Report2009_Softsensor.dvi

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2 / 1 1 soft-sensor NIR Process Analytical Technology PAT NIR

3 / x m (m =1, 2,,M) 1 y M y = a m x m + e (1) m=1 x m, ȳ 0 x m y e a m N( M) X R N M, y R N a =[a 1,a 2,,a M ] T a = ( X T X ) 1 X T y (2) N

4 / 3 y, ŷ, x m M ŷ = a m x m = Xa (3) m=1 ŷ M x m M S y S e = y ŷ e ŷ y S ŷ e < ŷ, e >= a T (X T y X T Xa)=0 (4) e y ŷ θ cos θ = yt ŷ y ŷ = σ2 yŷ σ y σŷ = ρ yŷ (5) ρ yŷ y ŷ σyŷ 2 σ y,σŷ 2.2 a x m X T X/(N 1) x m a a e 2 + λ a 2 a = ( X T X + λi ) 1 X T y (6) λ PCAPCA

5 / 4 x m z r (r =1, 2,,R M) PCR 2.3 PCR Partial Least SquaresPLS [1] 2.4 Partial Least SquaresPLS PCR PLS ρ yŷ =cosθpcr/pca z r 2 PLS z r y < y, z r >= y z r cos θ r (7) z r cos θ r = ρ yzr PLS PCR PLS PLS PCR PLS

6 / PLS Chemistry Metrics Dynamic PLSDPLS DPLS PLS SSID [2] 2 TS-SSID1SSID 2 3SSID 3 [3] [4] T431/2 1 T431 T432 2 T431 2 Kano [5]

7 / 6 11 Purge T431 3 T Feed Product Ethylene 15, C351 Propylene compressor Ethane 1 T431/2 DPLS , 2, 3, 4, 5, , 7, 8, 9, 10, , 15, PPM

8 / 7 Ethane conc (A) (B) (C) Error Q T Time [hour] 2 Dynamic PLS 1 DPLS TS-SSID r RMSE D E D E DPLS TS-SSID TS-SSID 2 r (RMSE) DPLS TS-SSID 1 [3]TS-SSID 3.2 DPLS MSPC[6] MSPC

9 / 8 PCA/PLS SPC MSPC 2 T 2 Q PCA MSPC Hotelling s T 2 Q T 2 Q MSPC T 2 Q T 2 Q 3.3 Recursive PLSRPLS[7] RPLS x new y new [ ] [ ] X Y X new = x T, Y new = new ynew T (8) PLS [ ] [ ] P T Q T X new =, Y new = (9) x T new PLS [7]P R M R, Q R L R X, Y R y T new

10 / 9 (9) P Q β(0 <β 1) RPLS Lazy Learning Just-In- TimeJIT JIT [8,9,10,11]JIT [12] JIT JIT C-JIT[13] C-JIT RPLS JIT C-JIT [14]RPLS C-JIT 3 C-JIT 4

11 / 10 Aroma Conc.[%] Aroma Conc.[%] RMSE =1.33 r =0.67 LVs =2 RMSE =0.90 r =0.83 PCs =4 Estimation result by recursive PLS pressure change Measurement value Estimated value Day Estimation result by C-JIT modeling pressure change Day 3 PLS

12 / 11 [1],, :, (2008) [2] R.Amirthalingam and J.H.Lee : Subspace Identification Based Inferential Control Applied to a Continuous Pulp Digester, J. Proc. Cont., 9, 397/406 (1999) [3] M.Kano, S.Lee, and S.Hasebe : Two-Stage Subspace Identification for Softsensor Design and Disturbance Estimation, J. Proc. Cont., 19, 179/186 (2009) [4] 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, 37, 422/428 (2004) [5] M.Kano, K.Miyazaki, S.Hasebe, and I.Hashimoto : Inferential Control System of Distillation Compositions Using Dynamic Partial Least Squares Regression, J. Proc. Cont., 10, 157/166 (2000) [6] :, //, 48-5, 165/170 (2004) [7] S.J.Qin : Recursive PLS Algorithms for Adaptive Data Modeling, Comput. Chem. Engng, 22, 503/514 (1998) [8],, :,, 33-9, 947/954 (1997) [9], : Just-In-Time,, 37-7, 640/646 (2001) [10],,,,,, :,, (2004) [11],, : Just-In-Time,, 44-2, 116/119 (2005) [12],,,,,,, :,, 44-4, 325/332 (2008) [13],, : Just-In-Time,, 44-4, 317/324 (2008) [14] K.Fujiwara, M.Kano, S.Hasebe, and A.Takinami : Soft-Sensor Development using Correlation-Based Just-In-Time Modeling, AIChE J., accepted (2009)

report-MSPC.dvi

report-MSPC.dvi Multivariate Statistical Process Control 4 1 5 6 Copyright cfl4-5 by Manabu Kano. All rights reserved. 1 1 3 3.1 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :