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

1j

n

1jij,iij,ii

ii

P

1ppp,ii

]jk[z~d]jk[zb]k[z~

,]k[z~]k[ua]k[z

A1,1

]k[z~M

A1,M

u1[k]

AP,1

AP,M

uP[k]

N

N

w1[k]

wM[k]

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

]k[wM

]k[w1

]k[z]k[w 11

]k[z]k[w MM

z[k]

11PP,111,1 ]k[z~]k[ua]k[ua

u1[k] uP[k]

)q(D

)q(B1

1

11

]k[z~1

MMPP,M11,M ]k[z~]k[ua]k[ua

u1[k] uP[k]

)q(D

)q(B1

M

1M

]k[zM

]k[z1

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

2cx

e)x(

M,1i,])k[u(]k[wOP

1ppAii,2 i,p

M,1i,]k[w

]k[w]k[wO

M

1ji

iii,3

]k[zwO iii,4

M

1iii1,5 ]k[zw]k[zO

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

N

1k

2iiP,

oldnew

]),k[y]k[y(2

1E

;E

;

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%.