Optimal Design of Nonlinear Systems by Using the Low Dimension Associated Output Frequency Response Function (AOFRF)

In this study, the low dimension Associated Output Frequency Response Function (AOFRF) is applied to conduct the optimal design of nonlinear systems in the frequency domain. First, the Nonlinear Auto-Regressive with eXogenous inputs Model with design parameters for Design (NARX-M-for-D) is achieved by using system identification approaches. After that, the polynomial AOFRF representation of the NARX-M-for-D is derived, and the Complex-Valued Forward Regression Orthogonal Least Squares (CV-FROLS) algorithm is applied to reduce the dimension of the polynomial AOFRF representation. Finally, a case study on the design of an auxetic foam based vibration isolation system is discussed to demonstrate the effectiveness and the application of low dimension AOFRF representation in nonlinear system design.