Supervision, Fault-Detection and Fault-Diagnosis Methods - An Introduction - Isermann 1997
Supervision, Fault-Detection and Fault-Diagnosis Methods - An Introduction - Isermann 1997
Supervision, Fault-Detection and Fault-Diagnosis Methods - An Introduction - Isermann 1997
639-652, 1997
Copyright © 1997 Elsevier Science Ltd
Pergamon Printed in Great Britain. All fights reserved
0967-0661/97 $17.00 + 0.00
PII:S0967-0661(97)00046-4
Abstract: The operation of technical processes requires increasingly advanced supervision and
fault diagnosis to improve reliability, safety and economy. This paper gives an introduction to
the field of fault detection and diagnosis. It begins with a consideration of a knowledge-based
procedure that is based on analytical and heuristic information. Then different methods of fault
detection are considered, which extract features from measured signals and use process and
signal models. These methods are based on parameter estimation, state estimation and parity
equations. By comparison with the normal behaviour, analytic symptoms are generated. Human
operators are another source of information, and support the generation of heuristic symptoms.
For fault diagnosis, all symptoms have to be processed in order to determine possible faults.
This can be performed by classification methods or approximate reasoning, using probabilistic
or possibilistic (fuzzy) approaches based on if-then-rules.
Copyright © 1997 Elsevier Science Ltd
1. INTRODUCTION The classical methods (a) and (b) are suitable for the
overall supervision of the processes. To set the toler-
Within the automatic control of technical systems, ances, compromises have to be made between the
supervisory functions serve to indicate undesired or detection size of abnormal deviations and unnecessary
unpermitted process states, and to take appropriate alarms because of normal fluctuations of the vari-
actions in order to maintain the operation and to ables. Most frequently, simple limit value checking is
avoid damage or accidents. The following functions applied, which works especially well if the process
can be distinguished: operates approximately in a steady state. However,
the situation becomes more involved if the process
(a) monitoring: measurable variables are operating point changes rapidly. In the case of closed
checked with regard to tolerances, and loops, changes in the process are covered by control
alarms are generated for the operator. actions and cannot be detected from the output sig-
(b) automatic protection: in the case of a dan- nals, as long as the manipulated process inputs remain
gerous process state, the monitoring function in the normal range. Therefore, feedback systems
automatically initiates an appropriate coun- hinder the early detection of process faults.
teraction.
(c) supervision with fault diagnosis: based on The big advantage of the classical limit-value-based
measured variables, features are calculated, supervision methods is their simplicity and reliability.
symptoms are generated via change detec- However, they are only able to react after a relatively
tion, a fault diagnosis is performed and large change of a feature, i.e. after either a large sud-
decisions for counteractions are made. den fault or a long-lasting gradually increasing fault.
639
640 R. lsermann
In addition, an in-depth fault diagnosis is usually not are described in more detail in the subsequent papers.
possible.
Therefore (c) advanced methods of supervision and 2. FAULT DETECTION AND FAULT DIAGNOSIS
fault diagnosis are needed,which satisfy the following
requirements: Fig. 2 shows an overall scheme of knowledge-based
fault detection and diagnosis. The main tasks can be
(i) Early detection of small faults with abrupt or subdivided into fault detection by analytic and heuris-
incipient time behaviour. tic symptom generation, and fault diagnosis.
(ii) Diagnosis of faults in the actuator, process
components or sensors. 2.1 Analytic symptom generation
(iii) Detection of faults in closed loops.
(iv) Supervision of processes in transient states. The analytical knowledge about the process is used to
produce quantifiable, analytical information. To do
The goal for the early detection and diagnosis is to this, data processing based on measured process vari-
have enough time for counteractions such as other ables has to be performed, to generate first the char-
operations, reconfiguration, maintenance or repair. acteristic values by
The earlier detection can be achieved by gathering
more information, especially by using the relationship limit value checking of direct, measurable
between the measurable quantities in the form of signals. The characteristic values are the
mathematical models. For fault diagnosis, the know- exceeded signal tolerances.
ledge of cause-effect relations has to be used. A gen- signal analysis of directly measurable signals
eral scheme for all the supervisory functions and the by the use of signal models like correlation
resulting actions is given in Fig. 1. functions, frequency spectra, autoregressive
moving average (ARMA) or the characteris-
This paper introduces some basic problems and tic values (e.g., variances, amplitudes,
methods in supervision, fault detection and fault diag- frequencies or model parameters).
nosis. In Section 2 the main tasks of fault detection process analysis by using mathematical pro-
and fault diagnosis are considered. Then an overview cess models together with parameter estima-
of model-based fault-detection methods is given in tion, state estimation and parity equation
Section 3. This is followed by an introduction to fault methods. The characteristic values are para-
diagnosis procedures, Section 4. The various methods meters, state variables or residuals.
Stop ~ Signal
A
iF___qop tion[ I Alarm ~ e v a l u a t i o n ~
Moni-
toring
~ ..... 1. . . .
II "10perati°n
/ .~ F Faults Measure-
Me;
merits
Control
+
Process
II J Re,con- ~ , I W r--~--Ll ~ ~C- ] r[I/,~
Levels
, I figurati°nl
--" q : ~ C 1=~ P ~-"~
J
. . . . . I
\Piooos
Ii - Con+trol
"" Actions
In some cases, special features can then be extracted type, size and location of the fault as well as its time
from these characteristic values, e,g. physically of detection based on the observed analytical and heu-
defined process coefficients, or special filtered or ristic symptoms. If no further knowledge of fault-
transformed residuals. These features are then com- symptom causalities is available, classification
pared with the normal features of the non-faulty pro- methods can be applied which allow a mapping of
cess. For this, methods of change detection and clas- symptom vectors into fault vectors. To this end,
sification are applied. The resulting changes (discrep- methods like statistical and geometrical classification
ancies) in the described directly measured signals, or neural nets and fuzzy clustering can be used. If,
signal models or process models are considered as however, a-priori knowledge of fault-symptom causa-
analytic symptoms. lities is available, e.g. in the form of causal networks,
diagnostic reasoning strategies can be applied. For-
2.2 Heuristic symptom generation ward and backward chaining, with Boolean algebra
for binary facts and with approximate reasoning for
In addition to the symptom generation using probabilistic or possibilistic facts, are examples. Final-
quantifiable information, heuristic symptoms can be ly a fault decision indicates the type, size and location
produced by using qualitative information from of the most possible fault, as well as its time of de-
human operators. Through human observation and tection.
inspection, heuristic characteristic values in the form
of special noises, colours, smells, vibration, wear and The terminology used in this field is described in
tear, etc., are obtained. The process history, in the (Isermann and Ballr, 1997), based on definitions of
form of maintenance performed, repairs, former the IFAC Technical Committee SAFEPROCESS.
faults, lifetime and load measures, constitutes a fur-
ther source of heuristic information. Statistical data
(e.g. MTBF, fault probabilities) achieved from experi- 3. MODEL-BASED FAULT DETECTION
ence with the same or similar processes can be added. METHODS
In this way heuristic symptoms are generated, which
can be represented as linguistic variables (e.g., small, Different approaches for fault detection using math-
medium, large) or as vague numbers (e.g., around a ematical models have been developed in the last 20
certain value). years, see. e.g. (Willsky, 1976; Himmelblau, 1978;
Isermann, 1984, 1993, 1994a; Gertler, 1988; Frank,
2.3 Fault diagnosis 1990). In this section, basic methods are briefly
described.
The task of fault diagnosis consists of determining the
~ FAULTS
olmerved
HEURISTIC HEURISTIC
ANALYTICAL ANALY'IICALsyMPTOM ~ -m'~kJ
KNOWLEDOE
' tL
OBR~VATIOI~
+ MODm .
i FILTI~.ING, NORMAL
BBi~'VIINJR I
~TIMAII~q IIX'rlIACHI~I
ItlSIUItY
WlIII31t'I'II~
Vl Dm'Bml~ 8T/~.STICS
~V lamukl~
r
g
Clt[~,Jl,l~o I~CIIilON
FAULT-
DIAOIqC~II8
0---~
The task consists of the detection of faults in the pro- least one characteristic property of a variable from an
cesses, actuators and sensors by using the depen- acceptable behaviour. Therefore, the fault is a state
dencies between different measurable signals. These that may lead to a malfunction or failure of the sys-
dependencies are expressed by mathematical process tem.
models. Fig. 3 shows the basic structure of model-
based fault detection. Based on measured input sig- The time dependency of faults can be distinguished as
nals U and output signals Y__,the detection methods shown in Fig. 5:
generate residuals b parameter estimates 19 or state
estimates ~ which are called features. By comparison abrupt fault (stepwise)
with the normal features, changes of features are incipient fault (drift-like)
detected, leading to analytical symptoms s. intermittent fault.
FALIL'I~
With regard to the process models, the faults can be
further classified. According to Fig. 6 additive faults
influence a variable Y by an addition of the fault f,
and multiplicative faults by the product of another
variable U with f. Additive faults appear, e.g., as off-
sets of sensors, whereas multiplicative faults are para-
meter changes within a process.
t
.......
f
l¢0mhaAL
i ,amd~ S~pto~ a b
L. . . . . . . . . . . . . . . . . . . . . . ~ y =~ r ~ (2)
I f=-Aa
U . ~ - q y = (a + aa)O
Y. Y=Y.+ f "1__~ " = a l l + f U
a) b)
Fig. 6 Basic models of faults
a) additive faults b) multiplicative faults Fig. 9 State-space model for a SISO process and
faults
dr/dO = 0 (15)
Fig. 8 Linear input/output model and faults leads to the least-squares (LS) estimate
where
y~(O,s) = ~(s) u(s) (19)
A(s)
b)
is the model output, can also be used, see Fig. t0b).
Fig. 10 Model structures for parameter estimation
But then no direct calculation of the parameter esti-
a) equation error b) output error
mate O is possible, because e'(t) is nonlinear in the
parameters. Therefore the loss function as eq. (14) is
minimized by numerical optimization methods. The 3.3 Fault detection with state estimation and ob-
computational effort is then much larger, and on-line servers
real-time application is in general not possible. How-
ever, relatively precise parameter estimates may be The linear process under consideration is described in
obtained. If a fault within the process changes one or state-space form
several parameters by A0j, the output signal changes x_'(t) = A_x(t)+Bu(t) (23)
for small deviations according to
)~(t) = Cx_(t). (24)
Ay(0 =*r(OAO(t) + A~r(t) O + A gtr(t) A0(t), (20)
Here, p input signals u(t) and r output signals y(t) are
and the parameter estimator indicates a change A_0. assumed, as the methods described are especially
suitable for multivariable processes. Assuming that as
Generally, the process parameters .9_0depend on physi- well as the structure, all process parameters A, B, C
cal process coefficients P (like stiffness, damping are known (which is very restrictive) a state observer
factor, resistance) is used to reconstruct the unmeasurable state variables
0 = f(~) (21) based on the measured inputs and outputs
via nonlinear algebraic equations. If the inversion of g(0 = A_~(0 +~R(0 +H£(0 (25)
this relationship
¢(0 = 3(0 -C~(0. (26)
/2 = f-l(0) (22)
Compare Fig. 11, where e(t) is the output error. For
exists (Isermann, 1992b), changes Api of the process the state estimation error it follows from eq. (25) and
coefficients can be calculated. These changes in the (26), that
process coefficients are in many cases directly related
to faults. Therefore, the knowledge of Api facilitates (27)
fault diagnosis, but is not necessary for fault detection g(0 = ~(0 -g(0
only. Parameter estimation can also be applied for 4(0 = ~_-/-/~g(0.
nonlinear static process models (Isermann, 1993). The state error vanishes asymptotically
limx_-(t) = _0 (28)
Supervision, Fault-Detection and Fault-Diagnosis Methods 645
if the observer i s stable, which can be achieved by deviate from zero. x(t) as well as e(t) show a dynamic
proper design of the observer feedback H. The pro- behaviour which is different for f_L(t) and f.~(t). Both
cess is now influenced by disturbances and faults as x(t) or e(t) can be taken as residuals. In particular, the
follows, compare Fig. 12, residual e_(t) is the basis for different fault-detection
methods based on state estimation. For the generation
x_'(t) = A__~(t)+_Bu(t) +_Fv(t) +L_fL(t) (29) o f special properties, the design of the observer feed-
back H is of interest. Limiting conditions are the
stability and the sensitivity against output distur-
)~(t) = C~(t) +N_n(t) +M_M_fAf(t). (30) bances, n(t). If the signals are stochastic, Kalman-
Bucy filters are applied instead of observers.
Hereby are
v(t) non-measurable disturbances at the input If faults appear as changes AA~ AB or AC of the para-
n(t) non-measurable disturbances at the output meters, the process behavior becomes
f_L(t) fault signals at the input, acting through L on
x(t) (e.g., additive actuator or process faults) ~(t) = [A_+AA_].X(t)+[B_+A__Blu(t) (33)
f_.~(t) fault signals at the output, acting through M as
output changes Ay(t) (e.g. additive sensor )~(t) = [_C+ A ~Z]x(t) (34)
faults)
and the state estimation error
(35)
j--[,~ - ~ Z ( t ) + [aA_ - L/A £1~(t) + a ~ u ( t )
u Y
b) Fault-detection filters (fault-sensitive filters) for are independent of the process states _~(t), the known
multi-output processes input u and unknown inputs v (Fig. 12). In this way
- The feedback H of the state observer is chosen the residuals are dependent only on additive input
so that particular fault signals f_L(t)change in faults f~ and output faults f_u, see Fig. 12 and
a definite direction, and fault signals ~(t) in a (Hfifiing, 1996).
definite plane (Beard, 1971; Jones, 1973).
together with a special design of the observer feed- A straightforward model-based method, of fault detec-
back H. tion is to take a fixed model G Mand to run it parallel
to the process Gp, thereby forming an output error
c) Output observers
Another possibility is the use of output observers (or r ( s ) = [Ge(s ) -Gu(s)]u(s ) (42)
unknown input observers) if the reconstruction of the
state variable ~(t) is not of primary interest (Frank, as shown in Fig. 14a). However, as for observers, the
W/innenberg, 1989; Tsui, 1993). Through a linear process model parameters have to be known a priori.
transformation If Gp(s)--GM(s), the output error then becomes for
additive input and output faults, Fig. 8,
z(t) =/?~(t) (38)
r' (s) =Gt,(s)fu(s ) +fy(s). (43)
the state representation of the observer becomes (Fig.
13) Another possibility is to generate a polynomial error,
Fig. 14b),
~(0 =Eg(0 +du(O+Gx(O (39) r(s) =au(s)y(s) -B~(s)u(s) (44)
=Bp(s)fu (s) +Ap(s)fy(s).
and the residual is determined by
In both cases different time responses are obtained for
(40) an additive input or output fault, r'(s) corresponds to
the output error of parameter estimation, eq. (19),and
r(s) to the equation error, eq. (13). Eqs (43) and (44)
u generate residuals and are called parity equations
(Gertler, 1991). To generate specific properties the
residuals can be filtered
I i11 ° °°1
Yv(0 =~x(0 +t2 Uv(0.
(48) sities [y(ito) [ within a certain bandwidth ~t)min~f.l)~O.)ma x
of the signal by using of bandpass filters (Stearns,
1975).
By these kinds of fuzzy sets and corresponding mem- If no further knowledge is available for the relations
bership functions, all the analytic and heuristic symp- between features and faults, classification or pattern
toms can be represented in a unified way within the recognition methods can be used, Fig. 18. Here, refer-
range 0 < ~t(si) < 1. These integrated symptom repre- ence vectors S~ are determined for the normal behav-
sentations are then the inputs for the inference mech- iour. Then the corresponding input vectors S of the
anism, Fig. 1. features are determined experimentally for certain
faults Fj. The relationship between F u n d S is there-
fore learned (or trained) experimentally and stored,
forming an explicit knowledge base. By comparison
a) 0/ b) I of the observed S with the normal reference S_,, faults
' ~s, X ~ ''.as, F can be concluded.
~(S)I decreased increased
I I~FERENCE,-
PATTERN ]
I~, S, S
'r LASSIFICATIO ~
-AS +as
Fig. 17 Membership functions of symptoms Si=ASi
represented as fuzzy sets $1
e) Fault-symptom relationships
The propagation of faults to observable features or
symptoms in general follows physical cause-effect
relationships, where physical properties and variables Fig. 18 Fault diagnosis using classification methods
are connected to each other quantitatively and also as
functions of time. However, the underlying physical One distinguishes between statistical or geometrical
laws are frequently not known in analytical form, or classification methods, with or without certain prob-
are too complicated for calculations. If no information ability functions (Tou and Gonzalez, 1974). A further
is available on the fault-symptom causalities, experi- possibility is the use of neural networks because of
mentally trained classification methods can be applied their ability to approximate nonlinear relations and to
for fault diagnosis. This leads to an unstructured determine flexible decision regions for F in continu-
knowledge-base. In the case that the fault-symptom ous or discrete form (Barschdorff and Becker, 1990;
causalities can be expressed in the form of if-then Leonhardt, 1996). By fuzzy clustering the use of fuzzy
rules reasoning methods can be used. In the following separation areas is possible (Halgamuge, 1996). (If
subsections, both diagnostic procedures will be briefly features S are used for classification according to Fig.
described. As the timely behaviour (dynamics) 18 the generation of symptoms AS_ais not necessary
between causes and effects is not known in most because this is included in the classification pro-
cases, the relations are considered to be static. cedure, together with the reference S~)
4.2 Diagnosis using classification methods 4.3 Diagnosis using reasoning methods
In Section 3 it was shown how analytic and heuristic For some technical processes, the basic relationships
features S (or symptoms ASi) can be generated. These between faults and symptoms are at least partially
features are now represented in a feature vector known. Then this a-priori knowledge can be re-
presented in causal relations
$r=[$1,$2 .... ,S,]" (54)
fault --~ events ~ symptoms.
The corresponding faults are assumed to be known,
also in vector form Fig. 19a) shows a corresponding causal network, with
the nodes as states and edges as relations. The esta-
F T = IF1, F2 ..... Fm] (55) blishment of these causalitites follows the fault-tree
analysis (FTA), proceeding from faults through inter-
mediate events to symptoms (the physical causalitites)
The elements of F may be binary Fja [0,1] expressing or the event-tree analysis (ETA), proceeding from the
the faults as either "happened" or "not happened". symptoms to the faults (the diagnostic forward-chain-
They may also represent gradual measures for the ing causalities), see e.g. (Lee et al, 1985). To perform
size of the faults Fie [0...1]. a diagnosis, this qualitative knowledge can now be
expressed in form of rules
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