A Heuristic Neural Network Initialization Scheme for Modeling Nonlinear Functions in Engineering Mechanics

摘要

This paper introduces a heuristic methodology for designing multilayer feedforward neural networks to model the types of nonlinear functions common to many engineering mechanics applications. It is well known that a perfect way to determine the ideal architecture to initialize neural network training has not yet been established. This could be because this challenging issue can only be properly addressed by looking into the features of the function to be approximated and thus might be hard to tackle in a general sense. In this study, the authors do not presume to provide a universal method approximate an arbitrary function, rather the focus is given to modeling nonlinear hysteretic restoring forces, a significant domain function approximation problem. The governing physics and mathematics of nonlinear hysteretic dynamics as well as the strength of the sigmoidal basis function are exploited to determine both an efficient neural network architecture (e.g., the number of hidden nodes) as well as effective initial weight and bias values for those nodes. Training examples are presented to demonstrate and validate the proposed initial design methodology. Comparisons are made between the proposed methodology and the widely used Nguyen-Widrow Initialization. Future work is also identified.