DBN can be used for feature learning in industrial process modeling, monitoring and KPI prediction. However, building conventional large-sized DBN for industrial processes with large time delays could be tough and time-consuming. In this article, a pyramid DBN method is proposed to deal with the toughness of feature learning in long-time-delay processes, and to perform KPI prediction. The pyramid DBN framework performs multi-level feature learning with a sequence of low-resolution DBNs which can be quickly established and extract the feature information more completely. Besides, a feature filtering step with hill climbing based on Bayesian information criterion is designed to remove redundant variables. The proposed framework greatly improves modeling and prediction performance.

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 ...