Moving force identification based on learning dictionary with double sparsity

Moving force identification (MFI) is essential for the bridge safety as it is one of the major loads acting on the bridge deck. MFI techniques based on force dictionary are promising owing to their prominent performance in solving ill-posed problems and calculation efficiency. Since the specific forms of authentic moving forces are complex and unknown, a fixed dictionary normally adopted tends to fail in expressing moving forces sparsely enough. In this study, dictionary learning (DL) is introduced into the field of MFI to design a better fit force dictionary based on the measured response data. A novel MFI method based on learning dictionary with double sparsity is proposed. Firstly, the MFI equation in time domain which describes the relationship between moving force and measured structural responses is established. Then a sparse dictionary model is designed in which the force dictionary is assumed to be expressed sparsely over the base dictionary, and the moving force is sparse over the force dictionary simultaneously. Moreover, the sparse K-singular-value-decomposition (K-SVD) algorithm is employed to realize the learning process through alternatively updating between double sparse codes. Finally, the learned force dictionary and moving forces are estimated through base force dictionary and double sparse codes. Numerical simulations and experimental studies are carried out to investigate the performance of the proposed method, and the results clearly certify its effectiveness and robustness.