基于概率理论和AR/GARCH模型的非线性损伤识别

Structural nonlinear damage identification based on probability theory and AR/GARCH model

为了解决在不确定因素干扰下的结构非线性损伤识别问题,提出了基于概率理论和自回归/广义自回归条件异方差(AR/GARCH,autoregressive/generalized autoregressive conditional heteroskedasticity)混合模型的非线性损伤识别方法。描述了AR/GARCH模型的组合理论及其相应的组合公式,给出了模型参数估计和定阶方法。利用损伤前后的加速度响应信号构造AR/GARCH模型,并进一步提取出非线性损伤特征因子。采用概率理论和置信区间方法获取相应的损伤存在概率,并建立基于层间刚度的基本概率损伤指标。在此基础上,基于权化技术提出了改进概率损伤指标以提高识别可靠性。数值计算和实验验证结果表明,基于概率理论和AR/GARCH模型的损伤技术可以较好地解决不确定因素干扰下的非线性损伤问题,改进概率指标的识别效果明显优于基本概率指标。

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.