Quantifying uncertainty in material damage from vibrational data

T. Butler*, A. Huhtala, M. Juntunen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
4 Downloads (Pure)


The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks results in local reductions in stiffness parameters and may drastically alter the response of the beam. Data obtained from the vibrating beam are often subject to uncertainties and/or errors typically modeled using probability densities. The goal of this paper is to estimate and quantify the uncertainty in damage modeled as a local reduction in stiffness using uncertain data. We present various frameworks and methods for solving this parameter determination problem. We also describe a mathematical analysis to determine and compute useful output data for each method. We apply the various methods in a specified sequence that allows us to interface the various inputs and outputs of these methods in order to enhance the inferences drawn from the numerical results obtained from each method. Numerical results are presented using both simulated and experimentally obtained data from physically damaged beams.

Original languageEnglish
Pages (from-to)414-435
Number of pages22
JournalJournal of Computational Physics
Publication statusPublished - 5 Feb 2015
MoE publication typeA1 Journal article-refereed


  • Damage identification
  • Ensemble Kalman filter
  • Inverse problems
  • Measure theory
  • Parameter estimation
  • Tikhonov regularization


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