• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.839-851
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• 1997

Closed-form solutions are analytically derived for stochastic properties of earthquake ground motion fields, which are conditioned by an observed time series at certain observation sites and are characterized by spectra with uncertainties. The theoretical framework presented here can estimate not only the expectations of such simulated earthquake ground motions, but also the prediction errors which offer important information for the field of engineering. Before these derivations are made, the theory of conditional random fields is summarized for convenience in this study. Furthermore, a method for stochastic interpolation of power spectra is explained.

• Journal of Ship and Ocean Technology
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• v.12 no.2
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.537-549
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• 2001

The effect of partially restrained(PR) connections and the uncertainties in them on the reliability of steel frames subjected to seismic loading is addressed. A stochastic finite element method(SFEM) is proposed combining the concepts of the response surface method(RSM), the finite element method(FEM), the first-order reliability method (FORM), and the iterative linear interpolation scheme. The behavior of PR connections is captured using moment-relative rotation curves, and is represented by the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The seismic loading is applied in the time domain for realistic representation. The reliability of steel frames in the presence of PR connections is calculated considering all major sources of nonlinearity. The algorithm is clarified with the help of an example.

• Journal of computational fluids engineering
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• v.17 no.4
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• pp.32-40
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• 2012

Efficient Global Optimization (EGO) method is a global optimization technique which can select the next sample point automatically by infill sampling criteria (ISC) and search for the global minimum with less samples than what the conventional global optimization method needs. ISC function consists of the predictor and mean square error (MSE) provided from the kriging model which is a stochastic metamodel. Also the constrained EGO method can minimize the objective function dealing with the constraints under EGO concept. In this study the constrained EGO method applied to the RAE2822 airfoil shape design formulated with the constraint. But the noisy CFD data caused the kriging model to fail to depict the true function. The distorted kriging model would make the EGO deviate from the correct search. This distortion of kriging model can be handled with the interpolation(p=free) kriging model. With the interpolation(p=free) kriging model, however, the search of EGO solution was stalled in the narrow feasible region without the chance to update the objective and constraint functions. Then the accuracy of EGO solution was not good enough. So the three-step search method was proposed to obtain the accurate global minimum as well as prevent from the distortion of kriging model for the noisy constrained CFD problem.

• Nuclear Engineering and Technology
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• v.50 no.7
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• pp.1043-1050
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• 2018

For an efficient Monte Carlo (MC) burnup analysis, an accurate high-order depletion scheme to consider the nonlinear flux variation in a coarse burnup-step interval is crucial accompanied with an accurate depletion equation solver. In a Seoul National University MC code, McCARD, the high-order depletion schemes of the quadratic depletion method (QDM) and the linear extrapolation/quadratic interpolation (LEQI) method and a depletion equation solver by the Chebyshev rational approximation method (CRAM) have been newly implemented in addition to the existing constant extrapolation/backward extrapolation (CEBE) method using the matrix exponential method (MEM) solver with substeps. In this paper, the quadratic extrapolation/quadratic interpolation (QEQI) method is proposed as a new high-order depletion scheme. In order to examine the effectiveness of the newly-implemented depletion modules in McCARD, four problems in the VERA depletion benchmarks are solved by CEBE/MEM, CEBE/CRAM, LEQI/MEM, QEQI/MEM, and QDM for gadolinium isotopes. From the comparisons, it is shown that the QEQI/MEM predicts ${k_{inf}}^{\prime}s$ most accurately among the test cases. In addition, statistical uncertainty propagation analyses for a VERA pin cell problem are conducted by the sensitivity and uncertainty and the stochastic sampling methods.

• 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.

• Wind and Structures
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• v.9 no.3
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• pp.231-243
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• 2006

An improvement to the spectral representation algorithm for the simulation of wind velocity fields on large scale structures is proposed in this paper. The method proposed by Deodatis (1996) serves as the basis of the improved algorithm. Firstly, an interpolation approximation is introduced to simplify the computation of the lower triangular matrix with the Cholesky decomposition of the cross-spectral density (CSD) matrix, since each element of the triangular matrix varies continuously with the wind spectra frequency. Fast Fourier Transform (FFT) technique is used to further enhance the efficiency of computation. Secondly, as an alternative spectral representation, the vectors of the triangular matrix in the Deodatis formula are replaced using an appropriate number of eigenvectors with the spectral decomposition of the CSD matrix. Lastly, a turbulent wind velocity field through a vertical plane on a long-span bridge (span-wise) is simulated to illustrate the proposed schemes. It is noted that the proposed schemes require less computer memory and are more efficiently simulated than that obtained using the existing traditional method. Furthermore, the reliability of the interpolation approximation in the simulation of wind velocity field is confirmed.

• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.293-312
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• 2005

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.373-384
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• 2000

To assess the safety of nonlinear steel frame structures subjected to short duration dynamic loadings, especially seismic loading, a nonlinear time domain reliability analysis procedure is proposed in the context of the stochastic finite element concept. In the proposed algorithm, the finite element formulation is combined with concepts of the response surface method, the first order reliability method, and the iterative linear interpolation scheme. This leads to the stochastic finite element concept. Actual earthquake loading time-histories are used to excite structures, enabling a realistic representation of the loading conditions. The assumed stress-based finite element formulation is used to increase its efficiency. The algorithm also has the potential to evaluate the risk associated with any linear or nonlinear structure that can be represented by a finite element algorithm subjected to seismic loading or any short duration dynamic loading. The algorithm is explained with help of an example and verified using the Monte Carlo simulation technique.