Comparative studies of computation tools for moving force

Existing techniques to identify moving forces based on traditional finite element method (TFEM) is subject to a large number of elements with detailed description of a structure, which makes modeling complicated. A new modeling method for a vehicle-bridge system called wavelet finite element method (WFEM) is presented in this paper. It makes use of a multi-scale analysis whereby detailed description can be achieved to overcome this problem. The shape function of WFEM is formed by a scale function in a wavelet space and by a transformation matrix to connect the wavelet space to the physical one. To evaluate the properties of WFEM, simulations of two moving forces on a simply supported and a continuous bridge are conducted with subsequent comparison with TFEM. To smooth the noise and large fluctuations on the boundaries of the identified results in the time history, the first-order Tikhonov regularizations combined with the dynamic programming technique are adapted and compared with the zeroth-order Tikhonov regularization. White noise is added to the simulated dynamic responses. Some parameter effects, such as vehicle bridge parameters, measurement parameters are also considered. Numerical results demonstrate the WFEM method and the first-order Tikhonov regularization method to be effective for moving force identification. The first-order Tikhonov regularization has the property of smoothing noise and avoiding large fluctuations on the boundaries. Meanwhile, the parameters analyzed affect the identified results to some extent.