基于静力柔度灵敏度的网架结构损伤识别

采用模态参数来组集网架结构的柔度矩阵面临较多困难，如所需模态数量较多、测点数量有限和密集模态识别精度较低等．相比之下，基于静力测试的柔度矩阵具有测试精度较高、无截断误差的优点．文中提出一种基于静力柔度灵敏度、先定位后定量的网架结构损伤识别方法．首先，针对柔度灵敏度方程容易产生病态解的问题，构造一种奇异值贡献指标以合理截断柔度灵敏度矩阵的奇异值，从而提高解的精度．其次，结合前述奇异值截断策略，在不更新刚度矩阵的前提下，通过多次计算来逐步缩减疑似损伤杆件，从而降低未损杆件的干扰和实现损伤杆件的定位．最后，仅保留灵敏度矩阵中已定位损伤杆件对应的列，在迭代计算中不断更新刚度矩阵来进行损伤杆件的定量识别．以某网架结构为例进行数值分析．结果表明：提出的奇异值贡献指标具有明显的突变位置，可方便地指出灵敏度方程奇异值截断位置；提出的两步识别法在仅利用竖向自由度的情况下具有较好的抗噪能力，可有效定位和定量识别损伤杆件．

Detecting Damages of Space Trusses Based on Static Flexibility Sensitivity

Many difficulties could be encountered when assembling the flexibility matrix of a space truss based on modal parameters. For example, many modes are needed, sensor locations are limited and identification accuracy of densely distributed modes is poor. In contrast, flexibility matrix assembled by static testing takes advantages of higher testing precision and free truncation errors. A damage detection method for space trusses based on static flexibility matrix was proposed by quantifying damage severities after accurate damage location identification. Firstly, to solve the problem that flexibility equations could easily render ill-posed solutions, a singularity contribution index was introduced to properly truncate singular values of flexibility matrix and to improve the solution accuracy. Secondly, with the aforementioned singular value truncation strategy utilized and stiffness matrix not updated, suspicious damaged members were reduced step by step through several rounds of calculations. As a result, disturbances from undamaged members were decreased and the locations of damaged members were identified. Finally, with the columns associated with the identified damaged members reserved in the flexibility matrix, damage quantification was further conducted by iterative computations in which stiffness matrix was continuously updated. A space truss was taken as the numerical example. Analysis results show that the proposed singularity contribution index has an evident mutation location, which can be used to conveniently determine the truncation location of singular values of the flexibility matrix. The proposed two-stage damage detection method has good anti-noise ability and can achieve effective damage location identification and quantification, using merely vertical degrees of freedom.