Abstract
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.
Highlights
The dynamic loads acting on a structure cannot be directly measured in many cases, and it is necessary to use indirect methods
We proposed the augmented Tikhonov regularization method in combination with the Green kernel function to identify the external dynamic loads acting on a structure
We proposed a method for the initial values selection of the regularization parameters
Summary
The dynamic loads acting on a structure cannot be directly measured in many cases, and it is necessary to use indirect methods. The matching L-curve and GCV regularization parameter selection method may fail when L-curve is too smooth, without inflection points, or GCV function curve is too flat at the minimum value In these cases, it is difficult to accurately locate the regularization parameter, and an unsuitable parameter will lead to a large error in the load identification. This paper introduces the augmented Tikhonov regularization method in combination with the Green kernel function in dynamic load identification It proposes a new parameters selection method for the augmented Tikhonov regularization initial parameters, and the accuracy is compared to the standard Tikhonov regularization method.
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