Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems

This study attempts to demystify a powerful neural network approach for modelling non-linear hysteretic systems and in turn to streamline its architecture to achieve better computational efficiency. The recently developed neural network modelling approach, the Volterra/Wiener neural network (VWNN), demonstrated its usefulness in identifying the restoring forces for hysteretic systems in an off-line or even in an adaptive (on-line) mode, however, the mechanism of how and why it works has not been thoroughly explored especially in terms of a physical interpretation. Artificial neural network are often treated as “black box” modelling tools, in contrast, here the authors carry out a detailed analysis in terms of problem formulation and network architecture to explore the inner workings of this neural network. Based on the understanding of the dynamics of hysteretic systems, some simplifications and modifications are made to the original VWNN in predicting accelerations of hysteretic systems under arbitrary force excitations. Through further examination of the algorithm related to the VWNN applications, the efficiency of the previously published approach is improved by reducing the number of the hidden nodes without affecting the modelling accuracy of the network. One training example is presented to illustrate the application of the VWNN; and another is provided to demonstrate that the VWNN is able to yield a unique set of weights when the values of the controlling design parameters are fixed. The practical issue of how to choose the values of these important parameters is discussed to aid engineering applications.