Abstract The structural damage identification based on the dynamic condensation of finite element (FE) model can effectively deal with the mismatching between the measured degree of freedom (DOF) and the total DOFs of the entire FE model, and avoid the issues of mode pairing and repeated solution of the generalized eigenvalue problem of large-scale FE models. The proper configuration of master DOFs is essential for the successful application of the model reduction-based damage identification method, which determines the position of the sensors, the rearrangement of system matrices of the FE model according to the master/slave DOFs, and the specific form of the transformation matrix for the dynamic reduction method at the same time. The main purpose of this paper is to investigate the optimized choice of the master DOFs specifically for the dynamic reduction-based damage identification method through Bayesian experimental design, which is based on the Bayesian inference to interpret the data measured during the experiment. In the terminology of Bayesian experimental design, considering the configuration of master DOFs as a design of experiment, the utility function is defined through the Kullback–Leibler divergence, or relative entropy, which is employed as a scalar measure to quantitatively characterize the information gain caused by the measurement data between the prior and posterior probability distribution over the uncertain model parameters. By maximizing the expected utility under the marginal distribution for the data, the optimal experimental design, which is taken as the optimal configuration of the master DOFs, can be achieved. The proposed methodology for the optimal selection of master DOFs relevant to the dynamic reduction-based damage identification method is verified through both numerical case studies on a 40-DOF truss and experimental research on a real-life pedestrian bridge.

中文翻译：

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基于贝叶斯实验设计的动态减量化结构健康监测硕士选拔

摘要 基于有限元（FE）模型动态凝聚的结构损伤识别可以有效处理实测自由度（DOF）与整个有限元模型总自由度不匹配的问题，避免模态配对和大规模有限元模型广义特征值问题的重复求解。主自由度的正确配置对于基于模型减少的损伤识别方法的成功应用至关重要，该方法确定传感器的位置，根据主/从自由度重新排列有限元模型的系统矩阵，以及特定的同时为动态缩减方法的变换矩阵的形式。本文的主要目的是通过贝叶斯实验设计研究主自由度的优化选择，专门用于基于动态减少的损伤识别方法，该方法基于贝叶斯推理来解释实验过程中测量的数据。在贝叶斯实验设计的术语中，将主自由度的配置视为实验设计，效用函数是通过 Kullback-Leibler 散度或相对熵定义的，它被用作标量度量来定量表征所引起的信息增益通过不确定模型参数的先验和后验概率分布之间的测量数据。通过最大化数据边际分布下的预期效用，优化实验设计，这被视为主自由度的最佳配置，可以实现。通过对 40 自由度桁架的数值案例研究和对真实人行天桥的实验研究，验证了与基于动态减少的损伤识别方法相关的主自由度的最佳选择方法。