Modern industrial processes are large-scale, highly complex systems with many units and equipment. The complex flow of mass and energy, as well as the compensation effects of closed-loop control systems, cause significant cross-correlation and autocorrelation between process variables. To operate the process systems stably and efficiently, it is crucial to uncover the inherent characteristics of both the variance structure and dynamic relationship. Compared with the original slow feature analysis (SFA) that can only model the one-step time dependence, long-term dependency slow feature analysis (LTSFA) proposed in this paper can understand the longer-term dynamics by an explicit expression of latent states of the process. An iterative algorithm is developed for the model parameter optimization and its convergency is proved. The model properties and theoretical comparison with existing dynamic models are presented. A process monitoring strategy is designed based on LTSFA. The results of two simulation case studies show that LTSFA has better system dynamics extraction capability, which reduces the violation rate of the residual for the 95% confidence interval from 40.4% to 3.2% compared to the original SFA, and can disentangle the quickly- and slowly-varying features. Several typical disturbances can be correctly identified by LTSFA. The monitoring results on the Tennessee Eastman process benchmark show the overall advantages of the proposed method both in the dynamic and nominal deviation detection and the monitoring accuracy

现代工业过程是具有许多单元和设备的大规模、高度复杂的系统。复杂的质量和能量流动，以及闭环控制系统的补偿效应，导致过程变量之间存在显着的互相关和自相关。为了稳定高效地运行过程系统，揭示方差结构和动态关系的内在特征至关重要。与只能模拟一步时间依赖性的原始慢特征分析（SFA）相比，本文提出的长期依赖性慢特征分析（LTSFA）可以通过隐状态的显式表达来理解长期动态。过程。为模型参数优化开发了迭代算法并证明了其收敛性。介绍了模型特性以及与现有动态模型的理论比较。基于 LTSFA 设计了一种过程监控策略。两个仿真案例研究的结果表明，LTSFA 具有更好的系统动力学提取能力，与原始 SFA 相比，将 95% 置信区间的残差违反率从 40.4% 降低到 3.2%，并且可以快速解开缓慢变化的特征。LTSFA 可以正确识别几种典型的干扰。在田纳西州伊士曼过程基准上的监测结果表明了所提出的方法在动态和名义偏差检测以及监测精度方面的整体优势 两个仿真案例研究的结果表明，LTSFA 具有更好的系统动力学提取能力，与原始 SFA 相比，将 95% 置信区间的残差违反率从 40.4% 降低到 3.2%，并且可以快速解开缓慢变化的特征。LTSFA 可以正确识别几种典型的干扰。在田纳西州伊士曼过程基准上的监测结果表明了所提出的方法在动态和名义偏差检测以及监测精度方面的整体优势 两个仿真案例研究的结果表明，LTSFA 具有更好的系统动力学提取能力，与原始 SFA 相比，将 95% 置信区间的残差违反率从 40.4% 降低到 3.2%，并且可以快速解开缓慢变化的特征。LTSFA 可以正确识别几种典型的干扰。在田纳西州伊士曼过程基准上的监测结果表明了所提出的方法在动态和名义偏差检测以及监测精度方面的整体优势 LTSFA 可以正确识别几种典型的干扰。在田纳西州伊士曼过程基准上的监测结果表明了所提出的方法在动态和名义偏差检测以及监测精度方面的整体优势 LTSFA 可以正确识别几种典型的干扰。在田纳西州伊士曼过程基准上的监测结果表明了所提出的方法在动态和名义偏差检测以及监测精度方面的整体优势