A Structural Damage Localization Method Based on Empirical Probability Mass Function of ARMAX Model Residual and Kullback–Leibler Divergence

Abstract

Damage localization is very significant in engineering applications. The existing method based on the chi-square distribution of an autoregressive moving average with exogenous inputs (ARMAX) model residual is not applicable for these realistic excitations except Gaussian excitation. To solve the above problem, this paper presents a structural damage localization method based on the empirical probability mass function (EPMF) of the ARMAX model residual and Kullback–Leibler (KL) divergence. In detail, we employ empirical data analysis (EDA) approach to estimate the EPMF of the ARMAX model residual of the data generated by the arbitrary excitation because EDA does not need any a priori knowledge about the model residual. Moreover, the KL divergence is introduced to measure the dissimilarity of the EPMFs in undamaged and damaged states to prove that our method is effective for arbitrary excitation. Finally, the semi-parametric extreme value theory is used to estimate the reliable threshold for localizing the damage. Numerical simulated and experimental results illustrate that the proposed method localizes the damage under different excitations, respectively.