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Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework

Pushpa Pandey, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Tanmoy Chatterjee, Hadi Madinei Orcid Logo, Tom Deighan

Applied Mathematical Modelling, Start page: 115800

Swansea University Authors: Pushpa Pandey, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Hadi Madinei Orcid Logo

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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...

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Published in: Applied Mathematical Modelling
ISSN: 0307-904X
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa68223
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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. 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spelling 2024-11-11T11:14:54.2763044 v2 68223 2024-11-11 Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework c5b9c91974d44b88920ef13e914a9bdd Pushpa Pandey Pushpa Pandey true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false d9a10856ae9e6a71793eab2365cff8b6 0000-0002-3401-1467 Hadi Madinei Hadi Madinei true false 2024-11-11 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. Journal Article Applied Mathematical Modelling 0 115800 Elsevier BV 0307-904X Likelihood function; Backbone curves; Stochastic nonlinear dynamics; Bayesian inference; Markov Chain Monte Carlo; Model updating 8 11 2024 2024-11-08 10.1016/j.apm.2024.115800 COLLEGE NANME COLLEGE CODE Swansea University SU Library paid the OA fee (TA Institutional Deal) 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. 2024-11-11T11:14:54.2763044 2024-11-11T11:04:43.3111398 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Pushpa Pandey 1 Hamed Haddad Khodaparast 0000-0002-3721-4980 2 Michael Friswell 3 Tanmoy Chatterjee 4 Hadi Madinei 0000-0002-3401-1467 5 Tom Deighan 6
title Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
spellingShingle Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
Pushpa Pandey
Hamed Haddad Khodaparast
Michael Friswell
Hadi Madinei
title_short Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
title_full Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
title_fullStr Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
title_full_unstemmed Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
title_sort Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework
author_id_str_mv c5b9c91974d44b88920ef13e914a9bdd
f207b17edda9c4c3ea074cbb7555efc1
5894777b8f9c6e64bde3568d68078d40
d9a10856ae9e6a71793eab2365cff8b6
author_id_fullname_str_mv c5b9c91974d44b88920ef13e914a9bdd_***_Pushpa Pandey
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
d9a10856ae9e6a71793eab2365cff8b6_***_Hadi Madinei
author Pushpa Pandey
Hamed Haddad Khodaparast
Michael Friswell
Hadi Madinei
author2 Pushpa Pandey
Hamed Haddad Khodaparast
Michael Friswell
Tanmoy Chatterjee
Hadi Madinei
Tom Deighan
format Journal article
container_title Applied Mathematical Modelling
container_volume 0
container_start_page 115800
publishDate 2024
institution Swansea University
issn 0307-904X
doi_str_mv 10.1016/j.apm.2024.115800
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 0
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description 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.
published_date 2024-11-08T02:54:08Z
_version_ 1821372368658890752
score 11.04748

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