Structural nonlinear damage identification based on probability theory and AR/GARCH model
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Abstract:
In order to solve nonlinear damage detection problem under the disturbance of some uncertain factors, a damage identification method based on probability theory and AR/GARCH hybrid model was presented. First, the combination theory of an autoregressive (AR) model and a generalized autoregressive conditional heteroskedasticity (GARCH) model was described and the corresponding formulas were given. Parameter estimation and order determination strategies were proposed. Then, acceleration responses were utilized to establish the AR/GARCH model and extract nonlinear damage feature factor. Finally, probability theory and confidence interval approach were adopted for calculating probability of damage existence and a basic probability index was employed to detect inter-storey stiffness damage. An improved probability index based on weighting technique was further presented to raise the identification reliability. Simulation and experiment results show that the damage identification method based on probability theory and the AR/GARCH model can solve the nonlinear damage problem with uncertain factor disturbance and the identification results of improved probability index are obviously superior to those of the basic one.
