Fuzzy Logic Application for Fault Isolation of Actuators Jan Maciej Kościelny Michał Bartyś Paweł Rzepiejewski April 5-7, 2004 DAMADICS th DAMADICS Workshop on Integration of Qualitative/Quantitative Methods for Fault Diagnosis Presentation of Final Results Łagów/Poland Introduction Introduction Fault detection Fault detection Fuzzy residual evaluation Fuzzy residual evaluation Fuzzy reasoning rules Fuzzy reasoning rules Fault isolation algorithm Fault isolation algorithm Industrial benchmark problem Industrial benchmark problem Final remarks Final remarks Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Introduction Introduction Actuator FDI approaches Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project parity equation - (Massoumia and Van der Velde, 1988; Mediavilla et al.,1997) unknown input observer Phatak and Wiswandham, 1988) extended Kalman filter (Oehler et al., 1997) signal analysis (Deibert, 1994) fuzzy logic (Kościelny and Bartyś, 1997; 2000) b-spline (Benkhedda and Patton, 1997) spectral analysis (Previdi and Parisini, 2003) pattern recognition (Marciniak et al., 2003) structural analysis (Frisk et al., 2003) timed automata (Lunze and Supravatanakul, 2003)

Introduction Introduction Intelligent actuators supporting auto diagnostic and auto validation functions Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project  Bayart and Staroswiecki, 1991  Isermann and Raab, 1993  Kościelny and Bartyś, 1997  Yang und Clarke, 1997; 1999  Tombs, 2002

Introduction Introduction Fuzzy logic applications for development of FDI algorithms of actuators Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project  Frank, 1994  Garcia et al., 1997  Kościelny et al., 1999  Kościelny 1999; 2001  Sędziak, 2001  Calado et al  Korbicz et al  Yang und Clarke, 1997; 1999  Tombs, 2002

Introduction Fuzzy approach Introduction Model based fuzzy FDI system scheme Fuzzy approach Residual generation Fuzzy residual evaluation - + Fault isolation Set of pairs: Fault detection X={x i : i=1,2,...,I } Process data set R={r j : j=1,2,...,J } Set of residuals S={s j : j=1,2,...,J } The set of diagonostic signals Fuzzy reasoning Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Actuator fault detection Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project 3030

Fault detection Fault detection Feed forward perceptron neural networks (MLP) Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project - easiness of learning MA models because: - satisfactory modeling errors - no significant improvement of model quality - ability of fault learning ARMA models not because:

Fault detection Fault detection Examples of modelling results achieved Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project - easiness of learning Exemplification of flow rate model (3) quality in fault free state (normal process state). Flow rate in technical units [t/h] versus time in [s] is shown. Significant (ca. 50%) flow drop was observed. Illustration of fault sensitivity of the flow rate model (3).

Fuzzy residual evaluation Tri-valued fuzzy residuum evaluation (idea)  (r ) r nj T nj -T nj (r nj )  0 (r nj )  1 Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Definitions 1 0 Fuzzy fault symptom is the k dimensional fuzzy set such that for each residual r j assign k-plets 2 0 Fuzzy multiple-valued symptom where: - membership function of the j-th residual to the fuzzy set v ji Vj – the set of fuzzy values of j-th fuzzy diagnostic signal Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Setting parameters of membership functions Setting parameters of membership functions Statistical approach Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project Examples of experimental histograms of residual of flow rate model of control valve of Actuator Benchmark Problem in fault free process state. Additional filtering technique (low pass moving average filer) applied for the instrumentation measurements may reduce the span of residual distribution (right chart).

Setting parameters of membership functions Setting parameters of membership functions Abrupt fault occurrence Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project Examples of histograms of residual of flow rate model of control valve of Actuator Benchmark Problem in faulty process state. The occurrence of abrupt fault is documented. Additional filtering technique (low pass moving average filter) applied for the instrumentation measurements increase separation between neighbourhood residual values in fault free and faulty states an lower the number of intermediate residual values (right chart).

Fuzzy reasoning rules Reformulation DGN 1 DGN 2 DGN i DGN n s 1j s ij s nj s 2j Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project Example of rule isolating fault f1

Reference values of diagnostic signals used for fault reasoning Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Parallel reasoning scheme Fault signature Actual signals Diagnostic matrix PATTERN RECOGNITION V KJ V kJ sJsJ...… V kj SjSj...… V k1 S1S1 fKfK...fkfk f1f1 F/S SJSJ... SjSj S1S1 Diagnostic signals RulesRules Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

Fault isolation algorithm Operators DGN R( f ) Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project 1 0 Fulfillment degrees of rules’ premises 3 0 T-norm for fuzzy f k output 4 0 Diagnosis 2 0 k-th fuzzy rule output by fuzzy symptom s j

Industrial benchmark problem Elementary diagnosis Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project Theoretical diagnosis accuracy dacc ti L - the number of faults indicated in ist elementary diagnosis, for DGN0 the fault free state (OK) is also included Theoretical mean diagnosis accuracy dacc tm N is a number of elementary diagnosis

Industrial benchmark problem Fault f16 (supply air pressure drop) (OK - state)

Industrial benchmark problem Fault f18 (partly opened bypass valve)

Industrial benchmark problem Summary of experimental FDI performance indices of industrial benchmark Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project t dt - detection time r fd - false detection rate t dm - detection moment t irt - fault detection recovery time t it - isolation time r fi - false isolation rate r ti - true isolation rate t im - isolation moment t irt - fault isolation recovery time Remarks: 1. detection moment was captured when OK state certainty degree drop down below Isolation moment was captured when fault certainty degree rise above 0.25time

Final remarks Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project  Simple and practicable fuzzy fault isolation approach was presented.  The reasoning fuzzy system consists of fuzzyfication and inference procedures. Defuzzyfication is not being applied.  Diagnosis are pointing out particular faults related with the fault certainty degrees.  Improved robustness against measurement noise and model uncertainty.  Applicable for on-line diagnostics of industrial processes  Symptom uncertainty allows to improve the overall tolerance of diagnostic system on the disturbances and.  Fault certainty degree has no direct transformation onto the fault probability. It plays the auxiliary role and serves as an approximate estimation of the fault occurrence degree.  Fault certainty value depends on the selection of parameters of fuzzyfication process, method of fuzzy inferring and modelling quality  Fault certainty degree may be thought as practically acceptable because of intuitive acceptance and easy graphical interpretation.