A novel preconditioned range restricted GMRES algorithm for moving force identification and its experimental validation

Moving force identification (MFI) is a widely concerned inverse problem in structural dynamics and well-known as intrinsically existing ill-posedness. With the help of Arnoldi process and Krylov subspace method, the generalized minimal residual (GMRES) method can be improved to a range restricted generalized minimal residual (RRGMRES) method. Furthermore, by introducing the smoothing-norm preconditioning, a preconditioned range restricted generalized minimal residual (PRRGMRES) method is proposed to provide a stable solution to the ill-posed dynamic force identification problem. Simulations show that the novel method has significant improvement when compared to the classic time domain method and the RRGMRES method. In addition, to show the effectiveness and advantages of the proposed method, the PRRGMRES method is also compared with a newly-proposed regularization method named the preconditioned least square QR-factorization (PLSQR) method. Simulation results show that the PRRGMRES method has much better robustness and higher computational efficiency than the PLSQR method especially in dealing with highly inaccurate measurement cases. Finally, the accuracy and efficiency of the PRRGMRES method is verified by experimental studies. The PRRGMRES method has good performance in both overcoming ill-posed problems and improving computational efficiency, which should be of the highest priority in adoption for MFI.