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. Traditionallymoving vehicles are identified by identifying the equivalent moving forces,which is a well-known ill-conditioning problem, and hence is sensitive tonoise. Moreover identification of moving forces require the number ofsensors equal to or bigger than the number of unknown forces to obtain theunique solution. In order to avoid these drawbacks, this paper presents aneffective method to identify moving vehicles. Vehicle parameters are chosenas the variables, which are optimized by minimizing the square distancebetween the measured structural responses and estimated responses. Duringthe optimization, the computational work is reduced a lot by the proposedconcepts of dynamic moving influence matrix based on Virtual DistortionMethod (VDM), which consists of impulse response matrix with respect to thechanging positions of the moving masses and is independent of mass values,and only needs to be computed once in advance. In this way, the repeatedlyconstruction of the variant system matrix is avoided, and hence theoptimization efficiency is improved. In this method, a mass-spring dampingmodel with two degree of freedoms (Dofs) is used to simulate moving vehicleand its dynamic behavior. Moving vehicles and the bridge are analyzed asdifferent substructures. In addition the equivalent moving loads arereconstructed simultaneously, such that the well-conditioning of theidentification is ensured and makes the method be accurate and robust tonoise. Moreover the number of the necessary sensors is decreased. Thenumerical costs are considerably reduced further by using the concepts ofVDM, which belongs to fast reanalysis method, that is, the response of themodified structure equals to the response of an intact structure subjectedto the same external load and to certain virtual distortions which model thechanges of the actual structure. In this way, during the optimization, thestructural response under given optimization variables are estimated quicklywithout the whole analysis of the global structure. Numerical experiment ofa frame beam with 5\% Gaussian measurement error is used to verify theproposed method, where the effectiveness of different simplified vehiclemodels is compared. It demonstrates that masses of multiple moving vehiclescan be identified using fewer sensors. When the roughness of road surface isneglected, under normal speed, the structural response is mainly caused bythe weight of vehicles, and the coupling between the vehicle and bridge israther low, therefore the influence of the vehicle spring stiffness anddamping is very weak on the mass identification. For the identification ofmultiple vehicles, masses of the mass-spring damping model with two Dofs canbe identified satisfactorily with the stiffness and damping as the estimatedinitial values. The identification considering the road roughness or highspeed using the proposed method in this paper is undergoing.