Batch Process Monitoring Based on Multiway Global Preserving Kernel Slow Feature Analysis

As an effective nonlinear dynamic data analysis tool, kernel slow feature analysis (KSFA) has achieved great success in continuous process monitoring field during recent years. However, its application to batch process monitoring is unexploited, which is a more challenging task because of the complicated characteristics of batch process data. In this paper, we propose a novel batch process monitoring method based on the modified KSFA method, referred to as multiway global preserving kernel slow feature analysis (MGKSFA), to capture high nonlinearity and inherently time-varying dynamics of process data. In the proposed method, a two-step multiway data unfolding strategy is first utilized to convert the three-way batch process training data set into a two-way matrix. Then, the global structure preserving-based kernel slow feature analysis (GKSFA) is used to build the nonlinear statistical monitoring model, which not only explores the local dynamic data relationships but also considers the mining of global data structure information. Furthermore, a rule based on the cumulative slowness contribution is designed to determine the number of the retained slow features. Last, two monitoring statistics T-2 and SPE are built to detect the process faults. Two case studies, including one simple numerical nonlinear system and the benchmark fed-batch penicillin fermentation process, are used to demonstrate that the proposed MGKSFA method has the superior fault detection performance over the traditional batch process monitoring methods.