Identification of robust probabilistic slow feature regression model for process data contaminated with outliers

Abstract

Modeling of high dimensional dynamic process is considered as a challenging task. In this regard, probabilistic Slow Feature Analysis (PSFA), a dynamic latent variable model, is proven to be a useful tool which extracts temporally correlated dynamic features from the high-dimensional raw measurements. The extracted latent Slow Features (SFs) can capture process variations which are useful in developing dynamic models. Often times industrial data is affected by outliers, and modeling such data could result in inferior prediction performance. To deal with such scenarios, we propose a robust PSFA (RPSFA) based regression model that models outliers in the observation data using the Student's t-distribution. To estimate the parameters in RPSFA and to extract reduced dimension of SFs, we employ Expectation-Maximization (EM) algorithm under the Maximum Likelihood Estimation (MLE) framework considering SFs as hidden variables. To estimate the hidden SFs we propose a weighted gain Kalman filter based approach as the Normal distribution assumption of the observations is no longer valid. The validity and merits of the proposed approach are demonstrated though a simulated example, an industrial application and an experimental study.