Structural Nonlinear Damage Identification Method Based on the Kullback–Leibler Distance of Time Domain Model Residuals

Abstract

Under external load excitation, damage such as breathing cracks and bolt loosening will cause structural time domain acceleration to have nonlinear features. To solve the problem of time domain nonlinear damage identification, a damage identification method based on the Kullback–Leibler (KL) distance of time domain model residuals is proposed in this paper. First, an autoregressive (AR) model order was selected using the autocorrelation function (ACF) and Akaike information criterion (AIC). Then, an AR model was obtained based on the structural acceleration response time series, and the AR model residual was extracted. Finally, the KL distance was used as a damage indicator to judge the structural damage source location. The effectiveness of the proposed method was verified by using a multi-story, multi-span stand model experiment and a simulated eight-story shear structure. The results show that the proposed structural nonlinear damage identification method can effectively distinguish the structural damage location of multi-degree-of-freedom shear structures and complex stand structures, and it is robust enough to detect environmental noise and small damage.

Data-Driven Structural Health Monitoring: Leveraging Amplitude-Aware Permutation Entropy of Time Series Model Residuals for Nonlinear Damage Diagnosis

“…The coefficients of the AR model are reliable DSFs that can be obtained by the Euler–Walker method or the least squares method [ 26 ]. However, DSFs based on AR model residuals do not require recalculation of model coefficients and are more compatible with unsupervised learning for damage detection.…”

“…For example, Chen et al [ 25 ] used the AR/ARCH model in economics for nonlinear damage detection in structures and proposed the use of a second-order variance index (SOVI) as a damage indicator. Zuo and Guo [ 26 ] developed an AR model for structural response acceleration data and proposed a damage identification method based on the residual Kullback–Leibler distance of the AR model to identify the nonlinear damage location of the structure more effectively. However, most of the previous studies have focused on the statistical characteristics of the model residuals, emphasizing the capability of the proposed damage classifiers in structural damage diagnosis and localization.…”

Exploration of Damage Identification Method for a Large-Span Timber Lattice Shell Structure in Taiyuan Botanical Garden based on Structural Health Monitoring

“…Both Equations ( 8) and ( 9) are linear equation sets about θ j , so θ j can be solved first according to Equation (9), and then ϕ i can be solved according to Equation (8).…”

“…The ARMA model, as an important component of time domain methods, is often used to fit regression structures to acceleration response data and extract DSF from it. Zuo and Guo [ 8 ] proposed a nonlinear damage identification method based on the autoregressive (AR) model and Kullback–Leibler distance, which has high sensitivity to minor damage. Razavi et al [ 4 ].…”