Optimization or Bayesian Strategy? Performance of the Bhattacharyya Distance in Different Algorithms of Stochastic Model Updating



Bi, Sifeng, Beer, Michael ORCID: 0000-0002-0611-0345, Zhang, Jingrui, Yang, Lechang and He, Kui
(2021) Optimization or Bayesian Strategy? Performance of the Bhattacharyya Distance in Different Algorithms of Stochastic Model Updating. ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg, 7 (2).

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Abstract

<jats:title>Abstract</jats:title> <jats:p>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.</jats:p>

Item Type: Article
Divisions: Faculty of Science and Engineering > School of Engineering
Depositing User: Symplectic Admin
Date Deposited: 25 Apr 2022 07:22
Last Modified: 21 Aug 2022 13:10
DOI: 10.1115/1.4050168
URI: https://livrepository.liverpool.ac.uk/id/eprint/3153875