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3 1 Statistical Process Control; SPC W.A. Schewhart 3ff μ ff μ ± 3ff.7% Univariate SPC; USPC.7% 1 Fig. 1(a) USPC Multivariate SPC; MSPC Principal Component Analysis; PCA MSPC Chemometrics Chemistry Metrics [1] MSPC PCA 3

4 USPC MSPC (a) USPC MSPC (b) PCA Fig. 1 (c) T (d) PCA-MSPC.1 PCA PCA Fig. 1(b) PCA 1 1 PCA PCA X < N P P N X X = USV T = h U R U i" S R S #h V R V i T (1) U V S s r R r Loading Matrix V R r v r r t r t r = Xv r = s r u r : () u r U R r R T R = XV R = U R S R : (3) 4

5 ± T 1 N 1 T T R T R = 1 N 1 S R (4) P R R P ^X = T R V T R = XV R V T R (5) ^X E = X ^X = X(I V R V T R) (6). PCA Fig. 1(b) Hotelling's T T = RX r=1 t r ff t r (7) ff tr r t r T T Fig. 1(c) T PCA Hotelling's T SPC Jackson[] PCA T PCA [3, 4] Fig. 1(d) T Q Q = PX p=1 (x p ^x p ) (8) Q Squared Prediction Error; SPE PCA T Q PCA-MSPC Hotelling's T PCA 5

6 T T Q T T Q Q T T Q PCA-MSPC 199 [5] USPC MSPC.3 T Q Contribution Plot Q p Q C [Q] p = (x p ^x p ) (9) T T p T C [T ] p = t± 1 T x pv p (1) [6] t v p p p [7] [8] PCA T Q T Q 6

7 [9] 3 MSPC 3.1 PCA PCA Principal Component Regression; PCR Partial Least Squares; PLS PLS Projection to Latent Structures Latent Variables [1] PLS PCR PLS PCR PLS PCR PCA-MSPC PLS-MSPC [5, 11] PLS PLS-MSPC PLS PLS-MSPC [1] 3. PCA PCA [13] t x(t) = h x 1 (t) x (t) ::: x p (t) PCA x D (t) = h x(t) x(t 1) ::: x(t s +1) Dynamic PCA PLS [14] i i (11) (1) 7

8 [15] PCA Multiscale PCA MSPC [16] 3.3 PCA-MSPC PCA/PLS Multiway PCA/PLS [17] PCA [18] [19] [] 3.4 SPC External Analysis [1] SPC SPC PCA-MSPC [] 3.5 MSPC PCA PCA-MSPC 8

9 s 1 x 1 z 1 y s x z y s x z y s 1 x 1 z 1 y 1 Fig. x z y x 1 - z 1 - y 1 Fig. 3 USPC PCA-MSPC ICA-MSPC Fig. Independent Component Analysis; ICA [3] ICA Fig. ICA Fast ICA[4] ICA Fig. 3 [5] ICA-MSPC 4 MSPC MSPC [6] [7] Statistical Quality Control; SQC MSPC PLS PLS [8] [1] B. M. Wise and N. B. Gallagher: The process chemometrics approach to process monitoring and fault detection; J. Proc. Cont., Vol. 6, pp (1996) 9

10 [] J. E. Jackson: Quality Control Methods for Several Related Variables; Technometrics, Vol. 1, pp (1959) [3] J. E. Jackson and G. S. Mudholkar: Control Procedures for Residuals Associated with Principal Component Analysis; Technometrics, Vol. 1, pp (1979) [4] J. E. Jackson: Principal Components and Factor Analysis: Part I Principal Components; J. of Quality Technology, Vol. 1, pp.1 13 (198) [5] J. V. Kresta, J. F. MacGregor, and T. E. Marlin: Multivariate Statistical Monitoring of Process Operating Performance; Can. J. Chem. Eng., Vol. 69, pp.35 47(1991) [6] P. Nomikos: Detection and Diagnosis of Abnormal Batch Operations Based on Multi-way Principal Component Analysis; ISA Trans., Vol. 35, pp (1996) [7] J. A. Westerhuis, S. P. Gurden, and A. K. Smilde: Generalized Contribution Plots in Multivariate Statistical Process Monitoring; Chemometrics and Intelligent Laboratory Systems, Vol. 51, pp () [8] A. Raich and A. Cinar: Statistical Process Monitoring and Disturbance Diagnosis in Multivariable Continuous Processes; AIChE J., Vol. 4, pp (1996) [9] M. Kano, S. Hasebe, I. Hashimoto, and H. Ohno: Statistical Process Monitoring Based on Dissimilarity of Process Data; AIChE J., Vol. 48, pp () [1] W. G. Glen, W. J. Dun III, and D. R. Scott: Principal Component Analysis and Partial Least Squares; Tetrahedron Computer Methodology, Vol., pp (1989) [11] J. F. MacGregor, C. Jaeckle, C. Kiparissides, and M. Koutoudi: Process Monitoring and Diagnosis by Multiblock Methods; AIChE J., Vol. 4, pp (1994) [1] H. Kamohara, A. Takinami, M. Takeda, M. Kano, S. Hasebe, and I. Hashimoto: Product Quality Estimation and Operating Condition Monitoring for Industrial Ethylene Fractionator; J. Chem. Eng. Japan (accepted) [13] W. Ku, R. H. Storer, and C. Georgakis: Disturbance Detection and Isolation by Dynamic Principal Component Analysis; Chemometrics and Intelligent Laboratory Systems, Vol. 3, pp (1995) [14] M. Kano, K. Miyazaki, S. Hasebe, and I. Hashimoto: Inferential Control System of Distillation Compositions Using Dynamic Partial Least Squares Regression; J. Proc. Cont., Vol. 1, pp () [15] B. R. Bakshi: Multiscale PCA with Application to Multivariate Statistical Process Monitoring. AIChE J., Vol. 44, pp (1998) [16] M. Kano, K. Nagao, H. Ohno, S. Hasebe, I. Hashimoto, R. Strauss, and B. R. Bakshi: Comparison of Multivariate Statistical Process Monitoring Methods with Applications to the Eastman Challenge Problem; Comput. Chem. Engng, Vol. 6, pp () [17] S. Wold, P. Geladi, K. Esbesen, and J. Ohman: Multi-way Principal Components- and PLS-Analysis; J. Chemometrics, Vol. 1, pp (1987) 1

11 [18] P. Nomikos and J. F. MacGregor: Monitoring Batch Processes Using Multiway Principal Component Analysis; AIChE J., Vol. 4, pp (1994) [19] P. Nomikos and J. F. MacGregor: Multivariate SPC Charts for Monitoring Batch Processes. Technometrics, Vol. 37, pp (1995) [] B. M. Wise, N. B. Gallagher, S. W. Butler, D. D. White Jr., and G. G. Barna: A comparison of principal component analysis, multiway principal component analysis, trilinear decomposition and parallel factor analysis for fault detection in a semiconductor etch process; J. Chemometrics, Vol. 13, pp (1999) [1],,, : ;, Vol. 38, pp () [] T. Yamamoto, A. Shimameguri, M. Ogawa, M. Kano, and I. Hashimoto: Application of Statistical Process Monitoring with External Analysis to an Industrial Monomer Plant; IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM) (4) [3] C. Jutten and J. Herault: Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetic Architecture; Signal Processing, Vol. 4, pp.1 1 (1991) [4] A. Hyvarinen and E. Oja: A Fast Fixed-Point Algorithm for Independent Component Analysis; Neural Computation, Vol. 9, pp (1997) [5] M. Kano, S. Tanaka, S. Hasebe, I. Hashimoto, and H. Ohno: Monitoring Independent Components for Fault Detection; AIChE J., Vol. 49, pp (3) [6] T. Kourti and J. F. MacGregor: Process Analysis, Monitoring and Diagnosis, Using Multivariate Projection Methods; Chemometrics and Intelligent Laboratory Systems, Vol. 8, pp.3 1 (1995) [7] L. H. Chiang, E. L. Russell, and R. D. Braatz: Fault Detection and Diagnosis in Industrial Systems; Springer (1) [8] : ; (1995) 11

Report2009_Softsensor.dvi

Report2009_Softsensor.dvi / http://www-pse.cheme.kyoto-u.ac.jp/ kano/ 2009 03 Copyright c 2009 Manabu Kano. All rights reserved. / 1 1 soft-sensor NIR Process Analytical Technology PAT NIR / 2 2 2.1 x m (m =1, 2,,M) 1 y M y = a