Virtual Sensor Modeling for Nonlinear Dynamic Processes Based on Local Weighted PSFA

Modern industrial processes are featured with complex dynamic, nonlinear, and noisy characteristics. It is of great significance to apply the probabilistic latent variable models (LVMs) to mine the pivotal features of the industrial processes. A probabilistic slow feature analysis (PSFA) can extract slowly varying features in rapidly changing data sequences as a dynamic LVM. However, the performance of PSFA is limited because of its linear assumption. In this article, a locally weighted PSFA (LWPSFA) is proposed for nonlinear dynamic modeling of industrial data with random noises. Two different kinds of weighting techniques are designed to approximate the nonlinear slow feature transition and emission functions. After that, the expectation maximum (EM) algorithm is adopted to estimate the parameters of LWPSFA with a weighted log-likelihood function (W-LLF). Eventually, a debutanizer column and a hydrocracking process are used to validate the effectiveness of LWPSFA.