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.
Highlights
Batch process mainly exists in food, semiconductor, chemical production, and so on
The regular methods combine kernel mapping, which linearizes the relationship with high-dimensional projection, such as kernel principal component analysis (KPCA),[13,14] kernel independent component analysis (KICA),[15] and kernel Fisher discriminant analysis (KFDA).[16]
Multiway dynamic nonlinear global neighborhood preserving embedding (MDNGNPE) method is proposed for dynamic nonlinear batch process monitoring
Summary
Batch process mainly exists in food, semiconductor, chemical production, and so on. It is vital to develop approaches that ensure product quality and production safety requirements. As one of the manifold learning algorithms, neighborhood preserving embedding (NPE) can preserve the local structure of data and has been widely used in processing monitoring.[17,18,19,20,21] As a nonlinear extension of NPE,[22] kernel NPE tries to preserve local topology relationship. The radial basis kernel is widely used to solve nonlinear relationships between variables by providing an infinite-order mapping.[31] But the infinite-order mapping would lead to a higher computational complexity; especially for batch process, it needs to unfold the three-array data into two-array data. Multiway dynamic nonlinear global neighborhood preserving embedding (MDNGNPE) method is proposed for dynamic nonlinear batch process monitoring.
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