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
Recently, was
the by
graph
atic
memories
we
with
recall
same
fore,
the
as
as to
mation
us
to
ity/decomposability.
Authors
fault
diagnostic
FCM10).
The
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)
It
Fisystem
can
Kosko's
represent
and
all
of
causal
full
other
valeffects.
matrix The
of
E
ith
the
row
connec-
Ci
and,
into
Cj.
only
the If the
{-1,0,1},
structure, branch
SDG
is
useful
system
has
spe-
relationon
Tree based
in
accommodate
FCM
Analysis diagnostic
forward
loops
diftake
because
based
Fault
originally
feedback
easily
SDG causal
to
is
can
a rather
than
knowledge
Analysis
it
the
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
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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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