• Title, Summary, Keyword: Latin hypercube sampling

### Asymptotic Comparison of Latin Hypercube Sampling and Its Stratified Version

• Lee, Jooho
• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.135-150
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• 1999
• Latin hypercube sampling(LHS) introduced by McKay et al. (1979) is a widely used method for Monte Carlo integration. Stratified Latin hypercube sampling(SLHS) proposed by Choi and Lee(1993) improves LHS by combining it with stratified sampling. In this article it is shown that SLHS yields an asymptotically more accurate than both stratified sampling and LHS.

### Uncertainty Analysis of Concrete Structures Using Modified Latin Hypercube Sampling Method

• Yang, In-Hwan
• International Journal of Concrete Structures and Materials
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• v.18 no.2E
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• pp.89-95
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• 2006
• This paper proposes a modified method of Latin Hypercube sampling to reduce the variance of statistical parameters in uncertainty analysis of concrete structures. The proposed method is a modification of Latin Hypercube sampling method. This analysis method uses specifically modified tables of random permutations of ranked numbers. In addition, the Spearman coefficient is used to make modified tables. Numerical analysis is carried out to predict the uncertainty of axial shortening in prestressed concrete bridge. Statistical parameters obtained from modified Latin Hypercube sampling method and conventional Latin Hypercube sampling method are compared and evaluated by a numeric analysis. The results show that the proposed method results in a decrease in the variance of statistical parameters. This indicates the method is efficient and effective in the uncertainty analysis of complex structural system such as prestressed concrete bridges.

### Two-stage Latin hypercube sampling and its application (이단계 Latin Hypercube 추출법과 그 응용)

• 임미정;권우주;이주호
• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.99-108
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• 1995
• When modeling a complicated system with a computer model, it is of vital importance to choos input values efficiently. The Latin Hypercube sampling (LHS) proposed by MaKay et al.(1979) has been most widely used for choosing input values for a computer model. We propose the two-stage Latin Hypercube sampling(TLHS) which is an improved version of the LHS for procucing input values in estimating the excectation of a function of the output variable. The proposed method is applied to simulation study of the performance of a printer actuator and it is shown to outperform the other sampling methods including the LHS in accuracy.

### Weighted Latin Hypercube Sampling to Estimate Clearance-to-stop for Probabilistic Design of Seismically Isolated Structures in Nuclear Power Plants

• Han, Minsoo;Hong, Kee-Jeung;Cho, Sung-Gook
• Journal of the Earthquake Engineering Society of Korea
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• v.22 no.2
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• pp.63-75
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• 2018
• This paper proposes extension of Latin Hypercube Sampling (LHS) to avoid the necessity of using intervals with the same probability area where intervals with different probability areas are used. This method is called Weighted Latin Hypercube Sampling (WLHS). This paper describes equations and detail procedure necessary to apply weight function to WLHS. WLHS is verified through numerical examples by comparing the estimated distribution parameters with those from other methods such as Random Sampling and Latin Hypercube Sampling. WLHS provides more flexible way on selecting samples than LHS. Accuracy of WLHS estimation on distribution parameters is depending on the selection of weight function. The proposed WLHS is applied to seismically isolated structures in nuclear power plants. In this application, clearance-to-stops (CSs) calculated using LHS proposed by Huang et al. [1] and WLHS proposed in this paper, respectively, are compared to investigate the effect of choosing different sampling techniques.

### Effects of Latin hypercube sampling on surrogate modeling and optimization

• International Journal of Fluid Machinery and Systems
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• v.10 no.3
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• pp.240-253
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• 2017
• Latin hypercube sampling is widely used design-of-experiment technique to select design points for simulation which are then used to construct a surrogate model. The exploration/exploitation properties of surrogate models depend on the size and distribution of design points in the chosen design space. The present study aimed at evaluating the performance characteristics of various surrogate models depending on the Latin hypercube sampling (LHS) procedure (sample size and spatial distribution) for a diverse set of optimization problems. The analysis was carried out for two types of problems: (1) thermal-fluid design problems (optimizations of convergent-divergent micromixer coupled with pulsatile flow and boot-shaped ribs), and (2) analytical test functions (six-hump camel back, Branin-Hoo, Hartman 3, and Hartman 6 functions). The three surrogate models, namely, response surface approximation, Kriging, and radial basis neural networks were tested. The important findings are illustrated using Box-plots. The surrogate models were analyzed in terms of global exploration (accuracy over the domain space) and local exploitation (ease of finding the global optimum point). Radial basis neural networks showed the best overall performance in global exploration characteristics as well as tendency to find the approximate optimal solution for the majority of tested problems. To build a surrogate model, it is recommended to use an initial sample size equal to 15 times the number of design variables. The study will provide useful guidelines on the effect of initial sample size and distribution on surrogate construction and subsequent optimization using LHS sampling plan.

### Study on a Robust Optimization Algorithm Using Latin Hypercube Sampling Experiment and Multiquadric Radial Basis Function (Latin Hypercube Sampling Experiment와 Multiquadric Radial Basis Function을 이용한 최적화 알고리즘에 대한 연구)

• Zhang, Yanli;Yoon, Hee-Sung;Koh, Chang-Seop
• Proceedings of the KIEE Conference
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• pp.162-164
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• 2007
• This paper presents a "window-zoom-out" optimization strategy with relatively fewer sampling data. In this method, an optimal Latin hypercube sampling experiment based on multi-objective Pareto optimization is developed to obtain the sampling data. The response surface method with multiquadric radial basis function combined with (1+$\lambda$) evolution strategy is used to find the global optimal point. The proposed method is verified with numerical experiments.

### Effect of Rocking Behavior of Isolated Nuclear Structures and Sampling Technique for Isolation-System Properties on Clearance-to-stop (면진 원전구조물의 전도거동과 면진시스템 특성에 대한 샘플링 기법이 정지거리에 미치는 영향)

• Han, Min Soo;Hong, Kee Jeung;Cho, Sung Gook
• Journal of the Earthquake Engineering Society of Korea
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• v.19 no.6
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• pp.293-302
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• 2015
• ASCE 4 requires that a hard stop be built around the seismic isolation system in nuclear power plants. In order to maintain the function of the isolation system, this hard stop is required to have clearance-to-stop, which should be no less than the 90th-percentile displacements for 150% Design Basis Earthquake (DBE) shaking. Huang et al. calculated clearance-to-stop by using a Latin Hypercube Sampling technique, without considering the rocking behavior of the isolated structure. This paper investigates the effects on estimation of clearance-to-stop due to 1) rocking behavior of the isolated structure and 2) sampling technique for considering the uncertainties of isolation system. This paper explains the simplified analysis model to consider the rocking behavior of the isolated structure, and the input earthquakes recorded at Diablo Canyon in the western United States. In order to more accurately approximate the distribution tail of the horizontal displacement in the isolated structure, a modified Latin Hypercube Sampling technique is proposed, and then this technique was applied to consider the uncertainty of the isolation system. Through the use of this technique, it was found that rocking behavior has no significant effect on horizontal displacement (and thus clearance-to-stop) of the isolated structure, and the modified Latin Hypercube Sampling technique more accurately approximates the distribution tail of the horizontal displacement than the existing Latin Hypercube Sampling technique.

### Latin Hypercube Sampling Based Probabilistic Small Signal Stability Analysis Considering Load Correlation

• Zuo, Jian;Li, Yinhong;Cai, Defu;Shi, Dongyuan
• Journal of Electrical Engineering and Technology
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• v.9 no.6
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• pp.1832-1842
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• 2014
• A novel probabilistic small signal stability analysis (PSSSA) method considering load correlation is proposed in this paper. The superiority Latin hypercube sampling (LHS) technique combined with Monte Carlo simulation (MCS) is utilized to investigate the probabilistic small signal stability of power system in presence of load correlation. LHS helps to reduce the sampling size, meanwhile guarantees the accuracy and robustness of the solutions. The correlation coefficient matrix is adopted to represent the correlations between loads. Simulation results of the two-area, four-machine system prove that the proposed method is an efficient and robust sampling method. Simulation results of the 16-machine, 68-bus test system indicate that load correlation has a significant impact on the probabilistic analysis result of the critical oscillation mode under a certain degree of load uncertainty.

### A Study of Cogging Torque Minimization for a 6MW BLDC Motor by using Latin Hypercube Sampling strategy (LHS를 이용한 6MW BLDC 전동기의 코깅토크 최소화 연구)

• Woo, Sung-Hyun;Shin, Pan-Seok
• Proceedings of the KIEE Conference
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• pp.32-34
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• 2008
• Latin Hypercube sampling strategy(LHS)는 출력변수에 의한 목적함수들의 기댓값의 추정을 위한 입력변수를 생성하는데 사용할 수 있는 샘플링 포인트 추출 방법으로, 샘플링 포인트의 "quality"를 향상시켜준다. multi-objective Pare optimization 에 근거한 LHS와 ($1+\lambda$) 진화기법으로 이루어진 최적화 algorithm을 제안 하였고, 이를 이용하여 6MW BLDC 전동기의 코깅토크를 최소화 하였다, 총 2단계의 최적 설계를 통해 초기형상의 코킹토크에 비해 19%로 감소하였다.

### Assessment of statistical sampling methods and approximation models applied to aeroacoustic and vibroacoustic problems

• Biedermann, Till M.;Reich, Marius;Kameier, Frank;Adam, Mario;Paschereit, C.O.
• Advances in aircraft and spacecraft science
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• v.6 no.6
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• pp.529-550
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• 2019
• The effect of multiple process parameters on a set of continuous response variables is, especially in experimental designs, difficult and intricate to determine. Due to the complexity in aeroacoustic and vibroacoustic studies, the often-performed simple one-factor-at-a-time method turns out to be the least effective approach. In contrast, the statistical Design of Experiments is a technique used with the objective to maximize the obtained information while keeping the experimental effort at a minimum. The presented work aims at giving insights on Design of Experiments applied to aeroacoustic and vibroacoustic problems while comparing different experimental designs and approximation models. For this purpose, an experimental rig of a ducted low-pressure fan is developed that allows gathering data of both, aerodynamic and aeroacoustic nature while analysing three independent process parameters. The experimental designs used to sample the design space are a Central Composite design and a Box-Behnken design, both used to model a response surface regression, and Latin Hypercube sampling to model an Artificial Neural network. The results indicate that Latin Hypercube sampling extracts information that is more diverse and, in combination with an Artificial Neural network, outperforms the quadratic response surface regressions. It is shown that the Latin Hypercube sampling, initially developed for computer-aided experiments, can also be used as an experimental design. To further increase the benefit of the presented approach, spectral information of every experimental test point is extracted and Artificial Neural networks are chosen for modelling the spectral information since they show to be the most universal approximators.