基于不完备模态信息的结构损伤识别方法

针对结构损伤识别中的有限测点问题和测试噪声问题,提出一种基于模型修正法的损伤识别方法,仅利用结构的低阶频率和相应的不完备振型进行损伤识别。基于动力缩聚法构造参数化的振型扩展矩阵,解决振型不完备的问题,然后根据交叉模型交叉模态法CMCM(cross-model cross-mode)构造约束方程,并使用Hestenes-Powell增广拉格朗日乘子法求解约束优化问题,从而根据优化问题的最优解判断出损伤位置和损伤程度。在模态数据包含测试噪声的情况下,提出一种改进的CMCM方法,以减小测试噪声对损伤识别结果的影响。对一个25杆平面桁架进行数值仿真实验,结果表明,在3%的噪声水平下,仅需测得损伤结构的前5阶不完备模态,本文方法就能较准确地识别结构损伤。

Damage detection method using incomplete modal information

A new method based on model updating was developed in this paper to identify damage with the low-order frequencies and incomplete modes of vibration.It aims to deal with a finite number of measure points and measurement noise.Mode shapes are expanded with parameterized expansion matrixes based on a dynamic condensation method.Constraint equations are established based on the CMCM (cross-model cross-mode) method.The Hestenes-Powell extended Lagrange multiplier method is adopted to solve this constrained optimization problem.The optimal solution indicates the positions and degrees of damages.When the modal data contains measurement noise,an improved CMCM method is proposed to decrease its influence of test noise.The proposed method is verified against the numerical simulation test of a 25-bar truss structure.The results show that this method can identify damages accurately using the first five incomplete modes when the modal data contains 3% measurement noise.