An Effective Method for Evaluation of the Nonlinear Output Frequency Response Functions from System Input-Output Data

Abstract

The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was introduced in [1] for the analysis of nonlinear systems in the frequency domain where a least-squares (LS) method was proposed for the evaluation of the NOFRFs using system input-output data. However, this leastsquares (LS) based approach may experience numerical errors due to matrix inversion and consequently cannot produce accurate NOFRFs sometimes. In order to mitigate this problem, in the present study, a modified LS method (M-LS) is proposed to make sure that the information matrix to be inverted for the LS solution is appropriately constructed so as to improve the condition number of the information matrix and reduce the numerical errors. Simulation results have demonstrated the effectiveness of the newly proposed method and indicated that the new method will enable a more accurate evaluation of the NOFRFs and facilitate the frequency analysis of nonlinear systems directly using system input-output data.