• 대한기계학회논문집A
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• 제31권4호
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• pp.490-495
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• 2007

This research aims to examine accuracy and efficiency of the first four moments corresponding to mean, standard deviation, skewness, and kurtosis, which are estimated by a function approximation moment method (FAMM). In FAMM, the moments are estimated from an approximating quadratic function of a system response function. The function approximation is performed on a specially selected experimental region for accuracy, and the number of function evaluations is taken equal to that of the unknown coefficients for efficiency. For this purpose, three error-minimizing conditions are utilized and corresponding canonical experimental regions constructed accordingly. An interpolation function is then obtained using a D-optimal design and then the first four moments of it are obtained as the estimates for the system response function. In order to verify accuracy and efficiency of FAMM, several non-linear examples are considered including a polynomial of order 4, an exponential function, and a rational function. The moments calculated from various coefficients of variation show very good accuracy and efficiency in comparison with those from analytic integration or the Monte Carlo simulation and the experimental design technique proposed by Taguchi and updated by D'Errico and Zaino.

• 대한기계학회논문집A
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• 제35권2호
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• pp.163-168
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• 2011

설계단계에서 시스템의 불확실성을 반영하려는 노력이 다양하게 이루어지고 있으며, 강건 최적설계 혹은 신뢰도 기반 최적설계는 이에 대한 대표적인 설계 방법론이다. 실제 문제에 이러한 방법론을 적용하기 위해서는 성능함수의 통계적 모멘트와 손상확률에 대한 정확하고 효율적인 추정 방법이 필요하고, 더불어 최적화를 위한 방향탐색과정에서 요구되는 민감도 해석의 정확성 및 효율성이 확보되어야 한다. 본 연구에서는 함수근사모멘트 방법을 기존에 유도된 적분 형태의 민감도 해석 식에 적용하여 그 민감도 해석 결과의 정확성을 확인하고, 이를 대표적인 신뢰도 기반 최적설계 문제에 적용하고자 한다. 민감도 해석 결과 및 신뢰도 기반 최적설계 결과를 타방법의 결과와 비교하여 함수근사모멘트 방법의 타당성을 입증하고자 한다. 활용된 적분 형태의 민감도 해석은 손상확률 혹은 통계적 모멘트가 계산된 경우 추가적인 함수 계산 없이 민감도를 얻을 수 있는 효율적인 방법이다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.602-606
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• 2005

A systematic procedure of probability analysis for general distributions is developed based on the first four moments estimated from polynomial interpolation of the system response function and the Pearson system. The function approximation is based on a specially selected experimental region for accuracy and the number of function evaluations is taken equal to that of the unknown coefficient for efficiency. For this purpose, three error-minimizing conditions are proposed and corresponding canonical experimental regions are formed for popular probability. This approach is applied to study the stochastic properties of the performance functions of a MEMS structure, which has quite large fabrication errors compared to other structures. Especially, the vibratory micro-gyroscope is studied using the statistical moments and probability density function (PDF) of the performance function to be the difference between resonant frequencies corresponding to sensing and driving mode. The results show that it is very sensitive to the fabrication errors and that the types of PDF of each variable also affect the stochastic properties of the performance function although they have same the mean and variance.

• 품질경영학회지
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• 제22권3호
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• pp.111-118
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• 1994

In this paper we propose a parametric and a nonparametric small sample estimators for the mean residual life (MRL) under the random censorship model using the partial moment approximation. We also compare the proposed nonparametric estimator with the well-known nonparametric MRL estimator based on Kaplan-Meier estimator of the survival function, and present the efficiency of the nonparametric method relative to the Weibull model for small samples.

• 대한기계학회논문집A
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• 제30권8호
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• pp.985-992
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• 2006

Many methods for reliability analysis have been studied and one of them, a moment method, has the advantage that it doesn't require sensitivities of performance functions. The moment method for reliability analysis requires the first four moments of a performance function and then Pearson system is used for the probability of failure where the accuracy of the probability of failure greatly depends on that of the first four moments. But it is generally impossible to assess them analytically for multidimensional functions, and numerical integration is mainly used to estimate the moment. However, numerical integration requires many function evaluations and in case of involving finite element analyses, the calculation of the first fo 따 moments is very time-consuming. To solve the problem, this research proposes a new method of approximating the first four moments based on kriging metamodel. The proposed method substitutes the kriging metamodel for the performance function and can also evaluate the accuracy of the calculated moments adjusting the approximation range. Numerical examples show the proposed method can approximate the moments accurately with the less function evaluations and evaluate the accuracy of the calculated moments.

• 한국통신학회논문지
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• 제15권11호
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• pp.879-885
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• 1990

준정적 근사법을 적용하여 평탄한 단면(End cap)을 포함하는 회전체에 유기되는 전류에 대한 적분방정식을 유도하고 모멘트법을 이용해서 해석하였다. 수체해석시 기저함수로 Cubic B Spline 함수, 가중함수로 델타함수를 사용한 Point Matching Method를 사용하였다. 또한 끝단에 둥근타원체(Spheroidal end cap)를 갖는 경우 및 평탄한 단면을 갖는 원통주의 구조변수 변화에 따른 영향관계를 해석하였다.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Computers and Concrete
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• 제26권1호
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• pp.1-10
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• 2020

In this paper, a procedure for automated optimized design of reinforced concrete frames has been presented. The procedure consists of formulation and solution of the design problem in the form of an optimization problem. The minimization of total cost of R/C frame has been taken as the objective of optimization problem. In this research, consistent approximation method is applied to explicitly formulate constraints and objective function in terms of the design variables. In the presented method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the Sequential Quadratic Programming (SQP) method. The proposed method is demonstrated through a four-story frame and an eight-story frame, and the optimum results are compared with those in the available literature. It is shown that the proposed method can be easily applied to obtain rational, reliable, economical and practical designs for Reinforced Concrete Moment Resisting Frames (RCMRFs) while it is converged after a few analyses.

• 대한기계학회논문집A
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• 제30권8호
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• pp.1001-1007
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• 2006

In this paper we present robust optimal supporting positions for large glass panels used for TFT-LCD monitors when they are stored in a cassette during manufacturing process. The criterion taken is to minimize their maximum deflection. Since they are supported by some supports and have large deformations, contact analysis with a geometrically nonlinear effect is necessary. In addition, the center of a panel can not be positioned exactly as intended and should be considered as uncertainties. To take into account of these effects, the mean and the standard deviation of system response functions, particularly the deflection of the panels, need be calculated. A function approximation moment method (FAMM) is utilized to estimate them. It is a special type of response surface methodology for structural reliability analysis and can be efficiently used to estimate the two stochastic properties, that is, the system performance and the perturbations caused by uncertainties. For a design purpose, they are to be minimized simultaneously by some optimization algorithm to obtain robust optimal supporting positions.

• 대한기계학회논문집A
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• 제29권9호
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• pp.1243-1252
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• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.