结构在服役期间可能会产生裂纹等损伤，裂纹的张开和闭合效应使损伤呈现出时域非线性特性.另外，基于时域模型的方法主要反映了刚度损伤引起相邻节点自由度处的特征改变，难以直接反映层间刚度的损伤信息.为了解决这些问题，提出了一种基于GARCH模型和改进罚指标的损伤识别方法.首先描述了GARCH模型的基本原理，并给出了GARCH模型的定阶方法和模型参数估计法.然后分析了时域非线性的双线性刚度特性，并提出了基于GARCH模型的非线性损伤识别原理和基于刚度的基本GARCH指标.最后利用罚函数原理，对层间刚度损伤提出了一种改进GARCH罚指标方法以提高识别可靠性.数值计算和实验研究结果表明，采用改进GARCH罚指标可以较好识别出结构非线性损伤，其识别效果要好于基本GARCH指标以及基于线性自回归模型和倒谱测距的方法.
In service period, some structures may exist damages like cracks, and the opening and closing of cracks make the damage display a time-domain nonlinear characteristic. In addition，time-domain model methods mainly provide the characteristic change of degree of freedom of adjacent nodes caused by stiffness damage, but it is difficult to directly show the inter-storey stiffness information. To solve these problems, a damage detection method based on GARCH model and improved penalty index was presented. Firstly, basic theory of GARCH model was described, and the order estimation and the parameter estimation of GARCH model were proposed. Then, the bilinear stiffness characteristic of time-domain nonlinearity was analyzed, and the nonlinear damage identification principle and basic GARCH index of stiffness identification were presented. Finally, an improved GARCH penalty index method was established to enhance the identification reliability for the inter-storey stiffness damage. Simulation and experiment results indicate that the improved GARCH penalty index can well identify the structural nonlinear damage, and the identification effect of the proposed index is obviously better than those of the basic GARCH index and those combined with autoregressive model and the cepstral metric index.
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