MULTIPLE FAULTS FUZZY DETECTION APPROACH IMPROVED BY PARTICLE SWARM OPTIMIZATION

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1 8 th International Conference of Modeling and Simulation - MOSIM 0 - May 0-2, Hammamet - Tunisia Evaluation and optimization of innovative production systems of goods and services MULTIPLE FAULTS FUZZY DETECTION APPROACH IMPROVED BY PARTICLE SWARM OPTIMIZATION Imtiez FLISS LI3 Laboratory / University of Manouba, National School of Computer Sciences 200 Manouba, Tunisia ensi.rnu.tn Moncef TAGINA LI3 Laboratory / University of Manouba, National School of Computer Sciences 200 Manouba, Tunisia ensi.rnu.tn ABSTRACT: In this paper an on-line multiple faults detection approach is proposed and improved by the use of Particle Swarm Optimization (PSO) to optimally adjust the membership functions parameters. The residuals obtained by Analytical Redundancy Relations are used as inputs to our system. The Analytical Redundancy Relations are generated by the use of bond graph modelling. The results of the fuzzy detection module are presented as a colored causal graph. The causal graph represents the state of different variables from the green nominal state to the red faulty state. The proposed approaches are then tested through a simulation of the three-tank hydraulic system. A comparison between the results obtained by using PSO and those given by the use of Genetic Algorithms (GA) is finally made. KEYWORDS: multiple faults detection, fuzzy logic reasoning, Particle Swarm Optimization, causal graph, bond graph, Genetic Algorithms. INTRODUCTION With the hasty progress of science and technology, the security and reliability of industrial systems become more and more fundamental. Proper and timely fault detection is one of the key technologies that can guarantee the system safety and reliability. If multiple faults occur, consequences can be extremely serious in terms of human lives, environmental impact and economic loss. Higher performances and more accurate security necessities have invoked an ever rising demand to develop online multiple faults detection systems. Knowledge about a given situation is generally imperfect. Doubts can arise either about knowledge validity (it is said to be uncertain), or about how to express knowledge clearly (it is vague or imprecise). These two types of imperfections are different but often intimately linked. Noise measurements and modelling approximations are sources of uncertainty in the decision to classify on-line a process state with measurements (Evsukoff A., et al., 2000). It is, then, difficult to distinguish between the effects of an actual fault and those caused by uncertainty and disturbance. The fuzzy logic reasoning is a solution to avoid instable decisions in these cases. The use of fuzzy logic in the field of fault detection has been considerably increasing. However, the success of fuzzy reasoning fault detection module depends essentially on the parameters of the fuzzy logic such as the fuzzy membership functions. For efficiency, an optimal design of membership functions is desired (Zhou, Y.S., and L.Y. Lai, 2000). Therefore, we have chosen to use an optimization technique to adjust the parameters of the fuzzy membership functions: the particle swarm optimization (PSO). Generally, PSO is characterized as a simple concept, easy to implement, and computationally efficient. Unlike the other heuristic techniques, PSO has a flexible and well-balanced mechanism to enhance local exploration abilities (Abido, M. A., 2002). In this paper, we proposed an on-line multiple faults fuzzy detection approach that we improved by using Particle Swarm Optimization. The inputs of these systems are residuals which are consistency indicators and represent the numerical evaluation of the Analytical Redundancy Relations (ARRs) or also called the parity relations. Analytical Redundancy Relations (ARRs) are symbolic equations representing constraints between different known process variables (parameters, measurements and sources). When a process operates under normal mode conditions, evaluation of the constraints should reveal values within certain small error bounds. Theoretically, these values, also called residuals, should be zero under no fault condition. ARRs are obtained from the behavioral model of the system through different procedures of elimination of unknown variables (Evsukoff A., et al., 2000). To get these ARRs, we were based on the bond graph modelling (Dauphin-Tanguy, G., 2000) which allows to deal with the enormous amount of equations describing the process behavior and to display explicitly the power exchange between the process components starting from the instrumentation architecture. Bond graph is a unified language for all engineering science domains that con-

2 siders energy and information channels. Indeed, that is very useful since multidisciplinary systems constitute the majority of industrial products that exist nowadays. The fuzzy detection conclusions are finally displayed through a colored causal graph. In this step we were inspired from (Evsukoff A., et al., 2000), representing the state of system variables through a gradual colored palette from the green nominal state to the red faulty state. This leads to stable decisions and allows gradual information processing that can be easily understood by the human operator. To test the performance of the proposed approaches we rely on a simulation of the three- tank hydraulic system. This paper is organized as follows: the second section presents the proposed multiple faults Fuzzy fault detection approaches without and with PSO. While Section 3 introduces the simulation example, Section 4 is devoted to the presentation of simulation results. In this part we will expose the fault detection results we get in case of both proposed approaches with and without PSO. To make evidence of the effectiveness of using PSO, we intend to compare, in section 5, the multiple faults detection rate given using PSO to the one given by Genetic Algorithms (GA). Finally, some concluding remarks are made. 2 THE FUZZY APPROACH FOR MULTIPLE FAULTS DETECTION There has been an increasing interest in fault detection in recent years, as a result of the increased degree of automation and the growing demand for higher performance, efficiency, reliability and safety in industrial systems. Fault detection is crucial in the process of system supervision. It consists in deciding if the physical process is faulty or not regardless disturbances. In fact, the purpose of detection is to establish a rule of decision that can detect the earliest possible passage of a normal operating condition, called Hypothesis H 0, to a state of abnormal, where there are failures, noted Hypothesis H, corresponding to an unpredictable change of some parameters related to the process. When using such a decision rule, the operator wants to reduce the delay in detection and the rate of false alarms. To avoid instable decisions in this case of uncertainties and disturbances, many techniques have been used. A considerably increasing interest in the development of diagnostic methods based on fuzzy logic (Koscielny J- M., and M. Syfert, 2006). In fact, fuzzy logic is a very efficient tool for the conversion of uncertain and inaccurate information. It is considered in (Bouchon-Meunier, B., 995) as the best framework in which we can handle uncertainties and which also allows the treatment of some incompleteness. This method can take into account the uncertainties by the gradual nature of belonging to a fuzzy set. The development of on line fault detection systems improves the operational reliability of industrial systems and reduces the operational and maintenance costs. With the continual expansion of industrial applications which are becoming increasingly complex, the problems of multiple faults occur. This means that several faults affect variables at the same time. In this context, our work consists in proposing two fuzzy approaches for on-line multiple faults detection. While, the first one detects faults without optimizing the parameters of membership functions, the second, uses PSO to optimally adjust these parameters. 2. Fuzzy detection approach without PSO Fuzzy logic fault detection consists in interpreting the residuals by generating a value of belonging to the class AL (alarm) between 0 and that allows to decide whether the measurement is normal or not. The gradual evolution of this variable from 0 to represents the evolution of the variable to an abnormal state. In our work, we were inspired from (Evsukoff A., et al., 2000) in the defuzzification phase. Thus the gradual evolution is changed into an index characterizing a color code (green, red) to represent the state of different variables on a causal graph. The fuzzy logic detection approach involves three successive processes, namely: fuzzification, fuzzy inference, and defuzzification. 2.. Fuzzification Fuzzification module transforms the crisp inputs into fuzzy values. In fact, actual measure input values are mapped into fuzzy membership functions and each input's grade of membership in each membership function is evaluated. Then these values are processed in the fuzzy domain by Inference system, which, is based on the rule base provided by the Knowledge base (KB). The Analytical Redundancy Relations (ARR), symbolic equations which are only function of known variables, can provide information on the consistency of the model with the real working of the system of the system. Therefore they are equal to zeros in normal running, different of zero at the time of a failing of one or several components of system. These relations are used as inputs of our fuzzy logic detection module. The linguistic set {NB, N, Z, P, PB} meaning negative big, negative, zero, positive and positive big respectively describes the inputs (ARRi). The supports of the membership functions of the inputs are as the following: =,,,

3 =,,, =,,, =,,, =,,, With a domain characteristic variable which is obtained from experts' knowledge. Symmetrical trapezoidal membership functions are used for the input fuzzy partitions (see figure ). Symmetry is justified here by the fact that in the absence of a fault, residuals are zero, and positive or negative faults have the same importance (Evsukoff A., et al., 2000). The symmetry leads to a simple parameterization of the residual value fuzzy partition with only four parameters: a i, a i2, a i3 and a i4 (instead of eight) corresponding to the trapezoid boundaries. Where: a i : the maximum value of ARR i in fault-free case. a i2 : minimum value of ARR i in fault case. a i3 : maximum value of ARR i in fault case in limited interval. a i4 : maximum value of ARR i in fault case. Note that a i, a i2, a i3 and ai4 are absolute values; they can take only positive values. The membership functions of inputs are shown in figure Defuzzification After determining the relationship between residuals and system variable states and creating the fuzzy connections between the two, the final step is to defuzzify these sets. Defuzzification is the process of converting the fuzzy information into crisp values. The outputs of our fuzzy detection module are the variables' states. An output can be OK or AL. Figure 2 shows the different outputs' membership functions. Figure 2: Output Fuzzy Partitions Where: a i : minimum negative value of the system variable i in fault case. b i : minimum value of the system variable i in fault-free case. c i : maximum value of the system variable i in fault-free case. d i : minimum positive value of the system variable i in fault case. Note that a i, b i take only negative values while c i and d i take only positive values. Figure : Input Fuzzy partitions 2..2 Fuzzy inference system The second step in the fuzzy logic process involves the inference of the residual values. The fuzzy inference system (FIS) is responsible for drawing conclusions from the knowledge-based fuzzy rule set of if-then linguistic statements. In general, the task of fault decision is to infer variables' states from a set of residuals (ARRs). The set of fuzzy inputs (N Analytical Redundancy Relations) with their respective membership functions form the premise part of a fuzzy logic analysis. A fuzzy rule set (linguistic if-then statements) is then used to form judgment on the fuzzy inputs derived from the N ARRs. In our case, a large set of inference rules is established, for instance: If all ARRs are Z then all variables are OK. If all ARRs are NB then all variables are AL. If all ARRs are PB then all variables are AL. We used the MIN-MAX inference method consisting in using the operator min for AND and the operator max for OR. In this step we inspired from (Evsukoff A., et al., 2000). Each conclusion is associated with a color. In fact, the description obtained as an output of fuzzy reasoning in detection module is defuzzified into an index associated with a color shade to represent how each of the conclusions is matched. In our case, the conclusions are defuzzified into an index of a color map from green (normal state) to red (faulty state). Colors codes have been widely used in human-machine interfaces to represent qualitative numerical results. Using colors enables concepts that gradually evolve with time to be represented. A graduated color code translates the detection algorithm results into a mass visualization of the variable states, which allows operators to analyze a large amount of qualitative information (Evsukoff A., et al., 2000). The result of the fuzzy detection approach is then presented as a colored causal graph. The performance of fuzzy detection is intimately linked to the fuzzy membership functions. For efficiency, an optimal design of membership functions is desired (Zhou, Y.S., and L.Y. Lai, 2000). Therefore, we have chosen to use an optimization technique to adjust the parameters of the fuzzy membership functions: the Particle Swarm Optimization (PSO).

4 2.2 Overview of Particle Swarm Optimization (PSO) K= (3) Particle Swarm Optimization PSO (Kennedy, J., and R.C. Eberhart, 995) (Shi, Y., And R.C. Eberhart, 998) is one of the artificial life or multiple agents type techniques. It is a population-based optimization technique first introduced by Kennedy and Eberhart (995). It uses a principle of social behavior of a group. A group can achieve the objective effectively by using the common information of every agent, and the information owned by the agent itself. The motivation for the development of the PSO was based on a simple simulation of animal social behaviors such as bird flocking or fish schooling. Some of the attractive features of PSO include the ease of implementation and the fact that no gradient information is required (Clerc, M., 999). The population in PSO is called a swarm and the individuals, referred to as particles, are candidate solutions to the optimization problem at hand in the multidimensional search space (D dimensional). Each dimension of this space represents a parameter of the problem to be optimized. The position and velocity of all particles are usually updated synchronously in each iteration of the algorithm. A particle adjusts its velocity according to its own flight experience and the flight experience of other particles in the swarm in such a way that it accelerates towards positions that have had high objective (fitness) values in previous iterations. The algorithm does not require the objective function to be differentiable and continuous and it can be applied to nonlinear and non-continuous cases to solve a wide array of different optimization problems. There are two kinds of position towards which a particle is accelerated in common use. The first one, a particle s personal best position achieved up to the current iteration, is called Pbest i. The other is the global best position obtained so far by all particles, called Gbest (Yisu, J., et al., 2008). There are several versions of the Particle Swarm Optimization in the literature. We have chosen the one with constriction factor for its speed of convergence (Clerc, M., 999). In this case, the modified velocity (v i ) and position (x i ) of each particle can be calculated using the current velocity, Pbest i and Gbest as shown in the following formulas: t + t t + = K * ( v + c * rand()* ( Pbesti x ) + c * rand() * ( Gbest x t + )) i i i 2 i v () t+ t x i = x i + v i Where K: the constriction factor, (2) With c=c +c 2 and c>4 (Clerc, M., and J. Kennedy, 2002), t x i : Current position of the i th particle at the t th iteration, t v i : Velocity of the particle n i at the t th iteration, Pbest i : Best previous position of the i th particle, Gbest: Best particle position among all particles in the population, Rand (): Random number between 0 and, c : self confidence factor, c 2 : swarm confidence factor, c and c 2 are positive constants empirically determined knowing that (c +c 2 >4). 2.3 Fuzzy detection approach using PSO In this approach, we intend to optimally adjust the inputs' parameters: a i, a i2, a i3 and a i4 and the output's membership functions parameters a j, b j, c j and d j using PSO with.., N is the total number of residuals,.. and P is the total number of system variables Initialization Initial swarm population is composed of 30 particles. This choice is based on the study done in (Carlisle, A., and G. Dozier, 200). This population size is small enough to be efficient, yet large enough to produce reliable results. Initial positions and velocities of particles are generated by using random values. The initial fitness value of each particle is initialized to a big positive constant. The local best of each particle Pbest i is set to its current fitness value. The global best value of the position Gbest is set to the best value of all Pbest i Fitness function The fitness function or the objective function is the performance index of a population. The fitness value is bigger, and the performance is better. For the present problem the aim is to have the proper fault decision. Thus, the used fitness function fixes the rate the fault detection error which ought to be minimized Algorithm The evolution procedure of PSO Algorithm can be summed up as following:

5 ) Begin 2) Definition of the problem dimension 3) Initialization 4) Calculate membership parameters. 5) Evaluation of objective function 6) Updating local best memory Pbest i and the best memory of population Gbest 7) Update each particle velocity and position using the equations () and (2) 8) If the maximum iteration number is reached stop 9) Else loop to 4. and the energy flow paths appear as links or bonds (Dauphin-Tanguy, G., 2000). The bond graph model of the three- tank system is giving in figure 4. 3 SIMULATION EXAMPLE 3. PROCESS DESCRIPTION To illustrate the applicability of the presented methods a three- tank hydraulic system shown in figure 3 is taken as example. The process consists of three cylindrical tanks. Tanks communicate through feeding valves func- tioning in binary mode. Msf and Msf 2 corresponding to volume flows applied to the system are the two inputs of the process. We put five sensors: effort sensors De, De 2 and De 3 to measure pressure of C, C 2 and C 3 and flow sensors Df and Df 2 measuring flow level of the valves and 2. The global purpose of the three- tank system is to keep a steady flumiddle. id level in the tank n 2, the one in the Figure 4: Bond Graph model of the three-tank system The tanks are modeled as capacitances that hold fluid, and the valves as resistances to flow. 0 and junctions represent the common effort (i.e., pressure) and common flow (i.e., flow rate) points in the system, respectively. Each junction in the reference model represents a constitutive equation for efforts or flows. Measurement points, shown as Dei and Dfi com- detectors and flow detec- ponents, are respectively effort tors not consuming power (supposed ideal) and con- nected to junctions. Thanks to structural behavioral and causal properties (Gentil, S., 2007) of Bond Graph, the causal graph of the three- tank process can be generated as given in figure 5. Figure 3: The three-tank system 3.2 Bond Graph Modelling To ensure the best precision and reliability in fault detecmodel of the physi- tion, we have to choose carefully the cal system. In fact, the quality of diagnostic system de- models of pends on the quality of the model. Dynamic physical systems may be represented in different ways: logical statements, mathematic equations, bond graph, digraphs In our case, we focus on bond graph modelling (Dau- multidiscip- phin-tanguy, G., 2000) which is a powerful linary tool for modelling, analysis and ARRs generation. Bond graphs are labeled, directed graphs, which present a topological, domain-independent, energy-based mebehavior of physi- thodology for modeling the dynamic cal systems (Samantaray, A. and B. Bouamama, 2008) Bond graphs provide an easy way to put up multi- system models domain energy-based models. Building follows an intuitive approach where energy flow paths between system components are captured by a topologi- cal structure where system components appear as nodes, Figure 5: Influence Graph of the three- tank system In this case, the graph nodes represent the system va- the normal relations riables; the directed arcs symbolize among them (for instance Msf ->De means that modificause changes of De ). cations of Msf will necessary 3.3 ARR determination For the generation of Analytic Redundancy Relations directly from the bond graph model, we were based on the bond graph model given in figure 4 and we used the procedure described in (Tagina, M., and al., 996a) (Ta- the constituent rela- gina, M., and al., 996b) exploiting tions of set of junctions of the model, that are function of known variable or unknown (the effort and the flow in link with the considered junction), that are deduced by the covering of causal path. In this case, we obtain the following Analytical Redun- dancy Relations:

6 ARR: MSf ( + ) De Df = 0 (4) sc R C s C s ARR2: sc 2 ARR3: Df ( + ) De2 Df 2 = 0 (5) R C s C s ( + ) De3 = 0 C s MSf Df (6) C s R C s 3 ARR4: De De 3 2 Df2 = R23 ARR5: De De 3 2 Df = R The bond graph model is then converted into synopsis diagram simulated within Simulink/Matlab environment. (7) (8) In free-fault context, it is confirmed that all Analytical Redundancy Relations describing the residuals are null. Note that we consider in our work additional faults modeled as additive signals added to the three- tank system variables to be monitored. 4 SIMULATION RESULTS We have used 50 data to test the performance of the proposed approaches to give proper faults decisions. We first expose the results given in case of using our multiple faults fuzzy detection approach without Particle Swarm Optimization. 4. Multiple Faults Fuzzy detection without PSO The multiple faults fuzzy approach without PSO gives a bad detection in case of faults affecting De 2 and Msf 2. In fact, the proposed approach doesn't detect any faults and the result of this case is given in figure 6. Figure 6: Result of injecting De 2 and Msf 2 using the fault detection module without PSO We also notice a delay of 0 seconds in fault detection in case of injecting Msf, Msf 2 and De 2 at 30s. These results can be improved by using Particle Swarm Optimization. 4.2 Multiple Faults Fuzzy detection using PSO The first step in our work is to determine the membership functions' parameters The optimal membership functions The membership functions' parameters are [a, a2, a3, a4] for each input (in this case we have five inputs {arr, arr2, arr3, arr4 and arr5}) and [a, b, c and d] for each output {Msf, Msf2, De, De2, De3, Df and Df2}. Table lists the parameters of the PSO algorithm used in our work. We have based our choice of the population size, c and c 2 on the study done in (Carlisle, A., and G. Dozier, 200). Population Size 30 Number of Iterations 0000 c 2.8 c 2.3 a i with iϵ [,5 ] [0, ] a i2 with iϵ [,5 ] [0,.5] a i3 with iϵ [,5 ] [, 5] a i4 with iϵ [,5 ] [.5, 5] a j with jϵ [,7 ] [-5, 0] b j with jϵ [,7 ] [-0.5, 0] c j with jϵ [,7 ] [0, 5] d j with jϵ [,7 ] [0.5, 5] Table : Parameters of PSO algorithm With {a i, a i2, a i3, a i4 } the parameters of the input n i; {iϵ [, 5 ]} and {a j, b j, c j, d j } the parameters of the j th output; {jϵ [, 7 ]}. After the evolution process of PSO, we obtain as a result: a 0.46 a a a a b a 3.57 a c a 4.73 a d a a a a b b a c c a d d a a a a b b a c c a d d a a a a b b a c c a d d Table 2: Simulation results

7 The optimal membership functions consequently obtained are shown in figure 7. Figure 7: The optimal membership functions Once the parameters of membership functions are adreasoning to determine the justed, we proceed by fuzzy status of the system: normal or faulty displaying the re- the state of the dif- sults as a causal graph representing ferent variables through a gradual palette of colors from the green nominal state to the red faulty state Multiple Faults Fuzzy detection The detection results are satisfactory in this case. For instance figure 8 and figure 9 show faults detection reand Msf 2 } and {Msf, Msf 2 sults when faults affect {De 2 and De 2 } respectively. Figure 8: Result of injecting De 2 and Msf 2 using the fault detection module with PSO Figure 9: Result of injecting Msf, Msf 2 and De 2 using the fault detection module with PSO In case of injecting faults to Msf, Msf 2 and De 2, we nowithout any delay. tice a proper decision at time These results prove evidence of the effectiveness of the use of PSO to improve fault detection Discussion Comparison between the results obtained using the mul- without and with PSO in tiple fault detection approaches the case of the three- tank system is resumed in table 3 and figure 0.

8 Multiple Faults Fuzzy Detection approach using PSO 98% Rate of proper decision Average delay in.8s detection Table 3: Simulation results 00% 80% 60% 40% 20% 0% 98% 78% Proper decision rate Using PSO Without PSO Figure 0: Simulation results Results prove evidence that the use of PSO in our on-line multiple faults Fuzzy detection module gives the proper decisions in majority of cases with a small delay. It is also clear that the use of PSO presents an average reducin the case of the tion of 20% of bad detections giving use of our approach without PSO and a reducing of fault delay of proximately 8 s. The application of the PSO algorithm in our case shows that this technique presents a great promise for detection process. In fact, the use of PSO in our study case im- proved the performance of our fuzzy fault detection module, decreases the possibility of bad detections and reduced the detection delay. To make evidence of the effectivenesss of using PSO, it would be interesting to compare its performance in case of multiple faults detection with an evolutionary tech- the Genetic nique that has attracted considerable attention: Algorithms (GA). 5 MULTIPLE FAULTS FUZZY DETECTION WITH GA 5. Overview of Genetic Algorithms Multiple Faults Fuzzy Detection approach without PSO 78% 9.06 s The GA is an optimization routine based on the prin- genetics. It has ciples of Darwinian Theory and natural primarily been utilized as an off-line technique for per- solution to a forming a directed search for the optimal problem. The GA performs a parallel, directed, random search for the fittest element of a population within a search space. The population simply consists of strings of numbers, called chromosomes that hold possible solu- M.E.-S., 2007). tions of a problem (El-Telbany, Like PSO, the GA begins its search from a randomly generated population of designs that evolve over succeseliminating the need for a sive generations (iterations), user-supplied starting point. To perform its optimization- like process, the GA employs three operators called seand replacement, to propa- lection, crossover, mutation, gate its population from one generation to another (Has- san, R., B. Cohanim and O. De Weck, 2005). By creating successive generations which continue to evolve, the GA will tend to search for a global optimal solution. The key to the search is the fitness evaluation. The fitness of each of the members of the population is calculated using a fitness function that characterizes how well each particular member solves the given problem. Parents for the next generationn are selected based on the fitness value of the strings. That is, strings that have a higher fitness value are more likely to be selected as par- to survive to the next ents, and, thus, are more likely generation. 5.2 Detection approach using GA 5.2. Algorithm The following outline summarizes how the genetic algo- rithm we used works:. The algorithm begins by creating a random initial population. 2. The algorithm then creates a sequence of new popualgorithm uses the individ- lations. At each step, the uals in the current generation to create the next pop- ulation. To create the new population, the algorithm performs the following steps: a) Scores each member of the current population by computing its fitness value. b) Scales the raw fitnesss scores to convert them in- of values. to a more usable range c) Selects members, called parents, based on their fitness. d) Some of the individuals in the current populafitness are chosen as elite. tion that have lower These elite individuals are passed to the next population. e) Produces children from the parents. Children are produced either by making random changes to a single parent mutation or by combin- of a pair of parents ing the vector entries crossover. f) Replaces the current population with the childgeneration. ren to form the next

9 3. The algorithm stops when one of the following stopping criteria is met: faults detection results when faults affect {De 2 and Msf 2 }. a) The maximum number of generations is reaches (in our study we use 00 as a maximum number). b) There is no improvement in the best fitness value for 50 generations Parameters optimization: simulation The first step in our work is to determine the membership functions' parameters which are [a, a2, a3, a4] for each input and [a, b, c and d] for each output. Table 4 lists the parameters of GA used in our work. Population Size 30 Maximum number of generations 00 Genome representation X Mutation function Uniform mutation Crossover function Intermediate Scaling function Rank Table 4: Parameters of GA With the genome representation X= [a, a 2, a 3, a 4, a 2, a 22, a 23, a 24, a 3, a 32, a 33, a 34, a 4, a 42, a 43, a 44, a 5, a 52, a 53, a 54, a, b, c, d, a 2, b 2, c 2, d 2, a 3, b 3, c 3, d 3, a 4, b 4, c 4, d 4, a 5, b 5, c 5, d 5, a 6, b 6, c 6, d 6, a 7, b 7, c 7, d 7 ]. After the evolution process of GA described in (5.2.) and using the parameters given in table 4, we obtain as a result: a 0.06 a a a a b a 3.07 a c a 4.73 a d a a a a b b a c c a d d a a a a b b a c c a d d a a a a b b a c c a d d Table 5: Simulation results Multiple Faults Fuzzy detection using GA The detection approach using Genetic Algorithms gives a small rate of bad detections 8%. We can say then that the results are acceptable. For instance figure shows Figure : Result of injecting De 2 and Msf 2 using the fault detection module using GA In this case, we notice a proper decision with a delay in detection of 2s in case of injecting Msf 2 and De 2 at 40s. 5.3 Discussion Comparison between the results obtained using the multiple fault detection approaches with PSO and with GA in the case of the three- tank system is resumed in table 6. Rate of proper decision Average delay in detection Fuzzy Fault Detection Fuzzy Fault De- Module tection Module using PSO using GA 98% 92%.8s 2.26 s Table 6: comparisons between Genetic Algorithms and PSO We notice that both used optimization techniques give good rate of proper decision (more than 90%) and a small average delay in detection (less than 3s) in the case of the three-hydraulic system with the choices we made in tables and 4. According to the simulation results given in our study case, PSO proves its effectiveness giving the proper fault decision in 49/50 cases and reducing the delay in detection. This can be explained by the fact that the best finally solutions (membership functions parameters) are obtained from bad intermediate solutions that were eliminated in the case of GA. This influences the performance of the multiple faults fuzzy detection particles which is sensitive to its membership functions parameters. It is also to notice that, compared to GA, the advantages of PSO are that it is easy to implement and there are few parameters to adjust (Hassan, R., B. Cohanim and O. De Weck, 2005). In fact, PSO does not have genetic operators like crossover and mutation. Particles update themselves with the internal velocity. They also have memory, which is important to the algorithm.

10 We can then conclude that the use of PSO presents a great improvement and promise of our on-line multiple faults fuzzy detection approach. 6 CONCLUSION In this paper, we have proposed a fuzzy approach for online multiple faults detection. In fact, fuzzy systems are convenient and efficient for solution for such a problem. However, the major drawback of the fuzzy logic systems is insufficient analytical technique design (like parameterization of the membership functions). This paper presents an improvement of the proposed approach using Particle Swarm Optimization in order to adjust the membership functions' parameters of a fault detection module. The inputs of the detection modules are Analytical Redundancy Relations obtained from bond graph model. The conclusions of the fuzzy reasoning detection module are then defuzzified into an index of a color map from green (normal state) to red (faulty state) and given as a colored causal graph. A simulation of the three-tank system proves that the improved multiple faults fuzzy detection module gives very good results compared to the one without optimization. Finally a comparison with GA is made to prove the effectiveness of the use of PSO in our study case. Simulations showed a good rate for proper detection and a small delay in detection in case of using PSO. REFERENCES Abido, M. A., Optimal Design of Power-System Stabilizers Using Particle Swarm Optimization. IEEE Trans. Energy Conversion, Vol. 7, p Bouchon-Meunier, B., 995. La logique floue et ses applications, Addison-Wesley, France. Carlisle, A., and G. Dozier, 200. An Off-The-Shelf PSO. Proceedings of the Particle Swarm Optimization Workshop, Indianapolis, Ind, Usa, p. 6. Clerc, M., 999. The Swarm and the Queen: Towards A Deterministic and Adaptive Particle Swarm Optimization. Proceedings of the Congress of Evolutionary Computation, Washington, Dc, p Clerc, M., and J. Kennedy, The Particle Swarm: Explosion, Stability and Convergence in a Multi- Dimensional Complex Space. IEEE Transactions on Evolutionary Computation, Vol. 6. Dauphin-Tanguy, G., Les Bond Graph. Hermes Sciences Publications. El-Telbany, M.E.-S., Employing Particle Swarm Optimizer and Genetic Algorithms for Optimal Tuning of PID Controllers: A Comparative Study. ICGST-ACSE Journal, Volume 7, Issue 2, p Evsukoff, A., S. Gentil and J. Montmain, Fuzzy Reasoning in Cooperative Supervision Systems. Control Engineering Practice, p Gentil, S., Supervision des procédés complexes, Hermès Science Publication, Paris. Hassan, R., B. Cohanim and O. De Weck, A Comparison of Particle Swarm Optimization and the Genetic Algorithm. 46th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics & Materials Conference, Austin, Texas. Kennedy, J., and R.C. Eberhart, 995. Particle Swarm Optimization. Proceeding of The IEEE International Conference On Neural Networks, Perth, Australia, Vol. 4, p Koscielny J-M., and M. Syfert, 2006, Fuzzy diagnostic reasoning that takes into account the uncertainty of the relation between faults and symptoms..int. J. Appl. Math. Comput. Sci., Vol. 6, No., p Samantaray, A. and B. Bouamama, Model-Based Process Supervision: A Bond Graph Approach, Springer Verlag, London, UK. Shi, Y., and R.C. Eberhart, 998. A Modified Particle Swarm Optimiser. IEEE International Conference on Evolutionary Computation, Anchorage, Alaska. Tagina, M., J.P. Cassar, G. Dauphin-Tanguy and M. Staroswiecki, 996. The Bond Graph Use for the Design and The Improvement Of Instrumentation Architecture For System Monitoring. Int Mechanical Engineering Congress and Exhibition, Publication Dans Dynamics Systems and Control Division's Proceedings, Atlanta, Georgia, USA. Tagina, M., J.P. Cassar, G. Dauphin-Tanguy and M. Staroswiecki, 996. Bond Graph Models For Direct Generation Of Formal Fault Detection Systems. International Journal of Systems Analysis Modelling and Simulation, Vol.23, p Yisu, J., J. Knowles, L. Hongmei, L. Yizeng and D.B. Kell, The Landscape Adaptive Particle Swarm Optimizer. Applied Soft Computing, 8, p Zhou, Y.S., and L.Y. Lai, Optimal Design for Fuzzy Controllers by Genetic Algorithms. IEEETrans. On Industry Application, Vol. 36, No., p