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

Wang, Nengjian; Ren, Chunping; Liu, Chunsheng

doi:10.1155/2018/4790950

Cited by 2 publications

(2 citation statements)

References 53 publications

(59 reference statements)

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“…Image reconstruction is an ill-posed problem, and it is generally known that Tikhonov regularization is an efficient way to solve ill-posed problems. Its basic idea is to transform equation (1) into an optimization problem [20][21][22][23][24]:…”

Section: Image Reconstructionmentioning

confidence: 99%

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

Liu

Ren

2019

Journal of Electrical and Computer Engineering

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Aiming at the conventional image edge detection algorithm, the first-order differential edge detection method is easy to lose the image details and the second-order differential edge detection method is more sensitive to noise. To deal with the problem, the Tikhonov regularization method is adopted to reconstruct the input coal-rock infrared images, so as to reduce the noise interference, and then, the reconstructed image is transformed by gray level. Finally, we consider the frequency characteristics and long memory properties of fractional differential, the classical first-order Sobel and second-order Laplacian edge detection algorithms are extended to fractional order pattern, and a new pattern of fractional order differential image edge detection is constructed to realize the coal-rock fracture edge features identification. The results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller. From the point of view of location criteria and location accuracy, the fractional order differential algorithm is better than the integer order. In addition, the proposed method is compared with Canny algorithm, B-spline wavelet transform, and multidirection fuzzy morphological edge detection method, can detect more coal-rock fracture infrared image edge details, and is more robust to noise.

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Section: Image Reconstructionmentioning

confidence: 99%

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

Liu

Ren

2019

Journal of Electrical and Computer Engineering

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“…It still retains its researchable charm in the field of force identification (Jayalakshmi et al, 2018; Li and Lu, 2018; Wang et al, 2018a). Many regularization techniques have been introduced for solving the problem of force identification, for example, Tikhonov method (He et al, 2019; Wang et al, 2018b), truncated singular value decomposition (Chen et al, 2019), multiplicative regularization (Aucejo and De Smet, 2018), sparse regularization (Qiao et al, 2019), and so on. Among these methods, the sparse regularization method is a comparatively new technology.…”

Section: Introductionmentioning

confidence: 99%

Force identification under unknown initial conditions by using concomitant mapping matrix and sparse regularization

Pan

2020

Journal of Vibration and Control

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Unknown initial conditions can affect the identified accuracy of dynamic forces. Direct measurement of initial conditions is relatively difficult. This study proposes a sparse regularization–based method for identifying forces considering influences of unknown initial conditions. The initial conditions are embedded in a classical governing equation of force identification. The key idea is to introduce a concept of concomitant mapping matrix for reasonably expressing the initial conditions. First, a dictionary is introduced for expanding the dynamic forces. Then, the concomitant mapping matrix is formulated by using free vibrating responses, which correspond to structural responses happening after the structure is subjected to each atom of the force dictionary. A sparse regularization strategy is applied for solving the ill-conditioned equation. After that, the problem of force identification is converted into an optimization problem, and it can be solved by using a one-step strategy. Numerical simulations are carried out for verifying the feasibility and effectiveness of the proposed method. Illustrated results clearly show the applicability and robustness of the proposed method for dealing with force reconstruction and moving force identification.

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

Cited by 2 publications

References 53 publications

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

Force identification under unknown initial conditions by using concomitant mapping matrix and sparse regularization

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