Step-wise segment partition based stationary subspace analysis and Gaussian mixture model for nonstationary process performance assessment

Abstract

This article focuses on solving the problem of performance assessment for nonstationary processes without significant cointegrated correlations, which is a basic assumption of traditional methods. The time axis is replaced by indicator axis of working condition. Thus, the irregular non-stationarity along time axis could turns to be typical piecewise stationarity along indicator axis of working condition. The proposed method provides a general tool to deal with non-stationarities and relax the cointegrated restriction on variable correlations. Since a nonstationary process has specific working patterns under different conditions, the process can thus be divided into multiple segments along the axis of working condition. To characterize the properties of different performances within a segment meticulously, random sampling-based stationary subspace analysis (SSA) is conducted to separate the Gaussian and non-Gaussian subspaces. Since the operating performance is mainly distinguied by the non-Gaussian information, the non-Gaussian subspace obtained by SSA is further characterized by Gaussian mixture model (GMM). For online application, the segment model is selected by the indicator of working condition, and then the performance is assessed using Bayesian inference to provide a probabilistic result. The efficacy of the proposed method is validated by a coal mill from a real thermal power plant.