NARX neural networks for nonlinear analysis of structures in frequency domain

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.