• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.549-561
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• 2018

Sobol method is applied as a powerful variance decomposition technique in the field of global sensitivity analysis (GSA). The paper is devoted to increase convergence speed of the extracted Sobol indices using a new proposed sampling technique called genetic based Latine hypercube sampling (GBLHS). This technique is indeed an improved version of restricted Latine hypercube sampling (LHS) and the optimization algorithm is inspired from genetic algorithm in a new approach. The new approach is based on the optimization of minimax value of LHS arrays using manipulation of array indices as chromosomes in genetic algorithm. The improved Sobol method is implemented to perform factor prioritization and fixing of an uncertain comprehensive high speed rotor-bearing system. The finite element method is employed for rotor-bearing modeling by considering Eshleman-Eubanks assumption and interaction of axial force on the rotor whirling behavior. The performance of the GBLHS technique are compared with the Monte Carlo Simulation (MCS), LHS and Optimized LHS (Minimax. criteria). Comparison of the GBLHS with other techniques demonstrates its capability for increasing convergence speed of the sensitivity indices and improving computational time of the GSA.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.36 no.5
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• pp.177-185
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• 2020

The building energy performance indicator, called Energy Performance Index (EPI), has been used for the past decades in South Korea. It has a list of design variables assigned with weighting factors (a, b). Unfortunately, the current EPI method is not performance-based but very close to a prescriptive rating. With this in mind, this study aims to propose a new performance-based EPI method. For this purpose, a global sensitivity analysis method, Sobol, is employed. The Sobol method is suitable for complex nonlinear models and can decompose all the output variance due to every input. The Sobol sensitivity index of each variable is defined as 0 to 1 (0 to 100%), and the sum of all sensitivity indices is equal to 1 (100%). In this study, an office building was modeled using EnergyPlus and then the Latin Hypercube Sampling (LHS) was conducted to generate a surrogate model to EnergyPlus. The sensitivity index was suggested to replace weight (a) in the existing EPI. In addition, the discrete weight (b) in the existing EPI was replaced by a set of continuous regression functions. Due to the introduction of the sensitivity index and the continuous regression functions, the new proposed approach can provide far more accurate outcome than the existing EPI (R²: 0.83 vs. R²: 0.01 for cooling, R²: 0.66 vs. R²: 0.01 for total energy). The new proposed approach proves to be more rational, objective and performance-based than the existing EPI method.

• Journal of Ocean Engineering and Technology
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• v.34 no.5
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• pp.316-324
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• 2020

This paper presents comparative studies of reliability analysis and meta-modeling using the sampling method of Monte Carlo simulation for the structure design of an automatic ocean salt collector (AOSC). The thickness sizing variables of structure members are considered as random variables. Probabilistic performance functions are selected from strength performances evaluated via the finite element analysis of an AOSC. The sampling methods used in the comparative studies are simple random sampling and Sobol sequences with varied numbers of sampling. Approximation methods such as the Kriging model is applied to the meta-model generation. Reliability performances such as the probability failure and distribution are compared based on the variation of the sampling method of Monte Carlo simulation. The meta-modeling accuracy is evaluated for the Kriging model generated from the Monte Carlo simulation and Sobol sequence results. It is discovered that the Sobol sequence method is applicable to not only to the reliability analysis for the structural design of marine equipment such as the AOSC, but also to Kriging meta-modeling owing to its high numerical efficiency.

• Computers and Concrete
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• v.2 no.5
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• pp.411-421
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• 2005

A linear programming problem of the optimal proportioning of concrete aggregates is discussed; and a self-adaptive genetic algorithm is developed to solve this problem. The proposed method is based on changing a range of variables for capturing the feasible region of the optimum solution. A computational verification of this method is compared with the results of the linear programming.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.115-125
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• 2021

Simulation-based hull form optimization is a typical HEB (high-dimensional, expensive computationally, black-box) problem. Conventional optimization algorithms easily fall into the "curse of dimensionality" when dealing with HEB problems. A recently proposed Cross-Entropy (CE) optimization algorithm is an advanced stochastic optimization algorithm based on a probability model, which has the potential to deal with high-dimensional optimization problems. Currently, the CE algorithm is still in the theoretical research stage and rarely applied to actual engineering optimization. One reason is that the Monte Carlo (MC) method is used to estimate the high-dimensional integrals in parameter update, leading to a large sample size. This paper proposes an improved CE algorithm based on quasi-Monte Carlo (QMC) estimation using high-dimensional truncated Sobol subsequence, referred to as the QMC-CE algorithm. The optimization performance of the proposed algorithm is better than that of the original CE algorithm. With a set of identical control parameters, the tests on six standard test functions and a hull form optimization problem show that the proposed algorithm not only has faster convergence but can also apply to complex simulation optimization problems.

• Journal of Magnetics
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• v.19 no.4
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• pp.385-392
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• 2014

Uncertainties in loads, materials and manufacturing quality must be considered during electromagnetic devices design. This paper presents an effective methodology for robust optimization design based on the variance decomposition in order to keep higher accuracy of the robustness prediction. Sobol' theory is employed to estimate the response variance under some specific tolerance in design variables. Then, an optimal design is obtained by adding a criterion of response variance upon typical optimization problems as a constraint of the optimization. The main contribution of this paper is that the proposed method applies the variance decomposition to obtain a more accurate variance of the response, as well save the computational cost. The performance and robustness of the proposed algorithms are investigated through a numerical experiment with both an analytic function and the TEAM 22 problem.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1001-1004
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• 1987

In this study mathematical properties of variational solution and solution of the boundary integral equation of the linear elasticity problem are studied. It is first reviewed that a variational solution for the three-dimensional linear elasticity problem exists in the Sobolev space [ $H^{1}$(.OMEGA.)]$^{3}$ and, then, it is shown that a unique solution of the boundary integral equation is identical to the variational solution in [ $H^{1}$(.OMEGA.)]$^{3}$. To represent the boundary integral equation, the Green's formula in the Sobolev space is utilized on the solution domain excluding a ball, with small radius .rho., centered at the point where the point load is applied. By letting .rho. tend to zero, it is shown that, for the linear elasticity problem, boundary integral equation is valid for the variational solution. From this fact, one can obtain a numerical approximatiion of the variational solution by the boundary element method even when the classical solution does not exist.exist.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.299-319
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• 1997

Since a convergence strategy in interactive procedure is the origin of a lot of the restrictions and inconvenience of many methods, a new flexible convergence strategy is necessary for developing that is applicable for interactive MOLP as well as interactive multiple objective integer programming(MOIP). A method for computing the volume of the interval defined subsets of weighting vector space is developed using Sobol's LP$_{i}$, Generator. Since the interactive procedure requires a number of iterations, with a fixed number of solutions presented per iteration, a convergence strategy is needed to control the rate at which the interactive procedure converges to a final solution. Thus, in this paper, a new convergency strategy is developed.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.669-677
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• 2013

Quasi-Monte Carlo method is known to have lower convergence rate than the standard Monte Carlo method. Quasi-Monte Carlo methods are using low discrepancy sequences as quasi-random numbers. They include Halton sequence, Faure sequence, and Sobol sequence. In this article, we compared standard Monte Carlo method, quasi-Monte Carlo methods and three scrambling methods of Owen, Faure-Tezuka, Owen-Faure-Tezuka in valuation of multi-asset European call option through simulations. Moro inversion method is used in generating random numbers from normal distribution. It has been shown that three scrambling methods are superior in estimating option prices regardless of the number of assets, volatility, and correlations between assets. However, there are no big differences between them.

• Korean Journal of Weed Science
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• v.3 no.2
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• pp.120-128
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• 1983

The nationwide survey of weed population covering 1,800 wheat and barley fields in 60 Cities and Guns all around Korea was conducted in December of 1982 and March-April of 1983. In this survey result, two species of gresses and 35 species of broadleaves were identified, and among them 36 and 29 species were found in the wheat and barley fields of upland and paddy, respectively. In the scope of weed life cycle, biennials were more dominant than perennials and annuals in these fields. The most dominant weed species in upland fields were Stellaria media, Cyrillus and Alopecurus aequalis Sobol var. amurensis Ohwi while those in paddy fields were Stellaria alsine Grimm. var. undulata Ohwi and Alopecurus aequalis Sobol var. amurensis Ohwi. In addition, the more weeds were observed in the conventional row seeding method than in other seeding methods including drill seeding and also in no-tillage than in tillage method. In the other hand, the successive use of herbicide for several years greatly influenced the pattern of weed occurrence; broadleaved weeds increased and grasses decreased with the successive use of herbicides.