Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can be used to perform inverse analysis for the case of sparse damage. In this paper, we propose a novel two-stage sensitivity analysis-based framework for both model updating and sparse damage identification. Specifically, an $\ell_2$ Bayesian learning method is firstly developed for updating the intact model and uncertainty quantification so as to set forward a baseline for damage detection. A sparse representation pipeline built on a quasi-$\ell_0$ method, e.g., Sequential Threshold Least Squares (STLS) regression, is then presented for damage localization and quantification. Additionally, Bayesian optimization together with cross validation is developed to heuristically learn hyperparameters from data, which saves the computational cost of hyperparameter tuning and produces more reliable identification result. The proposed framework is verified by three examples, including a 10-story shear-type building, a complex truss structure, and a shake table test of an eight-story steel frame. Results show that the proposed approach is capable of both localizing and quantifying structural damage with high accuracy.

中文翻译：

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结构系统损伤识别的稀疏表示

识别结构系统的损坏通常被表征为一个逆问题，由于测量噪声和建模错误引起的随机和认知不确定性，该问题可能是病态的。稀疏表示可用于对稀疏损坏的情况进行逆分析。在本文中，我们提出了一种新的基于两阶段敏感性分析的框架，用于模型更新和稀疏损伤识别。具体而言，首先开发了 $\ell_2$ 贝叶斯学习方法，用于更新完整模型和不确定性量化，从而为损伤检测设定基线。然后呈现基于准$\ell_0$ 方法（例如，顺序阈值最小二乘法（STLS）回归）的稀疏表示管道，用于损伤定位和量化。此外，贝叶斯优化与交叉验证相结合，启发式地从数据中学习超参数，节省了超参数调整的计算成本，并产生更可靠的识别结果。所提出的框架通过三个实例进行验证，包括10层剪力式建筑、复杂桁架结构和8层钢框架的振动台试验。结果表明，所提出的方法能够以高精度定位和量化结构损伤。和八层钢框架的振动台试验。结果表明，所提出的方法能够以高精度定位和量化结构损伤。和八层钢框架的振动台试验。结果表明，所提出的方法能够以高精度定位和量化结构损伤。