Novel Sparsity Adaptive Matching Pursuit for Moving Force Identification Using Atomic Coherence Discrimination and Variable Step-Size Strategies

Moving force identification (MFI) through dictionary learning is substantial for advancing bridge structural health monitoring (BSHM). However, the existing methods face challenges such as the storage and transmission expenses associated with large-scale data, as well as the uncertainty of prior information of sparsity parameters in subsequent MFI computations. Therefore, a novel MFI framework of dictionary learning under compressed sensing (DLCS) is first developed based on dictionary learning and compressed sensing theories, and sparse representation characteristics of dictionaries. In the DLCS framework, a novel sparsity adaptive matching pursuit algorithm is then proposed by considering the atomic screening and variable step-size strategies, which resolves the unknown sparsity problem in the calculation of the sparsity coefficient. The best coherence threshold parameters for atomic screening are optimized based on the Bayesian information criterion. Finally, the validation of the proposed method is conducted by numerical simulations, and experiments via bridge–vehicle system models in the laboratory. The results indicate that all the relative percentage errors in the identification of gross vehicle weight by the proposed method keep under 2.84% in all experimental cases, and the computational efficiency is markedly higher than that by the other two conventional methods, DL-OMP and DL-SAMP, with its computational time being approximately half of the former and about one-fifth of the latter, respectively, which provide new potential tools and innovative perspectives for BSHM.