The role of the Bhattacharyya distance in stochastic model updating

Sifeng Bi, Matteo Broggi, Michael Beer

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)
344 Downloads (Pure)


The Bhattacharyya distance is a stochastic measurement between two samples and taking into account their probability distributions. The objective of this work is to further generalize the application of the Bhattacharyya distance as a novel uncertainty quantification metric by developing an approximate Bayesian computation model updating framework, in which the Bhattacharyya distance is fully embedded. The Bhattacharyya distance between sample sets is evaluated via a binning algorithm. And then the approximate likelihood function built upon the concept of the distance is developed in a two-step Bayesian updating framework, where the Euclidian and Bhattacharyya distances are utilized in the first and second steps, respectively. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated mass-spring example and a quite challenging benchmark problem for uncertainty treatment. These examples demonstrate a gain in quality of the stochastic updating by utilizing the superior features of the Bhattacharyya distance, representing a convenient, efficient, and capable metric for stochastic model updating and uncertainty characterization.

Original languageEnglish
Pages (from-to)437-452
Number of pages16
JournalMechanical Systems and Signal Processing
Early online date17 Aug 2018
Publication statusPublished - 15 Feb 2019


  • approximate Bayesian computation
  • Bayesian updating
  • model validation
  • stochastic model updating
  • uncertainty quantification


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