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

• Published in: KSCE journal of civil engineering Vol. 27; no. 5; pp. 2104 - 2115
• Main Authors: Park, Kwang-Yeun, Jeon, Sang-Bum, Park, Yeun Chul, Lee, Hae Sung
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Civil Engineers 01.05.2023; Springer Nature B.V; 대한토목학회
• Subjects: Acceleration; Civil Engineering; Engineering; Fourier transforms; Geotechnical Engineering & Applied Earth Sciences; Girder bridges; Girders; Industrial Pollution Prevention; Mathematical analysis; Mathematical models; Optimization; Regularization; Spatial filtering; Strain; Structural Engineering; Velocity; 토목공학; De-noising; Velocity and acceleration; Reconstruction of displacement; Strain-displacement relation; Bernoulli beam; Temporal filter; Spatial filter
• ISSN: 1226-7988; 1976-3808
• DOI: 10.1007/s12205-023-1278-3

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.