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Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
,
Michael Friswell,
Tanmoy Chatterjee,
Hadi Madinei ,
Tom Deighan
Applied Mathematical Modelling, Start page: 115800
Swansea University Authors:
Pushpa Pandey, Hamed Haddad Khodaparast , Michael Friswell, Hadi Madinei
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.1016/j.apm.2024.115800
Abstract
The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated likelihood function. The proposed methodology is applied to bo...
| Published in: | Applied Mathematical Modelling |
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| ISSN: | 0307-904X |
| Published: |
Elsevier BV
2024
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa68223 |
| Abstract: |
The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated likelihood function. The proposed methodology is applied to both numerical and experimental cases. The paper commences by introducing Bayesian inference and its constituents: the likelihood function, prior distribution, and posterior distribution. The resonant decay method is employed to extract backbone curves, which capture the non-linear behaviour of the system. A mathematical model based on a single degree of freedom (SDOF) system is formulated, and backbone curves are obtained from time response data. Subsequently, MCMC sampling is employed to estimate the parameters using both numerical and experimental data. The obtained results demonstrate the convergence of the Markov chain, present parameter trace plots, and provide estimates of posterior distributions of updated parameters along with their uncertainties. Experimental validation is performed on a cantilever beam system equipped with permanent magnets and electromagnets. The proposed methodology demonstrates promising results in estimating parameters of stochastic non-linear dynamical systems. Through the use of the proposed likelihood functions using backbone curves, the probability distributions of both linear and non-linear parameters are simultaneously identified. Based on this view, the necessity to segregate stochastic linear and non-linear model updating is eliminated. |
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| Keywords: |
Likelihood function; Backbone curves; Stochastic nonlinear dynamics; Bayesian inference; Markov Chain Monte Carlo; Model updating |
| College: |
Faculty of Science and Engineering |
| Funders: |
This research work has been partly funded by the RCUK Energy Programme [grant number EP/T012250/1]. The author also acknowledges the funding from the Engineering Physical Science Research Council (EPSRC) through a program grant EP/R006768/1. The views and options expressed herein do not necessarily reflect those of UKAEA. The support of the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government is also acknowledged. |
| Start Page: |
115800 |