Pyramid Dynamic Bayesian Networks for Key Performance Indicator Prediction in Long Time-Delay Industrial Processes

Building dynamic Bayesian networks (DBNs) for time-delay industrial processes has always been tough, since the structure learning of the DBN is a NP-hard problem. In this article, a pyramid DBN (PDBN) framework is proposed to speed up modeling and improve feature learning for industrial processes with large time delays. In the PDBN framework, a sequence of small-sized DBNs are established, each of which is a progressively simpler representation of the previous layer, and the feature information learned by the DBN sequence corresponds to the layers in the pyramid. With information fusion of the feature pyramid and a further feature filtering with hill climbing based on Bayesian information criterion, we can restore the feature information of the time-delay industrial processes. Regression models are built based on the features learned by the PDBN framework for further key performance indicator estimation. Advantages of the method have been effectively validated on two actual industrial cases. With multilevel feature learning and filtering, both modeling speed and prediction accuracy have been greatly improved. The proposed method outperforms other similar works on identifying important features in industrial processes and existing DBN-based soft sensors.