Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

In this paper, a nonlinear auto regressive with eXegenous input (NARX) model of nonlinear systems, where the physical parameters of interest for the system design appear explicitly as coefficients in the model, is introduced. The model is referred to as the NARX model with parameters of interest for design (NARX-M-for-D). The output frequency response function (OFRF) in terms of these physical parameters is then introduced for the NARX-M-for-D, and an efficient algorithm is derived to determine the OFRF so as to facilitate the design of nonlinear systems in the frequency domain. Moreover, a general procedure for the design of the physical parameters of the NARX-M-for-D in the frequency domain is proposed, which has the potential to be applied to design a wide range of engineering systems and structures. Finally, two case studies are provided to demonstrate the new OFRF-based nonlinear system design and its significance in engineering applications.