NARX neural networks for nonlinear analysis of structures in frequency domain

Abstract

The Volterra series is a powerful tool in the analysis of nonlinear systems. The nonlinear behavior of a system can be interpreted from investigation of Fourier transforms of Volterra kernels (so called higher‐order frequency response function, HFRFs). The Volterra series are highly promising for nonlinear analysis of civil structures where the nonlinear nature of structures must often be considered. However, a major limitation of Volterra series is the difficulty involved in the calculation of Volterra kernels. Chance et al. (1998) developed a method to obtain HFRFs of a single‐input system directly from the weights of the NARX (Nonlinear AutoRegressive with eXogenous) neural network which identified the system. In order to analyze nonlinear seismic behavior of multi‐input large civil structures such as bridges, this study extends the work of Chance et al. (1998) to a multi‐input Volterra series. Moreover, a numerical example and a real application example (nonlinear seismic behavior analysis of Bai‐Ho bridge, the first seismic isolation bridge in Taiwan) demonstrate the feasibility of applying the proposed method for nonlinear analysis of a multi‐input system.