Applying matrix regularization to identification of traffic-induced equivalent loads and multi-vehicle weight on beam-like bridge

Abstract

Identification of traffic-induced forces is an important topic in the field of bridge structural health monitoring (B-SHM). It can provide reliable data to support the great demand for monitoring and evaluating the working conditions of bridges. Bridges may serve under consistent moving vehicles and this requires that the methods of moving force identification (MFI) should be applicable under circumstances such as multiple-vehicle loading and long-term monitoring. Centering on cases containing multiple vehicles, this study proposed a matrix regularization-based method for the identification of traffic-induced equivalent loads and multi-vehicle weights. Herein, multiple moving forces in the spatial domain are converted into a certain number of equivalent loads which virtually act at fixed locations on the bridge as a kind of coordinate transformation. The MFI problem then can be transformed into tasks of identifying some concentrated forces. To solve the problem of equivalent load identification, the structural input-output relationship is firstly reorganized in a matrix-matrix-matrix form with the help of segmentation via time windows and consideration of unknown structural initial conditions. Then the matrix regularization with a sparse penalty term is introduced to formulate an identified equation so that, it can ensure the strong noise robustness of the identified results. Finally, the total weight of multiple vehicles can be empirically estimated from the sum of the identified equivalent loads. Numerical simulations and model experiments are performed to verify the proposed method's performance. The effects of vehicle speeds, measuring noise, number of modal orders, number of vehicles, and vehicle spacings are investigated. The illustrated results show that the proposed method turns out to be effective and precise in identifying the traffic-induced equivalent loads and the weight of multiple vehicles.