Structural nonlinear damage identification using penalty conversion index of GARCH model

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.