New Approach to Designing Multilayer Feedforward Neural Network Architecture for Modeling Nonlinear Restoring Forces. I: Formulation

Abstract

This paper addresses the modeling problem of nonlinear and hysteretic dynamic behaviors through a constructive modeling approach which exploits existing mathematical concepts in artificial neural network modeling. In contrast with many neural network applications, which often result in large and complex “black-box” models, here, the writers strive to produce phenomenologically accurate model behavior starting with network architecture of manageable/small sizes. This affords the potential of creating relationships between model parameter values and observed phenomenological behaviors. Here a linear sum of basis functions is used in modeling nonlinear hysteretic restoring forces. In particular, nonlinear sigmoidal activation functions are chosen as the core building block for their robustness in approximating arbitrary functions. The appropriateness and effectiveness of this set of basis function in modeling a wide variety of nonlinear dynamic behaviors observed in structural mechanics are depicted from an algebraic and geometric perspective.