Sparse representation for damage identification of structural systems

TL;DR

This paper introduces a two-stage sensitivity analysis framework combining Bayesian updating and sparse representation techniques to accurately identify and quantify structural damage, even under uncertainties.

Contribution

It presents a novel two-stage approach integrating Bayesian learning and sparse regression for damage detection and quantification in structural systems.

Findings

Successfully localized and quantified damage in three structural examples.

Achieved high accuracy in damage detection despite uncertainties.

Reduced computational cost through hyperparameter optimization.

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 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.