Deep Cascade Gradient RBF Networks With Output-Relevant Feature Extraction and Adaptation for Nonlinear and Nonstationary Processes.

The main challenge for industrial predictive models is how to effectively deal with big data from high-dimensional processes with nonstationary characteristics. Although deep networks, such as the stacked autoencoder (SAE), can learn useful features from massive data with multilevel architecture, it is difficult to adapt them online to track fast time-varying process dynamics. To integrate feature learning and online adaptation, this article proposes a deep cascade gradient radial basis function (GRBF) network for online modeling and prediction of nonlinear and nonstationary processes. The proposed deep learning method consists of three modules. First, a preliminary prediction result is generated by a GRBF weak predictor, which is further combined with raw input data for feature extraction. By incorporating the prior weak prediction information, deep output-relevant features are extracted using a SAE. Online prediction is finally produced upon the extracted features with a GRBF predictor, whose weights and structure are updated online to capture fast time-varying process characteristics. Three real-world industrial case studies demonstrate that the proposed deep cascade GRBF network outperforms existing state-of-the-art online modeling approaches as well as deep networks, in terms of both online prediction accuracy and computational complexity.