NEURAL AND NEURO-FUZZY NETWORKS IN FAULT DIAGNOSIS OF DYNAMIC SYSTEMS Józef Korbicz University of Zielona Góra Institute of Control and Computation Engineering Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 2011

Outline of the talk Introduction Model-based diagnosis systems Soft computing in fault diagnosis artificial neural networks fuzzy logic neuro-fuzzy networks Applications – intelligent actuators, DC motor Conclusions Futher reading and research directions Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20112

Introduction Fault diagnosis : determination of the kind, size, locations and time of the occurrence of a fault Fault diagnosis problem in : automatic control systems telecommunications networks transmission pipelines and lines electrical and electronic circuites and others Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20113

Diagnostic steps Fault diagnosis most important and difficult task to achieve fault accommodation Goals of fault diagnosis detection and isolation of occurring faults as well as providing information about their size and source Isolation Detection Identification Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20114

Two-step procedure of the diagnosis process Symptom generation (fault detection) generation of signals or symptoms which reflect the faults Symptom evaluation (fault classification) logical decision-making on the time of the occurrence and location of a fault Fault analysis determination of the type of fault as well as its size and cause SYSTEM Inputs Residual generation Classification Fault analysis Residual evaluation Measurements Residuals Time and location of faults Type and case of faults Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20115

Fault diagnostic strategies Model-based approach analytical models (e.g. Luenberger observers, Kalman filters) knowledge-based models (neural networks, fuzzy logic, neuro-fuzzy networks) combination of both along with analytical or heuristic reasoning Data-based approaches pattern recognition statistic methods Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20116

Model-based approach PROCESS MODEL Classifier R=>S Relation S=>F Residual evaluation Fault isolation faults outputs R-residual inputs S-diagnostics signals F-faults Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20117

Data-based approach PROCESS Relation S=>F Generator of diagnostic signal Fault isolation faults Y-outputsU-inputs S-diagnostics signals F-faults Classifier U Y=>S ∩ University of West Bohemia, Czech Republic, 12 May 2011Józef Korbicz8

Importance of research IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, SAFEPROCESS since 1991 every 3 years, next: Mexico, 2011 Polish National Conference on Diagnostics of Processes and Systems, DPS since 1996 every 2 years, next: Warsaw, 2011 Applications, i.e. chemical industry, power plants, automotive and aircraft industries, etc. Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20119

Models for symptom generation Parity space DETECTION MODELS AnalyticalKnowledge-based Data-Based Observers Parameter identification Expert systems Qualitative (fuzzy) Fuzzy Neural Neuro-fuzzy Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Why do we need so many models? Diagnosed system can be: complex: processes, actuators, measurements non-linear dynamic noised and disturbed – unknown input with imprecise mathematical models Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Models for symptom evaluation Thresholds Pattern Classification Neural SYMPTOM EVALUATION Approximate Reasoning Adaptive analytical fuzzy neural Constant Parametric geometrical distance fuzzy neural neuro-fuzzy Parametric statistical Probabilistic fuzzy Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Fault tolerant control system Multidisciplinary feature FTC is a control system that possesses the ability to accommodate system component faults/failures automatically and is capable of maintaining overall system stability and acceptable performance in the event of such failures Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Modern control and fault diagnosis system Problem how to design a robust fault diagnosis system for non-linear systems? Solution with analytical or soft computing techniques Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Where can fault tolerant control systems be applied? Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Neural networks in fault diagnosis Main advantage of ANNs  do not require an accurate analytical model of the diagnosed process  need representative training data ANNs in fault diagnosis Modelling problem dynamics of the diagnosed processes Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Networks with external dynamics Neural residual generator with external Tapped Delay Lines (TDLs) Input-output representation where - non-linear function of the network - non-linear function of the diagnosed process Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Networks with internal dynamics Dynamic neural networks with global recurrence: drawback – the stability problem local recurrence: dynamic neuron models Dynamic neuron model Mathematical description adder module filter module activation module... w1w1 w2w2 wPwP IIR Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Dynamic multilayered neural network Training algorithm  Extended Dynamic Back-Propagation (EDBP) Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Application problems of neural networks Architecture designing there are no effective formal methods kind of network and its structure is selected based on: - known properties of various networks, e.g. MLP, RBF or GMDH - character and complexity of the process considered, e.g. nonlinear, dynamic, multi-input and multi-output Training and learning needs representative data convergence is a pretty slow Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Examples of fault diagnosis systems Two-tank system with delay aim of system control: to keep up a constant level of water in Tank 2 possible faults: - Valve V2 closed and blocked - Valve V2 opened and blocked - leak in Tank 1 Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Residual generation Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Fuzzy logic General fuzzy-logic systems Advantages of fuzzy systems transparent representation of the system under study linguistic interpretation in the form of rules rules extracted from data can be validated by an expert Knowledge Base Rules Data Inference mechanism Crisp/Numerical Outputs Crisp/Numerical Inputrs Fuzzy inference system Fuzzy sets Fuzzy sets FuzzyficationDefuzzyfication Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Fuzzy residual generation Known fuzzy observers qualitative observer functional observer relational observer PROCESS z-1 z-1 z-1 z-1 z-1 z-1 z-1 z-1 Fuzzy Relatio n Fuzzy- fication Fuzzy Cartezi an Produc t Defuzzi - fication Fuzzy relation model + – Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Neuro-fuzzy networks Combination of the fuzzy system with neural networks Mamdani neuro-fuzzy networks Takagi-Sugeno neuro-fuzzy networks i -th rule : IF x 1 is A 1 i and … and x n is A n i THEN y 1 = b 1 i and … and y n = b m i i- th rule : IF x 1 is A 1 i and … and x n is A n i THEN y 1 =b 0,1 i +b 1,1 i x 1 +…+b n,1 i x n and and y m =b 0,m i +b 1,m i x 1 +…+b n,m i x n where x 1,…,x n are inputs A 1 i,…,A n i are fuzzy sets b 0,1 i,…,b n,m i are parameters of linear consequents y 1,…,y m are outputs Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Neuro-fuzzy networks where x 1,..., x n - inputs y 1,..., y m - outputs n - no. of inputs, m - no. of outputs N - no. of rules, L.1,...,L.4 - layers N 1,...,N n - no. of fuzzy partitions b j i - singletons where x 1,..., x n - inputs y 1,..., y m - outputs n - no. of inputs, m - no. of outputs N - no. of rules, L.1,...,L.4 - layers N 1,...,N n - no. of fuzzy partitions b j i - singletons Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Neuro-fuzzy networks Advantages of neuro-fuzzy networks  ability to represent some kind of uncertainty present in real processes  ability to combine quantitative and qualitative knowledge  non-linear mappings parameters of membership functions are adjusted by the training process, i.e. the mean value and variance of bell-shaped membership functions Disadvantages for large numbers of fuzzy sets the number of adjusted parameters increases drastically Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Models uncertainty Sources of model uncertainty mathematical or/and neural and neuro-fuzzy models of supervised systems are never perfectly accurate and complete parameters of the systems may vary with time in an uncertain manner characteristics of disturbances and noise are unknown Conclusion there is always a mismatch between the actual process and its model even if there are no process faults Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Robustness in model-based fault diagnosis Robust model-based FDI methods insensitive or even invariant to modelling uncertainty Why do we need robust methods? to increase robustness to modeling uncertainty without losing fault sensitivity to minimise false alarms and improve the quality of the diagnosis Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Uncertainty problem in diagnostics and its solution Robust observer unknown input observer, unknown input filter design strategy: minimization the effect of unknown inputs Model uncertainty statistical techniques (many restrictive assumptions) Neural and neuro-fuzzy models uncertainty design strategy: using the Bounded-Error Approach (BEA) Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Approaches to robust fault detection Active approaches principle : to eliminate model uncertainty - unknown input observers (Witczak, 2007) - parity relation (Chen and Patton, 1999) Passive approaches principle : to provide and adaptive threshold taking into account model uncertainty (approaches for linear systems (Frank, 2002)) key design principle : to estimate the parameters of the model and the associated model uncertainty and then use this information for adaptive threshold determination main tool : least-square method-based approaches Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Adaptive threshold n Concept Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Uncertainty of soft computing models Takagi-Sugeno fuzzy model Korbicz and Kowal, 2007 GMDH neural model Witczak, Korbicz, Mrugalski and Patton, 2006 Multi-layer perceptron model Mrugalski and Korbicz, 2007 Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Dynamic neural networks of GMDH (Group Method of Data Handling) Why GMDH? successful identification depends on proper selection of the model structure determination of the appropriate structure and parameters of a non-linear model is a very complex task GMDH approach can be successfully employed to automatic selection of the neural network structure, based only on the measured data structure of the network is designed by gradually increasing its complexity Idea of GMDH replacing the complex model of the process with partial models (neurons) by using the rules of variable selection Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Network development procedure GMDH Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n Dynamic GMDH neural network Dynamic neuron structure System description Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

GMDH networks Uncertainty determination and fault detection BEA-based parameter estimation non-linear parameter estimation problem due to the invertibility of the activation function it is possible to write this makes it possible to use the error-in-regressor BEA As a result of using the BEA, we have - an estimate of - the feasible parameter set Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

GMDH networks Uncertainty determination and fault detection Termination condition procedures of - parameter identification - partial models evaluation - partial models selection are repeated over till the transition error starts growing Uncertainty propagation uncertainty of the neurons is propagated through the layers during the development of the GMDH network Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

GMDH networks Uncertainty determination and fault detection Fault detection An adaptive threshold generated with the output neuron (Witczak, 2006): where Fault detection rule: When the output signal does not satisfy the constraints of the adaptive threshold then a fault symptom occurs Computational aspects: exact BEA : where V stands for the set of vertices of a polytope implicit BEA (e.g. OBE) : the adaptive threshold is described by analytical formulae (see e.g. Mrugalski, Witczak and Korbicz, 2007), i.e. there is no need for solving the max/minproblem Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Passive approach Adaptive threshold Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

DAMADICS benchmark Valve actuator case study Realization 5FP EC, RTN DAMADICS Industry Lublin Sugar Factory (Cukrownia Lublin S.A.) Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Intelligent actuator ACQ – data acquisition unit CPU – positioner central processing unit E/P – electro-pneumatic transducer V1,V2 and V3 – valves DT – displacement PT – pressure FT – value flow transducer CV – control value F – flow measurement T1 – juice temperature X – rod displacement P1 and P2 – juice pressures at the input and outlet of the control value T1T1 P1P1 V3V3 Control valve Pneumatic actuator Positioner P2P2 E/P CPU ACQ PT DT F CVCV V1V1 V2V2 FT X S Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Industrial application DAMADICS benchmark Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Pneumatic motor and valve models Model of the positioner and the pneumatic motor Model of the control valve Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Structure of GMDH models Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Robust detection of faults f4 and f7 with GMDH f4 – bushing frictionf7 – medium evaporation Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Robust detection of faults and with MLP Faults and Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n DC motor Laboratory stand  DC motor M1  DC motor M2  rotational speed sensor S  clutch K The shaft of the engine M1 is connected with the engine M2 by the clutch K Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n DC motor Model DC motor model where T – revolutions per minute (RPM) C m – motor excitation signal Neural network with dynamic neurons Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n DC motor Model DC motor response (solid line) and neural model response (dotted line) closed-loop system (Patan and Korbicz, 2007) Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n DC motor Fault detection Fault description (Korbicz and Kowal, 2007) Faults  incipient (I),  abrupt small (S),  abrupt medium (M) and abrupt big (B) Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

DC motor Fault detection Takagi-Sugeno neuro-fuzzy model with linear consequents where x i – input variable, y – output variable, N – number of fuzzy rules, N j – number of fuzzy partitions, μ – membership function, p – parameters of linear consequents Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

n DC motor Fault detection Takagi-Sugeno local linear models General data  number of rules: 9  number of faults: 7 where:- output of the i -th local linear model - motor control signal Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

DC motor Fault detection Confidence interval for DC motor and model outputs  small fault f1 Confidence interval for residuals  small fault f1 Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

DC motor Fault detection Confidence interval for DC motor and model outputs  incipient fault f2 Confidence interval for residuals  incipient fault f2 Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Conclusions General problem in fault diagnosis  how to design a system that will be - robust to uncertainties - sensitive to small changes Future research activity  combination of analytical methods and soft computing techniques, i.e. expert systems Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Further reading and research directions Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Further reading and research directions Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May

Thank you! Józef Korbicz University of Zielona Góra Institute of Control and Computation Engineering Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May