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Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity

Delei Yang, Chunyan Kang, Sihan Cheng, Zhongming Hu, Adesola Ademiloye Orcid Logo

Buildings, Volume: 15, Issue: 9, Start page: 1521

Swansea University Author: Adesola Ademiloye Orcid Logo

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DOI (Published version): 10.3390/buildings15091521

Abstract

In practical engineering, uncertainties inevitably exist in the models and measurement data used for structures. Therefore, a statistical strategy related to damage detection methods become crucial. In this paper, a probabilistic statistical damage detection method for FG Euler–Bernoulli beam struct...

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Published in: Buildings
ISSN: 2075-5309
Published: MDPI 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69654
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In this paper, a probabilistic statistical damage detection method for FG Euler&#x2013;Bernoulli beam structures is proposed, extending the approach originally developed for isotropic materials. Our approach determines the probability of damage occurrence for each element, which aids in evaluating whether beam structures have been damaged. This evaluation is based on integrating the sensitivity of modal strain energy for each element with the perturbation method. To demonstrate the effectiveness and accuracy of the proposed method, several numerical examples are investigated. These examples include a simply supported FG Euler&#x2013;Bernoulli beam subjected to both single and multiple element damages. The influence of gradient index, damage severity, boundary condition, and noise level on the accuracy of detection are also considered. The studies demonstrate that the probability of damage for each element remains relatively stable despite variations in the gradient indices. 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spelling 2025-06-09T14:18:03.0428835 v2 69654 2025-06-09 Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity e37960ed89a7e3eaeba2201762626594 0000-0002-9741-6488 Adesola Ademiloye Adesola Ademiloye true false 2025-06-09 EAAS In practical engineering, uncertainties inevitably exist in the models and measurement data used for structures. Therefore, a statistical strategy related to damage detection methods become crucial. In this paper, a probabilistic statistical damage detection method for FG Euler–Bernoulli beam structures is proposed, extending the approach originally developed for isotropic materials. Our approach determines the probability of damage occurrence for each element, which aids in evaluating whether beam structures have been damaged. This evaluation is based on integrating the sensitivity of modal strain energy for each element with the perturbation method. To demonstrate the effectiveness and accuracy of the proposed method, several numerical examples are investigated. These examples include a simply supported FG Euler–Bernoulli beam subjected to both single and multiple element damages. The influence of gradient index, damage severity, boundary condition, and noise level on the accuracy of detection are also considered. The studies demonstrate that the probability of damage for each element remains relatively stable despite variations in the gradient indices. For the damaged elements, these probabilities approach 1, indicating that the proposed method effectively identifies damage in FG beams even when the gradient index varies. Additionally, as the level of damage increases, the accuracy of damage detection tends to improve. However, varying boundary conditions can substantially affect the outcomes of damage identification, potentially leading to inconsistencies in results. Furthermore, our proposed method demonstrates excellent resistance against noise levels of up to 5%. We also found that different boundary conditions have a great impact on the damage detection. Journal Article Buildings 15 9 1521 MDPI 2075-5309 functionally graded Euler–Bernoulli beam; structural damage detection; modal strain energy sensitivity; statistical methods for damage identification 1 5 2025 2025-05-01 10.3390/buildings15091521 COLLEGE NANME Engineering and Applied Sciences School COLLEGE CODE EAAS Swansea University Another institution paid the OA fee The research presented in this paper is funded by grants from the Science and Technology Research Project of Henan Province (222102320320, 242102521034, 242102321169). A. S. Ademiloye thanks the Royal Society for the International Exchange grant (IES\NSFC\223217). 2025-06-09T14:18:03.0428835 2025-06-09T14:06:55.7604270 Faculty of Science and Engineering School of Engineering and Applied Sciences - Biomedical Engineering Delei Yang 1 Chunyan Kang 2 Sihan Cheng 3 Zhongming Hu 4 Adesola Ademiloye 0000-0002-9741-6488 5 69654__34427__bb8c7ba4125041f2804e735eaced3d11.pdf buildings-15-01521.pdf 2025-06-09T14:06:55.7353921 Output 3814318 application/pdf Version of Record true © 2025 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. true eng https://creativecommons.org/licenses/by/4.0/
title Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
spellingShingle Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
Adesola Ademiloye
title_short Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
title_full Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
title_fullStr Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
title_full_unstemmed Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
title_sort Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity
author_id_str_mv e37960ed89a7e3eaeba2201762626594
author_id_fullname_str_mv e37960ed89a7e3eaeba2201762626594_***_Adesola Ademiloye
author Adesola Ademiloye
author2 Delei Yang
Chunyan Kang
Sihan Cheng
Zhongming Hu
Adesola Ademiloye
format Journal article
container_title Buildings
container_volume 15
container_issue 9
container_start_page 1521
publishDate 2025
institution Swansea University
issn 2075-5309
doi_str_mv 10.3390/buildings15091521
publisher MDPI
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 Engineering and Applied Sciences - Biomedical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Biomedical Engineering
document_store_str 1
active_str 0
description In practical engineering, uncertainties inevitably exist in the models and measurement data used for structures. Therefore, a statistical strategy related to damage detection methods become crucial. In this paper, a probabilistic statistical damage detection method for FG Euler–Bernoulli beam structures is proposed, extending the approach originally developed for isotropic materials. Our approach determines the probability of damage occurrence for each element, which aids in evaluating whether beam structures have been damaged. This evaluation is based on integrating the sensitivity of modal strain energy for each element with the perturbation method. To demonstrate the effectiveness and accuracy of the proposed method, several numerical examples are investigated. These examples include a simply supported FG Euler–Bernoulli beam subjected to both single and multiple element damages. The influence of gradient index, damage severity, boundary condition, and noise level on the accuracy of detection are also considered. The studies demonstrate that the probability of damage for each element remains relatively stable despite variations in the gradient indices. For the damaged elements, these probabilities approach 1, indicating that the proposed method effectively identifies damage in FG beams even when the gradient index varies. Additionally, as the level of damage increases, the accuracy of damage detection tends to improve. However, varying boundary conditions can substantially affect the outcomes of damage identification, potentially leading to inconsistencies in results. Furthermore, our proposed method demonstrates excellent resistance against noise levels of up to 5%. We also found that different boundary conditions have a great impact on the damage detection.
published_date 2025-05-01T05:28:46Z
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score 11.089386

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