Diagnostics of technological processes faults

1. Real time diagnostics of technological processes and field equipment
L.A. Rusinov ⁎, I.V. Rudakova, V.V. Kurkina
Saint-Petersburg State Technological Institute (Technical University), Moskowsky pr. 26, 190013 Saint-Petersburg, Russia
Received 29 March 2006; received in revised form 25 October 2006; accepted 23 November 2006
Available online 29 January 2007
Abstract
Diagnostics of a state of potentially dangerous technological processes and field equipment enables to detect abnormal situations and hidden
(soft) failures at early stages of their development, when they are still reversible. In this paper, the combined method of diagnostics is considered.
The early detection of abnormal process situations is carried out with the help of the “moving PCA” method by matching the values of statistics T2
and Q with the thresholds. By the same method, the hidden faults of the field equipment (sensors, actuators etc.) are determined. However this
method does not allow us to simply identify the abnormal situations when many variables are changing simultaneously. For this case, the methods
of identification on the basis of production or frame-production diagnostic models (DM), in particular, systems on the basis of fuzzy production
rules, have shown the good results. The procedure of identification consists in estimation of degree of similarity between a current situation vector
S={s1, s2, … sJ} and vectors of possible abnormal situations registered in rules of a process diagnostic model Sm
⁎={s1m
⁎, s2m
⁎, … sJm
⁎}. Elements
si⁎=μS(ui⁎) reflect in opinion of the experts the “ideal” development of symptoms ui for the given fault. The quality of the method is illustrated by
diagnostics of a state of a high-pressure polyethylene polymerization process.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Diagnostics; Process faults; Sensor faults; PCA; Fuzzy production rules
1. Introduction
The majority of chemical technological processes refers to the
class of potentially dangerous (PDTP). Therefore there is a
necessity for continuous PDTP monitoring and diagnostics of
their state. The importance of the problem is due to the fact, that
the striving to intensification of PDTP very often results in the
necessity of operation near the boundaries of permissible safe
ranges and even near the hazardous zones, where intensity and
conversion, as a rule, are higher. In such cases, it is mandatory to
employ an automatic protection system, which, however,
deteriorates the qualitative and quantitative process characteristics
(including economic indices). This is because the system
functioning is usually accompanied by the emergency dumping
of reactionary mass, irreversible reaction depressing and other
actions resulted in essential losses [1–3]. Therefore it is important
to detect the process deviations from its normal state at early
stages of their development, when they are still reversible, and do
not bring them up to operating level of a protection system.
As a rule, PDTP are characterized by a high level of
uncertainties, large uncontrolled disturbances, essential interior
nonlinearity and, frequently, by bad observability. Very often they
have no mathematical descriptions. The abnormal situations,
which can arise during the process, are related to faults of two
kinds: process faults and faults of field equipment (sensors and
actuators) [4].
The process faults mostly stem from the large changes in
parameters of raw materials, ingress of forbidden impurities and
contaminations, degradation of catalyzers, variation of chemical
equipment parameters, etc. The sensor and actuator errors can
be divided into two main categories including hard failures
(complete failures), and hidden or soft failures caused by shifts
in sensor calibrations, aging drift, sticking of valves, etc. It is
easy to handle the hard failures, while it can hardly be said about
the soft failures. Therefore the latter are more dangerous, since
an operator usually finds out the soft failures too late, when the
essential violations are observed in the process [5].
A procedure for identification of an abnormal process
situation (FDI) consists of two stages: detection of a fault and its
Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25
www.elsevier.com/locate/chemolab
⁎ Corresponding author. Tel.: +7 812 4957453; fax: +7 812 7121191.
E-mail addresses: rusinov@ztel.spb.ru, rusinov@ws01.sapr.pu.ru
(L.A. Rusinov).
0169-7439/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemolab.2006.11.007

2. identification (determining the process block, where it hap-
pened, i.e., the localization of the fault, and then determination
the reasons, which caused the fault) [1,6,7].
Fault detection is made on the basis of a process model and it
includes comparison of observable process behavior with the
fault-free behavior represented by the model. At this step no
information concerning the kinds of faults and their effects is
required [6].
Among different methods of early detection of abnormal
situations, the method of the principal component analysis
(PCA) is most popular now [4,6,8–10]. The method allows us
to construct low dimensional models on the basis of process
data and laboratory analyses. These models reflect correlation
patterns between the process variables. Using these patterns we
can control the process state by monitoring only two statistics:
Hotelling T2
(further — simply T2
) and Q. The first statistics
represents the weighted sum of squared scores (sample variance
within the model), and the second one is the sum of squares of
residuals that describes the data which are not explained by the
model. Exceeding the threshold values by any of these statistics
indicates an occurrence of an abnormal situation.
The various PCA-based methods of fault detection differ in
approaches to model building. Normally a PCA model is cons-
tructed using the historical data that satisfy normal process
operation. After this, the model is further used without any
modification [8,9]. This approach is appropriate for stationary
continuous processes with parameters that are invariable in
time. The majority of chemical processes does not satisfy these
requirements. For these processes other ways of monitoring
methods such as moving PCA were developed. In that case, the
initial time-window of N measurements of the fault-free process
data is formed. Using these data, the PCA model is constructed
and the threshold values for statistics Hotelling T2
and Q are
computed. Then the next window is formed, and so on
[4,8,10,11]. The disadvantage of this method is that the use of
such “jumping” time-window deteriorates the fault detection
speed. At the same time, the sliding version of moving PCA
gives strong correlation between new and previous data samples
and, as a result, small amount of new information. Besides, the
frequent modification of PCA model parameters makes the
detection of faults more difficult. This is because of the incipient
and yet not detected faults change the PCA model irregularly.
The most frequently used method for localization of faults is
decomposition of the complex process into more simple and
autonomous structural units. Such decomposition can be carried
out for the global PCA model as well. In this case the iden-
tification of faults is carried out by comparing the contribution of
each variable to the faulty statistics with the contribution of this
variable to the statistics under normal process operation [4,5,9].
In the presence of a sensor or an actuator failure, this method
works effectively. However, its effectiveness becomes doubtful
if the situation is complicated by changes in many variables.
The method of identification by clusterization [12,13] has the
similar difficulties.
In these cases, the expert systems work quite well, in
particular, the systems based on the fuzzy production rules
[3,4,8,14–16]. So, we decided to combine the approaches by
using the moving PCA for the earlier detection of abnormal
situation, and the fuzzy production rules for fault identification.
The identification of an abnormal situation is performed by
comparison of the vector of the current process situation with
vectors of abnormal situations, which are included in the
conditional parts of rules of the diagnostic model (Fig. 1). By
the way, this method of identification can be used in the
statistical control by matching with PCA models of these
situations. In papers [11,17] this comparison is done using index
Ai that describes variations of the ith principal component (PC):
AiðkÞ ¼ 1 À jwiðkÞT
wi0j ð1Þ
where wi(k) is the ith PC, computed at step k (moving PCA), and
wi0 is the ith reference PC value. If wi0 is defined for the normal
operation data, then expression (1) is used for the fault detection.
If wi0 is defined for the process data with different faults, then
this expression can be used for the fault identification.
The method of identification in the PCA space has the
disadvantage that comes from the necessity to have a set of
diagnostic models (DM) that includes PCA models for the
abnormal situations. Unfortunately this is hardly ever possible
to carry out the active experiments on the real processes. The
chance to collect the necessary data using a passive waiting for
abnormal situations is problematic as well.
At the same time, experts can describe the process situations
on the basis of their experience and practical knowledge even at
the parametric level. They can usually range the importance of
the symptoms that makes it possible to increase reliability of
diagnostics.
Therefore in this paper we used a slightly modified moving
PCA method for the detection of abnormal situations, the
conventional process decomposition method for the fault
localization, and the fuzzy rule-based method for the identifica-
tion. The identification of a fault situation is executed by
evaluation of similarity of the fuzzy sets describing the situations.
The effectiveness of the method is illustrated by diagnostics of the
high-pressure polyethylene polymerization process.
2. Combined method for faults diagnostics
2.1. A) Detection of abnormal process situations
Taking into account the aforementioned arguments, we offer
the following fault detection method, which is based on the
moving PCA. At first, the initial PCA model for the normal
process state is formed, and the thresholds for statistics Q and
Fig. 1. The procedure for identification of abnormal situations.
19L.A. Rusinov et al. / Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25

3. T2
are computed. Then every new process data vector is pro-
jected on this PCA score space and the new values of statistics
Q and T2
are compared with the former threshold values. If
faults are not detected, the procedure continues until a new data
set of the process data vectors of size N will be formed. Then a
new PCA model is constructed for this new data set with
determination of the number of principal components, and
calculation of new cutoff values. Such approach accommodates
all natural modifications of the process. The data set size, N, is
chosen empirically and it depends on the dynamics of the
process.
Therefore, the procedure of monitoring and fault detection is
as follows:
1. Form the initial data set that is Xk
0
(k=0) matrix with N
rows (measurements) and p columns (process variables).
These are data obtained at the normal process operation.
Then normalize the matrix for zero mean and unit
variance. Check for outliers, for example, using the
median filter.
2. Form the PCA model and obtain the loading Pik and
score Tik matrices, e.g. by using the NIPALS algorithm
[18], and determine the number of principal components
I utilized in the model.
3. For a given significance value α, compute the threshold
values CQ and CT for statistics Q and T2
[4,19]:
CQ ¼ aðb þ czaÞd
ð2Þ
where
a ¼
Xp
i¼I
ki; b ¼ 1 þ ðh2h0ðh0 À 1Þ=a2
Þ;
h2 ¼
Xp
i¼I
k2
i ; h0 ¼ ð1 À 2ah3Þ=3h2
2; h3 ¼
Xp
i¼I
k3
i ;
c ¼
ffiffiffiffiffiffiffiffiffiffiffiffi
2h2h0
p
=a; d ¼ 1=h0;
zα is the α-percentile of the normal distribution; λi, i=I+
1,…, p are eigenvalues that explain variations of
reference data in a subspace of residuals, instead of all
p eigenvalues.
CTc
pðn À 1Þ
n À p
Faðn; n À pÞ ð3Þ
where Fα(n,n−p) is the α-percentile of the F-distribution
with n and (n−p) degrees of freedom.
4. Measure a new process data vector Xk+1, centre it by the
previous mean, and normalize it by the previous standard
deviation. Then, calculate statistics Q and T2
and
compare them with the previous threshold values.
5. If any of the statistics systematically exceeds its
threshold value during r (1brbN) consecutive steps,
the fault is considered to be detected.
If no exceeding of the threshold values happens during N
steps, the new data matrix Xk+1 is formed from the stored N
vectors {xk+1, …,xk+N}. New PCA model is constructed based on
these data and the new values of thresholds CQ and CT for
statistics Q and T2
are determined.
Then increase index k:=k+1 and return to step 4.
2.2. B) Identification of abnormal process situations
For identification of sensor and actuators faults and simple
process faults, variable contributions to statistics Q and T2
are
determined using the following expressions.
The complete contribution of variable xj to statistics T2
is
determined as follows:
CTð jÞ ¼
XI
i¼l
CTði; jÞ ð4Þ
where CT(i,j) is the contribution of variable xj into scores ti, that
have exceeded the threshold value [4]:
CTði; jÞ ¼
tixjPij
r2
i
ð5Þ
The contribution of variable xj to statistics Q [9] is given by
formula:
CQð jÞ ¼ ðxj À ¯xjÞ2
ð6Þ
To build the fuzzy diagnostic model for identification of
composite process faults that involves changes of large
number of variables, it is necessary to employ the fuzzification
of expert knowledge of abnormal situations. Fuzzification can
be carried out in a variety of ways [20]. Each situation is
represented by a fuzzy set A(ui), where ui are the elements of
universal set U. The universal set U includes all possible
conditions (symptoms) ui (ui ∈U) as its elements. The degrees
of symptom development in the given situation (membership
functions μS(ui)) are in the left parts of rules of DM. Thus, the
situation for each production rule is described in DM by
vector S⁎=(s1
⁎, s2
⁎,…sJ
⁎) with elements si
⁎=μS
⁎ (ui
⁎) that
reflect the “ideal” development of symptoms for a given fault
in opinion of the experts.
The current (actual) process situation is described by vector
S=(s1, s2,… sJ) formed by measured values of symptoms. The
rule is triggered by fulfillment of all conditions in its left part
(presence of all symptoms that are taken into account by a
given rule). In this case, the situation described by that rule is
considered to take place and the controls contained in the right
part of this rule should be implemented. But in practice
matching the vectors S⁎ and S is frequently incomplete and
we can talk about some degree of certainty in the inference
CF≤1.
Values of the linguistic variables that describe the develop-
ment of symptoms of abnormal situations can be represented by
intervals on the appropriate scales, so μS(ui) can be determined
by comparison of values of symptoms with this scale [21]. A
typical scale of such representation for some variable
(parameters of the technological process, translated beforehand
to dimensionless form and scaled in interval [0,1]) is shown in
20 L.A. Rusinov et al. / Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25

4. Table 1. Naturally the boundaries of intervals in the scale can be
changed by user.
The following two criteria for estimation of similarity of
situations were chosen after investigation as the most perspective
[15,16,21,22]:
1. Criterion SM1. The modified criterion with Euclidean
distance.
SMðS; S⁎Þ ¼
1
1 þ dðS; S⁎Þ
À
dðS; S⁎Þ
2
ð7Þ
where dðS; S⁎Þ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP
j gjðsj À s⁎
j Þ2
J
P
j gj
s
, J is the number of para-
meters in a precondition of a rule, γj is the weighting
coefficients determined, for example, from experts’
ranking of symptoms for the given fault.
2. Criterion SM4. The inner product of vectors S and S⁎.
SMðS; S⁎Þ ¼
X
j
ðsjds⁎
j Þ1=gj
max
X
j
ðsjdsjÞ1=gj
;
X
j
ðs⁎
j d s⁎
j Þ1=gj
! ð8Þ
The weighting coefficients underline the importance of this
or that symptom for identification of a given situation.
As it is mentioned above, the decomposition of the process
into a number of simpler structural units is employed for sim-
plification and better transparency of results of faults localiza-
tion. Then, each chosen structural process unit is described in
DM by its separate root frame that joins the common
information on the situations at this segment of the complex
process [23].
The abnormal situations that can arise in this part of the
process are described by the daughter frames subordinated to
the root frame (Fig. 2). The daughter frames contain the
database of fuzzy production rules that describe the concrete
faults and their causes. The rules are represented by matrices of
values of membership functions of symptoms in the given
situation and corresponding weighting coefficients describing
importance of jth symptom for diagnosing of the fault, defined
by lth production rule.
As a result, the procedure of fault identification includes the
following steps:
1. After detection of a fault, the root frame that contains a
structural unit where a fault happened, is activated. Then the
fuzzy vector of symptoms of the current situation is
compared to the vectors of matrix of cause– effect relations
and the appropriate daughter frame DM is activated.
2. Using one of the above stated criteria for estimation of
similarity of situations, the current and reference situations in
the rules of the daughter frame are matched.
3. The results of matching (value of criteria) are compared to
the threshold values defined empirically. The cycle is
repeated until the threshold is exceeded in several consec-
utive cycles.
The values of estimates of similarity of the competitive
situations (which have been grouped together in the daughter
frame) describe a degree of confidence CF of the diagnostic
system in the fact that the given fault takes place. These values
are returned to a process operator along with recommendations
for elimination of the recognized abnormal situation extracted
from right parts of the rules.
3. Case study
The case study for the proposed methods of detection and
identification of abnormal situations was carried out on the
process of the high-pressure polyethylene production [22],
specifically, on the block of the reactor of polymerization
chosen as a result of process decomposition. The block is
described by the root frame with three daughter frames related
to the faults in thermal conditions of the reactor, problems of
heat removal, and increase of loading on the agitator motor.
Three groups of contingencies can arise at the block caused by
10 different reasons in opinion of the experts. The operation of
the block is controlled by 15 process variables (about 20
diagnostic indices), and some of them are included into the
control loops. The evaluation of the method was carried out by
simulation using the simplified mathematical model of the
reactor block.
The abnormal situation «Overheat of agitator motor» caused
by two reasons (competing situations S3 and S4) was selected
for study of the method from all possible abnormal situations
that can appear at the block:
S3. If temperature of agitator motor shaft Heightened TE/D N
0.6; γ=0.7 & current in the agitator motor High IE/D N
0.75; γ=0.8 & temperature of gas at the reactor input
Fig. 2. Links of the process features with units of diagnostic model.
Table 1
The scale for quantitative representation of fuzziness
Fuzzy value Interval Fuzzy value Interval
Very strongly high 0.90–1.00 Reduced 0.30–0.44
Strongly high 0.80–0.89 Low 0.20–0.29
High 0.70–0.79 Strongly low 0.10–0.19
Heightened 0.55–0.69 Very strongly low 0.00–0.09
Mean (normal) 0.45–0.54
21L.A. Rusinov et al. / Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25

5. Reduced TINP b0.351
; γ=0.6, then the reason is as
follows: adhesion of the low-molecular polyethylene or
the normal polyethylene on the shaft of agitator motor in
the reactor. Recommendation is to increase the flow rate
of ethylene through the motor.
S4. If temperature of agitator motor shaft Heightened TE/D N0.6;
γ=0.7 & flow of polyethylene Reduced GPE b0.371
; γ=0.4
& temperature of gas at the input reactor Strongly high
TINP N0.83; γ=0.7 & temperature in the reactor Reduced
Tb0.441
; γ=0.4 & the differential pressure between the
compressor output and the reactor Normal ΔPb0.5; γ=0.5
& the initiator flow-rate Reduced GIN b0.41
; γ=0.4, then
the reason is as follows: increase of temperature of gas at
reactor input. Recommendation is to cool gas at reactor
input.
Values of membership functions for the “ideal” development
of these situations are obtained from the expert knowledge by
using the data in Table 1 for fuzzification [21]. The values of
weighting coefficients are obtained from experts who have
ranked the symptoms by their importance for identification of a
situation.
Fig. 3 shows the plots of statistics T2
and Q, and contribution
of variables into statistics Q for normal operation of the
polymerization process with normal noise. Evidently the values
of both statistics are much less than the threshold values.
However, statistics T2
is more sensitive to noise. This can increase
the number of false alarms. Since the main faults at the reactor are
related to deviations of the process from the model behavior, only
Q statistics is selected for the early fault detection.
After that, the linearly increasing disturbances were
introduced to the process (Fig. 4). They correspond to
development of situation S3. The algorithm of system operation
supposes that criteria evaluation procedure activates only after
exceeding the threshold for an abnormal situation. However
Fig. 4b shows the criteria values plot from the beginning of
development of situation S3. This demonstrates the sensitivity
to a competitive situation S4 as well.
The identification threshold is set for convenience of a process
operator only. If its value is too high, the system will inform the
1
For uniformity of behavior of elements in the criteria the values of
membership functions of parameters, active while decreasing below magni-
tudes indicated in rules, are taken inverse to the values in Table 1.
Fig. 3. Normal process operation. The plots of statistics Q — a) and statistics Hotelling T2
—b) and contributions plot of variables to statistics Q —c) as the function
of number of sensors’ sampling n. CQ and CT — threshold values of statistics calculated on expressions (2) and (3) for normal state of the process. The following
variables were controlled: T — temperature in the reactor; ΔP — differential pressure between compressor output and the reactor; GIN — initiator flow-rate; TE/D —
temperature of agitator motor shaft; IE/D — current of the agitator motor; TINP — temperature of gas at the reactor input, GPE — polyethylene flow-rate.
22 L.A. Rusinov et al. / Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25

6. operator only about the situations, which can be identified
confidently. Thus the diagnosis becomes more accurate due to
reduction of the number of possible abnormal situations.
However, the delay in the identification of the occurred abnormal
situation is increased, and, in a number of cases, it is possible to
miss an abnormal situation. If the threshold is low, the diagnosis is
fuzzier due to increasing the number of possible situations and the
operator should do additional analysis for identification of
abnormal situations.
Fig. 4b demonstrates that both criteria correctly identified a
cause of abnormal situation S3 at the background of competitive
situation S4. Early fault detection allows the operator to take
timely measures. The dynamically varying values of similarity
criteria are displayed as the trends and they provide the operator
with information on changes in the situation during and
after execution of the recommended corrective actions. The
modeling situation S3 is simple enough since it deals with
one dominating variable IE/D. Therefore it can also be iden-
tified from the contribution plot of this variable for statistics Q
(Fig. 4c).
In the case of development of situation S4 (Fig. 5) the similar
picture can be observed. The development of this situation is
more inertial, therefore the time interval between the moment of
the situation detection and the moment of its recognition is
longer then in the previous case. The contribution plot does not
allow us to specify the situation origin, since temperature
change in the reactor input results in violation of the thermal
conditions, which in turn are stabilized by the control system
(Fig. 5c). Therefore, if the plot is used for identification at the
beginning (during first 60 steps), the variation in ΔP may be
accepted as a primary reason for the situation. Only after the
completion of the transient process, parameter TINP begins to
increase step-by-step. However, the agitator motor temperature
increases as well, the electric motor current varies because of
the product density change, therefore there is no unique pattern
such as observed in case S3. At the same time, both criteria have
Fig. 4. Development of abnormal situation S3 at the background of competitive situation S4. The plot of statistics Q — a) and values of criteria of similarity estimation —
b) and the plot of the contributions of variables to statistics Q — c) as the function of number of sensors' sampling n. ζ — threshold for making the decision about similarity
of situations; the remaining notation is the same, as in Fig. 3.
23L.A. Rusinov et al. / Chemometrics and Intelligent Laboratory Systems 88 (2007) 18–25

7. confidently recognized the development of situation S4 at the
background of competitive situation S3.
4. Conclusion
The composite method for detection and identification of
abnormal situations that can arise at potentially dangerous and
hazardous technological processes is proposed.
The detection of origin of an abnormal situation is made by
the continuous monitoring of the process on the base of modified
moving PCA by tracking the behavior of statistics Hotelling T2
and Q. The identification of failures of sensors and actuators is
carried out by usual method by analysis of contribution plots of
each variable in the faulty statistics. However identification of
complicated situations accompanying with changing of many
variables is carried out by estimation of similarity of current
process situation with its reference patterns represented as the
fuzzy sets. The reference patterns of abnormal situations with
weighting coefficients for improving the effectiveness of iden-
tification are determined on the basis of the experts' knowledge.
The evaluation of the suggested method on the process of
polymerization in production of high-pressure polyethylene has
shown its effectiveness.
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