An estimation method of normalized nonlinear output frequency response functions for fatigue damage detection using stochastic response signal

Nonlinear output frequency response functions (NOFRFs) and its modified version, normalized NOFRFs (norm-NOFRFs), are composed of multiple spectra, which can sensitively indicate the occurrence of fatigue damage in machinery. However, their application is restricted to a certain extent. Currently, neither NOFRFs nor norm-NOFRFs can be estimated with only a single response signal. Aimed at this problem, the nonlinear auto-regressive (NAR) model was introduced, and an estimation method of norm-NOFRFs is proposed in this paper. Only one stochastic response signal is required in the proposed method, which removes the restrictions on the number and intensity of signals to identify norm-NOFRFs, and expands the range of scenarios for using norm-NOFRFs in damage detection. The feasibility and robustness of the proposed method are verified by the nonlinear model in numerical simulation. The effectiveness of revealing and quantifying the fatigue damage is verified by experimental study for three kinds of mechanical parts. A method for estimating normalized NOFRFs based on NAR model is proposed. The required signal for estimating normalized NOFRFs is reduced to one. Only response signal needs to be measured in NAR model-based estimation method. Fatigue damage can be detected through NAR model-based estimation method.