Saint-Petersburg State Technological Institute

1
Saint-Petersburg State Technological Institute
FAULT DIAGNOSIS IN CHEMICAL PROCESSES AND
EQUIPMENT WITH FEEDBACKS
L.A.Rusinov N.V.Vorobjev
V.V.Kurkina
I.V.Rudakova
2
FAULT DIAGNOSIS IN OBJECTS WITH FEEDBACKS

• The subject-matter of my report concerns the
  application of chemometrics approach to solving
  industrial problems relevant in particular to
  developing diagnostic systems for fault
  diagnosing in difficult cases.

3
Why is the diagnostics necessary?

• The majority of chemical technological
  processes refer to the class of potentially
  dangerous (PDTP) or hazardous.
• As a rule PDTP are characterized by
• high level of uncertainty,
• large uncontrollable disturbances,
• essential internal nonlinearity,
• bad observability.
• lack of mathematical descriptions (often).

4
Why is the diagnostics necessary?

• The operation of protection systems
  obligatory in the PDTP is usually accompanied
• by emergency dumping of a reactionary mass,
• irreversible repressing of a reaction and
• other operations resulting in essential losses.
• The early diagnostics can define the faults at
  their incipient stages and thus allows
  undertaking necessary acts to avoid the
  protection systems actuating.

5
What is necessary for diagnostics?
Continious monitoring and fault
diagnostics are carried out on the basis of a
diagnostic models (DM) connecting faults in the
process under control (abnormal situations) with
their observable symptoms. For this reason,
mathematical descriptions of PDP cannot often be
used as DM because they are usually valid only in
PDP working zones and unsuitable for abnormal
situations.

6
Classification of diagnostic models
Diagnostic Models
EKF
Fuzzy expert systems
Statistical
7
Slide 7,8
The object of diagnostics
PROCESS
100
Recycle or Regulator
0
Emergency situation
ABNORMAL SITUATION
Fault development
Normal regime
8
THE WAY OF SOLVING THE PROBLEM
For solving the problem, the diagnostic model
(DM) should be built for the process section or
equipment in the closed loop formed by feedback
(further - object). Deviations from this model
can be used in detecting the fact that an
abnormal situation has arisen. However, it is
impossible to identify a cause of the fault while
using deviations from the model. For this
purpose, the models describing all possible
abnormal situations are required. As a result,
it is necessary to have a bank of models
9
THE STRUCTURE FLOW CHART OF THE OBJECT DIAGNOSTIC
SYSTEM
10
THE FLOW-CHART OF THE DIAGNOSTICS PROCEDURE
1. THE OBJECT MONITORING FAULT
DETECTION THE FAULT DETECTION CRITERION
?igt? ? - threshold
2. INITIATION OF THE MODELS OF THE BANK
DESCRIBING OBJECT FAULTS
3. THE FAULT REASON (FR) IDENTIFICATION

• Restrictions of the method
• The necessity of the presence of diagnostic
  models, easy-in-use in real time.
• The necessity to obtain the knowledge of all
  possible faults of the object under control.

11
THE FUZZY DIAGNOSTIC MODEL
Each fault Fi is described by fuzzy rule Ri of
Takagi-Sugeno type
Ri IF x1 Ai1 AND... AND xn Ain, THEN yi
ai1x1 ... ain xn bi, where Ri i-th
rule of fuzzy model, i ?1,k k the number of
rules X xkj - a matrix of input variables
samples Nxn k ? 1, N N number of samples
j?1,n n - number of inputs ?i Aij - the
fuzzy terms-sets that enter into the conditional
part of each i-th rule yi - an output of i th
fuzzy rule ai ai1, , ai n and bi -
parameters of fuzzy model ?TiaTi, bi.
12
FLOW-CHART OF COMPUTING THE RESULT OF FUZZY MODEL
The result of fuzzy model computing is determined
by combination of contributions of all rules in a
common inference where ßi - the degree of
activation of i-th rule that is determined by
max-product composition ,
? 0,1 - the contribution of each
term-set Aij to the conditional part of the rule
Ri.
13
FLOW-CHART OF COMPUTING THE RESULT OF FUZZY MODEL
Coefficients of a right part of rules are
determined by solution of the system equations by
means of weighed ?LS yXch ? XchX,1 The
solution is - the diagonal matrix
with the degrees of activation ß on its
diagonal
14
THE DETERMINE OF MEMBERSHIP FUNCTIONS.
By means of fuzzy clustering of the data object
array, for example, by the algorithm of
Gustafson-Kessel, the number of clusters ? and
the matrix of their fuzzy separation U are
defined. Membership functions of fuzzy sets in
the conditional part of rules are extracted from
the matrix U which (g, s)-th member mgs?0,1
characterizes the value of membership of an
input-output combination in s-th column in the
cluster g.
15
THE DETERMINE OF MEMBERSHIP FUNCTIONS.
To obtain one-dimensional fuzzy set Ggj, the
multidimensional fuzzy sets, defined pointwise in
g-th row of the separation matrix U, are
projected into input variables space
Xj. Resulting fuzzy sets Ggj are usually
nonconvex. To obtain the convex (unimodal) fuzzy
sets, approximating by appropriate forms of
membership functions (for example, Gaussian) is
needed.
16
MEMBERSHIP FUNCTIONS OBTAINED BY CLUSTERISATION
6 clusters by threes clusters for a forward and
reverse valve strokes
MEMBERSHIP
FUNCTIONS
THE NORMALIZED VALUES OF INPUT VARIABLES
17
THE DIAGNOSTIC MODEL BASED ON THE KALMAN FILTER
In this case DM is developed in the space of
object states. The Kalman filter is actually
searching for an optimum estimate with the
least-squares method. The linear object model
for Kalman filter is of the form
where x(k) is the state vector, y(k)
- the vector of filter output variables at the
kth step, x(k-1) - the predicted
(extrapolated) state vector value at the (k1)th
step A, B, C - are known prediction,
control and observation matrices n,w
noises.
18
FLOW-CHART OF COMPUTING THE RESULT OF KALMAN
MODEL
The matrix of filter gain factors is given
as where , S(k) correlation
matrixes The specified estimation for the
system state vector is And finally, the
specified covariance matrix of estimation of the
system state vector is given in the form
19
THE DIAGNOSTIC MODEL BASED ON THE EXTENDED KALMAN
FILTER

For nonlinear objects the model is of the
form In this case, the filter does not use
fixed matrices A(x) and C(x), but linearizes them
recursively based on the previous state estimate
with the use of matrices of first partial
derivatives of the state equations These
matrices are calculated at every step and then
inserted into the standard Kalman filter
formulas.
20
CASE STUDY
Case study was carried out on two types of
objects 1. The object in control loop -
electropneumatic valve with the positioner 2. The
object in recycle circuit - Tennessee Eastman
process
21
THE STRUCTURE FLOW CHART OF THE ELECTROPNEUMATIC
VALVE WITH THE POSITIONER
22
THE STRUCTURE FLOW CHART OF THE TENNESSEE EASTMAN
PROCESS
) Applicability of the method to processes with
recycles is presented in the Vorobievs poster
presentation.
23
THE ELECTROPNEUMATIC VALVE WITH THE POSITIONER
The POSITIONER has the mathematical model
developed in the European Interuniversity Project
DAMADICS. 19 various positioner faults have been
considered by the model. But it does not fulfill
to the first restriction for diagnostic models of
objects of the class under study it is difficult
and not easy-to-use in real time. So, models on
the basis of fuzzy logic and Kalman filtering are
developed and the DAMADICS model was used for
their training.
24
MODELED POSITIONER FAULTS
F2 ABRUPT FAULT FLUID BOILING UP IN THE VALVE
CAVITY AT THE EXTREME FLOW RATE
F1 INCIPIENT FAULT SEDIMENTATION
CV1(k), CV1(k-1), CV1(k-2) Control signal
values entered from controller at kth, (k-1)th
and (k-2)th steps
ZT position of the valve plunger at the kth step
FT The flow rate through the valve
25
OUTPUT RESIDUALS OF FUZZY MODELS (INCIPIENT
FAULT F1)
DETECTION
RESIDUALS , (MODEL OF NORMAL REGIME)
time
RESIDUALS , (MODEL OF FAULT F1
time
RESIDUALS , (MODEL OF FAULT F2
IDENTIFICATION
time
26
OUTPUT RESIDUALS OF FUZZY MODELS (ABRUPT FAULT
F2)
DETECTION
Forward plunger stroke
RESIDUALS , (MODEL OF NORMAL REGIME)
time
Reverse plunger stroke
RESIDUALS , (MODEL OF FAULT F1
time
IDENTIFICATION
RESIDUALS , (MODEL OF FAULT F2
time
27
OUTPUT RESIDUALS OF MODELS BASED ON THE KALMAN
FILTERS (INCIPIENT FAULT F1)
DETECTION
RESIDUALS , (MODEL OF NORMAL REGIME)
time
RESIDUALS , (MODEL OF FAULT F1
time
IDENTIFICATION
RESIDUALS , (MODEL OF FAULT F2
time
28
OUTPUT RESIDUALS OF MODELS BASED ON THE KALMAN
FILTERS (ABRUPT FAULT F2)
DETECTION
RESIDUALS , (MODEL OF NORMAL REGIME)
time
RESIDUALS , (MODEL OF FAULT F1
time
IDENTIFICATION
RESIDUALS , (MODEL OF FAULT F2
time
29
CONCLUSIONS
?hemometrics methods are very effective for
execution the monitoring and diagnostics of
technological processes in chemical and related
industries, even in difficult cases at
diagnostics of the objects in circuits with
feedbacks because of feedback masking
effects Statistical methods allow constructing
diagnostic models on the base of the history
process data, not demanding the knowledge of
process chemism and the presence of its
mathematical descriptions.
30
CONCLUSIONS
For diagnosing such faults, it is suggested to
use the bank of diagnostic models describing
normal operation of the objects under control and
their operation when faults are available.
Applicability of the method is illustrated by
the example of system development with two types
of diagnostic models the model with fuzzy rules
of Takagi-Sugeno type and on the basis of
extended Kalman filters. Both models have
demonstrated approximately equal results when
diagnosing both incipient and abrupt faults.