A unified framework for enhancing inverse finite element method through strain pre-extrapolation and sensor placement optimization
•A novel framework is developed to enhance iFEM accuracy and robustness with limited sensors.•A new strain pre-extrapolation technique, GPR-MCKF, is proposed, accounting for spatio-temporal correlation in measurements.•The FIM of extrapolated strain is derived as an objective function, linking GPR-M...
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| Vydané v: | Mechanical systems and signal processing Ročník 234; s. 112836 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.07.2025
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| ISSN: | 0888-3270 |
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| Abstract | •A novel framework is developed to enhance iFEM accuracy and robustness with limited sensors.•A new strain pre-extrapolation technique, GPR-MCKF, is proposed, accounting for spatio-temporal correlation in measurements.•The FIM of extrapolated strain is derived as an objective function, linking GPR-MCKF and SPO.•SPO results mainly depend on structural geometry and are insensitive to other factors, such as loading conditions.•Numerical and experimental tests confirm the framework’s effectiveness, robustness, and general applicability.
The inverse finite element method (iFEM) is a powerful tool for shape sensing, but its effectiveness is often constrained by economic and spatial constraints that prevent sensor coverage. This paper presents a unified framework to enhance iFEM, comprising two key components. The first is a novel strain pre-extrapolation method, GPR-MCKF, which incorporates both spatial and temporal correlations from measurement data. To reduce the computational demand of Gaussian process regression (GPR) when handling large datasets, maximum correntropy Kalman filtering (MCKF) is used to handle temporal correlation, based on the space–time separability of the kernel and the state-space equation of Gaussian process. The second component is a sensor placement optimization (SPO) method with general applicability, introducing an innovative objective function based on the Fisher information matrix (FIM) of the extrapolated strain. This objective function links the two components. Moreover, with constant noise levels and a fixed kernel function, this objective function depends solely on the measurement locations, meaning the results of SPO are determined exclusively by the structural geometry. This objective function, combined with the number of sensors, forms a bi-objective optimization problem, which is solved using the multi-objective Lichtenberg algorithm (MOLA). Finally, numerical and experimental examples validate the framework’s effectiveness, robustness, and general applicability in shape sensing with limited sensors, demonstrating its potential for practical applications to complex and large-scale structures. |
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| AbstractList | •A novel framework is developed to enhance iFEM accuracy and robustness with limited sensors.•A new strain pre-extrapolation technique, GPR-MCKF, is proposed, accounting for spatio-temporal correlation in measurements.•The FIM of extrapolated strain is derived as an objective function, linking GPR-MCKF and SPO.•SPO results mainly depend on structural geometry and are insensitive to other factors, such as loading conditions.•Numerical and experimental tests confirm the framework’s effectiveness, robustness, and general applicability.
The inverse finite element method (iFEM) is a powerful tool for shape sensing, but its effectiveness is often constrained by economic and spatial constraints that prevent sensor coverage. This paper presents a unified framework to enhance iFEM, comprising two key components. The first is a novel strain pre-extrapolation method, GPR-MCKF, which incorporates both spatial and temporal correlations from measurement data. To reduce the computational demand of Gaussian process regression (GPR) when handling large datasets, maximum correntropy Kalman filtering (MCKF) is used to handle temporal correlation, based on the space–time separability of the kernel and the state-space equation of Gaussian process. The second component is a sensor placement optimization (SPO) method with general applicability, introducing an innovative objective function based on the Fisher information matrix (FIM) of the extrapolated strain. This objective function links the two components. Moreover, with constant noise levels and a fixed kernel function, this objective function depends solely on the measurement locations, meaning the results of SPO are determined exclusively by the structural geometry. This objective function, combined with the number of sensors, forms a bi-objective optimization problem, which is solved using the multi-objective Lichtenberg algorithm (MOLA). Finally, numerical and experimental examples validate the framework’s effectiveness, robustness, and general applicability in shape sensing with limited sensors, demonstrating its potential for practical applications to complex and large-scale structures. |
| ArticleNumber | 112836 |
| Author | Wei, Handi Xiao, Longfei Kou, Yufeng Li, Kelu Shan, Meng |
| Author_xml | – sequence: 1 givenname: Kelu surname: Li fullname: Li, Kelu organization: State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 2 givenname: Longfei orcidid: 0000-0003-3296-6427 surname: Xiao fullname: Xiao, Longfei organization: State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 3 givenname: Handi surname: Wei fullname: Wei, Handi email: weihandi@sjtu.edu.cn organization: State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 4 givenname: Yufeng orcidid: 0000-0003-3716-3674 surname: Kou fullname: Kou, Yufeng organization: State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 5 givenname: Meng surname: Shan fullname: Shan, Meng organization: State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Cites_doi | 10.1016/j.ymssp.2022.110056 10.1016/j.ymssp.2022.109466 10.1016/j.ymssp.2022.109167 10.1002/(SICI)1097-0207(19990410)44:10<1527::AID-NME497>3.0.CO;2-1 10.1016/j.cma.2004.03.015 10.1016/j.tws.2022.109798 10.1016/j.measurement.2021.110031 10.1016/j.measurement.2023.113502 10.1016/j.oceaneng.2019.106262 10.1016/j.tws.2024.112127 10.3390/s22239252 10.1016/j.paerosci.2018.04.001 10.1007/s11012-015-0146-8 10.3390/s20247049 10.1016/j.ymssp.2020.107163 10.1016/j.jsv.2022.117207 10.1016/j.automatica.2016.10.004 10.1016/j.compstruct.2023.117364 10.1016/j.ijnonlinmec.2022.104229 10.1016/j.ymssp.2021.108289 10.1016/j.ymssp.2021.107875 10.1016/S0045-7825(97)00135-7 10.1016/j.nimb.2018.11.019 10.1016/j.advengsoft.2013.07.002 10.1016/j.automatica.2020.109032 10.1016/j.tws.2023.110884 10.1016/j.compstruct.2021.113587 10.1016/j.jsv.2007.04.037 10.1016/j.tws.2023.110865 10.1016/j.tws.2022.109485 10.1016/j.tws.2024.111837 10.1016/j.oceaneng.2024.118293 10.1016/j.cma.2021.114520 |
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| Keywords | Gaussian process regression iFEM Maximum correntropy Kalman filter Sensor placement optimization Strain pre-extrapolation Fisher information |
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| SubjectTerms | Fisher information Gaussian process regression iFEM Maximum correntropy Kalman filter Sensor placement optimization Strain pre-extrapolation |
| Title | A unified framework for enhancing inverse finite element method through strain pre-extrapolation and sensor placement optimization |
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