Moving mass identification of vehicle-bridge coupled system based on virtual distortion method

In the inverse analysis of vehicle-bridge coupled system, moving vehicle (load) identification is a crucial problem. Traditionally moving vehicles are identified by identifying the equivalent moving forces, which is a well-known ill-conditioning problem, and hence is sensitive to noise. Moreover identification of moving forces require the number of sensors equal to or bigger than the number of unknown forces to obtain the unique solution. In order to avoid these drawbacks, this paper presents an effective method to identify moving vehicles. Vehicle parameters are chosen as the variables, which are optimized by minimizing the square distance between the measured structural responses and estimated responses. During the optimization, the computational work is reduced a lot by the proposed concepts of dynamic moving influence matrix based on Virtual Distortion Method (VDM), which consists of impulse response matrix with respect to the changing positions of the moving masses and is independent of mass values, and only needs to be computed once in advance. In this way, the repeatedly construction of the variant system matrix is avoided, and hence the optimization efficiency is improved. In this method, a mass-spring damping model with two degree of freedoms (Dofs) is used to simulate moving vehicle and its dynamic behavior. Moving vehicles and the bridge are analyzed as different substructures. In addition the equivalent moving loads are reconstructed simultaneously, such that the well-conditioning of the identification is ensured and makes the method be accurate and robust to noise. Moreover the number of the necessary sensors is decreased. The numerical costs are considerably reduced further by using the concepts of VDM, which belongs to fast reanalysis method, that is, the response of the modified structure equals to the response of an intact structure subjected to the same external load and to certain virtual distortions which model the changes of the actual structure. In this way, during the optimization, the structural response under given optimization variables are estimated quickly without the whole analysis of the global structure. Numerical experiment of a frame beam with 5% Gaussian measurement error is used to verify the proposed method, where the effectiveness of different simplified vehicle models is compared. It demonstrates that masses of multiple moving vehicles can be identified using fewer sensors. When the roughness of road surface is neglected, under normal speed, the structural response is mainly caused by the weight of vehicles, and the coupling between the vehicle and bridge is rather low, therefore the influence of the vehicle spring stiffness and damping is very weak on the mass identification. For the identification of multiple vehicles, masses of the mass-spring damping model with two Dofs can be identified satisfactorily with the stiffness and damping as the estimated initial values. The identification considering the road roughness or high speed using the proposed method in this paper is undergoing.