Distribution-free stochastic model updating of dynamic systems with parameter dependencies
Distribution-free stochastic model updating of dynamic systems with parameter dependencies
This work proposes a distribution-free stochastic model updating framework to calibrate the joint probabilistic distribution of the multivariate correlated parameters. In this framework, the marginal distributions are defined as the staircase density functions and the correlation structure is described by the Gaussian copula function. The first four moments of the staircase density functions and the correlation coefficients are updated by an approximate Bayesian computation, in which the Bhattacharyya distance-based metric is proposed to define an approximate likelihood that is capable of capturing the stochastic discrepancy between model outputs and observations. The feasibility of the framework is demonstrated on two illustrative examples and a followed engineering application to the updating of a nonlinear dynamic system using observed time signals. The results demonstrate the capability of the proposed updating procedure in the very challenging condition where the prior knowledge about the distribution of the parameters is extremely limited (i.e., no information on the marginal distribution families and correlation structure is available).
Bayesian model updating, Bhattacharyya distance, Gaussian copula function, Staircase density function, Uncertainty quantification
Kitahara, Masaru
6b8dae61-067b-41ca-a7ef-913ca2a42b6e
Bi, Sifeng
93deb24b-fda1-4b18-927b-6225976d8d3f
Broggi, Matteo
104881e3-cd8d-4909-9049-a914be5ee548
Beer, Michael
e44760ce-70c0-44f2-bb18-7197ba142788
3 May 2022
Kitahara, Masaru
6b8dae61-067b-41ca-a7ef-913ca2a42b6e
Bi, Sifeng
93deb24b-fda1-4b18-927b-6225976d8d3f
Broggi, Matteo
104881e3-cd8d-4909-9049-a914be5ee548
Beer, Michael
e44760ce-70c0-44f2-bb18-7197ba142788
Kitahara, Masaru, Bi, Sifeng, Broggi, Matteo and Beer, Michael
(2022)
Distribution-free stochastic model updating of dynamic systems with parameter dependencies.
Structural Safety, 97, [102227].
(doi:10.1016/j.strusafe.2022.102227).
Abstract
This work proposes a distribution-free stochastic model updating framework to calibrate the joint probabilistic distribution of the multivariate correlated parameters. In this framework, the marginal distributions are defined as the staircase density functions and the correlation structure is described by the Gaussian copula function. The first four moments of the staircase density functions and the correlation coefficients are updated by an approximate Bayesian computation, in which the Bhattacharyya distance-based metric is proposed to define an approximate likelihood that is capable of capturing the stochastic discrepancy between model outputs and observations. The feasibility of the framework is demonstrated on two illustrative examples and a followed engineering application to the updating of a nonlinear dynamic system using observed time signals. The results demonstrate the capability of the proposed updating procedure in the very challenging condition where the prior knowledge about the distribution of the parameters is extremely limited (i.e., no information on the marginal distribution families and correlation structure is available).
Text
Struct_Safety_Kitahara&Bi&Broggi&Beerr_preprint_20220214
More information
Accepted/In Press date: 25 April 2022
e-pub ahead of print date: 3 May 2022
Published date: 3 May 2022
Keywords:
Bayesian model updating, Bhattacharyya distance, Gaussian copula function, Staircase density function, Uncertainty quantification
Identifiers
Local EPrints ID: 490515
URI: http://eprints.soton.ac.uk/id/eprint/490515
ISSN: 0167-4730
PURE UUID: f9942875-c962-44a2-a916-193b30a6a0a3
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Date deposited: 29 May 2024 16:43
Last modified: 01 Jun 2024 02:09
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Contributors
Author:
Masaru Kitahara
Author:
Sifeng Bi
Author:
Matteo Broggi
Author:
Michael Beer
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