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<p>As critical components of cable-stayed bridges, stay cables suffer from complex loads and environmental effects. However, the inevitable loss of monitoring data poses a vital challenge to the safety and fatigue analysis of stay cables. This paper introduces a novel data-driven approach for estimating cable forces of cable-supported bridges based on the Koopman operator (KO) theory. The Koopman operator (KO) models the spatiotemporal correlations of the input–output cable force system, represented by differential–algebraic equations (DAE). It linearizes the nonlinear dynamics of the system using higher order state derivatives as observable functions to approximate the infinite-dimensional state space. The proposed method can effectively estimate the target cable force from input cable forces with high accuracy in time domain and stress range. The robustness of the proposed method is validated by considering data anomalies and input cable optimization. When using ten input cables without anomalies, the KO method achieves a mean absolute error (MAE) of 1.32&#xa0;kN and a mean error of 0.47&#xa0;kN, with the coefficient of determination (<i>R</i><sup>2</sup>) exceeding 99%. It outperforms conventional time-series prediction models in both accuracy and efficiency, requiring only 20% of the testing time of the second fastest model. These results demonstrate its potential as a reliable and efficient technique for data imputation in structural health monitoring (SHM).</p>

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Novel cable force estimation based on Koopman operator leveraging spatiotemporal correlation in cable networks

  • 期刊论文

  • 发表日期：

    2025年8月30日

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  • Chao Deng,
  • Yuan Ren,
  • Xiang Xu,
  • Ziyuan Fan,
  • Qiao Huang

摘要

As critical components of cable-stayed bridges, stay cables suffer from complex loads and environmental effects. However, the inevitable loss of monitoring data poses a vital challenge to the safety and fatigue analysis of stay cables. This paper introduces a novel data-driven approach for estimating cable forces of cable-supported bridges based on the Koopman operator (KO) theory. The Koopman operator (KO) models the spatiotemporal correlations of the input–output cable force system, represented by differential–algebraic equations (DAE). It linearizes the nonlinear dynamics of the system using higher order state derivatives as observable functions to approximate the infinite-dimensional state space. The proposed method can effectively estimate the target cable force from input cable forces with high accuracy in time domain and stress range. The robustness of the proposed method is validated by considering data anomalies and input cable optimization. When using ten input cables without anomalies, the KO method achieves a mean absolute error (MAE) of 1.32 kN and a mean error of 0.47 kN, with the coefficient of determination (R2) exceeding 99%. It outperforms conventional time-series prediction models in both accuracy and efficiency, requiring only 20% of the testing time of the second fastest model. These results demonstrate its potential as a reliable and efficient technique for data imputation in structural health monitoring (SHM).