Moving Force Identification Based On Wavelet Finite Element Method And First Order Tikhonov Regularization

The vehicles and bridges are always one of the significant parts for traffic engineering. It iscrucial for vehicle-bridge system to identify the moving forces, not only because the interactionforces induced by vehicles couldn't be simplified as static ones during the long time observation,but also because it is important and imperative to obtain the real-time moving forces on highwayand railway bridges for the safe estimation.This dissertation studies the modeling methods for vehicle-bridge system and identificdationmethods for moving forces on the system. The new methods for modeling and for moving forceidentification are compared with traditional methods to validate the properties of feasibility andcorrectness for different structures, with different influence factors, such as noise level,measurement parameters, vehicle-bridge system parameters, et al. According to the analysis, it iscapable of more accurate design for bridges and of more accurate monitoring for moving vehicle.The main contents of this dissertation are as follows:(1)In Chapter2, a modeling method called wavelet finite elemtent method (WFEM) forvehicle bridge system is studied. To parameterize the model, the B Spline Wavlet in theInterval (BSWI) is adopted to connect the physical and wavelet spaces throughtransformation matrix by expressing the physical parameters with wavelet functions. Theprecision of the model is controlled by the multi-scale and multi-resolution property ofWFEM, through which both the detail and coarse characteristics can be obtained. Thevibration analysis is applied to validate that fewer elements are needed for WFEMmodel and the precision is satisfied compared with traditional finite element method(TFEM), which is meaningful for the improvement of precision and efficient of large orcomplicated structure.(2)In Chapter3, a method for moving force identification based on the first order Tikhonov regularization and dynamic programming technique is studied. Fist, the relationshipbetween moving forces to be identified and the measured dynamic responses isestablished by the parameters in tiny time domain, which are discreted from the motionfunction in state space. Then, moving force is obtained using dynamic programmingtechnique by backward and forward iteration operation on optimal varialbes to gain theconnection of system parameters and optimal variables. The L-curve method isintroduced to find out the optimal parameter and the first order Tikhonov reguralizationis deduced for both smoothing the noise and avoiding the fluctuations when movingvehicles are moving in and out the bridge.(3)In Chapter4, identification of moving forces on simply supported and continuousbridges is studied. First to validate the feasibility and the commonatity of the newmodeling method compared with TFEM, then to certificate the advantage of firstTikhonov regularization by the comparision of the identified results of moving forceswith the results under zero order Tikhonov regularization. The effects of parameters onidentification accuracy are analyzed, and the numerical simulation gives the conclusionthat the influence parameters such as the sampling frequency, the vehicle speed, thenumber and the arrangement of the measurement sensors, the axle spacing of vehicles, etal affect the accuracy of identified results to some extent.