Identification of moving vehicle forces on bridge structures via moving average Tikhonov regularization

Traffic-induced moving force identification (MFI) is a typical inverse problem in the field of bridge structural health monitoring. Lots of regularization-based methods have been proposed for MFI. However, the MFI accuracy obtained from the existing methods is low when the moving forces enter into and exit a bridge deck due to low sensitivity of structural responses to the forces at these zones. To overcome this shortcoming, a novel moving average Tikhonov regularization method is proposed for MFI by combining with the moving average concepts. Firstly, the bridge-vehicle interaction moving force is assumed as a discrete finite signal with stable average value (DFS-SAV). Secondly, the reasonable signal feature of DFS-SAV is quantified and introduced for improving the penalty function (∣∣x∣∣22) defined in the classical Tikhonov regularization. Then, a feasible two-step strategy is proposed for selecting regularization parameter and balance coefficient defined in the improved penalty function. Finally, both numerical simulations on a simply-supported beam and laboratory experiments on a hollow tube beam are performed for assessing the accuracy and the feasibility of the proposed method. The illustrated results show that the moving forces can be accurately identified with a strong robustness. Some related issues, such as selection of moving window length, effect of different penalty functions, and effect of different car speeds, are discussed as well.