Uncorrelated multi-sources load identification in frequency domain based on improved Tikhonov regularization method

2016 ◽  
Vol 52 (3-4) ◽  
pp. 983-990 ◽  
Author(s):  
Jianying Wang ◽  
Cheng Wang ◽  
Bineng Zhong ◽  
Tian Wang ◽  
Wangping Guo ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Tikhonov Regularization Method ◽  
Load Identification

scholarly journals Augmented Tikhonov Regularization Method for Dynamic Load Identification

2020 ◽  
Vol 10 (18) ◽  
pp. 6348 ◽  
Author(s):  
Jinhui Jiang ◽  
Hongzhi Tang ◽  
M Shadi Mohamed ◽  
Shuyi Luo ◽  
Jianding Chen
Keyword(s):  
Kernel Function ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Identification Accuracy ◽  
Tikhonov Regularization Method ◽  
Load Identification ◽  
Structural Dynamic ◽  
Green Kernel ◽  
Ill Posed ◽  
Residual Norm

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.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

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