• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.378-381
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• 2005

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the fuzzy-model-based periodic control is employed, and the control input is changed n times during one sampling period; 2) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system, but its discretization error vanishes as n approaches the infinity. 3) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.6
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• pp.211-218
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• 1983

In this paper, an attempt is made to match the continuous state trajectory of the digital control system with that of its continuous data model. Matching the state trajectories instead of the output responses assures that the performances of the internal variables of the plant as well as the output variables are preserved in the discretization. The mathematical tool used in this research is an extended maximum principle of the Pontryagin type, which enables one to synthesize a staircase type of optimal control signals, such as the output signal of a zero-order hold asociated with a digital controller. A general mathematical expression of the digital controller which may be used to replace the analog controller of a general system while preserving as mauch as possible the performance characteristics of the original continuous-data control system is derived in this paper.

• Nuclear Engineering and Technology
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• v.55 no.1
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• pp.324-329
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• 2023

Different types of deterministic solution methods were used to solve neutron transport equations corresponding to half-space and slab albedo problems. In these types of solution methods, in addition to the error of the numerical solutions, the obtained results contain truncation and discretization errors. In the present work, a non-analog Monte Carlo method is provided to simulate the half-space and slab albedo problems with Inönü and Anlı-Güngör strongly anisotropic scattering functions. For each scattering function, the sampling method of the direction of the scattered neutrons is presented. The effects of different beams with different angular dependencies and the effects of different scattering parameters on the reflection probability are investigated using the developed Monte Carlo method. The validity of the Monte Carlo method is also confirmed through the comparison with the published data.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Geomechanics and Engineering
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• v.23 no.1
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• pp.51-59
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• 2020

In this paper, the WEKA platform was used to mine and analyze measured data of floor failure depth and a prediction system of floor failure depth was developed with Java. Based on the standardization and discretization of 35-set measured data of floor failure depth in China, the grey correlation degree analysis on five factors affecting the floor failure depth was carried out. The correlation order from big to small is: mining depth, working face length, floor failure resistance, mining thickness, dip angle of coal seams. Naive Bayes model, neural network model and decision tree model were used for learning and training, and the accuracy of the confusion matrix, detailed accuracy and node error rate were analyzed. Finally, artificial neural network was concluded to be the optimal model. Based on Java language, a prediction system of floor failure depth was developed. With the easy operation in the system, the prediction from measured data and error analyses were performed for nine sets of data. The results show that the WEKA prediction formula has the smallest relative error and the best prediction effect. Besides, the applicability of WEKA prediction formula was analyzed. The results show that WEKA prediction has a better applicability under the coal seam mining depth of 110 m~550 m, dip angle of coal seams of 0°~15° and working face length of 30 m~135 m.

• The Journal of the Acoustical Society of Korea
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• v.38 no.5
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• pp.543-548
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• 2019

The tonal signal caused by the machinery component of a vessel such as an engine, gearbox, and support elements, can be modeled as a sparse signal in the frequency domain. Recently, compressive sensing based techniques that recover an original signal using a small number of measurements in a short period of time, have been applied for the tonal frequency detection. These techniques, however, cannot avoid a basis mismatch error caused by the discretization of the frequency domain. In this paper, we propose a method to detect the tonal frequency with a small number of measurements in the continuous domain by using the atomic norm minimization technique. From the simulation results, we demonstrate that the proposed technique outperforms conventional methods in terms of the exact recovery ratio and mean square error.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Journal of the Korean earth science society
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• v.39 no.4
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• pp.317-326
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• 2018

Effect of the nonuniform grid on the two-dimensional transport equation was investigated in terms of theoretical analysis and finite difference method (FDM). The nonuniform grid having a typical structure of the numerical weather forecast model was incorporated in the vertical direction, while the uniform grid was used in the zonal direction. The staggered and non-staggered grid were placed in the vertical and zonal direction, respectively. Time stepping was performed with the third-order Runge Kutta scheme. An error analysis of the spatial discretization on the nonuniform grid was carried out, which indicated that the combined effect of the nonuniform grid and advection velocity produced either numerical diffusion or numerical adverse-diffusion. An analytic function is used for the quantitative evaluation of the errors associated with the discretized transport equation. Numerical experiments with the non-uniformity of vertical grid were found to support the analysis.

• Korean Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.175-185
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• 1997

Given the widespread use of the Finite Element Method in strength analysis, automatic mesh generation is an important component in the computer-aided design of parts and assemblies. For a given resolution of geometric accuracy, the purpose of mesh generators is to discretize the continuous model of a part within this error limit. Sticking to this condition often produces many small elements around small features in spite that these regions are usually of little interest and computer resources are thus wasted. Therefore, it is desirable to selectively suppress small features from the model before discretization. This can be achieved by low-pass filtering a CAD model. A spatial function of one dimension higher than the model of interest is represented using the Fourier basis functions and the region where the function yields a value greater than a prescribed value is considered as the extent of a shape. Subsequently, the spatial function is low-pass filtered, yielding a shape without the small features. As an undesirable effect to this operation, all sharp corners are rounded. Preservation of sharp corners is important since stress concentrations might occur there. This is why the LPF (low-pass filtered) model can not be directly used. Instead, the distances of the boundary elements of the original shape from the LPF model are calculated and those that are far from the LPF model are identified and removed. It is shown that the number of mesh elements generated on the simplified model is much less than that of the original model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.10-17
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• 1985

A new method is suggested for the solution of plane elasticity problems. With use of the dislocation model in the crack problems, the basic scheme of this method is to find equilibrium Burgers vectors of dislocations which are distributed along the boundary of the first fundamental boundary value problems. The stress distribution in the region can be found by superposition of the contributions of each dislocation. The method is applied to three cases with known analytical solutions, and to a V-notched specimen under uniaxial tension. The numerical results are compared with other available solutions. This method is effective and simple in its use, compared with other numerical methods. The method also provides very accurate solutions in the region except near the boundary where the discretization error is significant. The extrapolation method is suggested for the stresses in the boundary region. Extensive application are also suggested for a general estimate of the computational efficiency of the method.