Variational Bayesian Approach to Nonstationary and Oscillatory Slow Feature Analysis With Applications in Soft Sensing and Process Monitoring

Abstract

Extraction of underlying patterns from measured variables is central to various data-driven control applications, such as soft-sensor modeling, statistical process monitoring, and fault detection and diagnosis. More often than not, the observed variables display nonstationary characteristics and oscillations due to the changes in operating conditions and problems in controller tuning. Such variations pose a great challenge to conventional feature extraction methods. Hence, we present a probabilistic drift-type nonstationary oscillating slow feature model that can separate oscillating patterns and nonstationary variations from measured data. Furthermore, the measurement noise of each variable is independently modeled to account for the fact that not all the observed variables have the same level of uncertainty. Finally, the feature extractor parameters are estimated under a variational Bayesian framework to incorporate the prior information and obtain corresponding posterior distributions. The proposed methodology is applied to solve a fouling monitoring problem for an industrial oil production process.