• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2440-2443
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• 2008

This paper presents a three dimensional shape optimization procedure for a low-speed axial flow fan blade with a weighted average surrogate model. Reynolds-averaged Navier-Stokes equations with shear stress transport turbulence model are discretized by finite volume approximations. Six variables from airfoil profile and lean are selected as design variables. 3D RANS solver is used to evaluate the objective functions of total pressure efficiency. Surrogate approximation models for optimization have been employed to find the optimal design of fan blade. A search algorithm is used to find the optimal design in the design space from the constructed surrogate models for the objective function. The total pressure efficiency is increased by 0.31% with the weighted average surrogate model.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.461-472
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• 2015

In this paper, the nonlinear static response of curled cantilever beam actuators subjected to the one-sided electrostatic field is focused on. By assuming the deflection function of electrostatically actuated beam, analytical approximate solutions are established via using Galerkin method to solve the equilibrium equation. The Pull-In voltages which determine the stability of the curled beam actuators are also obtained. These approximate solutions show excellent agreements with numerical solutions obtained by the shooting method and the experimental data for a wide range of beam length. Expressions of these analytical approximate solutions are brief and could easily be used to derive the effects of various physical parameters on MEMS structures.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• International Journal of Fluid Machinery and Systems
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• v.3 no.1
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• pp.29-38
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• 2010

This paper presents a procedure for the design optimization of a centrifugal compressor. The centrifugal compressor consists of a centrifugal impeller, vaneless diffuser and volute. And, optimization techniques based on the radial basis neural network method are used to optimize the impeller of a centrifugal compressor. The Latin-hypercube sampling of design-of-experiments is used to generate the thirty design points within design spaces. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by using finite volume approximations and solved on hexahedral grids to evaluate the objective function of the total-to-total pressure ratio. Four variables defining the impeller hub and shroud contours are selected as design variables in this optimization. The results of optimization show that the total-to-total pressure ratio of the optimized shape at the design flow coefficient is enhanced by 2.46% and the total-to-total pressure ratios at the off-design points are also improved significantly by the design optimization.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.592-593
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• 2007

The complexity of modern power systems often makes it impractical to model it in its entirety for electromagnetic transient studies. Therefore areas outside the immediate area of interest must be represented by some form of Frequency Dependent Network Equivalent (FDNE). The advantage of using z-domain fitting is that it can be directly implemented in a digital simulation program without any loss of accuracy. Fitting in the s-domain always requires "discretizing" a continuous system and the inherent approximations. This paper presents z-domain rational function formulation and demonstrates the use of it for the assessment of the transient response of the Lower South Island of New Zealand.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.589-599
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• 2023

The object of this study is to introduce a new subclass of univalent analytic functions on the open unit disk. This subclass is created by utilizing univalent analytic functions with negative coefficients. We first explore the specific properties that functions in this subclass must possess before examining their coefficient characterization. By applying this approach, we observe several fascinating features, including coefficient approximations, growth and distortion theorems, extreme points and a demonstration of the radius of starlikeness and convexity for functions belonging to this subclass.

• Journal of the Korean Statistical Society
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• v.3 no.1
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• pp.3-12
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• 1974

The two-stage sequential test, suggested by Baker [2] for testing hypotheses $H_0:\mu=\mu_0$ and $H_1:\mu=\mu_1$ of $N(\mu,\sigma^2)$ with the unknown $\sigma^2$ would not be amenable for applications unles some cluses on the choice of the first-stage sample size are available. The study in this paper is intended to shed some light on the size of the first-stage sample. An approximate method is used to estimate an optimal initial sample size that minimizes the average sample number. In brief, the optimal size is a strictly monotone decreasing function of the quantity $(\mu_1-\mu_0)/\sigma$. Empirical and simulation results are used to ascertain the negligible effect of possible errors due to approximations and assumptions used.

• Journal of Communications and Networks
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• v.10 no.3
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• pp.351-361
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• 2008

This paper presents a delay-margin based traffic engineering (TE) approach to provide end-to-end quality of service (QoS) in multi-protocol label switching (MPLS) networks using differentiated services (DiffServ) at the link level. The TE, including delay, class, and route assignments, is formulated as a nonlinear optimization problem reflecting the inter-class and inter-link dependency introduced by DiffServ and end-to-end QoS requirements. Three algorithms are used to provide a solution to the problem: The first two, centralized offline route configuration and link-class delay assignment, operate in the convex areas of the feasible region to consecutively reduce the objective function using a per-link per-class decomposition of the objective function gradient. The third one is a heuristic that promotes/demotes connections at different links in order to deal with concave areas that may be produced by a trunk route usage of more than one class on a given link. Approximations of the three algorithms suitable for on-line distributed TE operation are also derived. Simulation is used to show that proposed approach can increase the number of users while maintaining end-to-end QoS requirements.

• Steel and Composite Structures
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• v.8 no.5
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• pp.343-359
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• 2008

In the present study, an efficient method for the optimum design of three-dimensional (3D) steel framed structures is proposed. In this method, in addition to choosing the best position of columns based on architectural requirements, the optimum cross-sectional dimensions of elements are determined. The preliminary design variables are considered as the number of columns in structural plan, which are determined by a direct optimization method suitable for discrete variables, without requiring the evaluation of derivatives. After forming the geometry of structure, the main variables of the cross-sectional dimensions are evaluated, which satisfy the design constraints and also achieve the least-weight of the structure. To reduce the number of finite element analyses and the overall computational time, a new third order approximate function is introduced which employs only the diagonal elements of the higher order derivatives matrices. This function produces a high quality approximation and also, a robust optimization process. The main feature of the proposed techniques that the higher order derivatives are established by the first order exact derivatives. Several examples are solved and efficiency of the new approximation method and also, the proposed method for the best position of columns in 3D steel framed structures is discussed.