多测点驱动随机移动荷载识别:AR(1)-Tikhonov-SVD-GCV框架
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兰州大学土木工程与力学学院

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Stochastic Moving Loads Identification Driven by Multi-Point Deflection Responses: An AR(1)-Tikhonov-SVD-GCV Framework
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    摘要:

    【目的】在桥梁健康监测领域,移动荷载的精准识别是桥梁安全评估的关键。现有方法在随机移动荷载时间相关性建模及反问题病态性处理方面仍有待改进。【方法】本文提出一种多测点挠度响应驱动的一阶自回归(first-order autoregressive,简称AR(1))-Tikhonov正则化-奇异值分解(singular value decomposition,简称SVD)-广义交叉验证(generalized cross-validation,简称GCV)(AR(1)-Tikhonov-SVD-GCV)框架。首先,通过AR(1)模型生成时间相关随机荷载因子序列,耦合基准荷载构建随机移动荷载模型;其次,结合Tikhonov正则化与奇异值分解SVD处理病态系统,并采用GCV准则自适应优化参数;最后,基于简支梁有限元模型与多测点挠度数据验证。【结果】结果表明:无噪声条件下相对百分比误差(relative percentage error,简称RPE)为8.41 %;在噪声水平为2 %时,RPE增加到15.15 %;且增加测点数量可提升随机荷载重构精度,验证了其鲁棒性。【结论】该方法有效突破传统确定性识别框架,为概率性桥梁安全评估提供了新思路。

    Abstract:

    [Purposes] In the field of bridge health monitoring, the precise identification of moving loads is crucial for bridge safety assessment. Existing methods still need improvement in terms of the modeling of temporal correlations in stochastic moving loads and handling the ill-posedness of inverse problems [Methods] This paper proposes a multi-point deflection response-driven first-order autoregressive (AR(1))-Tikhonov regularization-singular value decomposition (SVD)-generalized cross-validation (GCV) framework. First, temporally correlated stochastic loads factor sequences are generated via the AR(1) model and coupled with a baseline load to construct the stochastic moving loads model. Second, the ill-posed system is addressed by integrating Tikhonov regularization with SVD, and the regularization parameters are adaptively optimized using the GCV criterion. Finally, validation was performed using a simply supported beam finite element model with multi-point deflection data. [Findings] The results demonstrate that the relative percentage error (RPE) was 8.41% under noise-free conditions, which increased to 15.15% at a 2% noise level. Furthermore, increasing the number of measurement points improved the stochastic loads reconstruction accuracy, verifying the robustness of the framework. [Conclusions] This method breaks through the traditional deterministic identification framework and provides a new perspective for probabilistic bridge safety assessment.

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  • 收稿日期:2025-11-14
  • 最后修改日期:2025-12-04
  • 录用日期:2025-12-14
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