A Sparsely-Measured Fitting Method for Identifying the Coefficients in the Governing Equation of a Beam

This study proposes a method for identifying the coefficients in the governing equation of a beam from the sparsely measured response of bridge displacement. The following three steps constitute the procedure: First, the full-field displacement is reconstructed by the compressive sensing theory, which is innovatively applied in the spatial domain with a proposed general basis matrix. Then, the reconstructed displacement is fitted by the B-spline surface basis functions, and the derived control points are further adopted to compute the derivatives of displacement. The genetic algorithm is finally applied to seek the coefficients of the governing equation by substituting the fitted response into the equation. The proposed method is validated numerically and experimentally, including a parametric study to evaluate the performance subjected to various practical conditions. The salient advantages of the proposed method lie in that it requires few sensors for measurement, and the derivatives of displacement are computed robustly.