The role of the Bhattacharyya distance in stochastic model updating

• Published in: Mechanical systems and signal processing Vol. 117; pp. 437 - 452
• Main Authors: Bi, Sifeng, Broggi, Matteo, Beer, Michael
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15-02-2019; Elsevier BV
• Subjects: Algorithms; Approximate Bayesian computation; Bayesian analysis; Bayesian updating; Computer simulation; Model updating; Model validation; Stochastic model updating; Stochastic models; Uncertainty; Uncertainty quantification; Validation studies; Bayesian updating; Uncertainty quantification; Stochastic model updating; Model validation; Approximate Bayesian computation
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2018.08.017

•Bhattacharyya distance is proposed as a novel UQ metric in stochastic model updating.•The proposed likelihood is a capable connection between UQ metrics and updating tool.•Both Bhattacharyya and Euclidian distances are utilized in the updating framework.•Bhattacharyya distance is more comprehensive than Euclidian distance as a UQ metric.•Calculation is significantly reduced thanks to the approximate Bayesian computation.
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.