For industrial processes, operating conditions tend to be time varying, leading to the time-varying nonstationary characteristics. In this paper, an active nonstationary variables selection-based just-in-time co-integration analysis and slow feature analysis monitoring approach is proposed to explore the real-time variations in dynamic processes. To this end, by analyzing the time-varying stationarity of online data, active nonstationary variables are selected. Meanwhile, a just-in-time strategy is used to update the offline model. On this basis, co-integration analysis and slow feature analysis are developed for extracting long-run equilibrium relationships and slowly varying features. A comprehensive statistic is generated by Bayesian inference to monitor the operation status. With the active nonstationary information extraction, the proposed method emphasizes the online nonstationary characteristics, which allows the monitoring model to effectively capture the dynamic variations. Two case studies on benchmark processes show the advantages and feasibility of the proposed method.

对于工业过程，操作条件往往是随时间变化的，从而导致随时间变化的非平稳特性。在本文中，提出了一种基于主动非平稳变量选择的实时协整分析和慢速特征分析监测方法来探索动态过程中的实时变化。为此，通过分析在线数据的时变平稳性，选择活跃的非平稳变量。同时，采用即时策略更新离线模型。在此基础上，开发了协整分析和慢特征分析，用于提取长期均衡关系和慢变特征。通过贝叶斯推理生成全面的统计数据来监控运行状态。通过主动非平稳信息提取，该方法强调在线非平稳特性，使监测模型能够有效地捕捉动态变化。关于基准过程的两个案例研究表明了所提出方法的优点和可行性。