Confidence-aware multiscale learning for online modeling of distributed parameter systems with application to curing process

In industrial applications, the modeling of distributed parameter systems (DPSs) is of significance for process control and monitoring. Due to infinite dimension, spatiotemporal coupled dynamics, nonlinearity and model uncertainties, however, modeling and online applications of DPSs are very difficult. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. From the spacial-scale perspective, an evolutionary learning-based spatial basis function is designed by learning from two dimensionality reduction methods, including Karhunen-Lo <inline-formula><tex-math notation="LaTeX">$\grave{e}$</tex-math></inline-formula> ve and diffusion maps. From the temporal-scale perspective, an efficient broad learning system is developed as reduced-order model to online address temporal dynamics of DPSs. As for the spatiotemporal-scale learning, Gaussian process regression is proposed as confidence-aware estimator to compensate for model generalization errors caused by spatiotemporal coupled dynamics. Through integration with the three-scale learning, the proposed method enables online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of proposed method.