Process Chemometric Techniques and Applications

1. Process Chemometric Techniques and Applications S. Joe Qin Department of Chemical Engineering The University of Texas at Austin Austin, Texas 78712 512-471-4417 Qin@che.utexas.edu www.che.utexas.edu/qinlab

2. Outline • Introduction to Process Monitoring • Overview of Subspace Approaches • Fault Detection Methods • Fault Identification Methods • Fault Reconstruction • A Few Process Applications • Summary and Future Issues © S. Joe Qin

3. Goals of Multivariate Quality Control (Jackson, 1991) Any multivariate quality control procedure, whether or not PCA is employed, should fulfill four conditions: • A single answer should be available to answer the question: “Is the process in control?” • An overall Type I error should be specified. • The procedure should take into account the relationships among the variables. • Procedures should be available to answer the question: “If the process is out-of-control, what is the problem?” The same goals apply to process monitoring equally well © S. Joe Qin

4. PT PrT tk tr T Tr PCA for Fault Detection • Data Decomposition: • Projection to the PC subspace (PCS): • Projection to residual subspace (RS): • Fault detection indices: xk = + X © S. Joe Qin

5. PCS RS PCS RS Subspace Projection • PCS: Principal Component Subspace • RS: Residual Subspace © S. Joe Qin

6. Example: -x1=x2=x3 plus noise © S. Joe Qin

7. Combined Indices • Raich and Cinar (1996) suggest the following combined statistic, where is a constant. • Yue and Qin (1998, 2001) propose a combined index for fault detection, where Notice that is symmetric and positive definite. © S. Joe Qin

8. PCA for Sensor Validation • If a sensor fails, it will break the correlation. This can be used to detection sensor faults without duplicating sensors. • The SPE (squared prediction error) will detect the fault that deviates from the normal subspace. x2 Abnormal x1 © S. Joe Qin

9. Fault models (1) Bias (2) Complete Failure time time (3) Drifting (4) Precision Degradation time time : fault free data : corrupted data © S. Joe Qin

10. Reconstruction by Optimization Minimize the distance to the PC model subspace • x slides parallel to the x3 axis • An optimal location x3 is found x3,3 PCS x3 x (x1, x2) © S. Joe Qin

11. xr Reconstruction along an Arbitrary Direction Minimize the distance to the PC model subspace • x slides in the fault direction (or subspace) • An optimal reconstruction is found by least squares PCS Control limit x* © S. Joe Qin

12. Fault Identification via Reconstruction • Use multivariate correlation to validate sensors • build a normal model from data • reconstruct along all possible directions • the actual fault direction, when reconstructed, achieves the minimum reconstructed SPE • estimate fault magnitude • distinguish from process faults • multiple sensor faults take place in a subspace and can be reconstructed similarly x3 fault PC replace x2 x1 © S. Joe Qin

13. Identifying the Fault • Identification via reconstruction • If a fault j causes SPE to go above its limit, the reconstructed SPE(xj) will correct the fault and be below its limit. • Define a Fault Reconstruction Index for sensor j as © S. Joe Qin

14. Contribution Plots • SPE contribution is the composition of SPE: • About contribution plots • Quick and dirty • Has a portion of fault is all variables • Can be misleading x3 fault 3 PC 1 2 replace x2 x1 © S. Joe Qin

15. Simulation Example: 4 variables and 2 PCs • The data generating equation is • Generate 100 data samples to build a PCA model • Generate additional 12 samples with a bias fault in sensor 3. © S. Joe Qin

16. Fault Identification Results © S. Joe Qin

17. Unit A Unit B Unit C FI FI FI FI F3 F4 F1 F2 F5 Process Fault: Reconstruction vs. Contribution Plots • Example: Three units in series and four flow sensors. • Five candidate faults: each sensor fault and a leak in Unit B • 20% measurement noise added to the sensors • Create a leak (constant flow) in Unit B while the main flow varies randomly. • Calculate reconstruction indices along five directions • Calculate contributions for each sensor © S. Joe Qin

18. Results: Reconstruction vs. Contribution Plots © S. Joe Qin

19. Multi-dimensional Faults • Process and sensor faults can be multi-dimensional: • simultaneous multiple faults • single faults that occupy more than one dimension • Fault representation: • Example: © S. Joe Qin

20. Fault Reconstruction and Identification • Fault identification: assume each fault occurs and reconstruct it. Calculate © S. Joe Qin

21. x RS PCS x* Obtain Process Fault Directions • Collect and categorize historical fault data • For data in each category fit faulty data through the PCA model and calculate the residuals • Apply SVD on the residual data to extract significant singular directions • These directions are used as fault directions for diagnosing future faults • Extraction of fault directions can be done in RS as well as PCS © S. Joe Qin

22. Polyester Film Process • Polyester film process monitoring at Dupont • Decentralized monitoring for large scale processes • Process is divided into several blocks. Multiblock PCA models are built and local and global detection and contributions are analyzed • Historical fault signature can be modeled as deviation from the normal subspace (PCS), using singular value decomposition • The singular directions can be used to match future faults (via reconstruction) © S. Joe Qin

23. Decentralized FDD: Polyester Film Process • Detect problems early; improve product quality • Avoid rework/recycle of off-spec materials • Prevent abnormal, emergency situations © S. Joe Qin

24. Using the SPE index the faulty blocks are again block 2 and block 3. The variables contributing to the out-of-control situation in block 2 are mainly variables 16 and 19. In block 3 mainly variables 25 and 28 are responsible for the out-of-control situation. Decentralized monitoring approach gives much clearer indication of the faulty variables. Contributions in Faulty Blocks © S. Joe Qin

25. Fault directions are extracted from the SPE until it is under the limit. Three fault directions are necessary to deflate the SPE under the threshold. In the whole PCA model it was necessary to extract 9 directions. Making the Mask: Fault Direction for Block 2 © S. Joe Qin

26. 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 clearer than using the whole PCA model. Fault Directions © S. Joe Qin

27. 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 occurred to the system Fault Identification: Applying Masks © S. Joe Qin

28. Refinery Process Monitoring • Toto studied FCC unit monitoring at UT Austin and then applied it to a RCC unit in Indonesia © S. Joe Qin

29. Fault Diagnosis Results © S. Joe Qin

30. Summary • Fault detection can be done in PCS, RS and the combined space, depending on the application • Contribution plots are often used for fault diagnosis, but cautions should be exercised. Magnitude and sign of the contribution need to be used appropriately for diagnosis • Reconstruction is a reliable approach for fault diagnosis • Contribution plots and reconstruction based approaches use knowledge and data in different ways; the reconstruction approach reduces to the contribution approach with a single sample • Faults are modeled as directions or subspaces, which can be uni-dimensional or multi-dimensional © S. Joe Qin

31. Comments and Further Issues • Are PCS and RS equally reliable for fault detection and reconstruction? • PCS: normal variability, large variance, insensitive to small faults, could be non-stationary • RS: mostly noise with small variance, sensitive to small faults, include parity equation residuals, can be easily stationary and close to normal distribution • Further Issues: • Multi-way applications • Multi-block analysis for hierarchical monitoring • Recursive approaches for adaptive monitoring • Dynamic process monitoring • Multi-scale approaches using wavelets • Other multivariate methods such as PLS © S. Joe Qin

32. Acknowledgments • Financial Support from • NSF CAREER • NSF GOALI • Texas Advanced Research Program • DuPont Young Professor Award • Texas-Wisconsin Modeling and Control Consortium (TWMCC) Members AMD, Air Products, ALCOA Foundation, Aspen Technology,     Boise Cascade, DuPont Educational Aid Program,     Fisher-Rosemount Systems, Mitsubishi Chemical, Monsanto, National Instruments, Pertamina Indonesia, Union Camp, Union Carbide, and     Weyerhaeuser © S. Joe Qin

33. Related papers from Qin’s Group • Sensor Validation and Inferential Sensors • Qin, S.J., H. Yue and R. Dunia (1997). Self-validating inferential sensors with application to air emission monitoring. I&EC Research, vol.36, pp.1675-1685. • Fault Detection, Reconstruction, and Identification • R. Dunia and Qin, S.J. (1998). Joint diagnosis of process and sensor faults using principal component analysis. Control Engineering Practice, vol. 6, no. 4, 457-469. • R. Dunia and Qin, S.J. (1998). A unified geometric approach to process and sensor fault identification and reconstruction: the unidimensional fault case. Computer and Chem. Eng., 22, 927-943. • R. Dunia and Qin, S.J. (1998). A subspace approach to multidimensional fault identification and reconstruction. AIChE J., 44(8), 1813-1831. • Yue, H. and S.J. Qin (2001). Reconstruction based fault identification using a combined index, I&EC Research, 40, 4403-4414. © S. Joe Qin

34. Related papers from Qin’s Group • Determining the Number of Principal Components • Qin, S.J and R. Dunia (2000). Determining the number of principal components for best reconstruction. J. of Process Control, 10, 245-250. • Valle-Cervantes, S., W. Li, and S.J. Qin (1999). Selection of the number of principal- components: A new criterion with comparison to existing methods. I&EC Research, 38, 4389-4401. • Multiblock Analysis • Qin, S.J., S. Valle, and M.J. Piovoso (2001). On unifying multi-block analysis with application to decentralized process monitoring. J. Chemometrics, 10, 715-742. • Multiway Analysis for Batch Monitoring • H. Yue, S.J. Qin, R. Markle, C. Nauert, and M. Gatto (2000). Fault detection of plasma etchers using optical emission spectra. IEEE Trans. on Semiconductor Manufacturing, 13, 374-385. © S. Joe Qin

35. Related papers from Qin’s Group • Recursive Approaches for Adaptive Monitoring • Qin, S.J. (1998). Recursive PLS algorithms for adaptive data modeling. Comput. and Chem. Eng., 22, 503-514. • Li, W., H. Yue, S. Valle-Cervantes, and Qin, S.J. (2000). Recursive PCA for adaptive process monitoring. J. of Process Control, 10, 471 -- 486. • Multiscale Monitoring • Misra, M., S.J. Qin, H. Yue and C. Ling (2002). Multivariate process monitoring and fault identification using multi-scale PCA, accepted by Comput. Chem. Engng. • Process Monitoring under Feedback Control • Nugroho, Toto and S.J. Qin (2001). Sensor validation under feedback control of MPC, Control Engineering Practice, 9, 877-888. © S. Joe Qin