This paper presents a novel sparse-regularized minimum constitutive relation error (min-CRE) approach for structural damage identification with modal data. In this approach, the inverse identification problem is treated as a nonlinear optimization problem whose objective function is just the constitutive relation error (CRE). To circumvent the ill-posedness of the inverse problem that is caused by use of the possibly insufficient modal data and enhance the robustness of the identification process, the sparse regularization is introduced where a sparse (or ℓ1-norm) regularization term is added to the original CRE function. In regard to the minimum solution of the sparse-regularized CRE objective function, a two-step substitution algorithm is established. The attractive feature of the present damage identification approach is that no sensitivity analysis is involved herein and the additional introduction of the sparse regularization term introduces little computational complexity. The approach is applied to damage identification of one- or two-dimensional beam structures with experimental or simulated modal data. Results show that the sparse regularization indeed improves the effectiveness and robustness of the min-CRE approach under measurement noises and initial model errors, even in the case of large damages.
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