Abstract
In the service period, some engineering structures may have cracks or other nonlinear damages. The nonlinear damages are the major influence to the safety of engineering structures, which should be detected as early as possible. Currently, the effective nonlinear damage detection method is still lacking. Therefore, a penalty conversion index based on generalized autoregressive conditional heteroskedasticity (GARCH) model is presented to identify the nonlinear damage. First, an exact expression of GARCH model is described, the bilinear stiffness characteristic of nonlinear damage is given, and acceleration responses are used to establish the GARCH model. Then, through the GARCH model analysis of nonlinear damages responses, it can be found that the variance of conditional variance are sensitive to the nonlinear damage information of acceleration responses, so a basic conversion index based on the variance of conditional variance is proposed. Finally, a penalty conversion index based on GARCH model is presented, which can reduce the interference induced by the adjacent unrelated factors. Numerical and experimental examples show that the identification results of the proposed penalty conversion index based on GARCH model are superior to those of the basic conversion index and the cepstral metric (CM) index.
Highlights
The principle of vibration-based damage detection is that structural damage will change the dynamic characteristics of the structure, and the damage information can be acquired from the change of the dynamic characteristics.[4]
The nonlinear damage identification principle is studied, a novel index based on generalized autoregressive conditional heteroskedasticity (GARCH) model and penalty function is proposed
The maximum likelihood approach is utilized to estimate the model parameter, and Akaike information criterion is employed to calculate the order of GARCH model
Summary
In recent 30 years, vibration-based damage detection has received increasing attention.[1,2,3] The principle of vibration-based damage detection is that structural damage will change the dynamic characteristics of the structure, and the damage information can be acquired from the change of the dynamic characteristics.[4]. Keywords Damage identification, acceleration response, GARCH model, penalty function, nonlinearity A penalty GARCH conversion index is proposed, which is mainly based on GARCH effect of nonlinear responses and can directly identify the interstorey stiffness damage location.
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