基于改进解析冗余度的损伤识别方法

提出一种采用无损指标和损伤指标相结合进行损伤识别的改进解析冗余度方法。该方法通过剔除求解方程组中与损伤单元相关的方程，补充与损伤单元无关的方程，构造出新的求解方程组进行求解。在新模型中，与损伤单元无关的约束条件构成无损指标，相关的约束条件则构成损伤指标。同时，采用结构无阻尼振动方程建立约束满足问题模型，提出了改进解析冗余度方法在结构动力测试方面的理论。通过数值算例验证所提出方法在结构静动力方面单、多损伤识别的有效性，也证明了该方法在一定数据误差及模型误差下的适用性。最后，设计了钢梁静、动力试验。试验结果显示，所提出的方法能够定位结构较小的损伤，并且损伤指标较为明显。该方法在梁式结构的损伤识别和安全评估中具有一定的工程实用性。

Damage identification method based on improved analytical redundancy reduction method

An improved analytical redundancy reduction method combining undamaged index and damaged index to identify the damages is proposed in this paper. In this method, the new solving equation set is made up by getting rid of the equations related to assumed and damaged elements and adding the equations unrelated. Consequently, in the updated model, the relevant and irrelevant equations can form the damaged index and undamaged index respectively. In this paper, the CSP model is established via the undamped vibration equation and the theory of improved analytical redundancy reduction method in structural dynamic tests is also proposed simultaneously. In order to demonstrate the effectiveness in identifying either single or multiple damages and the feasibility under the circumstances of data error and modeling error, the static and dynamic numerical simulations are carried out in this paper. Eventually, static and dynamic tests of the steel beam are designed in this paper and the results have shown that the proposed method can locate the relatively small damages of the structure with obvious values of damaged index. In conclusion, the proposed method is practical in damage identification and assessment of the beam structure in engineering.