On-line monitoring of batch processes using generalized additive kernel principal component analysis

Based on analyzing the special structure of three-way array and generalizing the concept of additive kernels, this paper proposes the generalized additive kernel principal component analysis (GAKPCA) method for on-line monitoring of batch processes. The proposed method is a special nonlinear principal component analysis (PCA) method which can handle the nonlinear relationships between different monitoring variables and/or time intervals. It inherits the good properties of traditional multiway PCA (MPCA) method for on-line monitoring, and solves some problems that exist in traditional multiway kernel PCA (MKPCA) method. For example, based on the decomposition of batch samples in the feature space, the total squared prediction error (SPE) statistic of an entire batch can be divided into K components corresponding to K time intervals respectively, and its score vectors can be directly estimated on-line by the least squares approach without filling the unknown observations. As a special case, when the Gaussian kernel is used as the kernel function at each time interval, the proposed method is connected with the concept of correntropy which can bring robustness to our method. The experimental results on a fed-batch penicillin fermentation process demonstrate the validity of the proposed GAKPCA-based on-line monitoring method. (C) 2015 Elsevier Ltd. All rights reserved.