More transparent neural network approach for modeling nonlinear hysteretic systems

A powerful Volterra/Wiener Neural Network (VWNN) is designed to reflect the underlying dynamics of hysteretic systems. The nonlinear response of multi-degree-of-freedom systems subjected to force excitation can be tracked using this neural network. More importantly, the inner-workings of the network, such as the design parameters as well as the weights and biases, can be loosely related to physical properties of dynamic systems. This effort differs markedly from what is typically done for neural networks as well as the original version of the VWNN in Ref. 1. An adaptive training algorithm and improved formulation of high-order nodes are adopted to enable fast training and stable convergence. A training example is provided to demonstrate that the VWNN is able to yield a unique set of solutions (i.e., the weights) when the values of the controlling design parameters are fixed a priori. The selection of these design parameters in practical applications is discussed. The advantages of the VWNN illustrate the potential of applying highly flexible nonparametric identification techniques in a parametric fashion to suit the needs of structural health monitoring and damage detections.