• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.505-516
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• 2020

This study shows that image deblurring problems can be transformed into the multi-parameter Tikhonov type with multiple right hand sides. Also, this paper proposes the extension of the global generalized cross validation to obtain an appropriate choice of the regularization parameters for this problem. The experimental results of using the preconditioned Gl-CGLS algorithm were analyzed.

• Steel and Composite Structures
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• v.39 no.5
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• pp.511-528
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• 2021

There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.472-472
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• 2010

The tomography has played a key role in tokamak plasma diagnostics for image reconstruction. The Phillips-Tikhonov (P-T) regularization method was attempted in this work to reconstruct cross-sectional phantom images of the plasma by minimizing the gradient between adjacent pixel data. Recent studies about the comparison of the several tomographic reconstruction methods showed that the P-T method produced more accurate results. We have studied existing Laplacian matrix used in Phillips-Tikhonov regularization method and developed modified Laplacian matrix (Modified L). The comparison of the reconstruction result by the modified L and existing L showed that modified L produced more accurate result. The difference was significantly pronounced when a portion of plasma was reconstructed. These results can be utilized in the Edge Plasma diagnostics; especially in divertor diagnostics on tokamak a large impact is expected. In addition, accurate reconstruction results from received data in only one direction were confirmed through phantom test by using P-T method with modified L. These results can be applied to the tangentially viewing pin-hole camera diagnostics on tokamak.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.1
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• pp.161-166
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• 2020

This paper suggests an extension of the unified Bayesian Tikhonov regularization method. The unified method establishes the relationship between Tikhonov regularization parameter and Bayesian hyper-parameters, and presents a formula for obtaining the regularization parameter using the maximum posterior probability and the evidence framework. When the dimension of the data matrix is m by n (m >= n), we derive that the total misfit has the range of m ± n instead of m. Thus the search range is extended from one to 2n + 1 integer points. Golden section search rather than linear one is applied to reduce the time. A new benchmark for optimizing relative error and new model selection criteria to target it are suggested. The experimental results show the effectiveness of the proposed method in the image restoration problem.

• Smart Structures and Systems
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• v.31 no.3
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• pp.229-245
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• 2023

The absence of excitation measurements may pose a big challenge in the application of structural damage identification owing to the fact that substantial effort is needed to reconstruct or identify unknown input force. To address this issue, in this paper, an iterative strategy, a synergy of Tikhonov regularization method for force identification and modified Jaya algorithm (M-Jaya) for stiffness parameter identification, is developed for damage identification with partial output-only responses. On the one hand, the probabilistic clustering learning technique and nonlinear updating equation are introduced to improve the performance of standard Jaya algorithm. On the other hand, to deal with the difficulty of selection the appropriate regularization parameters in traditional Tikhonov regularization, an improved L-curve method based on B-spline interpolation function is presented. The applicability and effectiveness of the iterative strategy for simultaneous identification of structural damages and unknown input excitation is validated by numerical simulation on a 21-bar truss structure subjected to ambient excitation under noise free and contaminated measurements cases, as well as a series of experimental tests on a five-floor steel frame structure excited by sinusoidal force. The results from these numerical and experimental studies demonstrate that the proposed identification strategy can accurately and effectively identify damage locations and extents without the requirement of force measurements. The proposed M-Jaya algorithm provides more satisfactory performance than genetic algorithm, Gaussian bare-bones artificial bee colony and Jaya algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.8
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• pp.2718-2731
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• 2021

In the structural health monitoring of composite materials, in order to solve the ill-posed problem of impact force reconstruction, regularization techniques are often used to deal with it. Due to the poor convergence of the traditional Tikhonov regularization method, in order to accurately reconstruct the time history of the impact force, this paper improves Tikhonov regularization method and constructs homotopy function with strong convergence. Since the optimal regularization parameters need to be found in the homotopy function, the Newton downhill method is used to find the optimal parameters and the homotopy function can be calculated, which can accurately reconstruct the time history of the impact force. In order to verify the universality of the method in this paper, impact hammers of different materials were used in the experiment in this paper to study and compare the reconstruction effect of impact time history of different impact hammers.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.91-98
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• 2017

Electrical impedance tomography is a nondestructive imaging technique to reconstruct unknown conductivity distribution based on applied current data and measured voltage data through an array of electrodes attached on the periphery of a domain. In this paper, an inverse method based on truncated singular value decomposition is proposed to solve the inverse problem with the generalized Tikhonov regularization and to reconstruct the conductivity distribution. In order to reduce the inverse computational time, truncated singular value decomposition is applied to the inverse term after the generalized regularization matrix is taken out from the inverse matrix term. Numerical experiments and phantom experiments have been performed to verify the performance of the proposed method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.8
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• pp.41-46
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• 2006

The capability for reconstructing impact forces of an aircraft wing using impact response functions and regularization methods were examined. The impact response function which expresses the relation between the structure response and the impact force was derived using the information on mass and stiffness data of a finite element model for the wing. Iterative Tikhonov regularization method and generalized singular value decomposition method were used to inverse the impact response function that was generally ill-posed. For the numerical verification, a fighter aircraft wing was used. Strain and deflection histories obtained from finite element analysis were compared with the results calculated using impact response functions. And the impact forces were reconstructed with the strain histories obtained from finite element analysis. The numerical verification results showed that this method can be used to monitor impact forces on aircraft structures.

• Korea-Australia Rheology Journal
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• v.20 no.2
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• pp.51-58
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• 2008

This paper describes a two-step Tikhonov regularization procedure for converting the steady shear data generated by parallel-disk viscometers, in the presence of wall slip, into a shear stress-shear rate function and a wall shear stress-slip velocity functions. If the material under test has a yield stress or a critical wall shear stress below which no slip is observed the method will also provide an estimate of these stresses. Amplification of measurement noise is kept under control by the introduction of two separate regularization parameters and Generalized Cross Validation is used to guide the selection of these parameters. The performance of this procedure is demonstrated by applying it to the parallel disk data of an oil-in-water emulsion, of a foam and of a mayonnaise.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.4
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• pp.48-55
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• 1999

In this paper, the ill-posed inverse problem of surface waves caused by a two-dimensional pulsating pressure distribution on the free surface is studied using the regularization method. In order to exemplify the method, a cosine pressure distribution on a limited range of the undisturbed free surface is considered. By taking the resulting horizontal velocity as input data, the corresponding pressure is determined numerically by three different regularization schemes. It is found that the iterated Tikhonov method provides with the most accurate result, while solutions obtained from the Landweber-Friedman regularization are most stable.