1. Introduction 2. Fuzzy inference systems and fuzzy modelling 3. Adaptive neuro-fuzzy systems with local recurrent

1. FAULT DIAGNOSIS OF THE DAMADICS BENCHMARK ACTUATOR USING NEURO-FUZZY SYSTEMS WITH LOCAL RECURRENT STRUCTURELetitia Mirea*, Ron J. Patton*** ”Gh.Asachi” Technical University of Iaşi, Dept. of Automatic Control** University of Hull, Dept. of Engineering 1. Introduction 2. Fuzzy inference systems and fuzzy modelling 3. Adaptive neuro-fuzzy systems with local recurrent structure 4. Neuro-fuzzy design of an FDI system 4.1 Residual generation 4.2 Residual evaluation 5. Application

2. 2. Fuzzy inference systems and fuzzy modelling  Fuzzy Inference System (FIS): - rule base - data base - reasoning mechanism  Most applied FIS for system modelling  Sugeno fuzzy system Rule i: if x1 is A1 and x2 is A2and ... and xn is Anthen  Consequents of each fuzzy rule  local model  Antecedents of each fuzzy rule  define region in input space where local model applies  Sugeno model can be implemented as special type of neural network  Adaptive Neuro - Fuzzy System (ANFS)

3. 2. Fuzzy inference systems and fuzzy modelling  ANFS combines: - capability to handle uncertain & imprecise information (from fuzzy systems) - ability to learn from examples (from neural networks)  Identification of dynamic systems  models with adequate memory   ANFS should be provided with dynamic elements: - ANFS, external dynamic elements (ext. cascades of linear filters) - ANFS, internal dynamic elements (recurrent connections, internal filters)  ANFS with Local Recurrent Structure (ANFS-LRS)

4. 3. Adaptive NF systems with local recurrent structure  local model described by:

5. 3. Adaptive NF systems with local recurrent structure  Layer 1: adaptive, membership functions  Layer 2: computes the firing strengths of fuzzy rules  Layer 3: computes normalised firing strengths of the fuzzy rules  Layer 4: adaptive, outputs of local models  Layer 5: computes the overall output of the ANFS-LRS

6. 3. Adaptive NF systems with local recurrent structure  identification of MIMO system ANFS-LRS model for each output of process:  ANFS-LRS learning: - number of fuzzy rules and initial values of premise parameters  fuzzy clustering algorithm (Chiu, 1994) - ANFS-LRS parameters  gradient method: N - number of the training data yP,i - the i-th output of the process  - learning rate

7. 4. Neuro-fuzzy design of an FDI system4.1 Residual generation  FDI system: residual generation and residual evaluation  Residual generation: - an ANFS-LRS model for each system output is identified (MISO model) - MISO models  neuro-fuzzy observer scheme - generated symptoms (current state)  residuals  Neuro-Fuzzy Simplified Observer Scheme (NF-SOS): - MIMO process with I inputs uP,i[k], i=1,...,Iand O outputs yP,j[k], j=1,...,O - NF-ARX models: normal behaviour of the process - residuals  one-step ahead prediction error

8. 4. Neuro-fuzzy design of an FDI system4.2 Residual evaluation  Residual evaluation pattern classification using neural networks - pattern classifier  static Multi-Layer Perceptron - decision logic  Euclidean distance

9. 5. Application  Investigated process: actuator from the steam boiler used to control the water level in the 4th boiler station (Lublin sugar factory, Poland)  Real data corresponding to the normal behaviour of the process have been used to: - design the NF-SOS scheme using ANF-LRS - generate faulty data using the DAMADICS benchmark Considered faults: F1: Valve clogging F2: Valve plug or valve seat sedimentation F3: Servo-motor’s diaphragm perforation F4: Electro-pneumatic transducer fault F5: Rod displacement sensor fault F6: Positioner feedback fault F7: Fully or partly opened bypass valve F8: Flow rate sensor fault

10. 5. Application Methodology: Data filtering: low-pass Butterworth filters  noise reduction and data decimation Selection of used data:  training data set: 360 out of 3600 measurements – NORMAL behaviour  testing data sets: - data set 1: 3600 measurements (another hour, same day) - data set 2: 3600 measurements (previous day) - data set with faults Residual generation:  system identification using ANFS-LRS  neuro-fuzzy simplified observer scheme Residual evaluation:  static neural classifier (MLP/ BP)  decision mechanism based on the Euclidean distance

11. 5. Application inputs: u1 – level controller output u2 – valve input water pressure u3 – valve output water pressure u4 – temperature of the water outputs: y1 – servo-motor rod displacement y2 – water flow to steam boiler inlet Testing data set 1 Testing data set 2  Electro-pneumatic actuator:system identification using ANFS-LRS

12. 5. Application  data with faults  example for fault F3:  Residuals generated with NF-SOS based on ANFS-LRS corresponding to: - the normal behaviour - the considered faulty behaviours were evaluated using a neural classifier  Multi-Layer Perceptron  Obtained recognition rate: 93.67%

13. Conclusions  The present paper investigates the development of a neuro-fuzzy system with local recurrent structure and its application to fault diagnosis of an electro-pneumatic actuator (DAMADICS benchmark).  The advantages of using such a neuro-fuzzy system are: - it is abble to process uncertain information; - automatic extraction of the rule-base; - it is able to learn from examples; - it has a reduced input data space because of its locally recurrent structure.  The obtained experimental results by using the suggested neuro-fuzzy system reveal its good performances of approximation and generalisation.  Its application to fault diagnosis of an industrial process leads to good results reflected in a recognition rate greater than 90%.