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Sparse Bayesian learning for structural damage identification

机译：稀疏贝叶斯学习用于结构损伤识别

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摘要

Identification of structural parameters can be cast as the process of solving an inverse problem, in which regularization may be required when the problem is ill-posed. Bayesian inference provides a probabilistic interpretation of the regularization and yields a statistically stable/bounded solution. To this end, this paper presents a hierarchical Bayesian learning methodology with sensitivity analysis for identification of structural damage which has sparse characteristics. The proposed learning framework consists of two hierarchies: (1) the classical Bayesian learning and (2) the sparse Bayesian learning. Based on the incomplete modal quantities extracted from measurements such as the acceleration time histories, the classical Bayesian learning is utilized to update a parameterized baseline model followed by the sparse Bayesian learning which can accurately identify the sparsity of damage. The Bayesian learning procedures are formulated with the sensitivity analysis of model parameters, which compensate the linear truncation errors and produce accurate identification results through iterative optimization. The performance of the proposed approach has been illustrated through two numerical examples (a 10-story shear-type building and a 33-bar truss structure) and an experimental validation (a shake-table test of an 8-story frame). Results indicate that the proposed method is robust for structural damage identification even in the presence of high measurement noise and a limited number of sensor recordings. This hierarchical Bayesian learning approach is generally more efficient than classical regularization techniques such as the Tikhonov regularization.
机译：结构参数的识别可以作为解决反问题的过程，当问题不适当时可能需要进行正则化。贝叶斯推理提供了对正则化的概率解释，并产生了统计上稳定/有界的解。为此，本文提出了一种具有敏感性分析的层次贝叶斯学习方法，用于识别具有稀疏特征的结构损伤。拟议的学习框架包括两个层次结构：（1）经典贝叶斯学习和（2）稀疏贝叶斯学习。基于从测量值（如加速时间历史）中提取的不完整模态量，经典贝叶斯学习可用于更新参数化基线模型，然后进行稀疏贝叶斯学习，后者可准确识别损坏的稀疏性。贝叶斯学习程序是通过对模型参数进行敏感性分析而制定的，该方法可以补偿线性截断误差并通过迭代优化产生准确的识别结果。通过两个数值示例（一个10层的剪力型建筑和一个33杆的桁架结构）和一个实验验证（一个8层框架的振动台测试）说明了该方法的性能。结果表明，即使在存在高测量噪声和有限数量的传感器记录的情况下，所提出的方法对于结构损伤识别也是可靠的。这种分层贝叶斯学习方法通​​常比经典的正则化技术（如Tikhonov正则化）更有效。

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