Structural Nonlinear Damage Identification Algorithm Based on Time Series ARMA/GARCH Model

Abstract

In recent years, vibration based structural damage detection has been paid more and more attention by many researchers, especially for those based on the time series analysis. However, the traditional methods are mainly based on the linear time series analysis, which cannot deal with nonlinear damages effectively, such as the fatigue cracks that open and close upon dynamic loading. A new algorithm for the nonlinear damage detection is proposed based on a model of autoregressive moving average (ARMA) with generalized autoregressive conditional heteroscedasticity (GARCH) (ARMA/GARCH) in this paper. First, a reference ARMA model is constructed with the acceleration responses measured in a reference (healthy) state and the one-step-ahead error prediction are modeled as a GARCH model. Secondly, the new nonlinear damage-sensitive feature (DSF) is defined as the conditional standard deviation of the residual error of GARCH model in the reference and the unknown states, respectively. The performance of the presented algorithm is then evaluated by the experimental data of a three-story building structure provided by Los Alamos National Laboratory (LANL). Finally, the new algorithm is compared with the traditional methods based on the standard deviation ratio of the residual error of ARMA model. The illustrated results show that the proposed method can effectively estimate the extent of the nonlinear damage with higher accuracy. It has less computational cost and more robustness against operational and environmental variety. This makes it applicable for structural health monitoring in situ.