Structural response reconstruction of beam-like bridge based on equivalent loads under moving forces

Abstract

Response reconstruction has advantages in enriching monitoring data with high quality and it is of great importance to bridge structural health monitoring. However, there still are many current difficulties with response reconstruction due to the complex operation of bridges, e.g., hard to deal with time-varying positions of vehicles and inefficient reconstruction for cases with a long time. According to the theory of equivalent load identification, this paper proposes a model-based method for reconstructing responses induced by moving forces. The proposed method introduces moving time windows to extract the measured responses in an orderly manner and re-organizes them into a matrix form. The measured responses, expressed in matrix form, then serve as the input data to identify both equivalent loads and structural initial conditions, but not to estimate the actual moving forces. Herein, the equivalent loads represent some concentrated loads with time-invariant acting positions and are employed to approximately re-express the main information of moving forces. Matrix regularization with a sparse penalty term is used to ensure the robustness of identified results. Since the structural inputs have been estimated, the structural responses happening at the validation sensors then can be calculated as a forward problem. In this process, the role of identified structural inputs is an intermediate variable connecting the measuring sensors and the validation sensors so that, the transmissibility function (TF) discussed in the proposed method is expressed in an implicit pattern. Compared to the response reconstruction methods developed from moving force identification (MFI), an obvious characteristic is that information on the actual moving forces is no longer necessary. Therefore, it can bring convenience in practical application such as the time-varying positions of moving vehicles are not needed in advance. In addition, the application of matrix regularization has the potential for efficient computation. To verify the feasibility and effectiveness of the proposed method, both numerical simulations and experimental studies are finally carried out. The illustrated results indicate that the proposed method can accurately reconstruct the structural response. In addition, some related issues are also discussed.