Kernel-Regularized Latent-Variable Regression Models for Dynamic Processes

Abstract

Establishing relations between variables and realtime prediction of quality variables or other key indicators are critical for dynamic processes including industrial and biological processes. In this study, a novel multivariate statistical modeling method named "kernel-regularized latent variable regression (KrLVR) approach" is proposed for capturing the dynamics of a process by building KrLVR models with process and quality data. First, a regularization term based on a kernel matrix is incorporated into the objective of the latent variable regression model. Consequently, the proposed KrLVR method has the ability to overcome potential ill-conditioning resulting from collinearity in process data and has a stronger prediction power. Besides, the inner model is consistent with the outer model, which enables the proposed method to predict quality data with fewer latent variables. Second, the prior knowledge of dynamic processes such as exponential stability and smoothness can be integrated into the modeling process by using an appropriate kernel matrix. In addition, to meet the requirement of exponential stability of the model, the weights of the model should decay exponentially, that is, coincident with determining the number of historical observations for data augmentation (identification of the model structure). Therefore, the problem of tuning model complexity is eluded, and it becomes finding appropriate hyper-parameters of the kernel matrix. Moreover, the empirical Bayesian method is utilized for estimating hyper-parameters of the kernel matrix from augmented process and quality data. Three case studies illustrate the performance of the proposed KrLVR method by comparing with several other relevant methods.

Neural Component Analysis for Key Performance Indicator Monitoring

“…Multivariate statistics-based process monitoring (MSPM) − is one of the most attractive data-driven approaches for monitoring complex processes with high-dimensional data structures, for example, biopharmaceutical and chemical processes. Its core idea is to transform high-dimensional process data to low-dimensional principal components (PCs) and monitor them using several statistical indices. − …”