Process Fault Diagnosis by Using Fuzzy Cognitive Map Kee-Sang ...

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Kee-Sang LEE*, Sung-Ho KIM**, Masatoshi SAKAWA**. Masahiro INUIGUCHI*** and Kosuke KATO**. In this paper, a method of the fault diagnosis based on ...
Trans.

[

of the Society of Instrumen and Control Engineers Vol.33, No.12, 1155/1163 (1997)

Process

Fault

[

計 測 自 動 制 御 学 会 論 文 集 Vol.33, No.12, 1155/1163 (1997)

] Diagnosis

by

Using

Fuzzy

Cognitive

]

Map

Kee-Sang LEE*, Sung-Ho KIM**, Masatoshi SAKAWA** Masahiro INUIGUCHI*** and Kosuke KATO** In this paper, a method of the fault diagnosis based on FCM (Fuzzy Cognitive Map) is proposed. FCM which can store uncertain causal knowledge is essentially fuzzy signed directed graphs with feedback. The proposed basic fault diagnostic algorithm is considered as a simple transition from Shiozaki's signed directed graph method to FCM framework. It can simply identify the origin of the fault and can further be expanded to hierarchical fault diagnostic scheme. In particular, as the proposed scheme takes a shorter computing time in comparison with other methods, it can be used for on-line fault diagnosis of large and complex processes where conventional fault diagnostic methods can not be applied. Examples highlighting the use of the proposed scheme are presented. Key Words: fuzzy cognitive map, fault diagnosis system, hierarchical diagnosis

1.

paring actual parameters measured by a sensor with the values predicted by an analytical model of the system.

Introduction by

This kind of approach can accurately find out the ori-

Therefore, for guaran-

teeing the stability and reliability of the process, devel-

gins of faults and the magnitude of deviations. However, the quantitative approach generally requires as precise a

opment of the fault diagnostic systems is imperatively re-

model as possible in order to get a good fault diagnostic

quired more than ever before. The fault diagnosis is com-

result. In reality, such models for the system are not al-

posed of two stages: fault detection and fault isolation. The fault detection stage is characterized by a single, dis-

ways accessible due to the nonlinearity of the system and

tinct operation, that is, the observation that the system is not operating in a completely normal fashion. Whereas,

quantitative diagnostic approaches is quite limited. As pointed by many AI researchers, humans appears to

fault isolation requires the identification of the underly-

use a qualitative causal calculus in reasoning about the

ing cause of anomalous behavior.

behavior of a physical system. Therefore, this kind of di-

Recently industrial

processes can be characterized

large-scale and complex structure.

Idealy, fault isolation

the presence of noise. Therefore, the versatility of the

results in an accurate, unambiguous identification of the

agnostic scheme qualitatively representing the operation

component or components responsible for the root cause

of a physical system can be used to diagnose the system

of the anomalous behaviour.

malfunction3),4).

There are several different

Depending on the type of knowledge

ways of approaching the fault diagnosis problem. Gener-

employed, qualitative diagnostic approach can be divided

ally speaking, all fault detection and isolation schemes fall

further into shallow- and deep-knowledge-based

into two broad categories depending on the fault model

Shallow-knowledge-based

on which they are based:

relationships between irregularities in the system behav-

quantitative

approaches and

system.

system describes the empirical

qualitative approaches.

ior and system faults. Accordingly, it can be thought of

Quantitative approaches which have been studied by Willsky and Isermann 1),2) are based on the concept of

as the expert system, which is composed of knowledge

analytical redundancy.

system is effectively applied in the medical field but may

Their models are used for com-

base (heuristic rule) and inference engine. This kind of suffer from lack of completeness and consistency in the

* Department of Electrical Engineering , Faculty of Engineering, Dankook University, Seoul, Korea ** Department of Control and Instrumentation Engineering, Faculty of Engineering, Kunsan National University, Kunsan, Korea *** Department of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, HigashiHiroshima (Received October 25, 1995) (Revised June 30, 1997)

knowledge base. Deep-knowledge-based

systems provide

a systematic approach for reasoning about physical systems, i.e., can infer the propagation

of the malfunctions

or predict the effect of the fault utilizing extensive knowledge about the systems. In chemical engineering, most process knowledge is well defined and can be easily characterized

TR 0012/97/3312-1155 (c)1995 SICE

by well-known

1156

T. SICE

physical

principles.

based

Therefore,

system

is

more

knowledge-based

system.

sentative

qualitative

mention

the

Graph

(SDG)

is

not

of

deep

for

method

deep

knowledge

many

process

roneous

studied

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the by

graph

atic

memories

we

with

recall

same

fore,

the

as

as to

mation

us

to

ity/decomposability.

Authors

fault

diagnostic

FCM10).

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plicability

of

FCM

in

based

a

of

property,

faults. out

a

proposed

of

fault

by

be

impor-

tal

paper

structure

based this

is of

on

FCM

scheme

nally, are

a used

on

tank-pipe to

and

proposed recall

to

verify

the

forward/backward

lot

of

to

illustrate

is

basic

diagnostic presented.

the

and

the

scheme a

effectiveness

order

the

an a

carried

the

de-

3)

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Fisystem

can

Kosko's

represent

and

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other

valeffects.

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of

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ith

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Ci

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{-1,0,1},

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SDG

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system

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spe-

relationon

Tree based

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accommodate

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forward

loops

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based

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originally

feedback

easily

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to

is

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than

knowledge

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it

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uncertain

compared

method

struc-

the

systems.

physical

searching

fault

or

diagnostic

to by

by

the

several into

for

increased fault

con-

Hownot

applied fault

large expo-

tree. does

effectively

have even

diagnosis

is

operations. various

experts.

combination

is

system be

combine

many

the

decomposed

can

suitable

the

vector-matrix

impossible

allows

time

because

simple

not

of

thus

diagnosis

by

is

augmentation

and

fault

created be

in of

more

diagnositic

based

constructed

were di-

SDG

merits

the

FCM

approach

is

Analysis

drawback

is

Using

takes

Accordingly,

because

out

were

hierarchical

proposed

Tree

on-line

negative

loops.

with

such

in-

increase is

1

out

FCM

values

a fault

can

systems

ever,

1.

express

FCM

level

directed

represent

not

Fault

to the

FCM

feedback

2)

to

pipeline of

However,

to

extend

to

Tree

can

i and

respectively

of

is a traditional

Fault

it

of

nodes

connection

directed

similar

-1

following

As

a

branches

branch

effectively

nentially

is proposed.

bypassed

1)

Cj. and

levels

and

weights eij.

contains

that

Moreover,

ture,

of -1

Ck,

FCM.

FCM.

which

if a Cj,

levels

by

branches

is

from

the

E

two

effects

fuzzy

of the

sense

of

can

algorithm

structure, Third,

decomposition system

in

kind

scale

fundamen-

diagnostic

value

cial

system.

algorithm

the

FCM

any

out

of

directed

the

causal

described

a simple

in

method,

vector-matrix

the

the

ceptual find

of

called

of

SDG-

the

Second,

of

connection

weights of

is

an

of

general,

time

it

is

column

weights

ap-

decomposability

First,

positive

decrease

no

are

jth

connection

has

TAM

simple

follows.

the

presented.

hierarchical

scheme based

as

FCM are

into

composition diagnosis

organized

is

increase

different

FCM

the

ships.

operations. This

and

causal

denotes

elements

FCM

transfor-

diagnostic

using

a

to

Though

SDG

on

In

utilize requires

Whereas, origin

i.e.,

diagnosis.

algorithms which

is

j

causal

feednodes

concept,

measurable any

by

of

one

connecting

pro-

with

consists

represents have

to proposed

graph

FCM

Values

general,

ferent

composibil-

already

work

in

zero

value

can

two

based

this

fault

scheme

find

of

second

diagnostic

origin can

purpose the

have

a

correspond

SDG-

this

and

tion

has

Shiozaki's

recall

algorithm

hierarchical

searching

TAM

i to

in

results

ues

as

There-

aforementioned

i.e.,

it

and

versa.

Shiozaki's

However,

utilize

properties,

if

from

An

can eij2

been

directed

1.

that

results

approach has

fuzzy

node

branch

directed Ci

as-

can

FCM

framework.

from

framework.

enables

vice that

algorithm

transition

is

of

a

Fig.

Each

The

whose

FCM FCM

and

FCM

is in

branches.

In

temporal with

transform

FCM

shown

causality, di-

system-

large-scale

diagnostic

simple

FCM

FCM's

on-line

we

basic

a

(FCM)

inference.

consideration

into

is

signed

as

sub-FCMs,

SDG,

er-

and

allows

reason a

into

algorithm

proposed

approach

tant

several

structure

considered

can

An as

(FCM)

knowledge

convention, eij•¸[-1,1].

fuzzy

Map

Maps

causal

k=1,2,•c,N,

j

and

Maps

are

Kosko.

tensity.

method

merits

behaves

we

on

field.

Furthermore,

taking

diagnostic

many

structure

FCM

(TAM),

paper,

has

Cognitive

Cognitive

uncertain

and

causal

spurious

Fuzzy

Fuzzy

cessing

back

based

a forward-evolved

of

into

this

based

through

TAM.

decomposed

the

Its

is the

Cognitive

feedback.

inference

sociative

as

Fuzzy FCMs

reasoning

forward

In

of

al.

SDG

such

ex-

scheme

transient.

represent

engineering

Kosko9).

with

causal

Since

still

chemical

concept

proposed

rected

it

in

et

a

there this

Although

problems,

interpretations,

widely

be

variables.

unresolved

Iri

The

uses

during

easily

2. we

Directed

Analysis Since

by

can

method.

repre-

field,

Signed

diagnosis

1997

agnostic

the

processes,

developed

then

December

shallow-

this

knowledge.

fault

was and

the Tree

chemical

on-line

which

between

has

in

of in

and

shallow

of

some

Fault

No.12

deep-knowledgethat

shemes

Analysis

and

of

name

5)•`8).

loops

suitable

effects

Tree

control

SDG

To

method

of

a lot

use than

diagnostic

Fault

composite ist

the

attractive

Vol.33

fault

trees

However, of

various

experts

and

several

sub-FCMs.

moreover,

the FCMs

which FCM which

one

FCM

計 測 自動 制御 学 会論 文 集

第33巻

第12号

1997年12月

1157

nodes and consistent branches is called a cause and effect

(a)

(CE) graph. If there is an elementary path from a node on the SDG to all valid observed nodes, and if all the branches on these paths are consistent branches, then the tree which is composed of such a node and such consistent

(b)

Fig. 1 An exampleof a fuzzysigned directedgraph (a) and the FCM representation(b) 3.

Basic Fault

Diagnosis

Based on Sim-

ple FCM Basic fault diagnostic algorithm based on the simple FCM is developed in this section. It is composed of a preprocessing unit and a diagnostic algorithm. The preprocessing unit generates the fault pattern vectors which can be processed by the diagnostic algorithm. 3.1 Generation of The Fault Pattern Vector The first step for fault diagnosis is a generation of observed pattern vectors for some faults. First, we define DI

paths is known as a 'consistent rooted tree', and the node is its 'root'. The idea of consistent rooted-tree method is that the node which is the maximal strongly-connected component of the CE graph is the candidtate of the fault. The proposed diagnostic algorithm is discussed under the followingassumptions: 1. A single fault is assumed; 2. A single origin of the fault is also assumed. In what follows is the detailed basic diagnostic algorithm based on FCM. Let the connection matrix E and the observed pattern vector W be given. First, Extract Cause and Effect Relation matrix (CR) from the observed pattern vector and the FCM connection matrix. Second, Find origin of the fault. Step 1. Calculating CR matrix

(Deviation Index) and NOV (Normal Operating Value) to obtain the elements wi in the observed pattern vector w as in (1) and (2). DI=MeasuredValuei-NOV(1)iQ • NOV where

subscript

system

and Ģ

thresholds mal a

i indicates represents

to

be

right

vector

determined

as

operating

wi

of band,

and

carefully

normal

Thus,

variable

normal

be

the

onal

i.e.,

the

The

Basic proposed

iozaki's upon

iozaki's

has

of

pattern

fault

concept

That

algorithm

rooted-trees

method,

of SDG.

SDG

and signs

attached

to the

a directed

branch

in SDG

The

state

the

'0', '+',

as

the

tent

paths

which

has the same

of nodes

and

directed

branches.

has the

of a system

is built

structure

directed

same

on Sh-

The

sign

meaning

is expressed

as

branches, on

be

from

wj

the

calculated

plays

in

diag-

elements

threshold

off

function

According (3)

all

possible

role

of

can

to be

paths. removing

zero

in

removing in

Threshinconsisfor,

case all

CR

matrix

wi•EE(i,j)•E•†0. the

origin

of

fault

all

consis-

inconsistent is

about

The of

Sh-

thought

wi•EE(i,j)•Ewj than

after

identifying

the zero.

general,

whose

other

method,

information

for as

be

greater

satisfying

matrix all

is

the In

is

remaining

used

T

generating

Therefore,

(nodes) is

and

tree

WE.

and

branches.

variables

is based

of

square

to

rooted

(4)

a W

and

selected

in

wi

of

zero,

process

function

paths,

diagnosis

are

threshold

old

matrix

those

consistent

tent

is, it consists

in FCM.

a

nonzero

Algorithm

represents are

diagonal

with

follows.

Diagnostic

consistent the

FCM.

Fault

(4)

Diag(W)

get

1ifD12>1 wi=0if(DIi=1 and IN(k)=0) of the failure

then FDI algorithm

fails;

L100100

of the fault; source

E=F10-1010

>=2)

L200001

}

F2000-10

Diagnosistic part of the above algorithm is the same as Shiozaki's consistent rooted tree method for finding maximal strongly connected component. However, compared with Shiozaki's SDG-based approach, the proposed basic diagnostic algorithm is more simple and faster because it utilizes vector-matrix operations instead of forward/backward searching which usually requires a lot of computing time. 3.3 Application for Partially Observed Patterns In section 3.2, we assumed that all elements of the pattern vector are observed. However, there are virtually no real systems in which all of the state variables are measured accurately. Sometimes, owing to the high measurement cost and/or sensor faults, only partially observed pattern can be obtained. If there exist uncertain measurement elements in the pattern vector mainly induced by sensor faults, the aforementioned basic diagnostic algorithm can not be directly applied. In this case, after identifying the faulted sensors by the multiple sensor method and regarding them as unobserved states, the following expansion scheme should be done to get a right diagnosis result. Assume that r is the number of the unobserved states in the pattern vector. Let the following observed pattern vector be given. A=[a1

where

of the

(1) The case of the fully observed pattern Let's assume that the followingpattern is observedduring the operation of the system. FoL1F1L2F2

w=[o1-1-1-1 From

Step

1 of section

3.2,

FoL1F1L2F2 Fo00000 L100000 CR=F101010 L200001 F200000

From Step 2 in section 3.2, the decrease in F1 is identified to be an origin of the fault. (2) The case of the partially observed pattern Let's consider the followingobserved pattern. FoL1F1L2F2

a2…ai…aj…an]

n is the number

In general, FCM can be constructed according to either of the followings: 1. Plant data orrexperienced domain experts 2. A mathematical model In this example, the FCM for the system is built from the process model. Let's consider two cases:

whole

process

variables

and

w=[o1??-1

計 測 自動制 御 学 会論 文 集

第33巻

第12号

1997年12月

fectively tic

reduce

scheme

the complexity

applied

is accomplished

by breaking FCMs.

modular

construction

consider

'?'

indicates

variables

due

vectors

uncertainty

of the

the

to a sensor

derived

from

fault.

W are

All the

has

and

possible

are the generated

only pattern

origin of the fault. sources,

patterns

for

3.2 are applied

W2 indicates

that

their

diagnostic

results

the ith

impingement

and

on

of the

section

algorithm

Basic

algorithm

Diagnostic

Algo-

into FCM

transition

framework,

The first is that

of man-hour

to obtain

is required

The second is that

order

is obtained,

first, we introduce scheme

down

cal diagnostic

can

be

the

the

jth

impingement

sub-system

vari-

represents variables

constructed

together

the

on

by

into

one

expression. is

The

into

as

the ith

many

experts

modular The

FCM

detailed

for

decom-

follows.

whole

system

FCM for the

the

FCMs.

variables

scheme.

based on the overlapped

is proposed

for complex

Decomposition and modular

structure

and

This

The

are

rameter

hierarchi-

Scheme of FCM can ef-

variables

grouped

to-

within

are

or

functionally

variables. each

variables

sub-system

or

are

determined

(variable)•‚0).

which

affected

by

afother

(IN(variable)•‚0

These

variables

are

called

pa-

variables. 3.

Construct

only

struct Bij

from

belonging (Bji)

system's

to

(jth

4.

the

between

sub-systems.

further

the

number

reduced

of

sub-system's

of

if there

of

are

sub-

on

the jth

variables). describing

re-

belonging

the

parameter

con-

the ith

FCM

variables

dimension

between and

variables)

upper-level

parameter

The

to

influences

(ith

Construct

relations

sub-system,

sub-system's

variables

Step

the

the ith

considering

variables

sub-system's

to

upper-level

variables

physical

each

FCM but

it

equivalences

is

can

be

among

them.

decom-

and large-scale

structurally

coupled

variables

OUT

equal

by

strongly

sub-system's

lationships

problems,

Second,

2. other

subsystem's

due to a lot

aforementioned decompisition

fect

Step

a large amount

l sub-systems

overlapping

variables

of high dimension.

into several

processes. 4.2 Overlapped The hierarchical

sub-system

procedure

vari-

the FCM for the over-

even though

the

overlapped

algorithm

scheme

the jth

knowledge

1.

gives

utilizes the fact that FCM can be easily combined

or broken

position

systems,

it is not desirable

operations

to overcome

can be

However, its

and auto-pilot

rise to some problems.

In

which

which have many complex

plant

in

of the Sh-

of various processes.

to processes

like chemical

which was described

is the simple

used for fault diagnosis

of matrix-vector

(j=1,2,•c,l,j•‚i)

combined

reliable

Step

whole system

on

Bji

EBi

then

Step

rithm

all system.

EBi,

Decomposition

The basic diagnostic

ables,

FCMs,

variables.

general,

more

based

of

sub-system In

represents variables

Similarly,

gether

application

modular

of

..Bin(8)

sub-system

ables.

Since the other three

Diagnosis

Drawbacks

iozaki's

sys-

composed

structure.

(i=1,2,•c,‚Œ,j•‚i)

position

previous

for complex

system

by

system

facilitates

0...Bni...0

of

Hierarchical

the

system

complex

EBi=B21...•

pattern

where

patterns have two fault are all abandoned.

4.1

whole

architecture

corresponding

If Step 1 and Step 2 in section

Overlapped

processes.

i=1,2,..,1

to all the above patterns,

4.

the

diagnos-

as follows.

where the boldface numbers

F1 is a candidate

fault

0...B1...0

W=[0111-1] W1=[011-1-1] W2=[0.1-1-1-1] W3=[01-11-1] '?'s.

down

represented

the following

FL1F1L2F2

the

the

basic

large-scale

This

of a diagnostic

Let's

which

where

and

several

l sub-systems

System

to complex

into

tems.

Tank-pipeline

of the

This

the

Fig. 2

1159

Although above

the

dimension

procedure

is

cess

variables,

it

cess

variables

with

mension

of

the

equal

can

modular

be a

of to further

0-column FCM

the

the

EBi

number

of

reduced and facilitates

generated

by a

0-row. the

the

by whole

omitting Lowered construction

the proprodi-

1160

T. SICE

Vol.33

No.12

December

1997

2)

CRcan=T(WEcan)

3)

Identify

system

one

using

We

call

Hierarchical

representation

of FCM

general,

tween

each

within

a certain through

the

ement diagram

for

hierarchical

diagnostic

candidate in

each

origin

of

sub-

section

3.2.

sub-system.

the

fault

do

the

them.

Accordingly,

not

parameter

contain

from

the

that

the

true

origin

of

a candidate

occurred other

subsub-

element

nomelement.

the

as

be-

candidate

as

true

fault

a candidate

select

the

fault

fault

contains

to

paths

over

true

element

reasonable

as

the

spread all

the

which

act of

be

variable

nominate is

effect can

sub-system

it as

variables

sub-system

the will

able

true

for

parameter

fault

Therefore,

algo-

each

algorithm

element

sub-systems,

Whereas,

rithm

for

diagnostic

the

since

which

inate

Schematic

basic

candidate

Select

In

systems

4

element

elements.

systems

Fig.

a

4.

candidate

Fig. 3

the

this

Step

fault

el-

element.

non-parameter

fault

from

vari-

the

candidate

elements. of

fault

diagnosis

archical

representaion

shown

in

Fig.

modular

and

can

apply

level

one

the

is

Fig.

Its 4

which diagnosis

FCM,

A

is

consist

of

l

respectively.

plays have

a

detailed

is

the

to

system ered

out

as

follows.

only

related FCM

in

2.

Identify

the

fault

parameter

variables

as

order

to

in

diagnosis

2)

CRupper=T(WE(i,j))

3) the

Identify

Fig.

system

5 is

are rates.

the

Circles

each

are

variables

according

to

verify

bypassed

to

in

basic In

diagnostic

section

then

origins

we

sider

all

the of

parameter

algorithm

3.2,

discarded

two

fault

assumed failed

fault).

possible

in only

section one

diagnostic

However,

origins

variables

and

the

Fig.

obtained

origin

result in

(parameter

this

of (i.e.,

step variables)

we

fault,

and

more

decomposition

EB1=P20-1011

F500-100

F2P3F3P4F4

con-

of the

fault.

F201000 We

call

sub-system

which

contains

at

least

one

of

these

P3-10100 parameter Step

variables 3.

Extract

a candidate pattern

sub-system. vectors

(Wcan)

EB2=F30-1010 related

to

the

P400-101 candidate

sub-systems

and

apply

the

basic

diagnostic

al-

F4000-10 gorithm 1)

to

all

candidate

sub-systems.

WEcan=Diag(Wcan)•EFCMcan•EDiag(Wcan)

of

diagnostic

true

origin

applied The where

the Fi's

of

(i=1,..,8)

the

scheme

the

process FCM in

to

the

considthe

Pi's

are

sub-systems. and

upper-level

than

should

is

system

from the

F200-100

3.2.

a

fault,

origin

right

as

5 depict

fol-

using

a

the

effectiveness.

Pl01000

possible

get

(EB1•cEB4)

for

the

its pipeline

pressures

sub-systems (EB)

rameter

a

Fl-10100

all

the

simultane-

as

algorithm

PlFlP2F2F5 WE=Diag(W)•EFCMupper•EDiag(W)

of

which

variable

lows. 1)

origin

variable

(FCMupper). Step

true

sub-systems

parameter

hierarchical

FCM

upper-level

this

a

parameter

Therefore,

(i=1,..,8)

for

to

two

this

select

flow

within

than

is

fault.

4.

(variable).

element

(W)

in

Fig.

variable

more

fault.

The

finding

element

algorithm

contained

in of

fault

vector

nominate

the

upper-level

role

fault the

exist

ously the

scheme

shown

a

parameter

there

diagnostic

from is

a

result,

decomposition

pattern

variables

If

FCMs

Hierarchical

identifies

Extract

parameter

level

diagram

might

sub-systems. 1.

upper

Hier-

Algorithm

diagnosis

Lower-level

Step

modular

downward

upper-level

system.

by

level

diagnosis.

schematic

sub-systems

these

upper

synthesized

lower-level.

and

overlapped

fault

algorithm

complex

Diagnostic

hierarchical

In

Lower

Hierarchical

We

for

constructed

3.

FCMs

4.3

to

algorithm

the

FCMs upper-level model. are

section

Paselected 4.2.

計 測 自動 制 御 学 会 論 文集

第33巻

F5P5F6P6F7 F501000 P5-10100 EB3=F60-1010 P600-101 F7000-10

第12号

1997年12月

1161

P2F2F4F5F7P7 P2010000 F2000000 _F4000000CR upper-F 5100000 F7000001 P7001000

F4F7P7F8P8 F400100 F700100 EB4=P7-1-1010 F800-101 P800000 P2F2F4F5F7P7 P2010100 F2-100000 EB=F4000001 F5-100000 F7000001 P700-10-10 Let's consider the followingobserved patterns which describe the abnormal operation. P1F1P2F2P3F3P4F4 Wa=[0-1(1)(1)11-1(1) F5P5F6P6F7P7F8P8 (-1)1-11(-1)(-1)-10] where pattern Wa is observed when the decrease in F7 is an origin of the fault caused by the blockage of pipeline. The observed patterns are obtained from a simulation using the mathematical model of the process. Parenthesized variables are parameter variables included in upper-level FCM. The fault diagnosis is carried out by executing the followingtwo steps. -Diagnosis of upper-level FCMThe observed pattern for the upper-level FCM, Wa, obtained from Wa is as follows. P2F2F4F5F7P7 wa=111-1-1-1 Applying step 2 of section 4.4,

From step 2 of section 4.3, it can be found that F5 and F7 are fault parameter variables. From Fig. 5, sub-system 1,3 and 4 contain these elements and they are assumed to be candidate sub-systems for the fault. -Diagnosis of lower-level FCMThe diagnosis of lower-levelFCM should be applied to all the candidate sub-systems. The observed patterns for sub-system 3, 4 are as follows. P1F1P2F2F5 WB1=[0-111-1] F5P5F6P6F7 WB3=[-11-11-1] F4F7P7F8P8 WB4=[1-1-1-10] We can get the CR matrices for each candidate subsystems. In this way, we find that sub-system 3, 4 simultaneously nominate F7 and sub-system 1 nominates F5 as their candidate element, respectively. Therefore, F7 is selected as the true origin of the fault. If the candidate sub-system contains unobserved variables, these variables should be expanded according to the procedure described in section 3.3. Then all the derived pattern vectors for the candidate sub-system should be applied to the basic diagnostic algorithm. In general, the basic diagnostic algorithm can also be directly applied to the above case. However, it requires that all the sensors employed in the whole system should be as precise as possilbe for getting a good diagnostic result. This requirement is practically very severe because of high prices of sensor equipments. As we can see from the above example, if we utilize the hierarchical fault diagnostic scheme, this requirement gets loose. That is, if we can guarantee the reliability of the sensors placed in the parameter variables which belong to the upper-level FCM, we can get a better diagnostic result at a lower cost than the basic diagnostic algorithm. Furthermore, the hierarchical diagnosiscan save lots of computing time owing to the lowered FCM dimensions.

1162

T. SICE

Vol.33

Fig. 5 Structure of the bypassed pipeline system

5.

Conclusion

A new fault diagnosis scheme based on FCM has been developed.

No.12

December

1997

the Signed Directed Graph, Ind. Eng. Chem. Res., vol.29, pp. 1290 (1990) 7) J. Shiozaki, H. Matsuyama: Fault Diagnosis of Chemical Processes by the Use of Signed Directed Graphs. Extention to Five-Range Patterns of Abnormality, Int. Chemical Eng., vol.25, no.4, pp. 651 (1985) 8) Y. Tsuge, H. Matsuyama: Advanced Estimate of the Accuracy of the Diagnostic Result for the Fault Diagnosis by Use of the Signed Directed Graphs, Engineering, Kyushu Univ., vol.44, no.3 (1984) 9) B. Kosko: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice Hall (1992) 10) K.S. Lee, S.H. Kim, M. Sakawa: On-Line Fault Diagnosis by Using Fuzzy Cognitive Map, IEICE Trans. Fundamentals, vol.E79-A, no.6 (1996)

The proposed diagnosis scheme may be di-

vided into two parts: basic diagnostic algorithm and hier-

Kee-Sang

LEE

archical diagnostic algorithm. The basic diagnosis scheme can be viewed as a transition method to FCM framework.

Kee-sang

of the Shiozaki's SDG

Ph.D. Korea

The hierarchical diagnosis

and

scheme based on basic diagnosis algorithm utilizes a prop-

Lee received

the

B.S.,

M.S.

and

degrees in electrical engineering from University, Seoul, Korea, in 1978, 1981 1984

, respectively.

Since

1983,

he has

been a Professor with the Department of Electrical Engineering, DanKook University, Seoul,

erty of FCM, namely, that FCM can be decomposed structurally or functionally into modular FCMs with lower di-

Korea. Now he is a visiting scientist with the Department of Aeronautics and Astronautics,

mension.

University

Low dimensionality allows the proposed diag-

of Washington,

Seatle,

U.S.A.

His

nostic scheme to be used for fault diagnosis of large-scale

current

and complex processes to which conventional diagnostic

tion and diagnosis, fuzzy logic control, variable structure control theory and applications.

research

interests

include

fault

detec-

schemes can not be applied. The scheme has successfully been applied to a bypassed pipeline system to identify various simulated system faults. The result indicates that the proposed scheme is capable of identifying faults even in the case of a complex system by simple matrix-vector operations.

In this paper, we only deal with simple FCM.

Sung-Ho

KIM Sung-ho

Kim received

and Instrumentation

problem, e.g. spurious interpretations

tional University, interests include:

qualitative approaches. Currently, some researches are in progress for solving the problem by extending simple

M.S. and Ph.D.

1991 respectively. Currently, he is an Assistant Professor of the Department of Control

The proposed diagnostic algorithm entails some serious as in all kinds of

B.S.,

degrees in electrical engineering from Korea University, Seoul, Korea, in 1984, 1986 and

nostic

systems

Engineering,

Kunsan

Na-

Kunsan, Korea. His research intelligent control and diag-

using fuzzy logic and neural

net-

work.

FCM-based diagnostic algorithm into generic FCM-based one.

Masatoshi SAKAWA(Member) References

1) A.S. Willsky: A Survey of Design Methods for Failure Detection in Dynamic Systems, Automatica, vol.12, pp. 601 (1976) 2) R. Isermann: Process Fault Detection Based on Modeling and Estimation Method-a Survey, Automatica, vol.20, pp. 387 (1984) 3) M. Dalle, B.J. Kuipers: Qualitative Modeling and Simulation of Dynamic Systems, Comput. Chem. Eng., vol.12, pp. 853 (1988) 4) O.O. Oyeleye, M.A. Kramer: Qualitative Simulation of Chemical Process System:Steady-State Analysis, AIChE J. vol.34, pp. 1441 (1988) 5) M.A. Kramer, B.L. Palowitch: A Rule-Based Approach to Fault Diagnosis Using the Signed Directed Graph, AIChE J., vol.33, pp. 1067 (1987) 6) C.C. Chang, C.C. Yu: On-Line Fault Diagnosis Using

Masatoshi Sakawa received B.E., M.E. and D.E. degrees in applied mathematics and physics at Kyoto University, in 1970, 1972 and 1975, respectively. At present he is a Professor of Hiroshima University, Japan, and is working with the Department of Industrial and Systems Engineering, Hiroshima University. His research and teaching activities are in the area of systems engineering, especially, mathematical optimization, multiobjective decision making, fuzzy mathematical programming and game theory.

計測 自動制 御 学 会論 文 集

Masahiro

INUIGUCHI

(Member)

Masahiro Inuiguchi received B.E., D.E. degrees in industrial engineering Prefecture University, Since 1987, he worked Industrial versity

第33巻

Engineering, as a Research

M.E. and at Osaka

in 1985, 1987 and 1991. with the Department of Osaka

Prefecture

Associate.

to 1997, he was an Associate

From

Professor

Uni1992 of De-

partment of Industrial and Systems Engineering at Hiroshima University. At present he is an Associate Professor tronics and Information

of Department of ElecSystems at Osaka Uni-

versity. He is interested in possibility theory, fuzzy mathematical programming, DempsterShafer's

theory

of evidence

and

approximate

reasoning.

Kosuke

KATO

Kosuke Kato received B.E. and M.E. degrees in biophysical engineering at Osaka University, in 1991 and 1993, respectively. At present he is a Research Associate of Hiroshima University, Japan, and is working with the Department of Industrial and Systems Engineering, Hiroshima University. He is now interested in the area of large-scale mathematical optimization, multiobjective decision making and genetic algorithms.

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