FAULT DIAGNOSIS OF THE DAMADICS BENCHMARK FAULT DIAGNOSIS OF THE DAMADICS BENCHMARK
ACTUATOR USING NEURO-FUZZY SYSTEMS WITH ACTUATOR USING NEURO-FUZZY SYSTEMS WITH
LOCAL RECURRENT STRUCTURELOCAL RECURRENT STRUCTURE
Letitia 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. Fuzzy inference systems and fuzzy 2. Fuzzy inference systems and fuzzy modellingmodelling
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 A2 and ... and xn is An then )x,...,x,x(fz n21i
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)Adaptive Neuro - Fuzzy System (ANFS)
2. Fuzzy inference systems and fuzzy 2. Fuzzy inference systems and fuzzy modellingmodelling
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)ANFS with Local Recurrent Structure (ANFS-LRS)
ANFS combines:
- capability to handle uncertain & imprecise information (from fuzzy systems)
- ability to learn from examples (from neural networks)
3. Adaptive NF systems with local recurrent 3. Adaptive NF systems with local recurrent structurestructure
local model described by:
B Dn
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Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
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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
3. Adaptive NF systems with local recurrent structure3. Adaptive NF systems with local recurrent structure
P,1p,M,1i),u(O pAi,1 i,p
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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:
3. Adaptive NF systems with local recurrent structure
O,...,1i]),1k[],k[(f]k[y PPi yu
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1k
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N - number of the training datayP,i - the i-th output of the process - learning rate
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,...,I and O outputs yP,j[k], j=1,...,O
- NF-ARX models: normal behaviour of the process
- residuals one-step ahead prediction error
4. Neuro-fuzzy design of an FDI system4. Neuro-fuzzy design of an FDI system
4.1 Residual generation
O,...,1j]);1k[],k[(f]k[y PPjSOS-NFj yu
I,...,1ii,PP ]]k[u[]k[ u O,...,1jj,PP ]]1k[y[]1k[ y
O,...,1j];k[y]k[y:]k[ jj,Pj
Residual evaluation pattern classification using neural networks
4. Neuro-fuzzy design of an FDI system4. Neuro-fuzzy design of an FDI system
4.2 Residual evaluation
- pattern classifier static Multi-Layer Perceptron
- decision logic Euclidean distance
5. Application5. 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 cloggingF2: Valve plug or valve seat sedimentationF3: Servo-motor’s diaphragm perforationF4: Electro-pneumatic transducer faultF5: Rod displacement sensor faultF6: Positioner feedback faultF7: Fully or partly opened bypass valveF8: Flow rate sensor fault
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
5. Application5. Application
Electro-pneumatic actuator: system identification using ANFS-LRS
5. Application5. Application
inputs: u1 – level controller outputu2 – valve input water pressureu3 – valve output water pressureu4 – temperature of the water
outputs: y1 – servo-motor rod displacementy2 – water flow to steam boiler inlet
Testing data set 1 Testing data set 2
5. Application5. 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%
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%.