Bridge response reconstruction at unmeasured points based on major contributing modes selection and superposition
摘要
Response reconstruction plays an important role in bridge health monitoring when structural responses at critical locations cannot be directly measured. Conventional modal-analysis-based reconstruction methods usually estimate unmeasured responses by combining modal responses with mode shapes obtained from a finite element model (FEM). However, their accuracy can be compromised by discrepancies between FEM-derived mode shapes and real bridge mode shapes, as well as by inaccurate modal response extraction from limited measured data under spectral leakage, excitation characteristics, and measurement noise. To address these issues, this paper proposes a response reconstruction method based on the superposition of major contributing modes. First, a bridge-specific mode shape matrix is established by combining the bridge deflection influence line obtained from tests with mass information derived from design drawings, reducing the dependence on an idealized FEM. Then, the major contributing modes are identified through singular value decomposition of the measured response spectrum and the mode shape matrix. The modal responses of these modes are calculated by solving a system of linear equations, and the responses at unmeasured points are reconstructed through modal superposition. A numerical example and a bridge field test are conducted to validate the proposed method. In the numerical example, the proposed method reduces the Relative Percentage Error and Mean Absolute Error from 1.51 and 1.42 × 1–8 obtained by the traditional VMD-based method to 0.631 and 6.3 × 1–9, respectively, demonstrating improved reconstruction accuracy and practical applicability.