梁的控制微分方程在工程中有广泛的应用。本文提出了一种使用稀疏测量的位移估计梁结构控制方程系数的方法。首先使用压缩感知理论，由少量位移传感器测量的响应重构梁的全场位移。然后使用B-样条曲面基函数来拟合重构的位移场，获得的控制点将用于计算位移场的偏导数。最后将位移场偏导数代入控制方程，并通过遗传算法确定控制方程的系数。对所提方法的有效性进行了数值和实验验证，并通过参数研究考察了其性能。结果表明该方法具有所需传感器少，高阶导数计算稳健等优势。

The governing differential equations of beams have many engineering applications. This study proposes a method to identify the coefficients of the governing equation from sparsely measured displacement responses. First, the full-field displacement is reconstructed by the compressive sensing theory. The reconstructed displacement field is then fitted by B-spline surface basis functions, and the derived control points are further used to calculate other responses, which are derivatives of displacement. The genetic algorithm is finally utilized to seek the coefficients of the governing equation by substituting the fitted responses into the equation. The proposed method is both numerically and experimentally validated, together with a parametric study to evaluate its performance under various conditions. The salient advantages of the proposed method are that it requires only few sensors for measurement and the derivatives are calculated in a robust and easy way.