(177e) Keynote Talk: Modelling and Monitoring with Dynamic Auto-Regressive Latent Variable Methods

With the advent of Industry 4.0, industrial data can be collected at very high sampling rates, leading to more complicated relation between process and quality variables^{[1, 2]}. To extract valuable information from these variables and avoid the curse of dimensionality, multivariate latent variable methods (LVM) are widely used, such as partial least squares (PLS)^[3], canonical correlation analysis (CCA)^[4] and latent variable regression (LVR)^[5]. PLS and CCA are employed to construct the relations between process variables X and quality variables Y by maximizing their covariance and correlation respectively, while LVR aims to maximize the projection of Y in the latent space. Several variants of LVM are proposed to achieve better modeling and monitoring performance, including concurrent ones^[6-8] and nonlinear versions^{[9, 10]}.

The aforementioned models obtain satisfactory modeling and monitoring performance; however, only static variations are considered in these models, and this static assumption constrains their applicability in actual dynamic systems. Several dynamic variants were proposed to extract temporal information from the data. For instance, augmented matrices were formed to include lagged process and quality variables in the work of Ku et al.^[11] and Qin and McAvoy^[12]. However, it is hard to interpret their latent structures because of the augmentation matrices. To address this issue, dynamic inner LVM was proposed to construct dynamic outer model by maximizing the relations between current samples and a linear combination of past samples, and a dynamic inner model that is consistent with the dynamic outer model^[13-16]. Dynamic weighted variants were also proposed in [1, 17] to reduce the redundant information between adjacent historical samples by introducing basis functions. For aforementioned dynamic variants of LVM, only dynamic cross-correlations between the current quality variables and past process and quality variables are considered, leaving large portion of valuable quality information unexploited.

In this work, a series of dynamic auto regressive LVM (DALVM) algorithms are proposed to fully exploit the valuable information of both process and quality variables. DALVM aims to maximize the dynamic relations between current quality samples and past process and quality samples, and to achieve consistency, an auto-regressive exogenous (ARX) model is designed in the inner model. In DALVM, in addition to the auto-regressive relations of quality variables, the cross-correlations between X and Y are also constructed. Further, aiming for comprehensive modeling and monitoring, subsequent decompositions are proposed to decompose the process and quality variables concurrently into seven dynamic and static subspaces, and the corresponding monitoring scheme is designed for all subspaces. Two industrial dataset, Tennessee Eastman process and the three-phase flow facility, are used to illustrate the advantages of the proposed algorithms.

References

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[2] Xu, B. and Zhu, Q., 2020. Online quality-relevant monitoring with dynamic weighted partial least squares. Industrial & Engineering Chemistry Research, 59(48), pp.21124-21132.

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[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] Zhang, H. and Zhu, Q., 2021. Multi-layer fault monitoring with concurrent kernel latent variable regression. Submitted to Industrial & Engineering Chemistry Research.

[9] Melzer, T., Reiter, M. and Bischof, H., 2003. Appearance models based on kernel canonical correlation analysis. Pattern recognition, 36(9), pp.1961-1971.

[10] Zhang, Y., Zhou, H., Qin, S.J. and Chai, T., 2009. Decentralized fault diagnosis of large-scale processes using multiblock kernel partial least squares. IEEE Transactions on Industrial Informatics, 6(1), pp.3-10.

[11] Ku, W., Storer, R.H. and Georgakis, C., 1995. Disturbance detection and isolation by dynamic principal component analysis. Chemometrics and intelligent laboratory systems, 30(1), pp.179-196.

[12] 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.

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[14] Dong, Y., Liu, Y. and Qin, S.J., 2019. Efficient dynamic latent variable analysis for high-dimensional time series data. IEEE Transactions on Industrial Informatics, 16(6), pp.4068-4076.

[15] Zhu, Q., Qin, S.J. and Dong, Y., 2020. Dynamic latent variable regression for inferential sensor modeling and monitoring. Computers & Chemical Engineering, 137, p.106809.

[16] Qin, S.J., Dong, Y., Zhu, Q., Wang, J. and Liu, Q., 2020. Bridging systems theory and data science: A unifying review of dynamic latent variable analytics and process monitoring. Annual Reviews in Control.

[17] Xu, B. and Zhu, Q., 2020. Online Quality-Relevant Monitoring with Dynamic Weighted Partial Least Squares. Industrial & Engineering Chemistry Research, 59(48), pp.21124-21132.