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An Improved Metamodel-Based Algorithm Using Copula Theory for Assessing Reliability Analysis of Structures using FEM
Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.ORCID iD: 0000-0001-9493-9550
Trinity College Dublin, Dublin, Ireland.
Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.ORCID iD: 0000-0003-3548-6082
Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.ORCID iD: 0000-0002-8682-876X
2025 (English)In: Structural Engineering International, ISSN 1016-8664, E-ISSN 1683-0350Article in journal (Refereed) Epub ahead of print
Abstract [en]

Reliability analysis is crucial for evaluating structural performance, and advancements in computational technologies have enhanced the application of Finite Element Modeling (FEM) in this field. However, existing reliability methods face challenges, particularly with approximation methods that struggle with implicit limit state functions and simulation methods with cost. Metamodel-based approaches have gained popularity for their balance of efficiency and accuracy, yet most algorithms focus on independent variables. This paper presents an improved metamodel-based algorithm designed to assess structural reliability while considering variable dependency and FEM. The algorithm provides a methodology that ensures a rapid convergence of the iterative process when building the metamodel in the region of interest, i.e. where the Most Probable Point (MPP) is located. It uses a modified Design of Experiments (DoE) and integrates copula theory to model the joint probability distribution function (PDF). The algorithm enriches the experimental points matrix by finding points close to the Limit State Function (LSF) at 0 with high prediction variance using learning functions and with high joint PDF values using copula theory. Validation through various examples and an application example of a reinforced concrete bridge indicates that the proposed methodology is more efficient than most recent algorithms without reducing accuracy.

Place, publisher, year, edition, pages
Taylor & Francis, 2025.
Keywords [en]
reliability, structures, metamodel, kriging, copula, finite element modeling
National Category
Structural Engineering Building materials
Research subject
Structural Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-114331DOI: 10.1080/10168664.2025.2517059ISI: 001544553600001Scopus ID: 2-s2.0-105012557915OAI: oai:DiVA.org:ltu-114331DiVA, id: diva2:1989895
Funder
Svenska Byggbranschens Utvecklingsfond (SBUF), 13934Svenska Byggbranschens Utvecklingsfond (SBUF), 14354
Note

Fulltext license: CC BY

Available from: 2025-08-19 Created: 2025-08-19 Last updated: 2025-11-24
In thesis
1. Remaining service life estimation of existing concrete bridges through probabilistic and reliability analyses
Open this publication in new window or tab >>Remaining service life estimation of existing concrete bridges through probabilistic and reliability analyses
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis aims to assess the remaining useful life of two representative bridge types in Sweden by combining full-scale experimental tests, Finite Element Analysis (FEA), and time-dependent reliability analysis. The combination of these methods seeks to enhance solution accuracy and reduce uncertainties. As the bridge population approaches its intended design life, concerns regarding their current condition start to rise. Recent bridge failures are proof of the need for experts to increase their efforts to accurately assess existing bridges' remaining useful life. However, structural remaining lifetime prediction is a challenging task given the complexity of structural behavior and the various environmental threats the structure faces. Additionally, inherent uncertainties are part of any engineering problem, making an exact solution difficult to achieve. Therefore, introducing probabilistic-based concepts to determine the structure capacity helps account for those uncertainties typically addressed in structural reliability analysis. Time-dependent reliability analysis offers a tool to assess the remaining useful life of a structure, expressed in terms of its time to failure. 

The first case study corresponds to a road existing bridge in north Sweden that has been already demolished. The structure is a prestressed box-girder concrete bridge, and it was 66 years old at the time of experimental data collection. The second case is a reinforced concrete (RC) trough railway bridge, which is a representative bridge type in Sweden. The trough bridge was cast at LTU in 2021 as a replica of the design of a decommissioned trough bridge from the Iron Ore Line. The experiments performed in both case studies are used for two main purposes: the calibration of the Finite Element (FE) models and the update of the probability distributions of the parameters involved in the time-dependent reliability analysis. This will help a better FE model to represent structural behavior and more accurate probabilistic models. Different sensors were implemented during the experimental data collection, such as fiber optic sensors (FOS), traditional strain gauges, and linear variable differential transformers (LVDTs).

Given that the communication between FE and reliability analyses can be computational overwhelming, this thesis proposes an improved metamodel-based reliability algorithm which integrates the advantages of kriging, learning, and copula functions. The proposed algorithm aims to reduce the number of performance function evaluations, so the number of model runs is feasible when using FEA. 

The results of this research provide a practical understanding of the stochastic process for resistance deterioration in both cases.  This includes degradation due to prestressing losses for the Kalix bridge and fatigue for the trough bridge. By considering the stochastic process over the years and the random nature of the loads over time, we were able to calculate the remaining useful life for the cases of no experimental information and updated using experimental data. These findings have direct implications for the maintenance and management of similar structures, providing valuable insights for the field of civil engineering and structural reliability analysis. 

Place, publisher, year, edition, pages
Luleå University of Technology, 2025
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords
Existing bridges, reliability, remaining useful life, metamodel, Finite Element Modeling, full-scale tests
National Category
Infrastructure Engineering
Research subject
Structural Engineering
Identifiers
urn:nbn:se:ltu:diva-115519 (URN)978-91-8048-951-5 (ISBN)978-91-8048-952-2 (ISBN)
Public defence
2026-02-12, A117, Luleå University of Technology, Luleå, 09:00 (English)
Opponent
Supervisors
Funder
Swedish Transport Administration, 2024–011Svenska Byggbranschens Utvecklingsfond (SBUF), 14354
Available from: 2025-11-24 Created: 2025-11-24 Last updated: 2025-12-30Bibliographically approved

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Sarmiento, Silvia J.González-Libreros, JaimeSas, Gabriel

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