Batch process monitoring based on batch dynamic Kernel slow feature analysis

The traditional nonlinear dynamic batch process monitoring approaches are unable to extract the underlying driving forces of batch process. In this paper, a novel batch process monitoring method based on batch dynamic kernel slow feature analysis (BDKSFA) is proposed not only to capture nonlinear and dynamic characteristics but also to extract the underlying driving forces. The three-way data matrix is first unfolded and normalized and then rearranged into three-way matrix again. In order to contain stochastic variations and deviations among batches, the total average kernel matrix is computed as an average of I batch average kernel matrixes, each of which is also an average of I kernel matrixes for each batch. Based on the slow features extracted from BDKSFA model, two monitoring statistics are constructed to detect batch process fault. The simulation results obtained from the benchmark fed-batch penicillin fermentation process demonstrate the superiority of the developed method in terms of fault detection performance.