A methodology for structural nonlinear damage identification using higher-order spectral analysis of time series

Since obtaining the undamaged structural response information is challenging in practice, damage identification methods relying on undamaged response data face significant limitations in engineering applications. Furthermore, issues such as the influence of measurement noise, high computational costs, and the weak theoretical interpretability of damage identification methods constrain the development and application of structural health monitoring technologies. This paper aims to develop a simple, effective, and noise-resistant method for identifying structural nonlinear damage. To achieve this goal, a structural nonlinear damage identification method is proposed by combining the strong noise resistance of higher-order spectra with the advantages of the autoregressive (AR) model, which has clear physical interpretability and low computational cost. The proposed method establishes an AR model for the structural acceleration response, and regards the bispectral image fluctuation level of AR model residuals as a damage-sensitive feature, developing a damage indicator based on this feature for nonlinear damage localization. The analytical validation was conducted separately using nonlinear damage experiment data from the three-story frame model at Los Alamos National Laboratory and a scaled relay tower model. The analysis results verify that the proposed method can effectively identify and characterize nonlinear features within structural acceleration response. It can accurately identify nonlinear features caused by breathing cracks and bolt looseness, and efficiently determine the location of structural nonlinear damage sources.