Moving force identification based on the nonnegative flexible conjugate gradient least square method and experimental verification

Abstract

Moving force identification (MFI) is an approach aimed at acquiring the time history of unknown moving loads acting on a bridge, which is actually an inverse problem. The accuracy and efficiency of MFI are significantly influenced by the ill-posedness problem during the process of solving the vehicle-bridge interaction system, especially when the vehicle axles getting on or getting off the bridge. The objective of the study is thus to reduce the effect of ill-posedness problem on the accuracy and efficiency of MFI through numerical and experimental methods. A nonnegative flexible conjugate gradient least square (NN-FCGLS) method is first developed through enriching the conjugate gradient least square method with the flexible Krylov subspace technique and nonnegative constraint conditions. Then, the solution of the NN-FCGLS method is continuously updated with the Krylov subspace technique and the Karush-Kuhn-Tucker conditions at each iteration to obtain a stable solution for ill-posed dynamic force identification. Finally, laboratory experiments were carried out with a simply supported aluminum alloy beam. Numerical simulation results show that the NN-FCGLS method is insensitive to vehicle speed and vehicle wheelbase, and has better accuracy, stronger robustness and higher computational efficiency than the time domain method and the conjugate gradient least square method. The relative percent errors of all ten cases do not exceed 7.8 % under the interference of 20 % noise level. The experimental results shows that the correlation coefficients between measured responses and reconstructed responses are larger than 0.92 in all cases. Experimental studies demonstrate the accuracy and efficiency of the proposed NN-FCGLS method in the practice of MFI.