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Fuzzy Pattern Recognition Based Fault Diagnosis
Rafik Bensaadi, Leïla-Hayet Mouss, Mohamed Djamel Mouss, Mohamed
Benbouzid
To cite this version:
Rafik Bensaadi, Leïla-Hayet Mouss, Mohamed Djamel Mouss, Mohamed Benbouzid. Fuzzy Pattern
Recognition Based Fault Diagnosis. International Review on Modelling and Simulations (I.RE.MO.S.),
2011, 4 (6), pp.3361-3370. hal-00706004
Fuzzy Pattern Recognition Based Fault Diagnosis
Rafik Bensaadi
1
, Leïla H. Mouss
1
, Mohamed D. Mouss
1
and Mohamed Benbouzid
2
Abstract–
In order to avoid catastrophic situations when the dynamics of a physical system
(entity in Multi Agent System architecture) are evolving toward an undesirable operating mode,
particular and quick safety actions have to be programmed in the control design. Classic control
(PID and even state model based methods) becomes powerless for complex plants (nonlinear,
MIMO and ill-defined systems). A more efficient diagnosis requires an artificial intelligence
approach. We propose in this paper the design of a Fuzzy Pattern Recognition System (FPRS) that
solves, in real time, the main following problems: 1) Identification of an actual state; 2)
Identification of an eventual evolution towards a failure state; 3) Diagnosis and decision-making.
Simulations have been carried for a fictive complex process plant with the objective to evaluate
the consistency and the performance of the proposed diagnosis philosophy. The obtained results
seem to be encouraging and very promising for application to fault diagnosis of a real and
complex plant process. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved.
Keywords: Diagnosis, fault detection, pattern recognition, fuzzy control, conjugate gradients,
complex plant process.
Nomenclature
PID = Proportional, Integral and Derivative
controller;
MIMO = Multiple Input / Multiple Output systems;
FPRS = Fuzzy Pattern Recognition System;
FMEA = Failure Modes and Effects Analysis;
PCA = Principal Component Analysis;
FCM = Fuzzy
c-Means;
RBNN = Radial Basis Neural Network;
NP = crisp Nearest Prototype;
k-NN =
k-Nearest Neighbor;
CUSUM = CUmulative SUM;
FIR filter = Finite Impulse Response filter;
pdf = probability density function;
FIE = Fuzzy Inference Engine.
I. Introduction
There is an increasing interest in the development of
intelligent fault detection and diagnosis in industrial
systems because of increasing requirements for reliable,
safe and efficient operation of the plant and for
maintaining quality of the products [1-5]. Many variables,
unknown or not directly measured, have to be included in
the state vector to better describe the plant behavior:
model accuracy, a very difficult task, is necessary for the
effective processing of unpredictable and imprecise
information.
However, human expert can skillfully control plants,
localize a fault and in many times make a good diagnosis:
the human has the ability to learn, to manage imprecise
data and he acts in terms of a complex combination of
sensoring signals instead of separate information sources.
Because of complexity in modeling a real plant, we need
to achieve this sophisticated level of information
processing that the brain is capable of, to solve the
difficult task of fault detection and diagnosis [6-7].
Pattern Recognition is a field concerned with machine
recognition of meaningful regularities in noisy or
complex environments. It is based upon the numerical
representation of the
kth object observed in the process
(physical entity such as a induction motors, cables, etc.)
as a vector
xk = [
xk1
, . . . ,xkq]T, called the
pattern vector or
feature vector, where
xkj the
jth characteristic (feature)
associated with observation
k: temperature, pressure,
flow, sound noise frequency, etc. and
q the pattern vector
length [8-11]. Fuzzy logic concept is included to better
manage uncertainty and make useful quantification of
hard attributes [12-16].
In this paper, a technique for membership function
approximator design is presented. We discuss some
classification approaches and apply CUSUM algorithm
with additional criterions in fault detection problem [17-
18]. We propose a general diagnosis and decision making
scheme and give simulation results for a fictive complex
system.
II. FPRS Description
The pattern vector corresponds to a combination of
sensoring signals: temperature at point A, pressure level
at point B, incoming flow, etc. It is constructed in terms
of the human expert point of view about the plant, and the
effects listed in an FMEA [19]. Other mathematical
techniques like PCA help to design the pattern vector [20-
21].
For each new incoming observation, we need to
identify and quantify the actual plant status and any
possible convergence toward another state: in particular, a
failure state. We have to estimate the speed evolution and
execute the necessary safety actions in acceptable delays.
A general fault detection and diagnosis that meet these
requirements is presented in Fig. 1.
II.1 Membership Function Estimation
II.1.1 Fuzzy clustering. This first step of unsupervised
learning is necessary to produce a logic initialization of
the fault detection and diagnosis system. Given the
training set
X = {
x1,
x2, ��
xn}, where
xk = [
xk1
, . . . ,xkq]T
the pattern vector, the problem of fuzzy clustering in
X is
to assign to the objects {
xk} labels that identify „natural
subgroups‟ in
X. The
membership degrees are computed
as
U = [
uik] by the FCM algorithm with the following
considerations [12], [22]:
– A class set of observations that have similar
properties, corresponds to one operating or failure
mode, the number of clusters
c is assumed to be
known. It is also initialized in terms of the expert
point of view.
– The training set is considered, as representative of
the whole possible clusters, when its size is large
enough. It is obtained by causing the plant to
operate under different modes.
Fig. 1. A general FPRS design strategy.
The FCM algorithm converges from any initialization
to a local minimum. The prototypes and membership
degrees are iteratively updated by [12]
{ }
(
)
1
1
, ,
,
q
m
ik
k
k
i
n
m
ik
k
ik
k
i
j
u
u
u
f x v
v
m
=
=
⎧
��
��
=
��
⎨
��
��
��
=
⎩
��
��
x
v
for
i = 1,2,��,
c
(1)
where
uik is the membership degree of object
xk to class
i,
vi: is the prototype of class
i,
m �� [1, ��] is the weight
exponent on each fuzzy membership, until an error
threshold is reached.
Equation (1) is intuitively understood when we observe
the similarity with the
centre of gravity concept.
II.1.2 Nonlinear approximator design. At this step,
X =
{x
k} and
U = [
uik] feed the input of a nonlinear
approximator optimization algorithm. Let us consider the
structure of a RBNN as shown in Fig. 2 [23-24]. The
hidden layer typically comprises
p radial basis activation
functions with an associated Euclidean input mapping.
The output is taken as a linear activation function with an
inner product.
The input-output relationship, with
x = [
x1
,. . . , xq]T, is
given by
2
2
1
( , )
exp(
/ )
p
j
j
j
j
F
w
=
=
-
-
��
��
x ��
x c
(2)
where �� = [
w1
, . . . ,wp]T is the weight vector to be
adjusted during learning,
cj = [
cj1
, . . . ,cjn]T are the centers
of Gaussian functions.
Now, it is desired to cause
Fi(
x,��) matching a
membership function of class
i at the data points (
xk,
{
uik}) for
i = 1, ��,
c, previously estimated by the FCM.
Numerous optimization algorithms can be applied for
training purposes [25]. In this paper, we focus on the
conjugate gradient algorithm for training the
approximator. This algorithm can be considered as an
intermediate between first- and second-order methods. In
[26] a comparative study of five training algorithms
reveals that the gradient algorithm have reasonable
convergence speeds and require small memory storage.
Moreover, the use of Fletcher-Reeves or Polak-Ribiere
conjugated gradient methods can avoid main reasons of
convergence difficulties such as local minima [27].
The adopted algorithm is based upon the minimization
of
T
1
( )
n
k
k
i
k
J
e
e
=
= ��
where
ek = (
uik) –
Fi(
xk, ��), for
i = 1, ��,
c.
The algorithm is given as follow [25], [27].
1) Calculate
( )
( )
i
k
J
k
=
∂
��
=
∂
�� ��
��
.
Set the search direction equal to
d(
k) = –��(
k).
2) Find ��(
k+1) which minimizes
Ji(��) along
d(
k),
iteratively, by the Secant method:
a) Initialize �� < 1, set �� = ��(
k)
b) Set
[
]
[
]
[
]
T
T
T
( )
( )
(
( ))
( )
( )
( )
k
d k
k
d k
d k
k
d k
��
�� = -��
��
+ ��
- ��
c) �� = �� + ��
d(
k)
d) �� = ��
e) If |��
d(
k)| <
tol�� then return ��(
k+1) = ��
else go to b
3) Calculate �� (
k+1).
4) If
( )
(0)
k
tol��
��
<
��
then return ��(
k+1)
5) Set the next search direction
d(
k+1) = –��(
k+1) + ��(
k+1)
d (
k), where
[
]
[
]
T
T
(
1)
(
1)
(
1)
( )
( )
k
k
k
k
k
��
+
��
+
��
+
=
��
��
(Fletcher-Reeves update
[27]) or
[
]
[
]
T
T
(
1)
( )
(
1)
(
1)
( )
( )
k
k
k
k
k
k
��
+
- ��
��
+
��
+
=
��
��
(Polak-
Ribiere update [27]).
6) Set
k =
k+1 and goto 2.
c RBNNs are trained to estimate a membership
function for each corresponding class. Note that
Fi(
x,��)
may be outside [0,1] by a very small amount for the first
training, because (2) does not include a saturation factor.
The few false measures must be corrected (a value that is
negative or greater than 1 is taken, respectively, as 0 or 1)
to be processed correctly for fault detection. Another
procedure, that adds a sigmoid stage to the structure of
Fig. 2, can be tried in the future [26].
Fig. 2. RBNN based nonlinear approximator.
III. New Observation Processing
Once the membership approximator is well defined, a
new observation
z is labeled and classified. The
membership value of
z to class
i is
µi(
z) =
Fi(
z,��)
(3)
We define a hard classifier on ℜ
q as a decision
function
D imaged in the canonical (unit vector) basis of
Euclidean
c-space so that
D(
z) =
ei means that
z belongs
to class
i. This hard attribution is quantified by (3) to
explain how much
z is considered as
ith fault type and is
useful to identify the actual operating/failure mode. There
are many choices for classifier design.
Criterion 1:
z ��
i ⇔
µi(
z) = max {
µj(
z) }
j = 1, ∙∙∙
c
(4)
Criterion 2: Crisp nearest prototype rule (NP rule) [28].
z ��
i ⇔
DNP,
v(
z) =
ei ⇔ ||
z –
vi || �� ||
z –
vj ||
for
j = 1, ∙∙∙
c. (5)
Criterion 3: Fuzzy
k-nearest neighbor (
k-NN) rule [29].
– Compute and rank the distances
d(
z,
xi) as {
d1 ��
d2 �� ∙∙∙
dk ��
dk+1 �� ∙∙∙
dn}.
– Find the columns in
U corresponding to the
k
nearest neighbor indices {1, 2, ∙∙∙
k}.
– Calculate the vector
u(*|
z) = [
u(1|
z)
u(2|
z) ∙∙∙
u(
c|
z)]T
with the NN labels:
1
( )
k
ij
j
u
u i
k
=
= ��
z
for
j = 1, ∙∙∙
c.
– And finally decide
z ��
i ⇔
DNN,
k(
z) =
ei ⇔
u(
i|
z) = max {
u(
j|
z)}
j = 1, ∙∙∙
c
(6)
For a long training set and an efficient approximator,
the first criterion is the most adequate. NP and
k-NN may
be used as a redundant alternative to solve ambiguous
situations like the example illustrated in Fig. 3. It is easy
to see that (
z1 <
z* �� class 1) and (
z2 >
z* �� class 1), but
we need an additional/other criterion to classify (
z2 ��
z*).
We add the constraint
1
( )
c
i
th
i
µ
u
=
>
��
z
(7)
to reject observations with low membership degrees (
uth is
a small nonzero number taken lower than 0.5). When a
sufficient number of similar (low variance for a Gaussian
pdf approximation) observations are reached, a new
cluster is created. When a sufficient number of similar
(low variance for a Gaussian pdf approximation)
observations are reached, a new cluster is created.
Prototype and membership function parameters are
computed individually (partial FCM with
c = 1) or by
restarting a global membership function estimation
process.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z
m
e
m
b
e
rs
h
ip
fu
n
c
tio
n
µ1(z)
µ2(z)
z*
Fig. 3. Example of an ambiguous classification problem.
IV. Fault Detection and Forecasts
This is a more ambitious and potentially useful task in
maintenance monitoring. The detection of an actual or
future operating/failure mode requires getting and
processing, in real time, signals
z(
t) and µ
i(
z,
t), and taking
advantage of their stochastic properties. If the plant status
is efficiently described by the pattern vector, we note by
µ
i(
t) the membership degree of the plant state to class
i at
time
t, and we develop our approach through the
following steps.
Step 1: CUSUM algorithm is involved in change
detection by processing a sequence of independent
random variables with probability density function
p��(
z)
depending upon one parameter ��. It relies on a
fundamental concept: the log-likelihood ratio of an
observation
z
1
0
( )
( ) ln
( )
p
s
p
��
��
=
z
z
z
(8)
before an unknown change time
k0, �� is equal to ��0. At
time
k0, it changes to �� = ��1 �� ��0. The problem is to
detect the change time.
The cumulative sum
1
0
1
1
( ( ))
( )
( ( ))
ln
( ( ))
k
k
j
j
p
j
S k
s
j
p
j
��
��
=
=
=
=
��
��
z
z
z
(9)
where {
z(
j)}
j = 1, ∙∙∙
k a sequence of independent random
variables is expected to exhibit a negative drift before
change, and a positive drift after change. CUSUM
algorithm is derived under this idea and given as follow.
At each sample time:
(a) Acquire the new data
z(
k).
(b) Compute the decision function
g(
k) = max{0,
g(
k-1)+
s(
z(
k))}.
(c) Compute the number of successive observations
for which the decision function remains strictly positive:
N(
k) =
N(
k-1) 1{
g(
k-1)>0}+1
where 1{x}=1 when x is true and 1{x} = 0 otherwise.
(d) If
g(
k) >
h, issue an alarm (
h is a threshold
chosen to meet either a specified mean time for detection
or a specified mean time between false alarms). Find the
change occurrence time:
k0 =
ka –
N(
ka), where
ka is the
alarm time. Reinitialize the decision function to 0.
In many practical cases, �� is taken as the mean value
of a Gaussian distribution
p��(
z). In our problem, each
typical value ��
i indicates a class prototype
vi, and the
problem of change detection between failure modes will
require a prior knowledge about the class-statistical
properties. We only own a membership function database.
Step 2: Because of the fact stated above, CUSUM will
be applied with the following modification:
µ ( )
ln
µ ( )
i
j
z
z
is considered instead of
( )
ln
( )
i
j
p
p
��
��
z
z
where
i and
j are class-indexes. A membership value does
not have the same meaning as probability, but ratios
reflect the same information, so the ability to apply
CUSUM with taking
µ ( )
( ) ln
µ ( )
i
j
s
=
z
z
z
(10)
is intuitively concluded.
Step 3: Change time detection between two states is
presented. If the target class prototype remains far,
k0 may
be considered as an evolution detection occurrence and
safety decisions are executed in acceptable delay. When
the radius of target class membership function is very
small, the safety task will be more difficult, so we need
another tool to better quantify the evolution between
states and make an earlier alarm. An evolution towards a
fault is described by
( )
i
d
t
dt
��
A negative value means that the plant is leaving state
i, a
positive value means that it is evolving towards this state.
The evolution speed attributes
quick or
slow are
quantified by
2
2
( )
i
d
t
dt
��
The change in evolution speed is said to be
quick for
values greater than 0, an observation may leave quickly
state
i while converging slowly to state
j. Information
about the fault evolution direction are extracted from a
3��
c matrix defined by
1
2
1
2
2
2
2
1
2
2
2
2
...
...
...
c
c
c
d
d
d
E
dt
dt
dt
d
d
d
dt
dt
dt
⌈
⌉
��
��
��
��
��
��
��
��
��
��
��
��
��
��
=
��
��
��
��
��
��
��
��
��
��
��
⌊
⌋
(11)
The corresponding alarm time
ke is computed in terms
of constraints on the elements of
E. For example,
ke may
be defined as the delay time for which both
( )
i
d
t
dt
��
⎛
⎞
��
��
⎝
⎠
and
2
2
( )
( )
i
i
d
t d
t
dt
dt
⎛
⎞
��
��
∙
��
��
��
��
⎝
⎠
remain positive, and this corresponds to the alarm time
ka
computed by CUSUM. Other conditions may be added to
make an earlier alarm (optimization problem).
Because of external disturbances, a noise is added to
z
when reading. We will consider mean values instead of
instantaneous values. The problem is solved by a digital
FIR filter, the frequency bandwidth and sampling time are
chosen in terms of the noise properties and the response
time of all the mechanical/electrical plant parts considered
in the diagnosis design [30].
V. Diagnosis and Decision Making
A fault detection scheme has been completely
described. The
ith fault type effects (symptoms) may be
caused by more than one physical entity, and this fact is
described by conditional probabilities. Diagnosis is to
decide that element
ej (e.g. an induction motor rotor bar,
an inverter switch, etc.) is (or will be) the cause of the
detected (or expected) fault. Previous fault events feed a
statistical database with class-conditional pdf(s) {
p(
ith
fault |
ej-fault)}, used to compute
p(
ej-fault |
ith fault) by
Bayes rule [31-32]. The corresponding safety actions are
made according to the diagnosis conclusion, the fault
severity and the decision making scheme. One powerful
solution is built upon an
Inference Engine: this is a
software or hardware system, which gives a
conclusion
(output) from a
fact (input) and
knowledge (production
rules). If knowledge includes fuzzy linguistic terms, it is
referred to as FIE [33]. A conclusion may deal with:
– A new reference tracking (fuzzy control), the
knowledge base includes rules of the form:
if (mode 2)
and (low inflow),
then (tank 3 temperature
should be low)
– Diagnosis / binary logic instructions, a production
rule may be:
if (water outflow > 0.24 m3/sec)
and (valve 21 closed),
then (shut-off and repair/change element
e2)
if (
d2µ3/
dt2 > 0.12)
or (input control
u1 not set),
then (3rd
fault type in the next 3 min)
Beyond the construction/generation of production
rules, one difficult task when implementing a fuzzy
control algorithm is the accuracy of meaningful
membership functions for all the fuzzy linguistic terms
considered in the knowledge base [34-35]. We will
present later, through an example of temperature control,
the different steps involved in fuzzy control
implementation.
VI. Simulation Results
For the demonstration of the proposed diagnosis
method, we consider a fictive complex process plant. We
assume that a human expert is supervising the plant state
by observing three variables:
v1 (pressure at point A1),
v2
(temperature at point A2) and
v3 (sound noise frequency).
He makes detection and diagnosis upon two complex
combinations:
x1 =
f1(
v1,
v2,
v3) and
x2 =
f2(
v1,
v2,
v3) (PCA).
We want to apply the designed FPRS to act with a
similar reasoning faculty.
Simulation is run, by causing the plant to operate
during a sufficient time, under one normal (typical)
operating mode and two failure modes (plant parameters
randomly affected). PCA has reduced the pattern vector to
[
x1,
x2]T. The unsupervised learning step is applied with a
training set of 100 data points. Samples are labeled and
the prototypes identified as shown in Fig. 4.
The conjugate gradients method is successfully applied
to train an RBNN based membership function
approximator for each class (Fig. 5).
For classification and fault detection test, we caused
the system to evolve towards mode 3 by generating a
linear path sequence {
zk=[
zk1,
zk2]T}, each observation is
well labeled and classified (Fig. 6a). CUSUM is applied
with
3
1
µ ( )
( ) ln
µ ( )
s
=
z
z
z
(Fig. 6b).
-2
0
2
4
6
8
10
12
-6
-4
-2
0
2
4
6
8
x1
x2
Fig. 4. Fuzzy clustering with
c = 3,
q =2. The prototypes are marked as
red stars:
v1 = [1.823, -0.935]T,
v2 = [9.006, 2.151]T,
v3 = [6.297,
5.078]T.
(a) Plant status membership functions.
(b) Projection of (a) on
x1-
x2 plane: Similarity with Fig. 4 is proved.
0
5
10
15
20
25
10
-2
10
-1
10
0
10
1
10
2
number of iterations
J3
J2
J1
(c) Cost function during learning. There is a trade-off between the
learning time and accuracy requirements.
(d)
F1(
x, ��) matches the data pairs considered in training the RBNN.
Fig. 5. Membership approximator,
p = 25, �� = 2.5.
(a) New observation-path, plant is leaving mode1 towards mode 3.
0
5
10
15
20
25
30
35
40
45
-80
-70
-60
-50
-40
-30
-20
-10
time in number of samples
C
U
m
ula
tiv
e
S
U
M
: S
(b) Cumulative sum.
0
5
10
15
20
25
30
35
40
45
0
10
20
30
40
50
60
time in number of samples
cu
su
m
de
cis
io
n
fu
nc
tio
n: g
(c) Decision function.
Fig. 6. Fault change detection by CUSUM,
h = 1.2. The estimated
change occurrence is marked as circle; the alarm time as star.
Evolution towards fault 3 is detected earlier when
membership function derivatives are considered (Fig. 7b).
Temperature control problem is presented to describe
an example of a fuzzy inference engine (Fig. 8). A part of
the knowledge base is given as follow.
R1:
if (mode1)
and (quick evolution toward mode3),
then (
T5 should be low)
R2:
if (
P5 �� 0.4 bar) or (slow evolution toward mode3),
then (
T5 should be around 15��C)
R3:
if (mode2) and (high sound noise frequency),
then (
T5 should be high)
Facts:
z = [7, 3.7]T,
P5 = 1.27 bar,
dµ3/
dt = 0.2 /sec,
d2µ3/
dt2 = -0.18 /sec2,
fsn = 15 kHz.
Conclusion:
T5 should be?
0
5
10
15
20
25
30
35
40
45
0
0.2
0.4
0.6
0.8
1
time in number of samples
M
e
m
b
e
rs
h
ip
µ1(z(k))
µ2(z(k))
µ3(z(k))
0
5
10
15
20
25
30
35
40
45
0
1
2
3
4
5
time in number of samples
C
la
s
s
n
u
m
b
e
r
(a) Criterion 1 classification.
0
5
10
15
20
25
30
35
40
45
-0.04
-0.02
0
0.02
0.04
time in number of samples
m
e
m
b
e
rs
h
ip
firs
t d
e
riv
a
tiv
e
0
5
10
15
20
25
30
35
40
45
-4
-2
0
2
4
x 10
-3
time in number of samples
m
e
m
b
e
rs
h
ip
s
e
c
o
n
d
d
e
riv
a
tiv
e
(b) 1st and 2nd derivatives of µ1(
t) and µ3(
t).
The filled circle indicates earlier change detection.
Fig. 7. Future fault detection strategy
with additional derivative based criterions.
The fuzzy linguistic term
mode i is described by the
corresponding membership function
Fi(
x,��). The
membership function for each other fuzzy linguistic term
is initialized as shown but may be modified by learning to
update the shape form and parameters. The basic
operators, involved in fuzzy control, are defined as
follow.
AND: µA⋂B = MIN(µA,µB)
(12)
OR: µA��B = MAX(µA,µB)
(13)
NOT:
A
A
1
�� = - ��
(14)
For each rule, the compatibility of the fact to the
antecedent is obtained by projecting the fact to the
corresponding membership function. The resulting
membership degrees are combined by a conjunction AND
(rules 1, 3) or OR (rule 2). An individual conclusion is
obtained by truncating (minimizing) the consequent
membership function. All the rules are combined by a
conjunction ALSO (maximization of individual
conclusions) to construct a relatively complicated
membership function µ characterizing the final
conclusion. The final step is defuzzification.
The new reference
T5
* that must be tracked, given the
facts: (
z = [7, 3.7]T,
P5 = 1.27 bar,
dµ3/
dt = 0.2 /sec,
d2µ3/
dt2 = -0.18 /sec2,
fsn = 15 kHz), is computed by the
center of gravity method
( )
( )
5
5
5
*
5
5
5
34.8 C
T µ T
dT
T
µ T
dT
=
=
��
��
��
(15)
µ1
1
1
1
z2
Positive Sign
Quick Evolution
Low
�� 0.4 bar
Positive Sign
Slow Evolution
�� 15��C
µ2
high
high
z2
z = [7, 3.7]T
1.27 bar
0.2 /sec -0.18 /sec2
15 kHz
dµ3
/dt
d2µ3
/dt2
T5
P5
dµ3
/dt
d2µ3
/dt2
T5
T5
Sound noise frequency
0.319
0.024
0.210
0.550
0.740
34.8��C
Defuzzification
T5
T5
ALSO
µ
µ
Rule 1
Rule 2
Rule 3
µ1
1
1
1
z2
Positive Sign
Quick Evolution
Low
�� 0.4 bar
Positive Sign
Slow Evolution
�� 15��C
µ2
high
high
z2
z = [7, 3.7]T
1.27 bar
0.2 /sec -0.18 /sec2
15 kHz
dµ3
/dt
d2µ3
/dt2
T5
P5
dµ3
/dt
d2µ3
/dt2
T5
T5
Sound noise frequency
0.319
0.024
0.210
0.550
0.740
34.8��C
Defuzzification
T5
T5
ALSO
µ
µ
Rule 1
Rule 2
Rule 3
Fig. 8. Example of a fuzzy inference engine based decision process.
and
T5 remains continuously under this control.
VII. Conclusion
We have proposed a general FPRS design scheme for
fault detection and diagnosis in industrial systems. This
approach involves fuzzy clustering as a first partition of
the training set into a number of classes initialized by the
known operating/failure modes, and the conjugate
gradient method as the learning tool for training
membership
function
approximator.
Incoming
observations will be classified and new created classes are
taken into account.
Fault detection efficiency is first tested by applying
CUSUM with modified expression of the log-likelihood
ratio: membership degrees are considered instead of
probabilities. Then, another proposed method that takes
advantage of membership function derivatives is
investigated, evolution towards a fault type target is
quantified and safety actions will be executed in
acceptable delays.
There are many ways to design the decision system, we
proposed a an efficient knowledge based approach and
presented a
temperature fuzzy control as an example of a
safety action based on information about fault change
forecasts, extracted from the
E matrix.
The designed FPRS was successfully tested for a
fictive complex process plant and the obtained results
seem to be encouraging for application on a real and
complex plant process. The scheduled complex plant is an
agro-alimentary production system [4], [36]. However,
this will involve additional hardware and software
implementation and will be the subject of a future work.
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1University of Batna, LAP, 1, Rue Chahid Boukhlouf Mohamed El
Hadi, 05000 Batna, Algeria (email: hayet_mouss@yahoo.fr).
2University of Brest, EA 4325 LBMS, Rue de Kergoat, CS 93837,
29238 Brest Cedex 03, France (e-mail: Mohamed.Benbouzid@univ-
brest.fr).
Rafik BENSAADI received the B.Sc. degree
in Electronics and Control Systems and the
M.Sc degree in Industrial Engineering, from
the University of Batna, Batna, Algeria, in
1999 and 2006, respectively. He is currently
working toward the Ph.D. degree at the
University of Batna, Batna, Algeria.
His research interests include machine
learning, control theory, microcontroller-based
digital control design, DSP design, and
hardware implementation of fault detection,
diagnosis and decision-making scheme.
Leila Hayet MOUSS was born in Batna,
Algeria, in 1954. She received the B.Sc.
degree in Electrical Engineering, in 1979, from
the National Polytechnic School of Algiers,
Algeria; the M.Sc. and the Ph.D degrees in
Electrical and Computer Engineering from the
University of Bordeaux, Bordeaux, France, in
1982 and 1985, respectively, and the
University Habilitation degree from the
University of Batna, Batna, Algeria, in 2005.
After graduation, she joined the University
of Batna, Batna, Algeria, where she is an
Associate Professor of Electrical and Computer Engineering. Dr. Mouss
is the head of the Automatic and Computer Integrated Manufacturing
Laboratory (LAP). Her current research interests include diagnosis of
industrial production system using artificial intelligence techniques.
Mohamed Djamel MOUSS was born in
Batna, Algeria, in 1956. He received the B.Sc.
degree in Electrical Engineering, in 1982, from
the National Polytechnic School of Algiers,
Algiers, Algeria; the M.Sc. degree in Industrial
Electricity and the Ph.D degree in Industrial
Engineering, both from the University of
Batna, Batna, Algeria, in 1989 and 2006,
respectively; and the University Habilitation
degree from the University of Batna, Batna,
Algeria, in 2008.
After graduation, he joined the University
of Batna, Batna, Algeria, where he is an Associate Professor of
Electrical and Computer Engineering. Dr. Mouss is the leader of the S3
team (Sûret��, Supervision, Surveillance) of the Automatic and Computer
Integrated Manufacturing Laboratory (LAP). His current research
interests include diagnosis of industrial production system using
artificial intelligence techniques.
Mohamed El Hachemi Benbouzid was born
in Batna, Algeria, in 1968. He received the
B.Sc. degree in electrical engineering from the
University of Batna, Batna, Algeria, in 1990,
the M.Sc. and Ph.D. degrees in electrical and
computer engineering from the National
Polytechnic Institute of Grenoble, Grenoble,
France, in 1991 and 1994, respectively, and the
Habilitation �� Diriger des Recherches degree
from the University of Picardie ��Jules Verne,��
Amiens, France, in 2000.
After receiving the Ph.D. degree, he joined
the Professional Institute of Amiens, University of Picardie ��Jules
Verne,�� where he was an Associate Professor of electrical and computer
engineering. Since September 2004, he has been with the Institut
Universitaire de Technologie of Brest, University of Brest, Brest,
France, where he is a Professor of electrical engineering. His main
research interests and experience include analysis, design, and control of
electric machines, variable-speed drives for traction, propulsion, and
renewable energy applications, and fault diagnosis of electric machines.
Prof. Benbouzid is a Senior Member of the IEEE Power
Engineering, Industrial Electronics, Industry Applications, Power
Electronics, and Vehicular Technology Societies. He is an Associate
Editor of the IEEE TRANSACTIONS ON ENERGY CONVERSION, the IEEE
TRANSACTIONS
ON
INDUSTRIAL
ELECTRONICS, the IEEE
TRANSACTIONS ON VEHICULAR TECHNOLOGY, and the IEEE/ASME
TRANSACTIONS ON MECHATRONICS.
