• Title/Summary/Keyword: optimal approximation

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Optimization of Fermentation Processes with Singular Approximation and Minimum Principle (Singular Approximation과 Minimum Principle을 이용한 발효공정의 최적화)

  • 이중헌;정재철;박영훈
    • Microbiology and Biotechnology Letters
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    • v.27 no.3
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    • pp.223-229
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    • 1999
  • The two optimal control algorithms, singular approximation and minimum principle, were compared in this paper. The switching time with singular approximation was determined with mathematical derivation and the optimal control profile of specific growth rate was also calculated with minimum principle. The optimal control profiles were calculated by making simple model correlating the specific cell growth rate and specific product formation rate. The optimal control profiles calculated by singular approximation approach were similar to stepwise form of those calculatd by minimum principles. With the minimum principle, the product concentration was 8% more than that of singular approximation. This performance difference was due to a linearization of a nonlinear function with singular approximation. This optimal approaches were applicable to any system with different optimal cell growth and product formation.

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Accuracy Analysis of Optimal Trajectory Planning Methods Based on Function Approximation for a Four-DOF Biped Walking Model

  • Peng Chunye;ONO Kyosuke
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.452-460
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    • 2005
  • Based on an introduced optimal trajectory planning method, this paper mainly deals with the accuracy analysis during the function approximation process of the optimal trajectory planning method. The basis functions are composed of Hermit polynomials and Fourier series to improve the approximation accuracy. Since the approximation accuracy is affected by the given orders of each basis function, the accuracy of the optimal solution is examined by changing the combinations of the orders of Hermit polynomials and Fourier series as the approximation basis functions. As a result, it is found that the proper approximation basis functions are the $5^{th}$ order Hermit polynomials and the $7^{th}-10^{th}$ order of Fourier series.

A Study on the Optimal Shape Design of 2-D Structures (2차원 구조물의 최적형상설계에 관한 연구)

  • 김홍건;양성모;노홍길;나석찬;유기현;조남익
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.12 no.2
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    • pp.9-16
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    • 2003
  • A strategy of the optimal shape design with FEA(Finite Element Analysis) for 2-D structure is proposed by comparing subproblem approximation method with first order approximation method. A cantilever beam with two different loading conditions, a concentrated load and an evenly distribute load, and truss structure with a concentrated loading condition are implemented to optimize the shape. It gives a good design strategy on the optimal truss structure as well as the optimal cantilever beam shape. It is found that the convergence is quickly finished with the iteration number below ten. Optimized shapes of cantilever beam and truss structure are shown with stress contour plot by the results of the subproblem approximation method and the first order approximation methd.

OPTIMAL APPROXIMATION BY ONE GAUSSIAN FUNCTION TO PROBABILITY DENSITY FUNCTIONS

  • Gwang Il Kim;Seung Yeon Cho;Doobae Jun
    • East Asian mathematical journal
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    • v.39 no.5
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    • pp.537-547
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    • 2023
  • In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

Robust Optimal Design Method Using Two-Point Diagonal Quadratic Approximation and Statistical Constraints (이점 대각 이차 근사화 기법과 통계적 제한조건을 적용한 강건 최적설계 기법)

  • Kwon, Yong-Sam;Kim, Min-Soo;Kim, Jong-Rip;Choi, Dong-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.12
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    • pp.2483-2491
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    • 2002
  • This study presents an efficient method for robust optimal design. In order to avoid the excessive evaluations of the exact performance functions, two-point diagonal quadratic approximation method is employed for approximating them during optimization process. This approximation method is one of the two point approximation methods. Therefore, the second order sensitivity information of the approximated performance functions are calculated by an analytical method. As a result, this enables one to avoid the expensive evaluations of the exact $2^{nd}$ derivatives of the performance functions unlike the conventional robust optimal design methods based on the gradient information. Finally, in order to show the numerical performance of the proposed method, one mathematical problem and two mechanical design problems are solved and their results are compared with those of the conventional methods.

THE SOLVABILITY CONDITIONS FOR A CLASS OF CONSTRAINED INVERSE EIGENVALUE PROBLEM OF ANTISYMMETRIC MATRICES

  • PAN XIAO-PING;HU XI-YAN;ZHANG LEI
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.87-98
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    • 2006
  • In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

A Study on the LQG/LTR for Nonminimum phase plant : Optimal Approximation method (비 최소위상 시스팀에 대한 LQG/LTR 연구 - 최적 근사화 방법)

  • 서병설;강진식;이준영
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.191-196
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    • 1991
  • LQG/LTR method have a theoretical constraint that it cannot applied to nonminimum phase plant. In this paper, we suggest two methods of approximation of minimum phase plant for a given nonminimum phase plant to solve this constraint. Error is described by additive form which can reduce its magnitude in broad frequency range. A optimal approximation method was suggesetd by using Hankel operator theory and Nehari theory. It is showen by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.

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A Study on the LQG/LTR for Nonminimum Phase Plant (I) : Optimal Approximation Method (비 최소위상 플랜트에 대한 LQG/LTR에 관한 연구(I) : 최적 근사 방법)

  • 강진식;서병설
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.16 no.10
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    • pp.972-980
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    • 1991
  • LQG/LTR method have a theoretical constraint that it cannot applied to nonminimum phase plant. In this paper we suggest two methods of approximation of minimum phase plant for a given nonminimum phase plant to solve this constraint. Error is described by additive form which can reduce its magnitude in broad frequency range. A optimal approximation method was suggested by using Hankel operator theory and Nehan theory it is shown by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.

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기계고장을 고려한 생산및 품질검증 정책

  • 이창환
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1996.04a
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    • pp.298-301
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    • 1996
  • This paper addresses the effects of an imperfect production process on the optimal production quantity and quality inspection policies. The system is assumed to deteriorate during the production process. The results are either defective products or machine breakdown whether multiple quality inspection is worth or not. Furthermore, when multiple inspection policy is adopted, the optimal inspection schedule is shown to be equally spaced throughout the production cycle. Exact solution and approximation of the optimal production quantity and approximation of the optimal number of inspection are provided. Finally, to better understand the model of this paper, comparisons between this model and classical EMQ model are provided.

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