Bridge influence line identification based on adaptive B‐spline basis dictionary and sparse regularization

Summary Bridge influence line (BIL) is a promising tool for the real applications in the fields of bridge weight‐in‐motion (BWIM), model updating, damage identification, and load carrying capacity evaluation. The key of such applications is how to obtain the accurate results of BIL. To accurately identify BIL based on bridge dynamic responses induced by a moving vehicle, two critical problems, including how to construct a general representation function of BIL and how to deal with the ill‐posed inverse problem, should be properly resolved. This paper proposes a novel approach based on the adaptive B‐spline basis dictionary and sparse regularization technique for BIL identification. A representation of basis function is first established to construct BIL, and then integrated with a redundant B‐spline basis dictionary to ensure the sparsity of solution. A curvature‐based adaptive node optimization method is proposed to automatically adjust the spatial arrangement of nodes according to the shape of BILs. Numerical and experimental validations are conducted to verify the accuracy and robustness of the proposed approach. The identified BIL results are accurate, indicating that the proposed node‐adaptive optimization and sparse regularization techniques are effective to improve the quality of BIL identification. It is also shown that the proposed approach is not sensitive to the noise interference and configuration of testing vehicle. Through the robustness testing, it is proved that the proposed approach has the merits of high accuracy and strong robustness.