Sparse representation for damage identification of structural systems

Abstract

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 article, we propose a novel two-stage sensitivity analysis–based framework for both model updating and sparse damage identification. Specifically, an [Formula: see text] Bayesian learning method is first 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-[Formula: see text] method, for example, sequential threshold least squares regression, is then presented for damage localization and quantification. In addition, 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.

A fraction function regularization model for the structural damage identification

“…The updated stiffness parameter is utilized for locating and quantifying the structural damage. Among many techniques for model updating (e.g., heuristic algorithm (Sun et al, 2013), least squares based approaches (Xu et al, 2012), and filtering techniques (Chatzi and Smyth, 2002)), the sensitivity analysis is the most outstanding one because of its efficient computational capability and prominent sensitivity to small parameter changes (Mottershead et al, 2011; Zhao and Sun, 2020). However, the mathematical model of the sensitivity analysis-based model updating is generally underdetermined due to the fact that the number of available structural modal parameters is far less than that of structural elements.…”

“…More recently, the probabilistic models based on the regularization technique are proposed for the structural damage identification (Hou et al, 2019; Wang et al, 2020a, 2020b). For example, two-stage sensitivity analysis-based damage identification frameworks based on Bayesian l 1 learning are proposed for the reliable damage identification in Zhao and Sun (2020) and Zhao et al (2020).…”

Sparse Damage Detection with Complex Group Lasso and Adaptive Complex Group Lasso

“…One should note that such an approach calls for a sufficiently accurate model for the sensitivities of the baseline state to be obtained. Chen et al [13] applied a sensitivity analysis to express shifts of the modal parameters in terms of local stiffness degradation on the elemental level of a structural model. Sparse regression was then solved with a sequential threshold least squares algorithm.…”

A novel joint sparse regularization model to structural damage identification by the generalized fused lasso penalty

“…The variation of the physical parameters represents the damage information, which is used in locating the damage location and quantifying the damage severity simultaneously. Among techniques for model updating (e.g., filtering techniques (Chatzi and Smyth, 2009), least squares based approaches (Xu et al, 2012), and heuristic algorithms (Sun et al, 2013), the sensitivity analysis is the most classical one due to its high computational efficiency and excellent sensitivity to small parameter perturbations (Mottershead et al, 2011; Marwala, 2010; Chen and Sun, 2020). However, the mathematical model of sensitivity analysis is typically underdetermined because the order-number of the available modal parameters is usually less than the number of structural elements.…”