• Journal of the Korean Operations Research and Management Science Society
• /
• v.13 no.2
• /
• pp.25-33
• /
• 1988

An efficient heuristic solution procedure is developed for the minimum location problems. The gradient direction method and modified gradient approach are developed due to the differentiability of the objective functions. Suboptimal step size is obtained analytically. A Modified Gradient Procedure (NGP) is presented and compared with the hyperboloid approximation procedure (HAP) which is one of the best known methods.

• Proceedings of the IEEK Conference
• /
• 2007.07a
• /
• pp.389-390
• /
• 2007

In this paper, we propose a modified watershed algorithm to obtain exact edge of region. The proposed method adjusts priority at zero-crossing point of gradient in order to make the point of region decision time postponed. We compare the proposed method with a previous method and prove that this method can extract more correct edge of region.

• Journal of Ocean Engineering and Technology
• /
• v.20 no.6 s.73
• /
• pp.61-66
• /
• 2006

Two iterative solvers are applied to solve the modified mild slope equation. The elliptic formulation of the governing equation is selected for numerical treatment because it is partly suited for complex wave fields, like those encountered inside harbors. The requirement that the computational model should be capable of dealing with a large problem domain is addressed by implementing and testing two iterative solvers, which are based on the Stabilized Bi-Conjugate Gradient Method (BiCGSTAB) and Generalized Conjugate Gradient Method (GCGM). The characteristics of the solvers are compared, using the results for Berkhoff's shoal test, used widely as a benchmark in coastal modeling. It is shown that the GCGM algorithm has a better convergence rate than BiCGSTAB, and preconditioning of these algorithms gives more than half a reduction of computational cost.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.12
• /
• pp.1715-1725
• /
• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Structural Engineering and Mechanics
• /
• v.48 no.2
• /
• pp.195-205
• /
• 2013

The buckling problem of linearly tapered micro-columns is investigated on the basis of modified strain gradient elasticity theory. Bernoulli-Euler beam theory is used to model the non-uniform micro column. Rayleigh-Ritz solution method is utilized to obtain the critical buckling loads of the tapered cantilever micro-columns for different taper ratios. Some comparative results for the cases of rectangular and circular cross-sections are presented in graphical and tabular form to show the differences between the results obtained by modified strain gradient elasticity theory and those achieved by modified couple stress and classical theories. From the results, it is observed that the differences between critical buckling loads achieved by classical and those predicted by non-classical theories are considerable for smaller values of the ratio of the micro-column thickness (or diameter) at its bottom end to the additional material length scale parameters and the differences also increase due to increasing of the taper ratio.

• Advances in nano research
• /
• v.13 no.4
• /
• pp.393-406
• /
• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Journal of Biomedical Engineering Research
• /
• v.28 no.6
• /
• pp.817-824
• /
• 2007

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

• Smart Structures and Systems
• /
• v.18 no.5
• /
• pp.839-864
• /
• 2016

This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference between the recorded acceleration of a real damaged structure and a hypothetical damaged one. This is performed by updating physical parameters (module of elasticity in this study) in each step using iterative process of modified nonlinear conjugate gradient (M-NCG) and modified Broyden-Fletcher-Goldfarb-Shanno algorithm (M-BFGS) separately. These algorithms are based on sensitivity analysis and provide a solution for nonlinear damage detection problem. Three illustrative test examples are considered to assess the performance of the proposed method. Finally, it is demonstrated that the proposed method is satisfactory for detecting the location and ratio of structural damage in presence of noise.

• Bulletin of the Korean Chemical Society
• /
• v.15 no.11
• /
• pp.953-957
• /
• 1994

Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${\AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.

• Korean Journal of Food Science and Technology
• /
• v.52 no.3
• /
• pp.296-303
• /
• 2020

Hop-resistant lactic acid bacteria (LAB) are well-known, major beer-spoilage bacteria. The hop-gradient agar containing ethanol (c-HGA+E) method has been used to examine hop-resistance of beer-spoilage LAB. However, the selection of beer-spoilage bacteria by the c-HGA+E method is either too selective or too inclusive. Furthermore, it is accompanied by a complicated experimental procedure, high-cost and time. To overcome these disadvantages, the modified hop-gradient agar with ethanol (m-HGA+E) method was developed. The most remarkable modifications were the shape of the petri dish and the inoculation method for bacteria. The efficiency and validation of the m-HGA+E approach were proven by the formation of colonies at different hop concentrations in the bottom layer, co-culture with the bacteriocin producer and by PCR detection of hop-resistant genes. This study demonstrated that m-HGA+E is a rapid, economical, and easy method to monitor potential hop-resistant beer-spoilage LAB during the beer brewing process.