Moving force identification based on multi-task decomposition and sparse regularization

High-accuracy and efficient moving force identification (MFI) serves as an indirect approach that has the potential to meet real-time monitoring of vehicle-bridge interaction forces. The parallel computing-oriented method developed based on time-domain segmentation has demonstrated its advantages in the rapid identification of dynamic forces. However, this method has no strategy in place to highlight the global signal feature of dynamic forces. This study inherits a framework of the existing parallel computing-oriented method, attempting to identify the moving forces in a shorter amount of time by using a parallelizable multi-task optimal method. The proposed method establishes multiple MFI tasks based on a finite number of local time ranges. Each MFI task aims to estimate the moving forces happening within its local analysis duration and the corresponding initial vibration state of the structure. The identified equations for multiple tasks are built based on sparse regularization, intending to improve the ill-posed nature of the MFI inverse problems. To ensure that the identified moving force has an overall horizontal trend line, additional constraint conditions are defined mathematically and added to the sparse regularization-based equations, aiming to limit the differences among all the average values of the moving forces that are identified from different tasks, and resulting in a group of constrained identified equations. By relaxing the added constraints, a practical iterative algorithm is proposed for solving the multi-task MFI problem, wherein, the identified processes of different tasks in each iteration can be solved by parallel computing. Numerical and experimental studies verify the feasibility and effectiveness of the proposed method in identifying moving forces. The comparative analysis highlights its advantages in fast computation rather than the existing l1-norm regularization-based method in the considered cases. Some relative issues are discussed as well.