Multiway dynamic nonlinear global neighborhood preserving embedding method for monitoring batch process

Abstract

Aiming at the dynamic and nonlinear characteristics of batch process, a multiway dynamic nonlinear global neighborhood preserving embedding algorithm is proposed. For the nonlinear batch process monitoring, kernel mapping is widely used to eliminate nonlinearity by projecting the data into high-dimensional space, but the nonlinear relationships between batch process variables are limited by many physical constraints, and the infinite-order mapping is inefficient and redundant. Compared with the basic kernel mapping method which provides an infinite-order nonlinear mapping, the proposed method considers the dynamic and nonlinear characteristics with many physical constraints and preserves the global and local structures concurrently. First, the time-lagged window is used to remove the auto-correlation in time series of process variables. Second, a nonlinear method named constructive polynomial mapping is used to avoid unnecessary redundancy and reduce computational complexity. Third, the global neighborhood preserving embedding method is used to extract structures fully after the dynamic and nonlinear characteristics are processed. Finally, the effects of the proposed algorithm are demonstrated by a mathematical model and the penicillin fermentation process.

A Review on Data-Driven Process Monitoring Methods: Characterization and Mining of Industrial Data

“…Zhang and Qin proposed a multiway kernel ICA method to extract dominant independent components in batch processes [166]. More methods introduced previously in continuous process monitoring could be found to be combined with multiway methods, such as AE [167], kernel SFA [168], and manifold learning [168,169].…”

Quality-related batch process monitoring based on multi-way orthogonal signal correction enhanced total principal component regression

“…The total principal component regression processing method is used to continue to extract the part directly related to Ŷi in T pc . That is, PCA decomposition of Ŷi is performed again, and the new score matrix T ypc and load matrix Q ypc are shown in equation (12).…”

“…Therefore, Zhang et al 11 proposed a method to explore the dynamic and static characteristics in process statuses identification. Hui and Zhao 12 proposed a method that considered the nonlinear and dynamic in batch process monitoring. Zhu et al 13 proposed a dynamic time-slice multi-stage batch process monitoring method, dynamic behaviors of each phase can be captured from both single batch run and batch-to-batch evolutions.…”