Feasible and robust optimisation of cable forces in suspended bridges: A two-stage metaheuristic approach.

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Title: Feasible and robust optimisation of cable forces in suspended bridges: A two-stage metaheuristic approach.
Authors: Mascolo, Ida1 (AUTHOR), Sarfarazi, Sina1 (AUTHOR) sina.sarfarazi@unina.it, Modano, Mariano1 (AUTHOR)
Source: Mechanics Research Communications. Dec2025, Vol. 150, pN.PAG-N.PAG. 1p.
Subjects: Suspension bridges, Metaheuristic algorithms, Structural optimization, Tension loads, Particle swarm optimization, Grey Wolf Optimizer algorithm, Robust statistics, Stiffness (Engineering)
Abstract: • A two-stage framework for feasible and robust cable retensioning is proposed. • A reduced-order banded influence operator links cable actions to deck response. • Scale relation between hanger spacing and deck stiffness governs operator bandwidth. • PSO and GWO deliver symmetric, bounded, and constructible adjustment patterns. • Robustness and reproducibility are demonstrated under structured perturbations. The adjustment of cable pretension in suspended-deck bridges is a critical inverse design problem, where feasibility and robustness are as important as accuracy. Conventional methods such as finite-element (FE) re-analysis or the Influence Matrix Method (IMM) provide algebraic solutions but often produce oscillatory or infeasible patterns once field constraints are applied. This study introduces a two-stage framework that integrates stiffness-based sensitivity analysis with constrained metaheuristic optimisation. In stage-1 a reduced-order banded influence operator is introduced, which reflects how changes at the cable scale propagate over a limited range before combining into the global deck deformation. The effective bandwidth is tied to hanger spacing and deck stiffness, giving a natural connection between actuator-level inputs and system-level response. In Stage-2, cable adjustments are determined through multi-objective optimisation that balances target matching, smoothness, symmetry, and bounded jack capacities. Two population-based strategies, Particle Swarm Optimisation (PSO) and Grey Wolf Optimisation (GWO), are benchmarked against convex regularization baselines on the Gravina Bridge (Italy). Both metaheuristics deliver symmetric, bounded, and contiguous force patterns that reproduce the target profile while remaining compatible with staged field operations. Robustness analysis under structured perturbations confirms near 14% reductions in mean and tail-risk errors relative to convex solutions, while reproducibility is ensured through constrained search and convex polishing. The results demonstrate that the framework provides accurate and constructible re-tensioning strategies, clarifying how scale interactions in cable–deck systems can be exploited for reliable design and maintenance. [ABSTRACT FROM AUTHOR]
Copyright of Mechanics Research Communications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Feasible and robust optimisation of cable forces in suspended bridges: A two-stage metaheuristic approach.
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  Data: <searchLink fieldCode="DE" term="%22Suspension+bridges%22">Suspension bridges</searchLink><br /><searchLink fieldCode="DE" term="%22Metaheuristic+algorithms%22">Metaheuristic algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Tension+loads%22">Tension loads</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+swarm+optimization%22">Particle swarm optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Grey+Wolf+Optimizer+algorithm%22">Grey Wolf Optimizer algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+statistics%22">Robust statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Stiffness+%28Engineering%29%22">Stiffness (Engineering)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: • A two-stage framework for feasible and robust cable retensioning is proposed. • A reduced-order banded influence operator links cable actions to deck response. • Scale relation between hanger spacing and deck stiffness governs operator bandwidth. • PSO and GWO deliver symmetric, bounded, and constructible adjustment patterns. • Robustness and reproducibility are demonstrated under structured perturbations. The adjustment of cable pretension in suspended-deck bridges is a critical inverse design problem, where feasibility and robustness are as important as accuracy. Conventional methods such as finite-element (FE) re-analysis or the Influence Matrix Method (IMM) provide algebraic solutions but often produce oscillatory or infeasible patterns once field constraints are applied. This study introduces a two-stage framework that integrates stiffness-based sensitivity analysis with constrained metaheuristic optimisation. In stage-1 a reduced-order banded influence operator is introduced, which reflects how changes at the cable scale propagate over a limited range before combining into the global deck deformation. The effective bandwidth is tied to hanger spacing and deck stiffness, giving a natural connection between actuator-level inputs and system-level response. In Stage-2, cable adjustments are determined through multi-objective optimisation that balances target matching, smoothness, symmetry, and bounded jack capacities. Two population-based strategies, Particle Swarm Optimisation (PSO) and Grey Wolf Optimisation (GWO), are benchmarked against convex regularization baselines on the Gravina Bridge (Italy). Both metaheuristics deliver symmetric, bounded, and contiguous force patterns that reproduce the target profile while remaining compatible with staged field operations. Robustness analysis under structured perturbations confirms near 14% reductions in mean and tail-risk errors relative to convex solutions, while reproducibility is ensured through constrained search and convex polishing. The results demonstrate that the framework provides accurate and constructible re-tensioning strategies, clarifying how scale interactions in cable–deck systems can be exploited for reliable design and maintenance. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mechanics Research Communications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.mechrescom.2025.104554
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Suspension bridges
        Type: general
      – SubjectFull: Metaheuristic algorithms
        Type: general
      – SubjectFull: Structural optimization
        Type: general
      – SubjectFull: Tension loads
        Type: general
      – SubjectFull: Particle swarm optimization
        Type: general
      – SubjectFull: Grey Wolf Optimizer algorithm
        Type: general
      – SubjectFull: Robust statistics
        Type: general
      – SubjectFull: Stiffness (Engineering)
        Type: general
    Titles:
      – TitleFull: Feasible and robust optimisation of cable forces in suspended bridges: A two-stage metaheuristic approach.
        Type: main
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          Name:
            NameFull: Mascolo, Ida
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          Name:
            NameFull: Sarfarazi, Sina
      – PersonEntity:
          Name:
            NameFull: Modano, Mariano
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          Dates:
            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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              Value: 00936413
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            – Type: volume
              Value: 150
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            – TitleFull: Mechanics Research Communications
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