time constant was about lh. Therefore it was decided to use a sampling rate of 10 samples by hour in order to gather the data set.

Figure 5. Outputs to step changes in inputs of CSTR.

The CSTR system was simulated in Matlab environment by using dynamic inputs as is the case in real applications. The inputs U1 and UJ were assumed to be variable (i.e., variable

concentration of reagent in inlet feed stream and jacket coolant temperature respectively), while; and the input U2 was

considered constant (i.e. inlet feed stream temperature). Random noise was added to every input and output. Fig. 6 shows typical results generated under the described conditions and for an operation time of 100 hours.

B. Training and Results

Based on the proposed approach (Fig. 3) two models must be constructed, such each sensor output is described by a model. Let assumed that the delay value's' in Fig. 3 is '5'.

During the training phase, the first 24 hours (240 samples) of the system operation are used, and the 240 samples are repeated toward obtaining a perfect representation of the system. The number of rules of the eTSl and eTS2 grows up to attain a constant level at 398 samples for eTSl and 205 for eTS2 (Fig. 7). By stopping the learning phase, the residuals of eTSl and eTS2 have been converged to be a white noise with the means is near to zero and the known standard deviation (Table II).

C. Validation of the Concept by Detection Multi-Sensor Fault

In this section, the effectiveness of the proposed MSFDI is assessed in operational zone. In this case study, we consider that only the sensors measuring the outputs may develop faults. The type of fault added to sensors is an artificial fault: Bias fault. The bias fault is a percentage of

Figure 6. Data form simulation the CSTR (10 samples/hour).


40

Number of Rules

'" eTSl Q,I '3 � 200 400 600 800 1000 1200 1400 ... 50 0 = 40 0 Number of Rules .: 30 = '0 20 � �

10 eTS2

00 200 400 600 800 1000 1200 1400 I I I I I I 0 20 40 60 80 100 120 140

Hours

Figure 7. Evolution of the fuzzy rules.

maximum variation of the nominal sensor output:

Bias =per%xl'l(y)=f3xl'l(y) (24)

The ranges of the sensor#1 and sensor#2:

(25)

Tow diagnosis scenarios have been considered to confIrm the effIciency of our approach. The index to assess the ability of the MSFDI to diagnosis is the detection time: time to tum on the alarm after the fault has occurred.

Scenario 1: In this scenario, it is assumed that no fault has occurred in the sensors, i.e. the bias value � is zero (24). The objective is to show the performance of the derived models for the output signals Yl and Y2 to capture the dynamic of the system. In order to test the generalization property of the derived models, different input patterns for the ones used in the training phase are selected for the input signals Ul and U2. As shown in Fig. 8, the two estimated outputs can perfectly track the real outputs of the system and the residual signals are so close to the residuals in training phase (Table III).

TABLE IT. TRAINING RESULTS

eTSI r1 = sTraln1

eTS2 r2 = sTraln2

TABLE Ill. TEST RESULTS

III = 0.0879

"I = 0.2500

112 = 0.014

"2 = 0.632

eTSI r1 = sTrain1

eTS2 r2 = sTrain2

111 = 0 .030

"I = 0.280

112 =0.019

"2 =0.516

Scenario 2: In this scenario, concurrent bias faults are

introduced to sensor#1 (Yl) and sensor#2 (Y2) at different

time instants. The performance of sensor fault detection and isolation depends on the level of the threshold (6"), the value

of the bias fault and the window length (L) of rj(t,L) . In

order to avoid false alarm, the above parameters as selected as L=20 and a =0.5 (Fig. 9).

By decreasing the threshold, the detection time will decrease, but the possibility of having false alarms will increase. It should be emphasized that for real application, the thresholds can be estimated by an expert on the process.

The 6 % bias faults are injected at two different time instants, 450lh and 400,h samples for the sensor#1 and sensor#2, respectively. In order to check the performance of the fault detections and isolation, two levels of the threshold are considered as a =0.5 and a =0.3 (Fig. 9).

For Sensor #1: At a =0.3, the MSFDI detects two faults, one is false alarm at the 140lh samples, and the second one is a true fault with detection time of 10 samples after the occurrence of the fault. At a =0.5 the MSFDI detects the injected fault with detection time of 20 samples (2 hours) without generating any false alarm.

For Sensor#2: At a =0.3, the MSFDI detects about 7 faults. One of them is a true fault and the others are false alarms. The MSFDI take 2 samples to detect the true fault. At a =0.5, the MSFDI only detects the injected fault at the 4041h

samples and hence the detection time is 4 samples (24 minutes).

The above simulation result show the effIciency of the proposed MSFDI to predict the dynamic of the highly nonlinear process and the capability of MSFDI to detect low severity sensor fault, i.e. 6% bias fault. However, the weakness in the proposed scheme is the time to detect the sensor fault especially in sensor#l, so further work must be conducted to improve the detection time. In addition, a future work can be developed to help the expert to select the threshold more quickly.

VI. CONCLUSION

Validation of the sensor measurement is crucial for monitoring the health of complex and nonlinear processes. This paper is concerned with the development of multiple sensor fault detection and isolation algorithm. Due to the


Figure 8. Operation zone without fault.

Time

Figure 9. Window average of the residuals without fault.

of the future directions of research will be in investigating the problem of actuator fault detection and isolation in nonlinear processes using the similar data-driven framework.

REFERENCES

[I] H. Wang, T. Y. Chai, 1. L. Ding and M. Brown, "Data Driven Fault Diagnosis and Fault Tolerant Control : Some Advances and Possible New Directions," ACTA AUTOMATlCA SINICA, vol. 35, pp. 739-747, 2009.

[2] 1. W. Hines and E. Davis, "Lessons learned from u. s. nuclear power," Progress in Nuclear Energy, vol. 46,2005.

"2(/,20)

05 04

01

15 6'1. btu fIIullllllb� -400� umilin

05

00��T�:�:�.�h02"�f��a�-�O�.5�)��4foo==��0�T�h��;hO�"�f(�a��'3�) Tome

Figure 10. Window average of the residuals with 6 % bias fault.

complexity and nonlinearity of the industrial process, datadriven techniques are more efficient for sensor fault diagnosis. In this work, an evolving Takagi-Sugeno approach is adopted and a new Multi-Model scheme is proposed for detection and isolation of multiple sensor faults. The proposed approach is validated by applying to a multiinput multi-output continue stirring tank reactor system. One

[3] H. Yang, S. Cho, C. Tae and M. Zaheeruddin, "Sequential Rule Based Algorithms for Temperature Sensor Fault Detection in Air Handling Units," Energy Conversion and Management, vol. 49, p. 2291-2306, 2008.

[4] I. Hwang, S. Kim, Y. Kim and C. Seah, "A Survey of Fault Detection, Isolation, and Reconfiguration Methods," IEEE TRANSACTlONS ON CONTROL SYSTEMS TECHNOLOGY, vol. 18, pp. 636-653, 2010.

[5] J. Gertler, Fault detection and diagnosis in engineering systems, Marcel Dekker, 1998.

[6] G. Heredia and A. Ollero, "Detection of Sensor Faults in Small


Helicopter UAVs Using Observer/Kalman Filter Identification," Mathematical Problems in Engineerin, 20 II.

[7] C. H. Zhao, F. L. Wang, F. R. Gao, N. Y. Lu and M. X. Jia, "Adaptive Monitoring Based on Independent Component Analysis for Multiphase Batch Processes with Limited Modeling Data," ind. Eng. Chem. Res., vol. 47, p. 3104-3113, 2008.

[8] R. Perla, S. Mukhopadhyay and A. Samanta" "Sensor fault detection and isolation using artificial neural networks," TENCON, iEEE Region 10 Cotif'., vol. 4, pp. 676-679, 2004.

[9] M. Najafi, Application of Auto-Associative Neural Networks for Sensor, Lap Lambert Academic Publishing, 2010.

[10] J. Jang and C. Sun, "Neuro-fuzzy modeling and control," iEEE Proceedings, vol. 83, p. 378-406,1995 . .

[II] W. Wang, M. Goldnaraghi and F . Ismail, "Prognosis of machine health condition using neurofuzzy systems," Mech. Systems and Signal Proc., vol. 18, p. 813-831,2004.

[12] P. Angelov and D. Filev, "An approach to online identification of takagisugeno fuzzy models," iEEE Trans. Syst. Man Cybern. - Part B: Cybernetics, vol. 34, p. 484-498, 2004.

[13] P. Angelov and C. Xydeas, "Fuzzy systems design: direct and indirect approaches," Soft Comp, vol. 10, p. 836-849,2006.

[14] 1. Hines and R. E. Uhrig, "Use of autoassociative neural networks for signal validation," Journal of intelligent and Robotic System, pp. 143 -154,1998.

[15] M. Najafi, C. Gulp and R. Langari, "Enhanced auto-associative neural networks for sensor diagnostics (E-AANN)," Fuzzy Systems, 2004. Proceedings. 2004 iEEE international Conference, vol. I, pp. 453 - 456, 2004.

[16] P. Frank, A. Garcia and B. Kppen-Seliger, "Modelling for fault detection and isolation versus modelling for control," Mathematics and Computers in Simulation, vol. 53, p. 259-271, 2000.

[17] T. Samy, T. Postlethwaite and D. W. Gu, "Survey and application of sensor fault detection and isolation schemes," Control Engineering Practice, vol. 19, p. 658-674, 2011.

[18] E. Balaban, A. Saxena, P. Bansal, K. F. Goebel and S. Curran, "Modeling, detection, and disambiguation of sensor faults for aerospace,"

iEEE SENSORS JOURNAL, vol. 9, p. 1907-1917,2009.

[19] B. W. Bequette, Process Dynamics: Modeling, Analysis and Simulation, Prentice-Hall, 1998.


Multiple sensor fault diagnosis for non-linear and dynamic system by evolving approach

Documents

Transcript of Multiple sensor fault diagnosis for non-linear and dynamic system by evolving approach