Efficient adaptive deep gradient RBF network for multi-output nonlinear and nonstationary industrial processes

Due to the complexity of process operation, industrial process data are often nonlinear and nonstationary, high dimensional, and multivariate with complex interactions between multiple outputs. To address all these issues, this paper proposes a novel industrial predictive model that integrates deep feature extraction and fast online adaptation, and can effectively deal with multiple process outputs. Specifically, a multi-output gradient radial basis function network (MGRBF) with excellent predictive capacity of nonstationary data is first used to provide preliminary prediction of target outputs. This prior quality information is combined with the original process input for deep feature learning and dimensional reduction. Through layer-wise feature extraction by the stacked autoencoder (SAE), deep quality-enhanced features can be obtained, which is further fed into a MGRBF tracker for online prediction. In order to timely capture the fast-changing process characteristics, the first two modules, namely, preliminary MGRBF predictor and SAE feature extractor are frozen after training, while the structure and parameters of the MGRBF tracker are updated online in an efficient manner. Two industrial case studies demonstrate that the proposed adaptive deep MGRBF network outperforms existing state-of-the-art online modeling approaches as well as deep learning models, in terms of both multi-output modeling accuracy and online computational complexity.