Global-local based wavelet functional principal component analysis for fault detection and diagnosis in batch processes

Functional data analysis has the natural advantages to handle the problems three-dimensional (3D) data, nonlinear and uneven-duration in batch processes. In this work, a global-local based wavelet functional principal component analysis (WFPCA) is developed to improve the detection performance and further diagnose the faulty variables in batch processes. Compared with the existing methods, the proposed global-local based WFPCA method has several merits. The trajectories of the process variables are analyzed as continuous functions rather than discrete vectors. Considering the diversity of those trajectories, the basis functions are separately specified and actively determined for each variable. Then the global WFPCA model is proposed on the basis of all the variables to detect the potential faults. If abnormal conditions are detected, local WFPCA models are applied within batches for each variable to diagnose the implied faulty variables. The merits and effectiveness of the proposed global-local based WFPCA methods are tested by a numerical case and an industrial penicillin fermentation process.