A supervised functional Bayesian inference model with transfer-learning for performance enhancement of monitoring target batches with limited data

Abstract

To increase the monitoring performance of the batch process with serious nonlinearity, uneven-length, and limited-data issues, a supervised transfer-learning based functional Bayesian inference method is developed in this study. The raw uneven-length batch data are firstly transformed into functional data by choosing appropriate orthogonal wavelet basis functions (WBFs). Using the approximation coefficients representing the latent features that are inherent to the raw data, a Gaussian process model and a Bayesian inference method are applied based on the coefficients in each source batch process and the established models are transferred to enhance modeling performance for the target process with limited batches. In the proposed functional method, the unfolding operation is not needed for preprocessing, avoiding distortion of the raw data structure. With the compact support property of WBFs, within-batch detection can be implemented effectively to recognize faults earlier. The advantages of the proposed model are verified using a numerical case and an industrial polytetrafluoroethylene process.