(341p) Modeling and Monitoring with Dynamic Weighted Partial Least Squares

In the past decades, supervised modeling and monitoring have achieved great success in modern industries to increase the safety and efficiency and reduce the operation cost ^[1-4]. The collected data in these processes are massive, high dimensional and highly correlated due to the complexity of physical conditions and process operations, leading to ill performance of traditional regression methods. To extract valuable information from the high-dimensional and correlated data effectively, multivariate statistical methods such as partial least squares (PLS) and canonical correlation analysis (CCA) are widely employed ^[5-7]. Among them, PLS is an efficient latent variable algorithm to extract cross-correlations between process variables (X) and quality variables (Y) ^[8-10]. Two sub-models are included in PLS: firstly, the loading vectors for X and Y are calculated in the outer model to maximize the covariance of latent variables, and a linear inner model is then developed between process scores and quality scores. Deflation is also performed to remove the effect of extracted latent variables from the original data X and Y.

An implicit assumption of PLS is that the relation between process and quality variables is static. However, it is not applicable for most industrial processes where dynamics are involved, and the dynamic covariance cannot be exploited fully and accurately by PLS. Thus, dynamic variants of PLS are proposed to deal with dynamic systems. Qin and McAvoy ^[11] modeled the dynamics by applying PLS on the data matrix including lagged values of both process and quality variables, which leads to a substantial increase in the dimension of X. Kaspar and Ray ^[12] designed filters to eliminate the dynamic components in X, and built a static model between filtered X and Y, where no lagged variables appear in the outer relations. Instead of using a static inner model, Lakshminarayanan et al. ^[13] proposed a dynamic inner model with time series models such as auto-regressive models with exogeneous variables. Li et al. ^[14] put forward a dynamic PLS by using a weighted vector to combine lagged process data, and an explicit dynamic outer model was developed between quality data and weighted process data. All of these methods modified the inner or outer relation only and paid no attention to the consistency of dynamic inner and outer relations. Recently, Dong and Qin ^[15] developed an improved dynamic PLS (DiPLS), where dynamics are incorporated in both inner and outer models.

Due to the high sampling rates in industrial processes, redundant and collinear information may be involved in successive sampled data, and modeling and monitoring with these data directly may result in sub-optimal performance. In this work, inspired by the work of dynamic weighted CCA (DWCCA) ^[16], a dynamic weighted PLS (DWPLS) method and its monitoring scheme are proposed to deal with the redundant information in neighboring samples. DWPLS reduces the dependency in adjacent samples by designing a series of basis functions such as polynomial and Gaussian bases. In the inner model, the quality scores are represented by a lagged vector auto-regressive model, which is constructed by a weighted combination of basis functions. In order to be consistent with the dynamic inner model, the outer model is to maximize the covariance between the quality latent scores and a weighted representation of lagged process scores. A dynamic monitoring scheme is also designed for DWPLS, where the prediction error of the quality scores are monitored for anomalies in the dynamic relations and the process scores are for faults about the static relations. The effectiveness of DWPLS over DiPLS is demonstrated through the Tennessee Eastman process (TEP) in terms of prediction and monitoring performance.

References

[1] Ge, Z., 2017. Review on data-driven modeling and monitoring for plant-wide industrial processes. Chemometrics and Intelligent Laboratory Systems, 171, pp.16-25.

[2] Shang, C., Yang, F., Huang, D. and Lyu, W., 2014. Data-driven soft sensor development based on deep learning technique. Journal of Process Control, 24(3), pp.223-233.

[3] Qin, Y. and Zhao, C., 2019. Comprehensive process decomposition for closed-loop process monitoring with quality-relevant slow feature analysis. Journal of Process Control, 77, pp.141-154.

[4] Zhu, Q. and Qin, S.J., 2019. Supervised diagnosis of quality and process faults with canonical correlation analysis. Industrial & Engineering Chemistry Research, 58(26), pp.11213-11223.

[5] Wise, B.M. and Gallagher, N.B., 1996. The process chemometrics approach to process monitoring and fault detection. Journal of Process Control, 6(6), pp.329-348.

[6] Qin, S.J., 2012. Survey on data-driven industrial process monitoring and diagnosis. Annual reviews in control, 36(2), pp.220-234.

[7] Zhu, Q., Liu, Q. and Qin, S.J., 2017. Concurrent quality and process monitoring with canonical correlation analysis. Journal of Process Control, 60, pp.95-103.

[8] Wold, H., 1975. Soft modelling by latent variables: the non-linear iterative partial least squares (NIPALS) approach. Journal of Applied Probability, 12(S1), pp.117-142.

[9] Dayal, B.S. and MacGregor, J.F., 1997. Recursive exponentially weighted PLS and its applications to adaptive control and prediction. Journal of Process Control, 7(3), pp.169-179.

[10] Pan, Y.C., Qin, S.J., Nguyen, P. and Barham, M., 2013. Hybrid inferential modeling for vapor pressure of hydrocarbon mixtures in oil production. Industrial & Engineering Chemistry Research, 52(35), pp.12420-12425.

[11] Qin, S.J. and McAvoy, T.J., 1996. Nonlinear FIR modeling via a neural net PLS approach. Computers & chemical engineering, 20(2), pp.147-159.

[12] Kaspar, M.H. and Ray, W.H., 1993. Dynamic PLS modelling for process control. Chemical Engineering Science, 48(20), pp.3447-3461.

[13] Lakshminarayanan, S., Shah, S.L. and Nandakumar, K., 1997. Modeling and control of multivariable processes: Dynamic PLS approach. AIChE Journal, 43(9), pp.2307-2322.

[14] Li, G., Liu, B., Qin, S.J. and Zhou, D., 2011. Quality relevant data-driven modeling and monitoring of multivariate dynamic processes: The dynamic T-PLS approach. IEEE transactions on neural networks, 22(12), pp.2262-2271.

[15] Dong, Y. and Qin, S.J., 2018. Regression on dynamic PLS structures for supervised learning of dynamic data. Journal of Process Control, 68, pp.64-72.

[16] Zhu, Q., 2019. Auto-regressive modeling with dynamic weighted canonical correlation analysis. Submitted to Journal of Process Control.