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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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/22/10615 |
| _version_ | 1827677445861408768 |
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| author | Jice Zeng Young Hoon Kim |
| author_facet | Jice Zeng Young Hoon Kim |
| author_sort | Jice Zeng |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:44:07Z |
| format | Article |
| id | doaj.art-5d7840ca81f64751a443e4f7e10ca606 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T05:44:07Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-5d7840ca81f64751a443e4f7e10ca6062023-11-22T22:16:24ZengMDPI AGApplied Sciences2076-34172021-11-0111221061510.3390/app112210615Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: FormulationsJice Zeng0Young Hoon Kim1Department of Civil and Environmental Engineering, University of Louisville, Louisville, KY 40292, USADepartment of Civil and Environmental Engineering, University of Louisville, Louisville, KY 40292, USAThe 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.https://www.mdpi.com/2076-3417/11/22/10615Bayesian model updating approachcoupling effectmodified systemstiffness modificationprobabilistic damage estimation |
| spellingShingle | Jice Zeng Young Hoon Kim Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations Applied Sciences Bayesian model updating approach coupling effect modified system stiffness modification probabilistic damage estimation |
| title | 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_short | 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 |
| topic | Bayesian model updating approach coupling effect modified system stiffness modification probabilistic damage estimation |
| url | https://www.mdpi.com/2076-3417/11/22/10615 |
| work_keys_str_mv | AT jicezeng stiffnessmodificationbasedbayesianfiniteelementmodelupdatingtosolvecouplingeffectofstructuralparametersformulations AT younghoonkim stiffnessmodificationbasedbayesianfiniteelementmodelupdatingtosolvecouplingeffectofstructuralparametersformulations |