• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.2
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• pp.163-168
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• 2011

Robust optimization or reliability-based design optimization are some of the methodologies that are employed to take into account the uncertainties of a system at the design stage. For applying such methodologies to solve industrial problems, accurate and efficient methods for estimating statistical moments and failure probability are required, and further, the results of sensitivity analysis, which is needed for searching direction during the optimization process, should also be accurate. The aim of this study is to employ the function approximation moment method into the sensitivity analysis formulation, which is expressed as an integral form, to verify the accuracy of the sensitivity results, and to solve a typical problem of reliability-based design optimization. These results are compared with those of other moment methods, and the feasibility of the function approximation moment method is verified. The sensitivity analysis formula with integral form is the efficient formulation for evaluating sensitivity because any additional function calculation is not needed provided the failure probability or statistical moments are calculated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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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.

• Journal of Korean Society for Quality Management
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• v.22 no.3
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.11
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• pp.879-885
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• 1990

An intergral equation is derived for surface current distribution of cylinders with end cap using quasistatic approximation method. The moment method is applied for numerical solution. Point matching method using Cubic B-spline function as a basis function, delta function as a weighting function is applied for moment method. And also, the influencial relation in accordance with structural variation is analized in case of spheroidal end up cap type and flat type.

• Structural Engineering and Mechanics
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• v.65 no.1
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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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• v.26 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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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.