一种仅使用静态响应的梁结构损伤识别方法

提出了一种仅使用静态响应的梁结构损伤识别方法。此方法引入了一种倒数变量。采用倒数变量后，位移的泰勒展开式中仅含有倒数增量的线性项。构建了基于倒数变量的损伤求解模型，然后应用非负最小二乘法求解损伤参数，可同时确定损伤位置和程度。与未引用倒数变量的方法对比，求解的损伤参数更加逼近真实的损伤情况，且讨论了噪声的影响。通过数值模拟对三跨连续梁结构进行仿真分析，结果表明，提出的方法能够对梁结构的损伤做出有效识别。

A beam structure damage detection method using only static response

In this paper,a damage identification method for a beam structure using only its static response is proposed.This method introduces reciprocal variables.The Taylor expansion of the displacement after adopting the reciprocal variables only contains the linear term of the reciprocal increments.We construct a damage solution model based on reciprocal variables,and then apply the non-negative least-squares method to obtain the damage parameters,which can determine the location and extent of the damage at the same time.Compared with the method that does not involve the reciprocal variables,the damage parameters obtained by this method are closer to the real damage situation.This paper also discusses the effects of noise.A three-span continuous beam structure is modelled and analyzed by numerical simulation.The results show that the proposed method can effectively identify the damage of the beam structure.