Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/79070
Title: Selection of regularization parameter for l(1)-regularized damage detection
Authors: Hou, RR 
Xia, Y 
Bao, YQ
Zhou, XQ
Keywords: Damage detection
Sparsity
L(1) regularization
Regularization parameter
Vibration method
Issue Date: 2018
Publisher: Academic Press
Source: Journal of sound and vibration, 9 June 2018, v. 423, p. 141-160 How to cite?
Journal: Journal of sound and vibration 
Abstract: The l(1) regularization technique has been developed for structural health monitoring and damage detection through employing the sparsity condition of structural damage. The regularization parameter, which controls the trade-off between data fidelity and solution size of the regularization problem, exerts a crucial effect on the solution. However, the l(1) regularization problem has no closed-form solution, and the regularization parameter is usually selected by experience. This study proposes two strategies of selecting the regularization parameter for the l(1)-regularized damage detection problem. The first method utilizes the residual and solution norms of the optimization problem and ensures that they are both small. The other method is based on the discrepancy principle, which requires that the variance of the discrepancy between the calculated and measured responses is close to the variance of the measurement noise. The two methods are applied to a cantilever beam and a three-story frame. A range of the regularization parameter, rather than one single value, can be determined. When the regularization parameter in this range is selected, the damage can be accurately identified even for multiple damage scenarios. This range also indicates the sensitivity degree of the damage identification problem to the regularization parameter.
URI: http://hdl.handle.net/10397/79070
ISSN: 0022-460X
EISSN: 1095-8568
DOI: 10.1016/j.jsv.2018.02.064
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