A comprehensive process monitoring model based on nonstationary probabilistic predictable feature analysis
Dynamic industrial processes often operate under nonstationary conditions, where time-varying characteristics may reduce fault sensitivity and increase false alarms in conventional latent variable models. In practical production, nonstationary reflects the time-varying nature of the underlying process-generating mechanism, which may obscure the distinction between normal operating evolution and fault-induced deviations. This work aims to develop an interpretable probabilistic monitoring framework that captures both temporal dynamics and nonstationary variations. A nonstationary probabilistic predictable feature analysis (NS-PPFA) model is proposed. The latent space is decomposed into stationary and nonstationary components: stationary variables are described by stable autoregressive processes, while nonstationary variables are modeled as random walks. The resulting probabilistic state-space model jointly represents temporal correlations, measurement uncertainty, and operating-condition variations. Model parameters are estimated using an expectation–maximization strategy, where Kalman smoothing infers latent variables and genetic-algorithm optimization estimates lag-dependent regression coefficients. Multiple monitoring statistics are further constructed to evaluate stationary and nonstationary latent deviations, residual variations, and dynamic changes. Case studies on the three-phase flow facility benchmark, including top separator input blockage and slugging faults, show that NS-PPFA achieves higher fault detection rates and lower false alarm rates than conventional methods. These results demonstrate its effectiveness for robust and interpretable monitoring of nonstationary dynamic industrial processes.