Optimization analysis and experimental study of preconditioned least square QR-factorization for moving force identification

Based on the theory of moving force identification in time domain, a preconditioned least square QR-factorization (PLSQR) algorithm is developed to overcome the typical ill-posed problem existing in inverse problems. A comprehensive numerical simulation is set up based on a beam model with biaxial time-varying forces to evaluate PLSQR by comparing this technique with the conventional counterpart SVD embedded in the time domain method (TDM). Investigations show that the PLSQR has higher precision, more noise immunity and less sensitive to perturbations with the ill-posed problems compared with TDM. By combining the improved Gram-Schmidt with iterative orthogonalization, iterative optimization analysis of PLSQR is carried out. Results indicate that the improved PLSQR(i-PLSQR) can more quickly and effectively identify the moving load on bridge without sacrificing the identification accuracy compared with the PLSQR, and the average optimal numbers of iterations reduce by at least two thirds in eight cases with three noise levels. The experimental results show that the identified force obtained from the i-PLSQR is very close to the true force and the identification accuracy is significantly higher than traditional TDM, which can be applied to the field moving force identification. The study results have important reference for the research of inverse problems identification of structural dynamics. © 2018, Nanjing Univ. of Aeronautics an Astronautics. All right reserved.