In this paper, a non-modal parametric method to identify structural damage using a regularized autoregressive moving average time series model under environmental excitation is proposed in combination with the virtual impulse response function. This method can use the structural vibration response to determine the damage caused to the structure during environmental excitation. Firstly, the virtual impulse response function is obtained by using the structural vibration response. Then, a regularized ARMA time series model is used to fit the virtual impulse response function. Based on the change of auto-regression coefficients in the regularization model under different damage cases, the structural damage is identified. The authors derive the regularization equation of an ARMA time series model to solve the problems in a time series model and obtain the regularization coefficient. Finally, this method is applied to a three-degrees-of-freedom chain structure and a three-floor shear structure of the Los Alamos National Laboratory (LANL). The experimental results show that the method based on the regularized ARMA time series model under environmental excitation can effectively identify the structural damage, which is a reliable method for damage identification. The regularized ARMA time series model can accurately extract signal features and has invaluable application prospects in the field of structural health monitoring.
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