We introduce the augmented Tikhonov regularization method motivated by Bayesian principle to improve the load identification accuracy in seriously ill-posed problems. Firstly, the Green kernel function of a structural dynamic response is established; then, the unknown external loads are identified. In order to reduce the identification error, the augmented Tikhonov regularization method is combined with the Green kernel function. It should be also noted that we propose a novel algorithm to determine the initial values of the regularization parameters. The initial value is selected by finding a local minimum value of the slope of the residual norm. To verify the effectiveness and the accuracy of the proposed method, three experiments are performed, and then the proposed algorithm is used to reproduce the experimental results numerically. Numerical comparisons with the standard Tikhonov regularization method show the advantages of the proposed method. Furthermore, the presented results show clear advantages when dealing with ill-posedness of the problem.
Jiang, J., Tang, H., Mohamed, M. S., Luo, S., & Chen, J. (2020). Augmented Tikhonov Regularization Method for Dynamic Load Identification. Applied Sciences, 10(18), . https://doi.org/10.3390/app10186348