Comparison of regularization methods for moving force identification with ill-posed problems

Four new methods have been developed to overcome the ill-posed problems inherently existing in moving force identification (MFI) in previous studies. This paper is an extension of the work to evaluate the overall performance of these presented methods by numerical simulations and experiment verifications in laboratory. A simply-supported bridge and two types of moving forces are adopted to evaluate the identification accuracy and ill-posed immunity of these new approaches. Bending moment and acceleration responses are measured when the time-varying forces moving across the bridge deck at constant speed. Numerical simulations of both uniaxial and biaxial forces include 12 cases, which are used to compare the identification accuracy and ill-posed immunity of these methods in detail. Finally, a hinge supported steel beam model and a vehicle model were designed and fabricated in laboratory. Then a series of experimental studies on MFI with these four methods are performed in laboratory. Both numerical and experimental results show that these four approaches can accurately identify moving forces with strong robustness and ill-posed immunity. Moreover, the truncated generalized singular value decomposition (TGSVD) method has higher identification accuracy than the piecewise polynomial truncated singular value decomposition (PP-TSVD) method, and the modified preconditioned conjugate gradient (M-PCG) method has higher identification efficiency than the preconditioned least square QR-factorization (PLSQR) method. To summarize, if the first goal in MFI is to improve the identification accuracy, the TGSVD method is recommended due to its high identification accuracy and stability in different cases. If the first goal in MFI is to improve the identification efficiency, the M-PCG method is recommended due to its high identification efficiency and easy to determine the optimal number of iterations. •Comparative studies have been carried out to evaluate the proposed four methods.•A guideline on selecting the best method for practical MFI has been provided.•Studies show that the PP-TSVD method is the worst among these four methods.•The TGSVD method is recommended for improving the identification accuracy.•The M-PCG method is recommended for improving the identification efficiency.