Selection of regularization parameter for l1-regularized damage detection

Rongrong Hou, Yong Xia, Yuequan Bao, Xiaoqing Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

35 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)141-160
Number of pages20
JournalJournal of Sound and Vibration
Volume423
DOIs
Publication statusPublished - 9 Jun 2018

Keywords

  • Damage detection
  • Regularization parameter
  • Sparsity
  • Vibration method
  • l regularization

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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