Plant-wide Monitoring of Processes Under Closed-loop Control

1
Plant-wide Monitoring of Processes Under
Closed-loop Control

• Sergio Valle-Cervantes
• Dr. S. J. Qin Advisor
• Chemical Engineering Department
• University of Texas at Austin

2
Outline

• Introduction
• Objective
• Selection of the number of principal components
• Extracting fault subspaces for fault
  identification of a polyester film process
• Multi-block analysis with application to
  decentralized process monitoring
• Extension to the MBPCA analysis with fault
  directions and wavelets.
• Conclusions

3
Introduction

• Faults in industry
• Among others, bad products, insecure conditions,
  damage to the equipment.
• In summary, lost of millions of dollars just
  because faults are not detected and identified on
  time
• Just in the U.S.A. petrochemical industries an
  annual loss of 20 billions in 1995 has been
  estimated because of poor monitoring and control
  of such abnormal situations
• Actually
• Chemical process highly automated
• The quantity of data captured by the information
  system is amazing

4
Introduction

• What can we do?
• Use this huge quantity of data to monitoring,
  control and optimize the process
• Actually, the modern computer systems are able to
  analyze that information, something in the past
  was not possible
• Therefore, efficient methods to on time fault
  detection and identification has been one of the
  main targets in industry to the afore mentioned.

5
Objectives

• Obtain novel methods for process monitoring,
  fault detection and identification using PCA.
• Use PCA and PLS models to identify the main
  factors that affect the process
• Determine the number of principal factors
  necessary to describe the process but not noise.
• Provide industry with new ways to improve the
  process operations.
• Develop new monitoring tools to increase process
  efficiency, thereby reducing costs and
  off-specification products.
• Develop plant-wide monitoring strategy under
  closed-loop control, including sensor fault
  detection, loop performance monitoring and
  disturbance detection.

6
Selection of the number of PCs

• One of the main difficulties in PCA selection of
  the of PCs.
• Most of the methods use monotonically increasing
  or decreasing indices.
• The decision to choose the of PCs is very
  subjective.
• A method based on the variance of the
  reconstruction error to select the of PCs.
• The method demonstrates a minimum over the of
  PCs.
• Ten other methods are compared with the proposed
  method.
• Data sets incinerator, boiler, and a batch
  reactor simulation.

7
Fewer or more PCs?

• Key issue in PCA ? of PCs
• If fewer PCs than required
• A poor model will be obtained
• An incomplete representation of the process
• If more PCs than necessary
• The model will be overparameterized
• Noise will be included

8
Methods to choose the of PCs

• Two approaches to obtain the of PCs
• Knowledge of the measurement error
• Use of statistical and empirical methods
• Akaike information criterion (AIC)
• Minimum description length (MDL)
• Imbedded error function (IEF)
• Cumulative percent variance (CPV)
• Scree test on residual percent variance (RPV)
• Average eigenvalue (AE)
• Parallel analysis (PA)
• Autocorrelation (AC)
• Cross validation based in Rratio
• Variance of the reconstruction error (VRE)

9
PCA notation
10
AIC, MDL, and IEF

• AIC and MDL popular in signal processing.
• IEF in factor analysis.
• Common attributes
• Work only with covariance-based PCA
• Variance of measurement noise in each variable
  are assumed to be identical
• A minimum over the number of PCs.

11
Selection Criteria in Chemometrics

• CPV measure of the percent variance captured by
  the first l PCs.
• Scree test on RPV the method looks for a knee
  point in the RPV plotted against the number of
  PCs.

• AE accepts all eigenvalues above the average
  eigenvalue and rejects those below the average.
• PA two models, original and uncorrelated data
  matrix. All the values above the intersection
  represent the process information and the values
  under the intersection are considered noise.

12
Selection Criteria in Chemometrics

• Autocorrelation use an autocorrelation function
  to separate the nosy eigenvectors from the smooth
  ones.
• Cross validation based on the R ratio
• R lt 1 the new component improve the prediction,
  then the calculation proceeds.
• R gt 1 the new component does not improve the
  prediction then should be deleted.

• Cross validation based on PRESS
• Use PRESS alone to determine the number of PCs.
• A minimum in PRESS(l) corresponds to the best
  number of PCs to choose.

13
Variance of the Reconstruction Error

• Based on the best reconstruction of the variables
• VRE index has a minimum, corresponding to the
  best reconstruction
• VRE is decomposed in two subspaces
• The portion in PCS has a tendency to increase
  with the number of PCs.
• The portion in the RS has a tendency to decrease.
• Result a minimum in VRE.

14
Examples Batch Reactor

• Simulated batch reactor
• Isothermal batch reactor
• 4 first order reactions
• 2 of noise
• 200 samples, 5 variables
• Boiler
• 630 samples, 7 variables
• T, P, F, and C.
• Incinerator
• 900 samples, 20 variables.
• T, P, F, and C.

15
Boiler and Incineration Process
16
Comparison
17
Summary

• Most of the methods have monotonically decreasing
  or increasing indices
• The IEF, AC, AIC, and MDL worked well with the
  simulated example, but they failed with the real
  data.
• The most reliable methods are CPV, AE, PA,
  PRESS, and VRE.
• Considering the effectiveness, reliability, and
  objectiveness, the PRESS method, and correlation
  based VRE method are superior to the others.
• VRE is preferred to the PRESS method in the
  consistency of the estimate, computational cost,
  and ability to include a particular disturbance
  or fault direction in the selection.

18
Extracting Fault Subspaces for Fault
Identification

• As chemical processes becomes more complex
• Tightly control the process
• Detect disturbances before they affect the
  process quality
• Monitoring and diagnosis of chemical processes
• Asses process performance
• Improve process efficiency
• Improve product quality
• More sensors gt more data.
• How to analyze the data to obtain the best
  process knowledge

19
Extracting Fault Subspaces for Fault
Identification

• Extracting the information is not trivial
• Extremely important for chemical processes
• The analysis of sensor conditions
• Process performance
• Fault detection and identification are essential
  for a good monitoring system
• Statistical process control
• Based on control charts for certain quality
  variables
• Multivariate statistical process control
• Model process correlation, detect and classify
  faults, control product quality with long time
  delays, monitoring dynamic processes, and detect
  and identify upsets in multiple sensors.

20
Extracting Fault Subspaces for Fault
Identification

• Two indices used in PCA or PLS based monitoring
• Hotellings statistics T2 gives a measure of the
  variation within the PCA model.
• Squared prediction error (SPE) of the residuals
  indicates how much each sample deviates from the
  PCA model.
• Often insufficient to identify the cause of the
  upsets. Then to identify the cause of the upsets
• Contribution plots
• Sensor validity index

21
New Approach

• To extract process fault subspaces from
  historical process faults using SVD.
• Historical process data are first analyzed using
  PCA to isolate between normal and abnormal
  operations.
• Process knowledge, operational and maintenance
  records are incorporated to assist the isolation
  of abnormal operation periods.
• The abnormal operation data are used to extract
  the fault subspaces.
• The extracted fault subspaces are used to
  reconstruct new abnormal data that are detected
  by the fault detection step.
• If the new faulty data can be reconstructed by
  one of the extracted fault subspaces, fault
  identification is completed for the new faulty
  data.
• Otherwise, the new faulty data are from a
  different type of fault that has not been
  recorded in the historical data.
• A new fault subspace is then extracted from the
  data and is added to the fault data base for
  future fault identification.

22
Detection and Identification of Process Faults

• The purpose of fault detection and identification
  is to improve the safety and reliability of the
  automated system
• PCA

• Detection indices
• SPE
• Hotellings T2

23
Contribution Plots

• Monitoring and Diagnosis Based on SPE

• Monitoring and Diagnosis Based on T2

24
Fault Subspace Extraction
25
Polyester Film Process

• Different grades of products are processed in the
  same equipment.
• A typical fault sudden oscillation of some
  temperature loops which swings in 10 degrees,
  then stop after a while.
• Hundred of sensors used in the process, including
  temperature, thickness, tension, etc., with a
  gauge.
• Grade changes for different products are
  frequent, approximately once a day.
• Changes in set points are made more frequently,
  and if it is needed the operators change the set
  points manually.
• Currently
• SPE always exceeds limits contribution plots
  indicate multiple suspects and no limits
  multiple grades with only one model ? clusters
  for different grades.

26
Data Analysis clusters

• 308 variables
• Process variables
• Set points
• Output variables
• Monitoring variables
• Process and monitoring variables were used in
  this analysis, 103 variables.
• Four clusters
• Red cluster normal
• Blue, green, and black clusters faulty.

27
Data Analysis PCs

• Determining the number of PCs.
• Four methods
• Average eigenvalue
• Parallel analysis
• Cumulative percent variance
• Variance of the reconstruction error.
• Fifteen PCs were used to build the model.

28
Data Analysis Contribution Plots

• The variables that are contributing to the out of
  control situation in this window of 250 samples
  are, mainly variable 28 and in a minor proportion
  variables 25 and 32
• In particular for sample 71
• Highest contribution variable 28
• Smaller contribution variables 25, 32, and 93

29
Fault Direction Extraction

• The fault directions are modeled from abnormal
  data.
• These directions are used to identify the true
  type of faults.
• Subplot(5,2,1)
• Highest direction variable 28
• Subplot(5,2,2)
• Highest direction variable 25
• Subplot(5,2,3)
• 32, 30, 29, 28, and 25
• Subplot(5,2,4)
• 34 and 40

30
SPE deflation

• The fault directions are extracted from the
  faulty SPE until it is under the limit defined by
  the PCA model.
• Nine fault directions are necessary to deflate
  the SPE under the threshold.
• Observe how the first peek in the original SPE is
  deflated immediately after the first direction is
  extracted (second plot). And the residual peek in
  the second plot is deflated after subtracting the
  next direction (third plot).

31
Fault Identification

• First subplot
• The SPE for a window of 125 samples in the
  testing data.
• Second subplot
• The reconstructed SPE on the testing data after
  extracting the fault directions. The fault is
  partially identified.
• Third subplot
• The fault identification index shows a tendency
  to increase after sample 80, that is because no
  fault was identified there. The fault has been
  identified in the first part, between sample 20
  and 80.

32
Summary

• With the extraction of fault directions from
  historical data, it is possible to identify
  process faults for the out-of-control situation.
• These directions are signatures that
  characterize certain types of faults.
• It is viable to use them to identify similar
  faults in the future.
• This technique requires only historical faulty
  data to model the fault directions and normal
  data to build a PCA process model.
• In the case that a new type of faults is
  identified, the new fault subspace is extracted
  and stored for future fault identification.
• In this way the number of fault subspaces can
  grow as more faults are encountered.

33
Multi-block Analysis

• Large processes
• Hundred of variables (difficult to detect and
  identify faults)
• Divide the plant in sections or blocks
• Using multi-block algorithms localize the faulty
  section or block.
• Basic idea divide the descriptor variable (X)
  into several blocks in the PCA case, to obtain
  local information (block scores) and global
  information (super scores) simultaneously from
  data.
• Use the regular PCA to calculate block scores and
  loadings based on the scores.
• The use of multi-block analysis methods for
  process monitoring and diagnosis can be directly
  obtained from regrouping contributions of regular
  PCA model.

34
Regular Algorithms

• Regular PCA algorithm

• Regular PLS algorithm

35
CPCA and MBPCA

• CPCA algorithm based on PCA scores

• MBPCA algorithm based on PCA loadings

36
Monitoring and Diagnosis

• Based on SPE

• Based on T2

No fault
No fault
37
Standard MSPC monitoring

• A standard PCA model is applied to all the
  variables.
• Identification of the out-of-control situation
  variables is difficult.
• SPE and T2 do not agree in all the variables.
• Contribution plots does not have a confidence
  limit.

38
SPE for each block

• Process data is divided in 7 blocks.
• Faulty block is located applying decentralized
  monitoring.
• Block 2 is where the main fault is located.

39
Identification of Faulty Blocks Using SPE

• In block 2 is identified the largest
  contribution.
• Variables 28 and 25 are mainly responsible for
  the out-of-control situation using contribution
  plots.
• Identification of the variables is clearer with
  CPCA than with standard MSPC monitoring.

40
Identification of Faulty Blocks Using T2

• T2 also shows that the main fault is located in
  the second block.
• Again variables 28 and 25 are identified.
• The decentralized monitoring approach gives a
  much clearer indication of the faulty variables.

41
Block SPE Index

• The SPE index is shown for all blocks along
  samples of data.
• Any significant departure from the horizontal
  plane is an indication of a fault.

42
Summary

• The use of multi-block PCA and PLS for
  decentralized monitoring and diagnosis is derived
  in terms of regular PCA and PLS scores and
  residuals.
• The decentralized monitoring method based on
  proper variable blocking is successfully applied
  to an industrial polyester film process.
• Using the subspace extraction method and
  decentralized monitoring PCA method, it is shown
  that the identification of the fault is clearer
  than using a whole PCA model.
• What we need is only good faulty data to extract
  the signature of the fault.
• Future task is use recursive PCA, or recursive
  PLS for adaptive decentralized monitoring.
• Develop fault identification index to uniquely
  identify the root cause of a fault instead of
  contribution plots.
• Integrate multi-scale monitoring approach in the
  decentralized monitoring approach for
  partitioning the data, to provide flexible
  partition and interpretation of information
  contained in the process data.

43
Multi-Block PCA and FII

• Instead of extracting the fault directions using
  one PCA model for the whole plant, now extract
  the directions only in the faulty block.
• The information required to identify a new fault
  is less than using the whole PCA model.

44
Fault Direction Extraction Block 2

• Fault directions are extracted from the SPE until
  it is under the limit defined by
• Three fault directions are necessary to deflate
  the SPE under the threshold. In the whole PCA
  model it was necessary to extract 9 directions.

45
Fault Directions

• Directions that will be used to identify the true
  faults in a new data set.
• Clearly it is shown that variables 19 and 16 are
  the variables mainly responsible for the
  out-of-control situation.
• The projections here are more clear that using
  the whole PCA model.

46
Fault Identification

• First subplot
• The SPE for 125 samples for the testing data is
  shown.
• Second subplot
• The reconstructed SPE on the testing data after
  extracting the fault directions, identifies the
  fault.
• Third subplot
• The fault identification index value goes to zero
  from sample 20 to sample 90, then the fault is
  identified. After sample 100 a new fault arrives
  to the system

47
Conclusions and Future Work

• The merging of MBPCA and the directions
  extraction has bettered the identification of the
  fault.
• Less quantity of information to needed to
  identify new faults.
• Integrate in this new approach the multi-scale
  monitoring approach for partitioning the data, to
  provide flexible partition and interpretation of
  information contained in the process data.
• Use dynamic PCA modeling to extract the full
  process model and capture the true
  characteristics of the process.

48
Related Publications

• S. Valle, W. Li, and S. J. Qin, Selection of the
  Number of Principal Components the Variance of
  the Reconstruction Error Criterion with a
  Comparison to Other Methods. Ind. Eng. Chem.
  Res., 38, 4389-4401 (1999)
• W. Li, H. Yue, S. Valle, and S. J. Qin,
  Recursive PCA for Adaptive Process Monitoring,
  J. of Process Control., 10 (5), 471-486 (2000)
• S. Valle,S. J. Qin, and M. Piovoso, Extracting
  Fault Subspaces for Fault Identification of a
  Polyester Film Process. Submitted to ACC-2001
• S. J. Qin, S. Valle, and M. Piovoso, On Unifying
  Multi-block Analysis with Application to
  Decentralized Process Monitoring. Accepted by
  J. Chemometrics

49
Acknowledgements

• National Science Foundation (CTS-9814340)
• Texas Higher Education Coordinating Board
• DuPont through a DuPont Young Professor Grant
• Consejo Nacional de Ciencia y Tecnología
  (CONACyT)
• Instituto Tecnológico de Durango (ITD)
• The authors are grateful to Mr. Mike Bachmann and
  Mr. Nori Mandokoro at DuPont plant in Richmond,
  Virginia for providing the data and process
  knowledge for this project