Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007, pp. 32-38 }- l mk om m s n oh k ÇmyqÇ Ç mk*çlm n 151-742 ne k e 56-1 * n 139-701 ne o o 447-1 (2006 11o 17p r, 2006 12o 13p }ˆ) Fault Detection & SPC of Batch Process using Multi-way Regression Method Kyoung Sup Woo, Chang Jun Lee, Kyoung Hoon Han, Jae Wook Ko* and En Sup Yoon School of Chemical & Biological Engineering Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-742, Korea *Department of Chemical Engineering Kwangwoon University, 447-1, Wolgye-dong, Nowon-gu, Seoul 139-701, Korea (Received 17 November 2006; accepted 13 December 2006) k rp r rl p e rl rn l, p rp e rp p, d rp ˆ v p edšp k. rp e rp p ~ e r e dˆp - ˆ l rp p pn l r m rp ˆ p l p p mp, p p (output) pn r r rl, e l rp p p p Ž k. e rp (multi-way) p p p (unfolding) rp ~p, p Support Vector Regression Partial Least Square p p pn m. l l (variable contribution chart) pn p p, ˆ p p l p l kp, p p o er k p p op v v p n p p p p pl. h Abstract A batch Process has a multi-way data structure that consists of batch-time-variable axis, so the statistical modeling of a batch process is a difficult and challenging issue to the process engineers. In this study, We applied a statistical process control technique to the general batch process data. and implemented a fault-detection and Statistical process control system that was able to detect, identify and diagnose the fault. Semiconductor etch process and semi-batch styrene-butadiene rubber process data are used to case study. Before the modeling, we pre-processed the data using the multi-way unfolding technique to decompose the data structure. Multivariate regression techniques like support vector regression and partial least squares were used to identify the relation between the process variables and process condition. Finally, we constructed the root mean squared error chart and variable contribution chart to diagnose the faults. Key words: Batch Process, Fault Detection, Statistical Process Control, Multi-way Unfolding, Support Vector Regression, Partial Least Squares 1. ƒ p rl ee p p p l p l p p pn rp r (multivariate statistical process control)p p p. rp r p sp rl l To whom correspondence should be addressed. E-mail: esyoon@pslab.snu.ac.kr rp q modeling rp v k rp p p d rp ˆ kk p rl prp v p. vr r p vp, r p v v pv k, l p ˆ ~rp Žk rp p o kk p. p r r rl l rp p p tl on r }k (robustness) (sensitivity)p e dšp p tn l, pl p l 32
- p pn e rp p v r rl 33 p lv p. e rp lp rk,, ~ l p l kl n rtp p. e rp t p r p p rp p n l rp p p s l r p vp p rl p rp n pp v l rrp m p. e rp p p rp r p } p (nonlinearity)p v p, e (two-way) p p lv l p r(continuous process) Batch e (tree-way) p p lv p p, batch sl e sl p Process drift batch-to-batch variation p r p sq [1]. l l rp r p Batch rl rn l, p rp e rp p, d rp ˆ p edšp k. (multi-way unfolding) p pn p r} (pre-processing) M-PLS(multiway-partial least square) M-SVR(multiwaysupport vector regression) p pn l rp p m r p ˆ p l kk p p mp, p pn rl (control chart) l e l e rp ˆ v, p p o Ž p edšp m. pm p p ~ e r(semiconductor etch process) dˆp - ˆ l (styrene-butadiene rubber) r p l rn l kp, rp rp p p v, n p p p p pl. 2. 2-1. m nz (preprocessing) e rp p p l r p m 3 p p. p l rp e p s batch sq p. p rp e rp p batch(i) (J) e (K) p 3 s(3-way structure) v. k batchp e p pr v k, batchl s j sensor shift process drift pl l rp p l n rp. pm p po l p p r} rp rp l rp rp p. vp p r} r p p, v batch p o p, w 3 p 2 p p meˆ p. v p p p p t m p p o d p rp ~. sensor shift process drift rl ql n p p t t (EWMA)[4] p pn pp l l e p v kp batch p pn mp rn v kk. ~ w batch p p n Fig. 1 p p p batch tp p p k p p ~ p n m, p n batch e p p r~ batch pl e pp r q l d pn Fig. 1. Preprocessing for the proposed modeling when batch lengths are different. Fig. 2. Two unfolding methods. p. p l Dynamic time wrapping[3]p Pseudo batch [8] k p n p. w 3 p p 2 p p meˆ o Multiway-unfolding p n m. Multiway-unfolding p e rp 3 p (I J K) tl p p l 2 p p meˆ p pƒ, l p l Batch-wise unfolding(i JK) Variable-wise unfolding(ik J)p p (Fig. 2). Batch-wise unfolding p p Batch ˆ ~rp Žk l o l, e l batch p ˆ m p l r l Variable-wise unfolding p n m. v p p l pl p v m p o Column auto-scaling p n l, p tr (standard normal distribution) p m. 2-2. r} p pn p Partial Least Square(PLS)m Support Vector Regression(SVR) p n m. p pn po rp p (op)m rp ˆ( ) p p Žk, rp p p rp Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007
34 n Ëp}tË Ë qnëop p p v p p o p. PLS p rp op pp p p op p n Žk l, l q m p p p p nk p. m l op X(m nx : m =, nx = op p )m Y(m ny : ny = p ) pp op p n t k, p n u k. t k m u k vector vector p p p ˆ. np< nx T T X= t k p k + E and Y= u k q k + F k = 1 np< nx k = 1 (1) Em F errorp p k m q k loading vectorp. p t k m u k vector l p, p n PLS, p n PLS. l l 2 e p pn (quadratic PLS)p m. SVR p AT&T Bell l p Vapnik(1992)l p Support Vector Machine k vl p, l p n p p p pv l [6]. rp kp l p X o p eˆ nonlinear mapping Φp l l p p, e (2)m p o l marginp (hyperplane)p } p. I y= w i Φ i + b marginp r, Risk r p, pl Risk (3) N min R(C) = C 1 (3) N --- L d 1 ε ( i, y i ) + --w 2 2 rk s l r Karush-Kuhn-Tucker(KKT) s l r (optimal seperating hyperplane)p }. Φ i (x) er ~rp ˆ k nlp p p rp ƒ (kernel function) n. Kx ( j, x j ) = Φ i x i ( ) T Φ i ( x j ) l l 2nd-order polynomial kernel ε-insensitive loss functionp n SV-Regressionp m. 2-3. p n y rp ˆ r p vp ˆ. v (quality variable). v p r p p v llv, ee p llv l n n p l, ee l pn l n. e l y o45 o1 2007 2k (2) (4) Fig. 3. Creating dummy ygvariable. Fig. 4. Creating output control chart. (dummy y variable) l p. [2, 5, 8] l l Fig. 3 p rp e (local batch time)p y l pn m. r r rp Batch t p v p pn Batch datam y p p p, Fig. 4 } dl pn r rp batch p (output) p rl m, dl n v kp r rp batch p p pn p r p v (cross-validation) p p p Ž k. p rl (control limit) qp p k r p v p p Ž p, p p p v r p Ž p l p rp rl l pn 3σ rl r m. p p p p rl l l l v Root mean square error(rmse) chart l p p p k. Error e (5)m p p p p r p p p p rl p l m. k ( ŷ i µ i ) 2 RMSE = ------------------------------ (5) 3σ i, r p mp p e (6) p l l (contribution) l l p p p m v k. n ( X i X i ) Contrib. = --------------------------- (6) n
3. i 3-1. z o(semiconductor etch process) ~ rp e r(etch)p p p lv, e rp p wafer pp v l e rp p. l l l rp pn Lam 9600 plasma etch toolp lp Al-stack etch rp machine p n m. p rp BCl 3 /Cl 2 plasma n l TiN/Al~0.5Í Cu/TiN/oxide stackp e rp, Al layer p pm p p tn. rp 6 v, ~ m w p (chamber) l d t, k p kr eˆ rp, w v (plasma) r, w Al p main etch, w k p TiN, oxide layerp overetch, l w p n (vent) v. p p p e p v 3 p e p llv 127 batch l pp, 20 p o p batch(induced-faults) p (Table 1). batch e p 1 p r 80 p time stepp, r 12 p lr p (127 12 80)(Table 2). 3-2. m - i o(sbr) l r t (emulsion polymerization)l p dˆp ˆ l (styrene-butadiene rubber) rp 1930 pl Buna-S p p k vp q v rp q p pn q rp p. l r t pp o (mild) r s l rp l r rll o, t (bulk polymerization)l r (viscosity) p r p. - p pn e rp p v r rl 35 Table 4. 5-quality variables 1 Composition 4 Cross Link 2 Particle Size 5 Polydispersion 3 Branching l l rn p semi-batch l r t rp, 53 p batch l pp, Table 3 p batch r 9 200 time point k p l p (53 9 200)., Table 4m p 53 batchp r r 5 p v (quality variables, 53 5) r p vp m p. 4. 4-1. z o r 34, p 9 j 43 p batch Exp 29 p pn p. n r batch t 17 p batch v SVRp pn dp v m, d p p rl (statistical control chart)l v 17 p r batch p m 9 p p p e k. Fig. 5m p r rp batchp p rl (control limit) l v k l, p p p batch p rl l p l p p pl, p p e p p pl. pp 9 p p l rl l l r (RMSE) Fig. 6. Table 1. 3-experiment batch data set Normal Fault Total Exp29 34 9 43 Exp31 36 5 41 Exp33 37 6 43 Total 107 20 107 Table 2. 12-measured variables 1 Endpoint A Detector 7 RF Impedance 2 Chamber Pressure 8 TCP Tuner 3 RF Tuner 9 TCP Phase Error 4 RF Load 10 TCP Reflected Power 5 RF Phase Error 11 TCP Load 6 RF Power 12 Vat Valve Table 3. 9-measured variables 1 Feed Styrene 6 T R. Jackt. 2 Feed Butadiene 7 Latex Density 3 Temp. Feed 8 Conversion 4 Temp. Reactor 9 Energy Rel 5 Temp. Cooling Fig. 5. Regression model output of Noramal data (a), Fault data (b). Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007
36 n Ëp}tË Ë qnëop Fig. 6. Root mean square error chart for all fault batches. Fig. 7. Variable contribution chart for all batches. o45 o1 2007 2k
- p pn e rp p v r rl 37 Fig. 8. Quality variable chart for all batches. Fig. 10. Regression model output for Normal batches(a), Fault 1(b), Fault 2(c). Fig. 9. Quality variable for batch 34(a), batch 37(b). Fig. 6 p p p p s l o e (intensity) v p p pl. p p p pl n batch p p p o s Ž p. pp p p l l Fig. 7. l batchl TCP + 50p p p p n, p p Fig. 6(a) } l k j rl 40 p rl l ˆ p, opp Fig. 7(a)l } 1, 4, 8, 11 p r p p p. Exp31(41batches, 5faults)m, Exp33(43batches, 6faults) e l p rn l v 11 v s p p p r e lp, p p l opp p l. 4-2. SBR o SBR rp p 5 p v (quality variable) v p rl ~ e r p m p. p v p batch rp r p v p 1 timep r p v l, n Fig. 8 p 53 batchp v p auto-scaling control chart l rl (LCL) l 2 p batch }k ppp p batch r m. ppp p batch 34m 37p scaling v p Fig. 9m. r p 51 t 27 PLS p pn l p v 24 r batchm 2 p p batchl rn k. Fig. 10l p m p r rp batch p p p rl mlp l v k l, Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007
38 n Ëp}tË Ë qnëop Fig. 11. RMSE Chart for Batch 34(a), Batch 37(b). SBR rl l rp p l k p vp p ( v r )p rk v ppp v mp, p v l, ee p r l nl rp op (cause variable) p r p p p p p m r l p p p. 5. l l n - p ~ e r Semi-batch SBR r l rn k. k p p rl, p p PC l n T 2 SPE(squared prediction error) }, RMSE, l pn p p p e, opp p m. l rk - p batch rp p v l n p p p k pl. rk p e l rp ˆ p v p l, ee l pn p rl p p. y Fig. 12. Contribution Chart for Batch34(a), Batch37(b). r p vl p p p batch 34m batch 37p p r l l p p p. p p l Error chartm contribution chart p p p Fig. 11 kp, p p op p Fig. 12m k. o45 o1 2007 2k 1. Nomikos, P. and MacGregor, J. F., Monitoring Batch Processes Using Multiway Principal Component Analysis, AIChE J., 40(8), 1361-1375(1994). 2. Wold, S., Kettaneh, N., Friden, H. and Holmberg, A., Modeling and Diagnostics of Batch Processes and Analogous Kinetic Experiments, Chemometrics Intell. Lab. Syst., 44(1), 331-340(1998). 3. Kassidas, A., Macgregor, J. F. and Taylor, P. A., Synchronization of Batch Trejectories Using Dynamic time Warping, AIChE J., 44(4), 864-875(1998). 4. Wise, B. M., Gallagher, N. B., Butler, S. W., White, Jr. D. D. and Barna, G. G., A Comparison of Principal Components Analysis, Multi-way Principal Components Analysis, Tri-linear Decomposition and Parallel Factor Analysis for Fault Detection in a Semiconductor Etch Process, J. Chemometrics., 13(3-4), 379-396(1999). 5. Theodora Kourti, Abnormal Situation Detection, Three-way Data and Projection Method; Robust Data Archiving and Modeling for Industrial Applications, Annual Rewiew in Control., 27(2), 131-139(2003). 6. Smola, A. J., Schölkopf, B., A Tutorial on Support Vector Regression, Statistics and Computing., 14(3), 199-222(2004). 7. Lee, J. M., Yoo, C. K. and Lee, I. B., Enhanced Process Monitoring of Fed Batch Penicillin Cultivation Using Time-varying and Multivariate Statistical Analysis, J. Biotechnology., 110(2), 119-136(2004). 8. Simoglou, A., Georgieva, P., Martin, E. B., Morris, A. J. and Feyo de Azevedo, S., On-line Monitoring of a Sugar Crystallization Process, Comp. Chem. Eng., 29(6), 1411-1422(2005). 9. Marjanovic, O., Lennox, B., Sandoz, D., Smith, K. and Crofts, M., Real-time Monitoring of an Industrial Batch Process, Comp. Chem. Eng., 30(10-12), 1476-1481(2006).