Load Identification Method Based on Interval Analysis and Tikhonov Regularization and Its Application

In order to study the dynamic force identification method of an end-plate pick of shearer, a dynamic force identification technique based on interval theory was proposed. The dynamic force interval identification model is established by describing and quantifying the identified parameters. By using the interval analysis method of the first-order Taylor expansion, the dynamic force identification is transformed into two kinds of deterministic inverse problems at the midpoint of the uncertain parameter and its gradient identification. The Tikhonov regularization method is used to solve two kinds of deterministic problems, and the upper and lower boundaries of dynamic force of the end-plate pick are determined. The results show that the deviations between the identified dynamic force and the actual dynamic force are basically within 2% and 5%, and the average uncertainties are up to 7% and 10%. Therefore, the proposed method can effectively determine the upper and lower boundaries of dynamic force of the end-plate pick, improve the solving efficiency, and provide a new research method for studying the coal rock mechanism of the pick cutting load.

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Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Mathematical Problems in Engineering ◽

10.1155/2019/6095184 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Chunping Ren ◽

Nengjian Wang ◽

Qinhui Liu ◽

Chunsheng Liu

Keyword(s):

Kernel Function ◽

Tikhonov Regularization ◽

Regularization Method ◽

Integral Form ◽

Identification Problem ◽

Tikhonov Regularization Method ◽

Dynamic Force ◽

Conical Pick ◽

Force Identification ◽

Green Kernel

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal-seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill-conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill-posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

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A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

Mathematical Problems in Engineering ◽

10.1155/2018/4790950 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Nengjian Wang ◽

Chunping Ren ◽

Chunsheng Liu

Keyword(s):

Tikhonov Regularization ◽

Present Method ◽

Optimal Solution ◽

Identification Problem ◽

Dynamic Force ◽

Inverse Identification ◽

Identification Problems ◽

Force Identification ◽

New Findings ◽

Ill Posed

This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to ill-posedness of the inverse problems, conventional numerical approach for solutions results in arbitrarily large errors in solution. However, in the field of engineering mathematics, there are famous mathematical algorithms to tackle the ill-posed problem, which are known as regularization techniques. In the current study, a novel fractional Tikhonov regularization (NFTR) method is proposed to perform an effective inverse identification, then the smoothing functional of the ill-posed problem processed by the proposed method is regarded as an optimization problem, and finally a stable optimal solution is obtained by using an improved super-memory gradient (ISMG) method. The result of the present method is compared with that of the standard TR method and FTR method; new findings can be obtained; that is, the present method can improve accuracy and stability of the inverse identification problem, robustness is stronger, and the rate of convergence is faster. The applicability and efficiency of the present method in this paper are demonstrated through a mathematical example and an engineering example.

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

Open Mathematics ◽

10.1515/math-2020-0111 ◽

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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