Nonparametric Dynamic Inner Kernel-Regularized Latent Variable Regression Algorithm for Process Modeling

Multivariate statistical methods are important for establishing the relationship between variables in a dynamic process. However, attention is rarely paid to utilizing prior knowledge and identifying the degree of process dynamics while extracting latent variables (LVs), which are vital in practice for improving modeling efficiency. In this article, a novel nonparametric dynamic inner LV regression algorithm is proposed for process modeling by extracting explicit dynamic LVs from highly correlated process and quality data. The inner-dynamic structure between LVs is modeled as an impulse response, where the model order defines the degree of dynamics in the process. The estimation of the inner model with a nonparametric system identification technique enables the model to achieve a good balance between model complexity and flexibility, thus realizing the estimation of the degree of dynamics in the process and ensuring the consistency of model performance. Prior knowledge of the impulse response is incorporated by a kernel-based regularization technique while searching for the inner model within an infinite-dimensional space to enhance the smoothness and stability of the model. Besides, prior knowledge is integrated into the progress of dynamic LV extraction as well, thereby improving the numerical properties of the dynamic LV regression model. Case studies based on chemical and biological processes are presented to demonstrate the effectiveness of the proposed method.