Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach

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Multiway kernel partial least squares method (MKPLS) has recently been developed for monitoring the operational performance of nonlinear batch or semi-batch processes. It has strong capability to handle batch trajectories and nonlinear process dynamics, which cannot be effectively dealt with by traditional multiway partial least squares (MPLS) technique. However, MKPLS method may not be effective in capturing significant non-Gaussian features of batch processes because only the second-order statistics instead of higher-order statistics are taken into account in the underlying model. On the other hand, multiway kernel independent component analysis (MKICA) has been proposed for nonlinear batch process monitoring and fault detection. Different from MKPLS, MKICA can extract not only nonlinear but also non-Gaussian features through maximizing the higher-order statistic of negentropy instead of second-order statistic of covariance within the high-dimensional kernel space. Nevertheless, MKICA based process monitoring approaches may not be well suited in many batch processes because only process measurement variables are utilized while quality variables are not considered in the multivariate models. In this paper, a novel multiway kernel based quality relevant non-Gaussian latent subspace projection (MKQNGLSP) approach is proposed in order to monitor the operational performance of batch processes with nonlinear and non-Gaussian dynamics by combining measurement and quality variables. First, both process measurement and quality variables are projected onto high-dimensional nonlinear kernel feature spaces, respectively. Then, the multidimensional latent directions within kernel feature subspaces corresponding to measurement and quality variables are concurrently searched for so that the maximized mutual information between the measurement and quality spaces is obtained. The I2 and SPE monitoring indices within the extracted latent subspaces are further defined to capture batch process faults resulting in abnormal product quality. The proposed MKQNGLSP method is applied to a fed-batch penicillin fermentation process and the operational performance monitoring results demonstrate the superiority of the developed method as apposed to the MKPLS based process monitoring approach.