Fault Detection in Control Systems via Evolutionary Algorithms

Transcription

1 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Fault Detection in Control Systems via Evolutionary Algorithms KLIMÁNEK, David 1 & ŠULC, Bohumil 2 1 Ing., Department of Instrumentation and Control Engineering, CTU in Prague, Technická 4, Praha, david.klimanek@fs.cvut.cz 2 Doc., Ing., CSc., sulc@fsid.cvut.cz Abstract: In control loops, there is always a problem how to detect small malfunctions of the control loop caused e.g. by changes of sensor properties that do not represent total failure, but only a deviation from assumed features. Sometimes, it is difficult to detect such changes because they are not apparent from the control loop behaviour and their detection may require very expensive measuring equipment. We are faced to a problem, that although the control loop seems to work properly, the consequences of such a small malfunction can be substantial and expensive (e.g. increase of harmful emissions in combustion processes). This paper describes a test how the above mentioned problem could be solved by means of Genetic Algorithms (GAs) that offer some aspects particularly appropriate for solution of this problem. Suitability evaluation shown in this paper is based on results from simulated experiments where the controlled object was a tank with SISO water level control. As an example of a malfunction, simulating change of sensor coefficients was chosen. This additive optimization of the sensor parameters does not have any effect on the control loop. The control loop works independently and does not depend on the system model. Keywords: Evolutionary algorithm, Genetic algorithm, Fault detection 1 Introduction In operation of control loops, we can be tackled by problem of a hidden malfunction of control system, usually caused by sensors for controlled variables. These sensors do not stop their operation completely; they only start to provide wrong measurement of controlled variable. If deviations of measured values from correct (real) values are not extreme there is only a very small chance for the operator to recognize something because all information he is provided with, is that intermediated by the faulty sensor. Only if there is a duplicity or even triplicity in data acquisition ensured then it is no problem to apply well known algorithms of selection two from three. Such hardware redundancy may represent additional costs and it has its raison d'etre in control of dangerous processes. However, to avoid additional costs, we are dealing with the idea to use genetic algorithm to detect malfunctions of the sensor properties. This detection can substitute one or two redundant measuring equipment. The aim of this paper is to present an attempt in finding another way towards malfunction detection than that represented by usual utilisation of redundant measuring equipment. Genetic Algorithms (GA) as a part of Evolutionary Algorithms are computational simulation techniques based on Darwinian principles. They have arisen from modelling biological processes (Holland, 1975). Evolutionary Algorithms comprise four main areas: Genetic Algorithms, Evolution Strategies, Genetic Programming and Simulated Annealing. All considered methods are heuristic, i.e. they contain a random component.

2 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Description of Genetic Algorithm Principles Although a large variety of different GAs is known, there is a standard genetic algorithm that has established the basis for many of the alterations (MAŘÍK 2001). Standard genetic algorithms (SGA) work with a population of potential solutions to a given problem. Each individual within the population represents a particular solution to the problem. The population is evolved, over generations, to produce better solutions to the problem. A diagram of the algorithm is shown in Figure 1. The SGA starts by creation of an initial population that is usually generated at random. Next an iterative process of evaluation, selection, crossover and mutation starts. This iteration runs until a termination condition is satisfied. A population of between twenty and one hundred is normally sufficient for majority application. (Michalewicz, 1996) Initialisation Fitess calculation ( Evalution) Genetic operators Selection Crossover Fitess calculation Mutation ( Evalution) New generation No Termination Condition Yes Result Found Figure 1 Diagram of Standard Genetic Algorithm In Figure 2 a pseudo code illustrating the SGA is shown. The algorithm runs in a loop which simulates evolution time. procedure SGA { t= 0; initialize P(t); evaluate P(t); while not terminal_condition do { t= t+1; select P(t) from P(t 1); reproduce pairs in P(t); mutate P(t) evaluate P(t) } } Figure 2 Schematic of Standard Genetic Algorithm

3 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, I. Initialization Time of evolution t = 0 Random initialization of generation P 0) = { P (0), i = 1,..., n }, n p size of population (1) ( i p Evaluate Fitness calculation Φ P(0)) = { Φ(P (0)), i = 1,..., n } (2) ( i p II. While Termination_Condition is not true Evolution time increases t = t + 1 Genetic operators Selection P ( t ) = { Pi ( t ) = sn( Pi ( t)), i = 1,..., np}, s n.selection method, n p population size (3) Crossover P ( t ) = { Pi ( t ) = pcross ( Pi ( t)), i = 1,..., n p} p cros probability of crossover (4) Mutation P ( t ) = { Pi ( t ) = mmut ( Pi ( t)), i = 1,..., n p} m mut probability of mutation (5) Evaluate Fitness calculation Φ ( P ( t)) = { Φ( Pi ( t )), i = 1,..., n p} (6) New generation P t + 1) = { P ( t + 1) = P ( t), i = 1,..., n } (7) ( i i p 3 Sensor Fault Detection by Means of GA Algorithm has been applied to a very simple application where simulated object is a tank with SISO water level control. Water level is controlled by PI controller; the water level is measured by sensor with linear characteristic. The sensor is an object where is demanded to verify whether simulated malfunction can be detected by genetic algorithms or not. Although implementation of fault detection methods is useable in more complex cases, this example was used because it is easy to verify results. Used example is simply, but inlet and outlet valves are modelled with butterfly characteristic which mimic real valve behaviour. The values of water level obtained from real system and simulation model are compared. The deviation represents sourcing signal for Genetic Algorithm block shown in Figure 3. As it was mentioned simulated changes of linear sensor properties (1) do not represent a total failure, but only a deviation from expected features.

4 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Figure 3 Simulation Scheme for malfunction function identification hreal ( t) = khsystem + q k, q sensor parameters, h water level (8) In Figure 3 influence of sensor coefficients changes have been tested. As long as no malfunction accrues sensor is providing exact data information. However, after simulated change detected sensor is providing altered information. Figure 4 Impact of sensor coefficients change During the whole simulation time GA block is trying to minimize deviation between real system and simulation model by evaluating potential sensor parameters. While no malfunction occurs the process is running with normally assumed coefficients k=0.3, q=0.2 and as it is apparent in Figure 2 value of water level is tracking desired value. The deviation of real system water level and simulation model is minimised (Figure 4). During the time simulated change of sensors parameters have occurred.

5 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Figure 5 Influence of parameter developing on deviation between model and real system When a malfunction occurs, parameters of sensor are changed, e.g. k = 0.45, q = 0.35 Genetic Algorithm block is trying evaluating such coefficients which real system is currently using. In each generation best coefficients are elected. In this attempt after 20 generations current parameters of sensor have been found (Table 1). Newly evaluated coefficients k, q are 0.45 and 0.23 respectively. Evaluated parameters are different from expected ones. Now the operator can be informed that some change has happened. In our case we just make manual correction i.e. decrease coefficients k and q. correc k = kcurrent kinit = = 0.15 correcq = qcurrent qinit = = After correction is made new parameters are set. After all necessary interactions are done In Figure 3 there can be seen no deviation between real model and simulated model. Table 1 Sensor parameter developing Number of Coefficients generation k q Genetic Algorithm block All genetic algorithms methods selection, crossover, mutation, representation of individuals were employed to genetic algorithm block. All considered functions are used from Genetic algorithm Toolbox (Chippefield A., Fleming, P. 1995). In Figure 6 there is the scheme of genetic algorithm block. The block consists of initialisation block and block for genetic operators. Initialisation block generates random

6 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, population of potential solutions; a vector of PopSize pairs is generated. Each pair is one potential solution i.e. it represents one possibility of sensors parameters [k, q]. Figure 6 Genetic Algorithms subsystem and its dialog panel As it has already been mentioned, while applying genetic algorithms, specifications of components such as the mutation and crossover probabilities, p cros and p mut, representation of individuals PopSize, fitness function and selection method, are also necessary. These parameters determinate whether or not algorithm will find optimum solution. Influences on results of those parameters have also been tested. Representation of individuals Each individual represents a solution of the optimization problem. In general there are two types of representing variables of GA. The first type is a bit string representation and the second type is a real number representation. The first type is used in this paper. All population of potential solutions are coded into the 10 bit string. For this operation Matlab functions have been contribution (Jan, 2002). In our experiment population of PopSize=30 individuals was necessary. Fitness calculation Each individual within the population is assigned a fitness value, which expresses how good the solution is at solving the problem. The fitness value probabilistically determines how successful the individual will be in selecting of reproduction. Better solutions are assigned using higher values of fitness than worse performing solutions. In assumed model of fault detection the fitness is the sum of deviations between the real system and the simulation model obtained during measuring period. For minimizing fitness function it is necessary to rankle fitness values. It is done by employing rankling function. The function generates a new vector of fitness values, by reassign 0 to the worst fitness value (maximum of fitness values vector ) and 2 to the best fitness value (minimum of fitness values vector) as it is shown in Table 1. Number of Individual Table 2 Rankling calculation Coefficients Fitness Value 10 4 k q Ranked fitness Value

7 Genetic manipulation XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Selection Roulette wheel selection was used in the experiment. The probability of each individual to be selected for reproduction is determined by the ratio. The wheel selection is based on principle of turning a roulette wheel having many holes and the number of holes marked by the particular individual is proportional to its fitness. The wheel is spun n p times and each time one member of the new population is picked up (MAŘÍK 2001). Crossover In this process couples of parents are randomly chosen and new individuals are created by copying a part from each parent (Figure 9) Parent x Parent x Offspring x ' Offspring x ' Figure 7 Single point crossover method The parameter of crossover is p cros. The usual value of p cross is In the considered application the probability was tested and the best results were obtained for probability p cross =0.6. Mutation Operator mimics the random mutations found in nature. The mutation operator makes small, random changes to an individual. For a binary encoding, it represents switch of randomly chosen bit with small probability, as shown in Figure 10. In the considered algorithm the probability of mutation p mut was Parent x 1 Offspring x1 Figure 8 Binary mutation operator Influences of mutation parameters to results have been tested. Their influence to fitness function is shown in Figure 11 and in Figure 12. Better results were obtained for probability of mutation p mut =0.1. Figure 9 The average fitness for 40 generations p mut =0.1 Figure 10 The average fitness for 40 generations p mut =0.6

8 XXIX. ASR '2004 Seminar, Instruments and Control, Ostrava, April 30, Conclusions The above mentioned algorithms have achieved detection of simulated change of sensor properties. Genetic algorithms have found new sensor parameters 40 interactions. Time necessary for evaluation lasted for several minutes. The evolution time depends on number of sensor coefficients. In case of more complex application with many parameters solution may takes very long. Detection by means of GAs is very time consuming process; it is not suitable for on line optimalisation where it is necessary to obtain results in few interactions. However, in the case of assumed application, this disadvantage does not matter, because malfunctions do not lead to fatal errors of controlled loop. However, by early detection we can avoid their harmful effects. In farther development we would like to try attempts to apply fault detection to applications where simulation model would be built up just of linearized blocks. Also confrontation with results obtained by other evolutionary methods i.e. Simulated Annealing will done. Research will focus on implementation GA to data from real system, validation of algorithms and incorporation of new experience into the algorithm. 5 Acknowledgements The research work has been supported by the grant No. 101/04/1182 of the Grant Agency of the Czech Republic. 6 References CHIPPEFIELD A., FLEMING, P The Matlab Genetic Algorithm Toolbox. Sheffield UK: IEE Colloquium on Applied Control Technology Using Matlab, JAN, A. J Computing in Object Oriented Nonlinear Modeling and Control of Thermo- Fluid Dynamic Systems. Ph.D. Thesis. Prague: Czech Technical University, NEUMAN, P., ŠULC, B., ZÍTEK, P.& DLOUHÝ,T Non-linear Engineering Simulator of a Coal Fired Steam Boiler Applied to Fault Detection of Optimum Combustion Control. Budapest, HU: Preprints, 4th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes Safe process 2000, MAŘÍK V., LAŽANSKÝ J. & ŠTĚPÁNKOVÁ O. 2001: Umělá inteligence 3. Praha, Academia Praha, s. ISBN FLEMING, P., PURSHOUSE, C IFAC Professional Brief- Genetic algorithms in control systems engineering [online]. Sheffield UK: <URL: > Ann Arbor,USA: The University of Michigan Press, WITCZAK M Identification and Fault Detection of Non-Linear Dynamic Systems. Zielona Gora, PL: University of Zielona Gora Press, HOLLAND, J. H. 1975: Adaptation in Natural and Artificial Systems. Ann Arbor,UK, The University of Michigan Press, GOLDBERG, D. E., 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Copany,1989.