The estimation method of normalized Nonlinear Output Frequency Response Functions with only response signals under stochastic excitation

The nonlinearity degree of the system can be sensitively revealed by the methods based on Nonlinear Output Frequency Response Functions (NOFRFs). However, there is a lack of methods based on NOFRFs that work with only response signals under stochastic excitation, which limits the application of NOFRFs in practical engineering. In this study, a new concept of normalized NOFRFs is proposed, and a corresponding estimation method that employs only stochastic output response is established. Firstly, a method of estimating NOFRFs by Power Spectral Density (PSD) is established, and therefrom the normalized NOFRFs and a corresponding nonlinearity index are proposed. Then, by taking the PSD of the excitation signal as the input and the PSD of the response signal as the output, a general estimation method of normalized NOFRFs is built, and an output measured only estimation method of normalized NOFRFs is further deduced and established. In these two estimation methods, the assumption of white noise excitation is not required, and the estimated results are insensitive to the change of excitation intensity. Finally, the experiments of fatigue damage detection of three-point bending fatigue steel plate specimens and reducer box cases under stochastic excitation are carried out. The results demonstrate that, compared with the NOFRFs, the degree of fatigue damage can be effectively revealed by the normalized NOFRFs with output.