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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 • The proposed model, LTSFA, can explicitly model the long-term time dependency. • An iterative algorithm is developed and convergence is proved. • The model properties and theoretical comparison with existing models are presented. • LTSFA can better extract dynamics compared to the original SFA. • The monitoring method based on LTSFA gives better monitoring performance. [ABSTRACT FROM AUTHOR]

• To highlight the local strong correlations, the data set is divided into highly correlated blocks and one remainder block. • The sparse loading vectors are obtained to produce interpretableprincipalcomponents. • The sparse, distributed PCA keeps the strong correlations and achieves sparsity, which improves monitoring performance. • Blockwise contribution plots are proposed to give accurate fault diagnosis results. Driven by the strong demand for sparsity in dimensional reduction techniques, a sparse modeling and monitoring approach based on sparse, distributed principal component analysis (SDPCA) is proposed to achieve sparsity. To this end, the data set is first divided into highly correlated blocks (HCBs) and one remainder block (RB) on the basis of the mutual-information-based correlation matrix. From this, the sparse loading vectors for the HCBs are obtained using the PCA models, while for the RB, it is obtained using the sparse PCA model. It is worth noting that the sparsity in SDPCA enables the sparse loading vectors to produce interpretable principal components, which keeps the correlations between the highly correlated variables and achieves the sparsity for the weakly correlated ones. Moreover, to fully appreciate the interpretation of the sparse principal components, a fault diagnosis strategy named blockwise contribution plots is proposed by first determining the faulty block, and then, identifying the faulty variables. Compared with PCA and SPCA, the proposed SDPCA detects more faulty samples and gives more accurate diagnosis results. [Display omitted] [ABSTRACT FROM AUTHOR]

Recent research has emphasized the successful application of canonical correlation analysis (CCA) to perform fault detection (FD) in both static and dynamic processes with additive faults. However, dealing with multiplicative faults has not been as successful. Thus, this paper considers the application of CCA to deal with the detection of incipient multiplicative faults in industrial processes. The new approaches incorporate the CCA-based FD with the statistical local approach. It is shown that the methods are effective in detecting incipient multiplicative faults. Experiments using a continuous stirred tank heater and simulations on the Tennessee Eastman process are provided to validate the proposed methods. [ABSTRACT FROM AUTHOR]