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<p>The conventional approach for measuring the flexibility matrix of bridge structures typically relies on the dynamic testing method, necessitating precise modal identification and mode shape expansion. Another alternative method for measuring the flexibility matrix is through static testing, which generally demonstrates a high level of testing accuracy. Nevertheless, directly measuring the static flexibility matrix is deemed inefficient due to the considerable number of independent load applications and sensor placements it necessitates. Consequently, an indirect method was proposed to enhance the efficiency of measuring the static flexibility matrix. First, the static displacements engendered by the load associated with each column of the flexibility matrix (termed column load) are approximated as linear combinations of several contributing modes. This transformation renders the problem of measuring complete static displacements into a task focused on determining the coefficients of contributing modes. Second, specialized measurements are systematically performed to estimate the coefficient of each contributing mode for all column loads. A transformation relationship between the coefficients of the mutual contributing mode shared by a column load and a testing load is established. The optimal testing load that maximizes the contribution of the mutual contributing mode is searched and then applied to the structure to carry out the static testing. By utilizing the transformation relationship, the coefficient of the mutual contributing mode of the column load is obtained. As long as the coefficients of all contributing modes for all column loads are indirectly acquired in this way, the complete static flexibility matrix can be naturally obtained. It is noted that the snow ablation optimizer is employed in this paper to find the optimal testing loads and corresponding optimal sensor deployments. The numerical analysis of a simply supported beam reveals that the proposed indirect method necessitates significantly fewer load applications and sensor locations while maintaining notable measurement accuracy. This assertion is corroborated by experimental validation, which attests to the exceptional efficacy of the proposed indirect approach.</p>

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Rapid measuring the static flexibility matrix of bridge structures using an indirect method

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Xiaoshun Wu,
  • Jiacheng Fu,
  • Shiyu Xu,
  • Cai Wu,
  • Feng Miao,
  • Daopei Zhu

摘要

The conventional approach for measuring the flexibility matrix of bridge structures typically relies on the dynamic testing method, necessitating precise modal identification and mode shape expansion. Another alternative method for measuring the flexibility matrix is through static testing, which generally demonstrates a high level of testing accuracy. Nevertheless, directly measuring the static flexibility matrix is deemed inefficient due to the considerable number of independent load applications and sensor placements it necessitates. Consequently, an indirect method was proposed to enhance the efficiency of measuring the static flexibility matrix. First, the static displacements engendered by the load associated with each column of the flexibility matrix (termed column load) are approximated as linear combinations of several contributing modes. This transformation renders the problem of measuring complete static displacements into a task focused on determining the coefficients of contributing modes. Second, specialized measurements are systematically performed to estimate the coefficient of each contributing mode for all column loads. A transformation relationship between the coefficients of the mutual contributing mode shared by a column load and a testing load is established. The optimal testing load that maximizes the contribution of the mutual contributing mode is searched and then applied to the structure to carry out the static testing. By utilizing the transformation relationship, the coefficient of the mutual contributing mode of the column load is obtained. As long as the coefficients of all contributing modes for all column loads are indirectly acquired in this way, the complete static flexibility matrix can be naturally obtained. It is noted that the snow ablation optimizer is employed in this paper to find the optimal testing loads and corresponding optimal sensor deployments. The numerical analysis of a simply supported beam reveals that the proposed indirect method necessitates significantly fewer load applications and sensor locations while maintaining notable measurement accuracy. This assertion is corroborated by experimental validation, which attests to the exceptional efficacy of the proposed indirect approach.