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Selection of masters in dynamic reduction-based structural health monitoring using Bayesian experimental design

机译：贝叶斯实验设计的动态减少结构健康监测硕士的选择

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摘要

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.
机译：基于有限元（FE）模型的动态凝结的结构损伤识别可以有效地处理测量的自由度（DOF）和整个FE模型的总DOF之间的不匹配，避免模式配对和重复的问题大规模FE模型的广义特征值问题的解决方案。主DOF的适当配置对于成功应用模型的基于模型的损伤识别方法是必不可少的，该损伤识别方法确定传感器的位置，根据主/从DOF和特定的FE模型的系统矩阵重新排列相互减少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专门针对基于动态的损伤识别方法的主DOF的优化选择，这是基于贝叶斯推断来解释在实验期间测量的数据。在贝叶斯实验设计的术语中，考虑到主DOF的配置作为实验的设计，通过Kullback-Leibler发散或相对熵定义了实用功能，或相对熵，其被用作标量测量来定量表征引起的信息增益通过不确定模型参数的先前和后验概率分布之间的测量数据。通过在数据的边际分布下最大化预期效用，可以实现最佳实验设计，作为主DOF的最佳配置。通过对现实行人步行桥的40-DOF桁架和实验研究的数值案例研究，验证了与动态缩减基于动态损伤识别方法相关的最佳选择的母DOF的方法。

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