Mass-Constrained hybrid Gaussian radial basis neural networks: Development, training, and applications to modeling nonlinear dynamic noisy chemical processes

Abstract

This paper develops sparse hybrid Gaussian Radial Basis Neural Networks (GRAB-NNs) for data-driven models. The proposed architectures are hidden-layered networks combining Gaussian and sigmoid hidden nodes. Efficient training algorithms are developed for solving the mixed integer nonlinear programming problem, where the optimal number of radial basis function (RBF) centers is obtained by a bidirectional branch and bound algorithm followed by optimal estimation of the coordinates of centers / widths and connection weights by minimizing the corrected Akaike Information Criterion. Algorithmic approaches are developed for exactly satisfying mass constraints both during the training and simulation problems. Sequential decomposition-based training approaches are developed by exploiting the structure of the hybrid model that facilitates use of different training algorithms for each sublayer of the hybrid structure thus leading to faster computation. The performance of the proposed network structures and training algorithms in presence / absence of constraints are evaluated for two nonlinear dynamic chemical systems.