Preconditioned Range Restricted Gmres Method For Moving Force Identification And Its Experimental Study

Moving force identification(MFI)is an important issue in the field of structural health monitoring.Due to the typical ill-posedness in the process of solving inverse problem,the method of MFI has some difficulty such as low accuracy and easily disturbed by noise.Overcoming the ill-posed problem in MFI has been greatly concerned by researchers.To overcome the ill-posed problem,relies on the Arnoldi process and Krylov subspace method,a preconditioned range restricted generalized minimal residual(PRRGMRES)method is proposed in this paper.Based on the range restricted generalized minimum residual method(RRGMRES),the PRRGMRES method is presented to provide a stable solution of MFI by introducing a smoothing-norm preconditioning.By setting 5 random noise levels and 12 response combinations,the influence rule of the regularization matrix L and iteration numbers j on identification results are studied.The relative percentage error(RPE)criterion is used to select the optimal regularization parameters and the feasibility and effectiveness of the proposed method are verified by numerical simulations.Simulation results show that the precision of the PRRGMRES method is superior to the TDM and RRGMRES method,which illustrate that the precondition process with smoothing norm is effective.In addition,the optimal number of iterations j of the PRRGMRES method is much less than the RRGMRES method,which indicate that the preconditioning process can be used to improve the identification efficiency.Moreover,with the increase of noise level,the PRRGMRES method has stronger robustness and higher ill-posed immunity than the RRGMRES method,which shows that the new method is more suitable for the engineering application.To verity the effectiveness and advantages of the proposed method,the proposed method is compared with a newly proposed Krylov subspace method,namely,the preconditioned least square QR-factorization(PLSQR)method.Identification accuracy and computational efficiency of the two methods are compared through numerical simulations and vehicle-bridge model experiment.Simulation results show that the PRRGMRES method has much stronger robustness and higher identification efficiency than PLSQR method.In addition,the PRRGMRES method has higher ill-posed immunity and significant advantages in dealing with the measurement response with high noise.Experimental results also show that PRRGMRES method has higher identification accuracy and saves at least 43% computation time than the PLSQR method.Due to the perfect performance in both numerical simulations and experimental studies,the PRRGMRES method is strongly recommended for MFI in field.