1. Real Time Diagnostics of Technological Processes and Field Equipment
Sanct-Petersburg Technological Institute (Technical University)
Department of process automation in chemical industry
Real Time Diagnostics of Technological Processes and Field Equipment
Rusinov L.A.,
Rudakova I.V.,
Kurkina V.V.
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2. POTENTIALLY DANGEROUS TECHNOLOGICAL PROCESSES (PDTP)
PDTP characterized by:
high level of uncertainties;
large uncontrolled disturbances;
essential interior nonlinearity;
bad observability (frequently);
large amount of abnormal situations (often).
Types of abnormal situations:
own process faults;
hard and soft failures of sensors;
actuators faults.
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3. FAULTS DETECTION BY PCA
PCA MODEL: X=TPT + E
where X - matrix of process variations [n x p],
n – number of measurements, p – number of variables;
T - scores matrix; [n x K], K – number of PC retained in the model;
P - loading matrix; [p x K]
Statistics for monitoring: ,
where ti – i-th component of score vector t=PTx,
s2ti – dispersion of ti.
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4. THRESHOLDS FOR STATISTICS
(1),
zα – is the value of α - percentile of normal distribution,
λi, i= I+1,..., p – eigenvalues.
(2),
where Fα (n,n-p) – is the value of α -percentile of Fisher
distribution at n, (n-p) degree of freedoms and significance level α.
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5. SUGGESTED METHOD OF FAULT DETECTION
Form matrix Х0k (k=0) with W rows (measurements) and р columns (variables) at normal conditions of process operation
Construct initial PCA-model by computing matrixes P and T for example by NIPALS algorithm
Compute threshold values СQ and СТ for statistics Q and Т2.
Measure new vector of observations хk+1, center it by previous mean, normalize on previous MSE. Evaluate statistics Q and Т2 and compare with threshold values.
If during r (1<r<W) sequential steps any of statistics exceeds the threshold values, the detection of fault is stated.
If during W steps such exceeding of threshold values do not happen, the new matrix Xk+1 is formed from stored W vectors {xk+1, …, xk+W}.
Construct new PCA-model, compute new values of thresholds CQ and CТ. Return to step 4.
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6. IDENTIFICATION of FAULTS
The contribution of a variable xj in a statistic Т2 is determined as:
where СТ (i, j) - contribution of a variable xj in one of the scores ti, that have exceed threshold value:
The contribution to a statistician Q by a variable xj will be:
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7. IDENTIFICATION of FAULTS
Evaluate the similarity
The pattern of current situation on process
Reference patterns of abnormal situations -
“ideal” development of situations (by experts’ opinion)
Criteria of similarity
Results of identification
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8. CRITERIA FOR EVALUATE THE SIMILARITY OF SITUATIONS
A) In space of PCA-model [Kano M. etc., 1999]:
Index of similarity Ai(k)=1-|wi(k)Twi0|
Both wi and wi0 - unit vectors.
Ai =0 when i-th PC representing current situation is equivalent reference РС.
Ai =1 when wi is orthogonal to wi0.
Disadvantage - the necessity to have in base of diagnostic model the set of РСА models for abnormal situations, that is seldom accessible.
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9. FUZZY MODELS of SITUATIONS
Situations represented by a fuzzy subset Si (sj) of universal set U, (SiU). Set U includes as members all possible conditions (symptoms) sj, the degrees of their development in the given situation are values of membership functions Si(sj)).
In DM situations represented by vectors S* ={s1*, s2*,… sJ*}, si*=Si (si*)
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10. CRITERIA FOR EVALUATE THE SIMILARITY OF SITUATIONS
B) In space of fuzzy models:
The modified criterion on base of Euclidean distance (SM4)
where , J - number of
parameters in a precondition of a rule, wj - weighting coefficients
2. The criterion on base of inner product of vectors (SM1) ,
wj – weighting coefficients
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11. DIAGNOSTIC FUZZY MODEL
Process plant
Diagnostic model
Root frame
Process
Structural unit
Net of root frames
Daughter frames
Abnormal situations
Faults
Fuzzy rules
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12. SUGGESTED METHOD OF FAULT IDENTIFICATION
Fuzzy vector of symptoms of the current situation is compared to vectors of matrix of cause - effect relations and the appropriate daughter frame DM is activated.
Estimation of situations' similarity by matching current and reference situations in the rules taking into consideration weighting coefficients from the appropriate matrix.
Criteria values are compared to thresholds, defined empirically. Cycle retries until exceeding a threshold in several sequential cycles will happen.
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13. CASE STUDY THE FLOW DIAGRAM OF THE PROCESS
The first cascade of compressing
Low-pressure recycle 1 2 3 4 5
Polyethylene
Ethylene
Initiator
High-pressure recycle
Polymerization
block
The second cascade of compressing
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14. CONSIDERED ABNORMAL SITUATIONS
S3. «Adhesion of low-molecular polyethylene or normal polyethylene on the shaft of agitator motor in the reactor»
If TE/D>0,6 (Heightened)  IE/D>0,75(High)  ТINP < 0,9 (Reduced) then increase flow rate of ethylene through the motor.
S4. «Overheat of motor because of increase of temperature of gas at reactor input»
If TE/D>0,6 (Heightened)  GPE<0,67(Reduced)  ТINP > 0,83(Heightened) then cool gas at reactor input.
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15. FRAGMENT of DIAGNOSTIC MODEL (SITUATIONS S3 AND S4)
The naming of the parameter
Designation
S3*
S4* wj
Si (si*)
Temperature of agitator motor
ТE/D 
0,7
0,6
Agitator motor current
IE/D 
0,8
0,75 -
Temperature of ethylene at the reactor input
ТINP 
0,9
ТINP
0,83
Productivity on polyethylene
GPE
0,4
0,67
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16. Q(n) FOR NORMAL OPERATION OF THE PROCESS70 60 30 20 90 80 50 40
100 Q
CQ = 100,83
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17. T2(n) FOR NORMAL OPERATION OF THE PROCESS70 60 30 20 90 80 50 40 Т2
CT = 23,1
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18. CONTRIBUTIONS  OF VARIABLES IN Q (NORMAL OPERATION)80 60 40 20
, %
GPE
ТINP
IE/D
ТE/D
GIn ΔР Т
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19. Q(n) FOR INCIPIENT DEVELOPMENT OF SITUATION S4
160
120
CQ = 100,83 80 40 n 20 30 40 50 60 70 80 90
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20. T2(n) FOR INCIPIENT DEVELOPMENT OF SITUATION S4Т2 20 80 60 70 50 40 30 90 n
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21. CONTRIBUTIONS  OF VARIABLES IN Q (INCIPIENT DEVELOPMENT OF S4 )
, % n 80 60 40 20
GPE
ТINP
IE/D
ТE/D
GIn ΔР Т
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22. IDENTIFICATION OF ABNORMAL SITUATIONS BY CRITERIA SM1 AND SM4
Increasing development of S4 at background of competitive S3 SM
SM1(S3)
SM1(S4)
SM4(S3)
SM4(S4)
 = 0,8 70 60 30 20 90 80 50 40
0.8
0.6
0.4 n
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23. Q(n) FOR INCIPIENT DEVELOPMENT OF SITUATION S370 60 30 20 90 80 50 40 Q
CQ = 100,83
600
400
200
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24. T2(n) FOR INCIPIENT DEVELOPMENT OF SITUATION S370 60 30 20 90 80 50 40 Т2
CТ = 23
200
100
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25. CONTRIBUTIONS  OF VARIABLES IN Q (INCIPIENT DEVELOPMENT OF S3 )80 60 40 20
, %
ТINP
GPE
IE/D
ТE/D
GIn ΔР Т
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26. IDENTIFICATION OF ABNORMAL SITUATIONS BY CRITERIA SM1 AND S4
Increasing development of S3 at background of competitive S4 SM
SM1(S3)
SM1(S4)
SM4(S3)
SM4(S4)
 = 0,8 70 60 30 20 90 80 50 40
0.8
0.6
0.4 n
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27. SUGGESTED METHOD for FDI
Detection of origin of an abnormal situation is carried out by modified moving РСА with tracking the behavior of statistics T2 and Q.
Identification of sensors and actuators failures is carried out by evaluation of contributions of each variable in faulty statistics.
Identification of complicated situations is carried out by estimation the similarity of current process situation with its reference patterns in rule-base diagnostic model at their representation as fuzzy sets.
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