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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 963424, 12 pages
Research Article

Simultaneous Identification of Moving Vehicles and Bridge Damages Considering Road Rough Surface

1College of Civil and Architecture Engineering, Dalian Nationalities University, Dalian 116650, China
2Smart-Tech Centre, Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland
3School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
4Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 5180553, China

Received 9 August 2013; Revised 19 October 2013; Accepted 3 November 2013

Academic Editor: Nawawi Chouw

Copyright © 2013 Qingxia Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method for the simultaneous identification of moving vehicles and the damages of the supporting structure from measured responses is presented. A two-axle vehicle model with two degrees of freedom (DOF) is adopted. The extent of the damage and the vehicle parameters were chosen as the optimisation variables, which allow ill conditioning to be avoided and decrease the number of sensors required. The identification is performed by minimising the distance between the measured responses and the computed responses to given optimisation variables. The virtual distortion method (VDM) was used, such that the response of the damaged structure can be computed from comparison with the intact structure subjected to the same vehicle excitation and to the response-coupled virtual distortions. These are related to the optimisation variables by the system impulse response matrix and are expressed by a linear system, which allowed both types of optimisation variables to be treated in a unified way. The numerical cost is reduced by using a moving influence matrix. The adjoint variable method is used for fast sensitivity analysis. A three-span bridge numerical example is presented, where the identification was verified with 5% root mean square (RMS) measurement, and model, error whilst also considering the surface roughness of the road.