Kernel-Regularized Latent-Variable Regression Models for Dynamic Processes

Establishing relations between variables and real-time prediction of quality variables or other key indicators arecritical for dynamic processes including industrial and biologicalprocesses. In this study, a novel multivariate statistical modelingmethod named"kernel-regularized latent variable regression(KrLVR) approach"is proposed for capturing the dynamics of aprocess by building KrLVR models with process and quality data.First, a regularization term based on a kernel matrix is incorporatedinto the objective of the latent variable regression model.Consequently, the proposed KrLVR method has the ability toovercome potential ill-conditioning resulting from collinearity inprocess data and has a stronger prediction power. Besides, the inner model is consistent with the outer model, which enables theproposed method to predict quality data with fewer latent variables. Second, the prior knowledge of dynamic processes such asexponential 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 becomesfinding appropriate hyper-parameters of the kernelmatrix. Moreover, the empirical Bayesian method is utilized for estimating hyper-parameters of the kernel matrix from augmentedprocess and quality data. Three case studies illustrate the performance of the proposed KrLVR method by comparing with severalother relevant methods