Reconstruction of Displacement, Velocity and Acceleration from Measured Dynamic Strain for Bernoulli-Beam Type Girders of Bridges

초록

This paper presents a new approach for reconstructing displacement, velocity and acceleration from measured strain in Bernoulli-beam type girders of bridges. A minimization problem is defined using the L-2-norm of the strain-displacement relation of the Bernoulli beam with a regularization function to form a low-cut, spatial filter converting measured strain into displacement. A standard finite element procedure is applied to discretize the minimization problem. Fundamental characteristics of the spatial filter are discussed using the spatial Fourier transform. A temporal filter is adopted to filter out temporal noise in the displacement reconstructed by the spatial filter and to reconstruct velocity. Acceleration is calculated by the 1(st)-order central finite difference of the reconstructed velocity by the temporal filter. The validity of the proposed approach is demonstrated through a numerical simulation and field measurement on two-span continuous Bernoulli beams. It is shown that the proposed approach yields a good estimation of displacement and its temporal derivatives even for sparsely measured strain in the spatial domain. Detailed results of the numerical study are presented and discussed.

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