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Data Mining for Knowledge Extractionin
Data Overloaded Process EnvironmentsPart 2
Sirish ShahProfessor and NSERC-Matrikon-ASRA Industrial Research Chair
University of Alberta, Canada
Credits: D. Chang, V. Kumar, H. Raghavan, S. Choudhury. S. Lakshminarayanan, H. Fujii
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Examples and Case Studiesof Process Monitoring
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Cluster Analysis
Hundreds of variables may be measured for a particular process.
An important but difficult task is the selection of useful variables for analysis.
Cluster analysis groups process variables according to their correlation structure.
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Numerical values in a correlation matrix!
1 -0.185294206 0.027055773 -0.171819975 0.093276222 -0.027994229 0.098787646 -0.020583535 0.032817213 -0.132101895 0.007443381-0.185294206 1 0.046731844 0.192725409 0.06221338 -0.121835155 0.007001147 0.072787318 0.256501727 -0.332697412 0.3011214280.027055773 0.046731844 1 0.497561061 0.097669495 -0.042977998 0.073150009 0.01752308 0.446311963 -0.065613281 0.577804913
-0.171819975 0.192725409 0.497561061 1 0.098720947 0.04428365 0.109814696 0.207062089 0.277424246 0.017018503 0.3740579680.093276222 0.06221338 0.097669495 0.098720947 1 -0.16665222 0.088320804 0.017838289 0.083761143 0.0118807 0.047680363
-0.027994229 -0.121835155 -0.042977998 0.04428365 -0.16665222 1 -0.083250958 -0.113249872 -0.066049714 0.083771862 -0.0246369920.098787646 0.007001147 0.073150009 0.109814696 0.088320804 -0.083250958 1 0.11444586 0.18562112 -0.115407265 0.14030574
-0.020583535 0.072787318 0.01752308 0.207062089 0.017838289 -0.113249872 0.11444586 1 0.008346999 -0.031577329 -0.0298117910.032817213 0.256501727 0.446311963 0.277424246 0.083761143 -0.066049714 0.18562112 0.008346999 1 -0.548843663 0.897175324
-0.132101895 -0.332697412 -0.065613281 0.017018503 0.0118807 0.083771862 -0.115407265 -0.031577329 -0.548843663 1 -0.4109610640.007443381 0.301121428 0.577804913 0.374057968 0.047680363 -0.024636992 0.14030574 -0.029811791 0.897175324 -0.410961064 10.074563952 -0.290999002 -0.166431901 -0.191828797 0.137354964 -0.318379029 0.361032714 0.140153123 0.041112456 0.020956227 -0.121890887
-0.113935147 0.096219583 -0.05286439 -0.015289902 0.019324048 0.016093852 0.079420974 0.30604406 0.012369794 -0.118651352 -0.024855722-0.004367924 0.415302265 0.212895416 0.422025428 0.121021716 -0.096013616 0.208845673 0.062699756 0.305190719 -0.192434667 0.383145433-0.041892367 0.292542753 0.088478765 0.242138917 0.091224942 -0.044085648 0.030151736 -0.048883722 -0.018817843 0.001127689 0.090586488-0.012796946 0.428193732 0.148027299 0.374229362 -0.036415302 0.031485232 0.014195414 0.093444237 0.111307503 -0.142990907 0.198198421-0.072987889 0.639653323 0.240224974 0.430130045 0.025582625 0.028934191 0.074669894 -0.003315806 0.264468969 -0.263129122 0.384595716-0.081425541 0.650446804 0.264165028 0.526494862 0.024959155 0.016578929 0.086833576 0.043588107 0.234276435 -0.236008471 0.3583759990.220771143 -0.298196834 -0.095225139 -0.369718105 0.018743973 0.082060135 -0.102865842 0.113548775 -0.131073669 0.077167167 -0.117265396
-0.024869432 -0.190880521 0.216974667 0.238447454 0.043845472 0.02495333 -0.005302967 -0.052698509 0.117642296 0.030820275 0.12686478-0.030647599 0.099397397 0.060271104 -0.149448693 0.101629373 0.107726218 0.138653219 -0.135938599 0.29944496 -0.143383865 0.324332399-0.105195337 -0.1838672 -0.148673467 -0.213141108 0.059956448 0.018061058 -0.017384883 -0.104230537 0.034619576 0.092101398 -0.0319182910.017414435 -0.037744275 0.109437444 -0.048190722 -0.019413361 0.085313857 -0.03284987 -0.090511989 0.148464685 -0.022750366 0.1854388330.038764349 -0.713947863 -0.052827235 -0.199718753 -0.077278511 0.145219414 -0.072139066 -0.148773823 -0.170502021 0.300067528 -0.221413011
-0.045966454 -0.478970547 0.019338226 0.217745669 -0.040564805 0.097708972 0.112071592 0.174626221 -0.127211683 0.192457187 -0.1987993940.004199633 -0.557289909 -0.28471802 -0.50961326 -0.10351578 0.076308499 -0.029991343 -0.086972975 -0.114870901 -0.040561871 -0.281984840.08599719 0.007025338 0.154179893 0.232546946 0.007835329 -0.086667223 0.156685077 0.023192903 -0.02996409 0.102102098 0.0147997420.07875747 -0.429241921 -0.344287431 -0.244148911 -0.023116012 -0.027914037 -0.035809918 0.05492866 -0.371758851 0.202342995 -0.500472826
-0.058448605 0.611130166 -0.119253918 0.057550975 0.117777025 -0.183408655 0.082432127 0.10213768 -0.008270005 -0.326478145 -0.006977244-0.02580405 -0.150816152 0.120793341 0.066957772 0.025269938 0.006378438 -0.075330271 0.07187571 -0.106953812 0.090117193 -0.0678767740.159960053 -0.46153707 -0.061782981 -0.275932869 0.000719008 0.025290936 0.007663131 -0.053698037 -0.101831356 0.058117208 -0.1733652060.026409868 -0.563862298 -0.386080423 -0.546002219 -0.101953064 0.031863056 -0.01116078 -0.088594064 -0.187499891 0.05573025 -0.3700930340.215815744 -0.782048799 -0.133757845 -0.413764596 -0.063567993 0.057507301 0.005673666 -0.045465041 -0.198905102 0.157678121 -0.2927683720.210107163 -0.762753731 -0.113514688 -0.377067501 -0.080202766 0.058553599 -0.013312535 -0.049311774 -0.178286335 0.116737358 -0.262262234
-0.160786539 0.822759906 0.082111296 0.319369724 0.073604799 -0.119269237 0.02934483 -0.005308015 0.179202768 -0.192898469 0.2390704920.17932223 -0.707919187 -0.147742155 -0.468437394 -0.086347239 0.046364378 0.023420083 -0.056932385 -0.199912109 0.13527489 -0.320831812
0.149319082 -0.752830887 -0.06056419 -0.348884293 -0.090379995 0.156053854 0.00402923 -0.087617203 -0.010696796 0.026324582 -0.10811970.010059676 0.616117603 0.346256652 0.323705183 0.037419038 -0.036121112 0.01731208 0.015883625 0.443358533 -0.280423399 0.559601776
Imagine looking at thousands of numerical values of data!
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Cluster Analysis
Correlationmatrix beforethe optimalordering ofvariables.(>150 variables!)
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Cluster Analysis
Correlationmatrix afterthe optimalordering ofvariables.
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Process Monitoring usingPrincipal Components Analysis
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Yet another motivational argument for Multivariate Statistics
FuelFlow
Abnormal Data
Steam Demand
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A different view of boiler data
FuelowRather than monitoringfuel flow and steam demand separately (which would anyway give misleading results),it makes sense to monitor a variablewhich is a linear combination of thetwo variables
Fl
Steam Demand Abnormal Data
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-20
24
6
0
0.5
1
1.50
0.5
1
1.5
2
2.5
PC1
PC2
23 →
Principal Components Analysis (PCA)
PCA is concerned with the coordinate transformation of data so that they can be represented in a reduced dimensional plane (e.g. )
The premise is that there is usually a simpler and inherent underlying structure to the process and therefore the data that originates from it. PC’s often have physical meaning.
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Principal Components Analysis
Given: Measurements of process variables, XMeasurements are possibly correlatedNumber of Samples: nsNumber of Variables: nx
Sample # X1 X2 X3 ………… Xnx
12345...ns
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-20
24
6
00.5
11.5
0
0.5
1
1.5
2
2.5
PC1
PC2
PC2
Analyze data in this reduced 2 dimensional plane
PC1
3D Euclidean basis space Principal
subspace
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Process Monitoring usingPrincipal Components Analysis
A simple example to illustrate the application of PCA
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Description of the process
Cold water Mixed water 1 Mixed water 2
F3F1 F4
F2 Hot water
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4
6
8
10
12
15
16
17
18
19
20
21
22
20
25
30
35
f2
3D V is ualiz at ion of F low Data
f1
f3
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567
891011
1416
1820
22
22
24
26
28
30
32
f2
3D V is ualiz at ion of F low Data
f1
f3
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-20
24
6
0
0.5
1
1.50
0.5
1
1.5
2
2.5
PC1
PC2
P defines the new coordinate system spanned by PC1 and PC2The scores are the projection of the data onto PC1 and PC2
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567891011
1416
1820
22
22
24
26
28
30
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f2
3D Visualization of Data
f1
f3
Prediction Error
Normal rangeof operation
(ellipse boundaries)
Large prediction error, i.e. correlation structure breaks
down. (This point will flare upon the SPE plot)
Correlation structure holds,but operation is outside normal range.These points show up on the T2 plots.
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Normal Operating Data
•Since the two mixed water flow rates are almost identical, only one of the flow rates (mixed water 1) is shown in this plot
•We take this flow rate data as normal operating data, and build a PCA model based on this data.
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Description of the process
Cold water Mixed water 1 Mixed water 2
F3F1 F4
F2 Hot water
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Square Prediction Error Plot
•If any of the measurements is wrong, i.e. if the model does not hold then the SPE plot will flare up.
•The SPE plot shown above is based on normal operating data, and therefore one should expect that almost all the data will lie within 99% confidence interval.
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0123456789
0 50 100 150 200 250 300 350 400 450 500
95%
99%
Hotelling's T²H
otel
ling'
s T
²
Sample
•The T2 chart show that all measurements are within 99% control limits.
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Since we have built a PCA model based on the normal operation data, we can now use this model to check:
•The shift of operating point of the plant
•Possible sensor fault in the online measurements
•The presence of any disturbance to the plant
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•In order to use the PCA model to check sensor faults, a bias or a drift in the measurement sensor of the total water flow rate is introduced between samples 501-700
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Many scores are out of the 99% control limits, indicating a possibly faulty sensor or an out of nominal zone excursion.
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T2 chart also indicates a out of control status beginning at sample 501
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•SPE chart is more sensitive than T2 chart to check for possible sensor failure. While T2 chart is more suitable for detecting any change in operating states of the process (assuming that the correlations among the variables still hold.)
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Process Monitoring
Data is often correlated in ways we don’t easily understand.Univariate analysis does not provide overall picture of the process.Multivariate techniques help us predict abnormal process operation before it becomes visible to operators.
Industrial Case Study:PCA-based Process Monitoring
Fault Detection and Diagnosis Decomposition in a Polymer Reactor
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H igh P ressure P rocess
P rim ary C o m presso rB ooste r S econdary C om p resso r
R eacto r
In itia tor P u m ps
S eparator
H opper
E x truderS ilos
C o-m ono m erP urgeM odifie r
E th ylen e
H eat E x ch
H eat E xch
P ackag in g
300ats20%
100%
74%6%
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Cooler cook onset
Fault
High Density Plot
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Modeling: Pre-filtered data
012345678
95 %
99 %
SPEDECOMP MODEL DEVELOPMENT
SP
E
Sample905 1810 2715 3620 4525 5430 6335 7240 8145 9050 9955
-3
-2
-1
0
1
2
3
-10 -5 0 5 10
PC-1 vs. PC-5DECOMP MODEL DEVELOPMENT
PC
-5 S
co
res
PC-1 Scores
PCA scores 2DPCA scores 2D
11 2 3 4 5 6
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EWMA data filteringOff-line analysis of reactor decomposition
0
5
10
95%
99%
SPEDECOMP
SP
E
Sample1027 2054 3081 4108 5135 6162 7189 8216 9243 10270
3456789
1011
95%
99%
SPEDECOMP
SP
E
Sample10836 10879 10922 10965 11008 11051 11094 11137 11180 11223 11266
Prediction time 9 minutes
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Contribution Plots fpr root cause diagnosis
05
10
SPE Contributions - (11195)Highest Contributors TIC52027D.PV ; PIC52021.PV;PI51135/64.PV
Per
cent
Con
tribu
tion
Tags
AI51001C
.PV
PI51135/64.P
V
PI52054.P
V R
FG
Pr
PIC
52021.OU
T
TI51015.P
V
TI51158.P
V1*disch
TI52024.P
V
TI52031A
.PV
TIC
52021D.P
V.
TIC
52027D.O
UT
TIC
52028D.P
V
Tags% Cntr. 1.664 7.765 3.660 3.075 0.293 0.174 0.453 1.535 1.047 3.560 3.661
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MRI Images
3 different MRI images of the same slice of the brain
Same slice with modified
“abnormality” in some of the images
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MRIA using PCAAxial T1 weighted
Axial FLAIR
Axial T2 weightedNeudecker product PCA
256X256X3X)
3X3P (loadings)
256X1
.
.
.Inverse Neudecker
productPC1
PC2
PC3X
256X256X3
Axial T1 weighted
Axial FLAIR
Axial T2 weighted
Score Images 256X256X3
2562X3T (scores)
2562X3
Score Plots 1024X1024
PC1 vs. PC2
(or other combination)
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Score images
Score images of original images
Score images with modified “abnormality”
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Scores plot (PC1 vs. PC2)
Scores plot of normal images Scores plot of image with modified “abnormality”
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Segmentation using scores plot
Building Softsensors via Partial Least Squares (PLS)
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PLS Modeling
X Y
Covariance Maximization
t1
t1
u1
PLS explains variationin both X and Y andsimultaneously alsomaximizes the X and Ycovariance
u1OUTER MODEL
Can fit a line or curve throughthis cluster ofpoints.
INNER MODEL
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Softsensor developmentIndustrial Case Study-1
Credits: Mitsubishi Chemicals, Japan
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PLS application to an industrial column: Modeling Results
0 1 2 3 4 5 6 7 8 9 10day
GC output Model output
0 1 2 3 4 5 6 7 8 9 10day
PLS model prediction
GC output Model output
Original model prediction1200
1000
800
ppm
600
400
1200
1000
800
ppm
600
400
Data are from the part of validation periods (Sep. 95)
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Inferential control using PLS model
FC
(R/D)
Reflux(R)
Distillate(D)
Condenser
Reboiler FC
FC
Bottoms
Steam
(D) sp
FC
FCFeedStreams
LC
Comp.Control
PLSModel
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Control Results
0
0
1 2 3 4 5 6 7 8 9 100day
p
GC output Model output
1 2 3 4 5 6 7 8 9 100
1000
day
p
Impurity after controlGC output Model output
On ControlSet Point Up
Specification Upper Limit
Impurity before control1500
1000
pm500
1500
pm
500
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Controller Performance Assessment
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Performance assessment
Performance of univariate or multivariate controllers ???Simplistically ask: How “healthy” is your controller?
ProcessControllerdr u y
Main benefit: Develop a tool that would help towardslow maintenance and optimal process performance.
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What is Performance Assessment?
Is your controller doing a satisfactory job? Can you get a measure of the ‘state of health’ of a closed loop system from routine operating data?
For diagnosis, look at system objects such as, actuators, constraints, disturbances, models etc.
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Quality and Variance
Remember that:
variables)d(controlle Variance1ProfitandQuality ∝
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Example of Variance Reduction
0 100 200 300 400 50092
94
96
98
100MOIC25276: Trend plots before and after tuning
Sample No.
0 100 200 300 400 50092
94
96
98
100
Sample No.
9293
9495
9697
9899
1000 10 20 30 40 50 60 70 80 90
9293
9495
9697
98
991000
10
20
30
40
50
60
70
80
90
Before tuning
After tuning
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Look at a real industrial process
Schematic Diagram of an Industrial Process
Loop to be evaluated
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Quality and Variance
❖ How good a job are we doing in regulating this temperature ?
❖ Can we do any better ?
310
Can this variance be reducedby retuning this loop?Te
mpe
ratu
re
300
290
2800 2 4 6 10 12 14 168
hrs
What is the lowest possible variance that we can achieve for this loop?
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Performance Assessment: SISO System
0 2 4 6 8 10 12 14 16280
Temperature
hrs0.6
Tighter temperatureregulation resulted in
22% increase in catalystlife
before tuning after tuning
310
300
290
02 4 6 8 10 12 14 16
0
0.2
0.4 Performance Index
hrs
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Flow control loop 2 (corroded valve)
500600700800900
1000110012001300
1015202530354045
Trend Plot of %LO-FC-0045.PV
Valu
e
Right Y Axis
Sample419 838 1257 1676 2095 2514 2933 3352 3771 4190 4609
%LO-FC-0045.PV LO-FC-0045.SP LO-FC-0045.OP
10 1000 2000 3000 4000 5000
-50
-40
-30
-20
-10
0
10
20
30
40
50
erro
rtime
error signal to controller
0 200 400 600 800 1000-50
-40
-30
-20
-10
0
10
20
30
40
50
mag
nitu
de o
f erro
r
no. of occurrence
Histogram of error signal
215 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
1170
1180
1190
1200
1210
1220
1230
1240
op
pv
3 0.00
0.05
0.10
PI(var) vs. Delay: %LO-FC-0045.PV
PI(v
ar)
Delay 1 2 3 4 5DelayPI(var) 0.012 0.036 0.063 0.092 0.125
4
0.0
0.5
1.0
0 5 10 15 20 25 30 35 40
Min DelayMax Delay
Auto Correlation - %LO-FC-0045.PV
ACF
Lag
ACF 95 % Confidence
5
0.0
0.5
1.0
1.5
2.0Impulse Response - %LO-FC-0045.PV
Impu
lse
Lag9 18 27 36 45 54 63 72 81 90 99
6
-10-505
101520253035
10-2 10-1
Closed-Loop vs. Min.Variance Output Response%LO-FC-0045.PV
Mag
nitu
de (d
B)
Normalized Frequency
Current Minimum Variance
7
f1
0.1
0.2
0.3
0.4
0.5
0.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
f2
Bicoherence estimated via the direct (FFT) method
89
10-2
10-1
1000
0.5
1
1.5
2
2.5
3
3.5
4 x 104
frequency, Hz
pow
er o
f the
sig
nal
Comments:pv – op shows distinct loops which are indicative of valve problemsPI plot along with ACF and IR show the time delay shows that theperformance is not satisfactory. IR plot indicates oscillations The bicoherence plot clearly indicates presence of significant nonlinearities
April data analysis
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Flow control loop 2: Corroded valve (cont’d)
July Data Analysis
0
500
1000
1500
0
10
20
30
40
50
60
Trend Plot of LO-FC-0045.PV
Valu
e
Right Y Axis
Sample756 1008 1260 1512 1764 2016 2268 2520 2772 3024 3276
LO-FC-0045.PV LO-FC-0045.SP LO-FC-0045.OP
1
0 1000 2000 3000 4000 5000-150
-100
-50
0
50
100
150
erro
rtime
error signal to controller
0 500 1000 1500-150
-100
-50
0
50
100
150
mag
nitu
de o
f erro
r
no. of occurence
Histogram of error signal
2
6 8 10 12 14 16 18 20 22 24 26400
500
600
700
800
900
1000
controller output, op
proc
ess
outp
ut, p
v
30.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9PI(var) vs. Delay: LO-FC-0045.PV
PI(v
ar)
Delay 1 2 3 4 5DelayPI(var) 0.222 0.485 0.667 0.791 0.879
4
0.0
0.5
1.0
0 5 10 15 20 25 30 35 40
Min DelayMax Delay
Auto Correlation - LO-FC-0045.PV
ACF
Lag
ACF 95 % Confidence
5
0.00.10.20.30.40.50.60.70.80.91.01.1
Impulse Response - LO-FC-0045.PV
Impu
lse
Lag4 8 12 16 20 24 28 32 36 40
6
-20-15-10-505
1015
10-2 10-1
Closed-Loop vs. Min.Variance Output ResponseLO-FC-0045.PV
Mag
nitu
de (d
B)
Normalized Frequency
Current Minimum Variance
7
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
f1
f2
Bicoherence estimated via the direct (FFT) method
89
10-2
10-1
1000
1
2
3
4
5
6
7
8 x 104
frequency, Hz
pow
er o
f the
sig
nal
Comments:Performance has been improved significantly (see the PI, ACF, and IR plots)pv – op plot indicates there may still be some nonlinearities in this loop.The bicoherence plots indicate that the nonlinearity has been decreased substantially.
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Turning data into knowledge: A New Paradigm
Information KnowledgeKnowledgeData
Process andPerformance Monitoring requiresturning rawdata into avalue addedresource
Develop virtual process variables that can give a proper insight into the workings of a process
scoresloadsmodelsperformance indicesothers
M
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Concluding Remarks
The real world is multivariate and NOTunivariate. So analyze data in a multivariate framework.Modeling, control, fault detection and diagnostics... etc. is possible via multivariate statistical analysis of process data. Process is monitored intelligently.Process monitoring in a predictive mode can avert serious plant upsets.
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Acknowledgments
NSERC, Matrikon Inc., ASRA and the University of AlbertaAT Plastics and Mitsubishi ChemicalsComputer Process Control Group@Ualberta