Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable c...

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Autores principales:	Jice Zeng, Young Hoon Kim
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Bayesian model updating approach coupling effect modified system stiffness modification probabilistic damage estimation Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/5d7840ca81f64751a443e4f7e10ca606
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spelling	oai:doaj.org-article:5d7840ca81f64751a443e4f7e10ca6062021-11-25T16:33:17ZStiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations10.3390/app1122106152076-3417https://doaj.org/article/5d7840ca81f64751a443e4f7e10ca6062021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/22/10615https://doaj.org/toc/2076-3417The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.Jice ZengYoung Hoon KimMDPI AGarticleBayesian model updating approachcoupling effectmodified systemstiffness modificationprobabilistic damage estimationTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10615, p 10615 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian model updating approach coupling effect modified system stiffness modification probabilistic damage estimation Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	Bayesian model updating approach coupling effect modified system stiffness modification probabilistic damage estimation Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Jice Zeng Young Hoon Kim Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
description	The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.
format	article
author	Jice Zeng Young Hoon Kim
author_facet	Jice Zeng Young Hoon Kim
author_sort	Jice Zeng
title	Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
title_short	Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
title_full	Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
title_fullStr	Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
title_full_unstemmed	Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations
title_sort	stiffness modification-based bayesian finite element model updating to solve coupling effect of structural parameters: formulations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/5d7840ca81f64751a443e4f7e10ca606
work_keys_str_mv	AT jicezeng stiffnessmodificationbasedbayesianfiniteelementmodelupdatingtosolvecouplingeffectofstructuralparametersformulations AT younghoonkim stiffnessmodificationbasedbayesianfiniteelementmodelupdatingtosolvecouplingeffectofstructuralparametersformulations
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Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

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