Nonlinear Bioprocess Monitoring Using Multiway Kernel Localized Fisher Discriminant Analysis

A novel batch bioprocess monitoring approach based on multiway kernel localized Fisher discriminant analysis (MKLFDA) is proposed in this article. For the routine bioprocess operation with some abnormal events, a supervised monitoring method is needed to handle the training data set that includes various types of faulty samples. Because of the inherent process nonlinearity and multimodality among normal and faulty clusters, the traditional multiway Fisher discriminant analysis (MFDA) method becomes inappropriate and unable to effectively detect or classify faulty samples. The newly developed MKLFDA approach, however, combines kernel function with the localized Fisher discriminant analysis so that the kernel feature can retain the process nonlinearity while the localized characteristic is able to extract the multi-Gaussianity within data clusters. Furthermore, the integrated multiway analysis uses batch-wise unfolding to convert the three-dimensional data set into a two-dimensional matrix that can be fed into the kernel localized Fisher discriminant analysis for fault detection and classification. The proposed MKLFDA approach is applied to three test scenarios in the fed-batch penicillin fermentation process and its batch monitoring performance is compared to that of the conventional MFDA method. The results indicate that the MKLFDA approach performs much better than MFDA method in detecting abnormal operating conditions as well as classifying various types of process faults occurring in fed-batch operation. The MKLFDA approach results in higher fault detection rate and lower false classifications.