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Sparse representation for damage identification of structural systems

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Document pages: 11 pages

Abstract: Identifying damage of structural systems is typically characterized as aninverse problem which might be ill-conditioned due to aleatory and epistemicuncertainties induced by measurement noise and modeling error. Sparserepresentation can be used to perform inverse analysis for the case of sparsedamage. In this paper, we propose a novel two-stage sensitivity analysis-basedframework for both model updating and sparse damage identification.Specifically, an $ ell 2$ Bayesian learning method is firstly developed forupdating the intact model and uncertainty quantification so as to set forward abaseline for damage detection. A sparse representation pipeline built on aquasi-$ 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 developedto heuristically learn hyperparameters from data, which saves the computationalcost of hyperparameter tuning and produces more reliable identification result.The proposed framework is verified by three examples, including a 10-storyshear-type building, a complex truss structure, and a shake table test of aneight-story steel frame. Results show that the proposed approach is capable ofboth localizing and quantifying structural damage with high accuracy.

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