Adaptive Multioutput Gradient RBF Tracker for Nonlinear and Nonstationary Regression

Multioutput regression of nonlinear and nonstationary data is largely understudied in both machine learning and control communities. This article develops an adaptive multioutput gradient radial basis function (MGRBF) tracker for online modeling of multioutput nonlinear and nonstationary processes. Specifically, a compact MGRBF network is first constructed with a new two-step training procedure to produce excellent predictive capacity. To improve its tracking ability in fast time-varying scenarios, an adaptive MGRBF (AMGRBF) tracker is proposed, which updates the MGRBF network structure online by replacing the worst performing node with a new node that automatically encodes the newly emerging system state and acts as a perfect local multioutput predictor for the current system state. Extensive experimental results confirm that the proposed AMGRBF tracker significantly outperforms existing state-of-the-art online multioutput regression methods as well as deep-learning-based models, in terms of adaptive modeling accuracy and online computational complexity.

Multi-Output Selective Ensemble Identification of Nonlinear and Nonstationary Industrial Processes

A key characteristic of biological systems is the ability to update the memory by learning new knowledge and removing out-of-date knowledge so that intelligent decision can be made based on the relevant knowledge acquired in the memory. Inspired by this fundamental biological principle, this article proposes a multi-output selective ensemble regression (SER) for online identification of multi-output nonlinear time-varying industrial processes. Specifically, an adaptive local learning approach is developed to automatically identify and encode a newly emerging process state by fitting a local multi-output linear model based on the multi-output hypothesis testing. This growth strategy ensures a highly diverse and independent local model set. The online modeling is constructed as a multi-output SER predictor by optimizing the combining weights of the selected local multi-output models based on a probability metric. An effective pruning strategy is also developed to remove the unwanted out-of-date local multi-output linear models in order to achieve low online computational complexity without scarifying the prediction accuracy. A simulated two-output process and two real-world identification problems are used to demonstrate the effectiveness of the proposed multi-output SER over a range of benchmark schemes for real-time identification of multi-output nonlinear and nonstationary processes, in terms of both online identification accuracy and computational complexity.