Structural nonlinear damage identification based on the information distance of GNPAX/GARCH model and its experimental study

Abstract

In the structural health monitoring (SHM) of civil engineering, most of the structural damage is nonlinear damage, such as breathing cracks and bolt looseness. Under the excitation of external loads, the time-domain response data of the structure produced by these nonlinear damages have nonlinear features. In order to solve the time-domain nonlinear damage identification problem of complex structures, this paper proposes a nonlinear damage identification method based on the information distance of GNPAX/GARCH (general expression of system identification for linear and nonlinear with polynomial approximation and exogenous inputs/generalized autoregressive conditional heteroskedasticity) model. First, an order determination method based on Bayesian optimization to select the order of the GNPAX/GARCH model was proposed, and the GNPAX/GARCH model was established for damage identification. Then, the redundant structural items of GNPAX/GARCH model were removed by the model optimization method based on the structural pruning algorithm. Finally, the information distance of the GNPAX/GARCH model conditional heteroscedasticity series between the baseline state and test state was derived, and the structural damage source locations were determined according to the information distance. A three-story frame structure experiment and a stand structure experiment were used to verify the effectiveness of the proposed method. The results show that the proposed method can effectively identify the nonlinear damages caused by the component breathing crack and joint bolt looseness, verifying its robustness to the nonlinear damage identification of the multi-story and multi-span complex structures.

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

“…The estimation of model coefficients oriented by a GARCH model gives us the estimated data with the following Table 5, where a is the true value of model (32), â is its estimators, and ns represents the number of simulations It can be observed that estimators of variable values in the bilinear model, as defined by its expression, yield efficient results when driven by Symmetric GARCH compared to Asymmetric GARCH, indicating that symmetry plays a crucial role in enhancing the accuracy of estimation for the proposed model [19][20][21][22][23][24][25].…”