Compressed sensing for moving force identification using redundant dictionaries

Abstract Moving force identification (MFI) techniques have been widely studied in recent years. However, the contradiction between response acquisition and energy consumption limits applications of existing MFI methods and has become one of the most prominent issues in the field of structural health monitoring (SHM). In fact, sample length of response data can be shortened by exploiting compressed coefficients of responses based on compressed sensing (CS) theory. In order to mitigate this contradiction and to study if these compressed coefficients can be efficiently exploited for MFI, a novel method is proposed for MFI based on CS with redundant dictionaries in this study. Firstly, a redundant dictionary is designed for creating a sparse expression on each moving force based on prior knowledge of moving forces. Then, by the aid of relationship between moving forces and responses, an indirect way is presented to design dictionaries for different types of structural responses, sparse expression of responses is established simultaneously, and a MFI governing equation is formulated by directly exploiting compressed coefficients of responses via CS. Moreover, sparse regularization is introduced to ensure the accuracy of MFI results. Finally, the proposed method is validated by both numerical simulations and experimental verifications. The illustrated results show that the sample length of each acquired data can be obviously shortened and the compressed coefficients rather than structural responses can be directly used for MFI. The identified moving forces are in good agreement with the true ones, which shows the effectiveness and applicability of the proposed method. In addition, the proposed method can estimate the total weight of the car with a good accuracy and a strong robustness to noise.