On-line batch process monitoring using batch dynamic kernel principal component analysis

In this paper, a new dynamic and nonlinear batch process monitoring method, referred to as BDKPCA, is developed for on-line batch process monitoring, tactfully integrating kernel PCA and ARMAX time series model through estimating the Average Kernel Matrix (AKM) of all batch runs. AKM is an average of I, the batch number, Single-Batch Kernel Matrixes (SBKM). Each of the I SBKM is also an average of I kernel matrixes for each batch. The AKM contains the information of the stochastic variations and deviations among batches. This information will be very useful for the BDKPCA model to characterize the batch process in detail. The structure of BDKPCA model is very simple, and BDKPCA calculates the Hotelling's T2 statistic and the Q-statistic for every time point, enhancing the method's sensitivity to the faults. Two cases are used to investigate the potential application of the proposed method, and its application to on-line batch process monitoring shows better performance than MKPCA.