Optimization or Bayesian strategy? Performance of the Bhattacharyya distance in different algorithms of stochastic model updating

Sifeng Bi*, Michael Beer, Jingrui Zhang, Lechang Yang, Kui He

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
69 Downloads (Pure)

Abstract

The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating.

Original languageEnglish
Article number020903
Number of pages10
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
Volume7
Issue number2
Early online date23 Apr 2021
DOIs
Publication statusPublished - 23 Apr 2021

Keywords

  • Bayesian model updating
  • Bhattacharyya distance
  • Markov chain Monte Carlo
  • optimization model updating
  • uncertainty quantification

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