An efficient and robust method for structural distributed load identification based on mesh superposition approach. (April 2021) - Liu, He; Liu, Quansheng; Liu, Bin; Tang, Xuhai; Ma, Hao; Pan, Yucong; Fish, Jacob
Highlights: The distributed loads are accurately approximated by the superimposed loading mesh. Well-posedness both in determined and underdetermined conditions by applying the modified 2nd TRM. Non-negativity of solution is ensured by employing the NNLS. High quality of proposed method in accuracy, robustness, and computational efficiency. Abstract: Accurate load identification is vital for the structural optimization design and the structural health monitoring in different engineering disciplines. However, the external loads usually are difficult to determine with direct measurements. In the present manuscript, an efficient and robust method is proposed to identify the distributed static or quasi-static loads on linear-elastic structures. The superimposed loading mesh approach is proposed to map the unknown loads, and nodal values of the superimposed loading mesh are taken as inverse variables in the inverse problem. With this strategy, the inverse problem is converted to solving a set of linear equations which maps the relationship between the inverse variables and measured responses. To find the optimal solution, the modified second-order Tikhonov regularization method (TRM) is employed. Furthermore, to ensure the non-negativity of the identified loads, the non-negative least squares (NNLS) is applied. Three numerical tests are employed to verify the feasibility of the proposed method. The results suggest that the distributed loads can be accurately identified, and that the inverse system is well-posed. The proposed method has been found to be robust that reasonable accuracy can be obtained even with significant measurement error.