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Simulação Sequencial Gaussiana usando Latin Hypercube Sampling : estudo de caso minério de ferro Carajás

Batiston, Evandro Lino
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Dissertação Formato: application/pdf
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A utilização de modelos de incerteza geológica é fundamental para a quantificação e avaliação da flutuação dos atributos analisados pelos departamentos de planejamento da indústria mineira. O método de simulação seqüencial Gaussiana (SSG) é amplamente utilizado para a construção destes modelos. O SSG caracteriza-se por representar adequadamente o espaço de incerteza da variável aleatória (VA) Z(u), desde que o número de realizações L seja adequado para reproduzi-lo. Existem dois algoritmos implementados em SSG que efetuam a tiragem aleatória da distribuição condicional local de probabilidade (dclp) cumulativa, visando gerar as realizações que vão compor a simulação. O algoritmo clássico, baseado na tiragem simples por Monte Carlo, denomina-se Simple Random Sampling (SRS), enquanto que o método alternativo é denominado Latin Hypercube Sampling (LHS). Esta dissertação compara a eficiência destes dois algoritmos, como forma de caracterizar o espaço de incerteza de algumas funções de transferência usadas na indústria mineral. O estudo de caso envolveu a análise do número de realizações necessárias para caracterizar adequadamente a variabilidade da resposta destas funções, como mecanismo para comparação...

Remote Sensing Data with the Conditional Latin Hypercube Sampling and Geostatistical Approach to Delineate Landscape Changes Induced by Large Chronological Physical Disturbances

Lin, Yu-Pin; Chu, Hone-Jay; Wang, Cheng-Long; Yu, Hsiao-Hsuan; Wang, Yung-Chieh
Fonte: Molecular Diversity Preservation International (MDPI) Publicador: Molecular Diversity Preservation International (MDPI)
Tipo: Artigo de Revista Científica
Publicado em 07/01/2008 Português
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This study applies variogram analyses of normalized difference vegetation index (NDVI) images derived from SPOT HRV images obtained before and after the ChiChi earthquake in the Chenyulan watershed, Taiwan, as well as images after four large typhoons, to delineate the spatial patterns, spatial structures and spatial variability of landscapes caused by these large disturbances. The conditional Latin hypercube sampling approach was applied to select samples from multiple NDVI images. Kriging and sequential Gaussian simulation with sufficient samples were then used to generate maps of NDVI images. The variography of NDVI image results demonstrate that spatial patterns of disturbed landscapes were successfully delineated by variogram analysis in study areas. The high-magnitude Chi-Chi earthquake created spatial landscape variations in the study area. After the earthquake, the cumulative impacts of typhoons on landscape patterns depended on the magnitudes and paths of typhoons, but were not always evident in the spatiotemporal variability of landscapes in the study area. The statistics and spatial structures of multiple NDVI images were captured by 3,000 samples from 62,500 grids in the NDVI images. Kriging and sequential Gaussian simulation with the 3...

A Novel Latin Hypercube Algorithm via Translational Propagation

Pan, Guang; Ye, Pengcheng; Wang, Peng
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
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Metamodels have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is directly related to the experimental designs used. Optimal Latin hypercube designs are frequently used and have been shown to have good space-filling and projective properties. However, the high cost in constructing them limits their use. In this paper, a methodology for creating novel Latin hypercube designs via translational propagation and successive local enumeration algorithm (TPSLE) is developed without using formal optimization. TPSLE algorithm is based on the inspiration that a near optimal Latin Hypercube design can be constructed by a simple initial block with a few points generated by algorithm SLE as a building block. In fact, TPSLE algorithm offers a balanced trade-off between the efficiency and sampling performance. The proposed algorithm is compared to two existing algorithms and is found to be much more efficient in terms of the computation time and has acceptable space-filling and projective properties.

Product Development Process Modeling Using Advanced Simulation

Cho, Soo-Haeng; Eppinger, Steven
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Trabalho em Andamento Formato: 102354 bytes; application/pdf
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This paper presents a product development process modeling and analysis technique using advanced simulation.The model computes the probability distribution of lead time in a resource-constrained project network where iterations take place among sequential, parallel and overlapped tasks. The model uses the design structure matrix representation to capture the information flows between tasks. In each simulation run, the expected durations of tasks are initially sampled using the Latin Hypercube Sampling method and decrease over time as the model simulates the progress of dynamic stochastic processes. It is assumed that the rework of a task occurs for the following reasons: (1) new information is obtained from overlapped tasks after starting to work with preliminary inputs, (2) inputs change when other tasks are reworked, and (3) outputs fail to meet established criteria. The model can be used for better project planning and control by identifying leverage points for process improvements and evaluating alternative planning and execution strategies. An industrial example is used to illustrate the utility of the model.; Center for Innovation in Product Development

Applying conditional latin hypercube (cLHS) for selecting soil sampling location for digital soil mapping at Parque Estadual da Mata Seca, MG, Brazil.

MENDONÇA-SANTOS, M. L.; DART, R. O.; BERBARA, R. L. L.
Fonte: In: GLOBAL WORKSHOP ON DIGITAL SOIL MAPPING, 3,, 30 Sept.- Oct. 3, 2008, Logan, Utah. Bridging research, production, and environmental applications: papers. Publicador: In: GLOBAL WORKSHOP ON DIGITAL SOIL MAPPING, 3,, 30 Sept.- Oct. 3, 2008, Logan, Utah. Bridging research, production, and environmental applications: papers.
Tipo: Resumo em anais de congresso (ALICE) Formato: 6 p.
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The use of the Conditional Latin Hypercube (cLHS) to select soil samples location to be used in the prediction of soil properties as soil organic carbon seems to be an important tool to decrease costs and subjectivity of sampling schemes. The main objective of this work was to test this method in a no sampled area, aiming to evaluate its efficiency in Digital Soil Mapping (DSM) procedures. The results show that this method was able to significantly increase the reliability in the spatial distribution of the sampled points in Parque Estadual da Mata Seca (PEMS). The study area is located in the North of Minas Gerais State, Brazil, in Tropical Dry Forest (TDF) ecosystems mainly. In this study, the cLHS algorithm developed by Minasny & McBratney (2006) was used, in addition to some ancillary data as Land Use/Land Cover and Normalized Difference Vegetation Index (NDVI), in order to select 60 soil sampling location to the study of soil organic carbon and others soil properties. The cLHS will be further analyzed in its performance to select representative points to be sampled and how this method could be helpful for DSM.; 2008

Selecting Random Latin Hypercube Dimensions and Designs through Estimation of Maximum Absolute Pairwise Correlation

Hernandez, Alejandro S.; Lucas, Thomas W.; Sanchez, Paul J.
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Artigo de Revista Científica
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Latin hypercubes are the most widely used class of design for high-dimensional computer experiments. However, the high correlations that can occur in developing these designs can complicate subsequent analyses. Efforts to reduce or eliminate correlations can be complex and computationally expensive. Consequently, researchers often use uncorrected Latin hypercube designs in their experiments and accept any resulting multicollinearity issues. In this paper, we establish guidelines for selecting the number of runs and/or the number of variables for random Latin hypercube designs that are likely to yield an acceptable degree of correlation. Applying our policies and tools, analysts can generate satisfactory random Latin hypercube designs without the need for complex algorithms.

Sliced Full Factorial-Based Latin Hypercube Designs as a Framework for a Batch Sequential Design Algorithm

Duan, Weitao; Ankenman, Bruce E.; Sanchez, Paul J.; Sanchez, Susan M.; Duan, Weitao; Ankenman, Bruce E.; Sanchez, Paul J.; Sanchez, Susan M.
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Artigo de Revista Científica
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SEED Paper; SEED Center Paper; Approved for public release; distribution is unlimited.; When tting complex models, such as nite element or discrete event simulations, the experiment design should exhibit good properties of both projectivity and orthogonality. To reduce experimental e ort, sequential design strategies allow experimenters to collect data only until some measure of prediction precision is reached. In this article, we present a batch sequential experiment design method that uses sliced Full Factorial-Based Latin Hypercube Designs (sFFLHDs), which are an extension to the concept of sliced Orthogonal Array-Based Latin Hypercube Designs (OALHD). At all stages of the sequential design, good univariate strati cation is achieved. The structure of the FFLHDs also tends to produce uniformity in higher dimensions, especially at certain stages of the design. We show that our batch sequential design approach has good sampling and tting qualities through both empirical studies and theoretical arguments.

Optimal design of piezoelectric materials for maximal energy harvesting

Nelson, Russell J.
Fonte: Monterey, California: Naval Postgraduate School Publicador: Monterey, California: Naval Postgraduate School
Tipo: Tese de Doutorado
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Approved for public release; distribution is unlimited; The military’s dependence on fossil fuels for electric power production in isolated settings is both logistically and monetarily expen-sive. Currently, the Department of Defense is actively seeking alternative methods to produce electricity, thus decreasing dependence on fossil fuels and increasing combat power.We believe piezoelectric generators have the ability to contribute to military applications of alternative electrical power generation in isolated and austere conditions. In this paper, we use three and six variable mathemat-ical models to analyze piezoelectric generator power generation capabilities. Using mk factorial sampling, nearly orthogonal and balanced Latin hypercube (NOBLH) design, and NOBLH iterative methods, we find optimal solutions to maximize piezoelectric gen-erator power output. We further analyze our optimal results using robustness analysis techniques to determine the sensitivity of our models to variable precision. With our results, we provide analysts and engineers the optimal designs involving material parameters in the piezoelectric generator, as well as the generator’s environment, in order to maximize electric output.; ; Captain, United States Army

Efficient nearly orthogonal and space-filling experimental designs for high-dimensional complex models

Cioppa, Thomas M.
Fonte: Monterey, California. Naval Postgraduate School Publicador: Monterey, California. Naval Postgraduate School
Formato: xvi, 128 p. : ill. (some col.) ; 28 cm.
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Approved for public release; distribution is unlimited.; The Department of Defense uses complex high-dimensional simulation models as an important tool in its decision-making process. To improve on the ability to efficiently explore larger subspaces of these models, this dissertation develops a set of experimental designs for searching over as many as 22 variables in as few as 129 runs. These new designs combine orthogonal Latin hypercubes and uniform designs to create designs having near orthogonality and excellent space-filling properties. Multiple measures are used to assess the quality of candidate designs and to identify the best one. For situations in which more than the minimum number of required runs are available, the designs can be permuted and appended to create additional design points that improve upon the design's orthogonality and space-filling. The designs are used to explore two surfaces. For a known 11 dimensional stochastic response function containing nonlinear and interaction terms, it is shown that the near orthogonal Latin hypercube is substantially better than the orthogonal Latin hypercube in estimating model coefficients. The other exploration uses the agent-based simulation MANA to analyze 22 variables in a complex military peace enforcement operation. The need for maintaining the initiative and speed of execution during these peace enforcement operations is identified.; Lieutenant Colonel...

Diagnostics of an Aircraft Engine Pumping Unit Using a Hybrid Approach based-on Surrogate Modeling

LAMOUREUX, Benjamin; MASSÉ, Jean-Rémi; MECHBAL, Nazih
Fonte: IEEE PHM Publicador: IEEE PHM
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This document introduces a hybrid approach for fault detection and identification of an aircraft engine pumping unit. It is based on the complementarity between a model-based approach accounting for uncertainties aimed at quantifying the degradation modes signatures and a data-driven approach aimed at recalibrating the healthy syndrome from measures. Because of the computational time costs of uncertainties propagation into the physics based model, a surrogate modeling technic called Kriging associated to Latin hypercube sampling is utilized. The hybrid approach is tested on a pumping unit of an aircraft engine and shows good results for computing the degradation modes signatures and performing their detection and identification.

Latin hypercube sampling with inequality constraints

Petelet, Matthieu; Iooss, Bertrand; Asserin, Olivier; Loredo, Alexandre
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical welding simulation, where the inequality constraints are caused by the physical decreasing of some material properties in function of the temperature.

Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties

Damblin, Guillaume; Couplet, Mathieu; Iooss, Bertrand
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/07/2013 Português
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Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about the output when the numerical simulations are expensive to run. This paper considers the problem of exploring the whole space of variations of the computer model input variables in the context of a large dimensional exploration space. Various properties of space filling designs are justified: interpoint-distance, discrepancy, minimum spanning tree criteria. A specific class of design, the optimized Latin Hypercube Sample, is considered. Several optimization algorithms, coming from the literature, are studied in terms of convergence speed, robustness to subprojection and space filling properties of the resulting design. Some recommendations for building such designs are given. Finally, another contribution of this paper is the deep analysis of the space filling properties of the design 2D-subprojections.

A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing

Aistleitner, Christoph; Hofer, Markus; Tichy, Robert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/11/2013 Português
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We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$, where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of dependent components of the random vector $(U^1, \ldots, U^d)$ one can achieve more accurate results by using Latin hypercube sampling with dependence (LHSD). We state a central limit theorem for the $d$-dimensional LHSD estimator, by this means generalising a result of Packham and Schmidt. Furthermore we give conditions on the function $f$ and the distribution of $(U^1, \ldots, U^d)$ under which a reduction of variance can be achieved. Finally we compare the effectiveness of Monte Carlo and LHSD estimators numerically in exotic basket option pricing problems.

The generalization of Latin hypercube sampling

Shields, Michael D.; Zhang, Jiaxin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/07/2015 Português
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Latin hypercube sampling (LHS) is generalized in terms of a spectrum of stratified sampling (SS) designs referred to as partially stratified sample (PSS) designs. True SS and LHS are shown to represent the extremes of the PSS spectrum. The variance of PSS estimates is derived along with some asymptotic properties. PSS designs are shown to reduce variance associated with variable interactions, whereas LHS reduces variance associated with main effects. Challenges associated with the use of PSS designs and their limitations are discussed. To overcome these challenges, the PSS method is coupled with a new method called Latinized stratified sampling (LSS) that produces sample sets that are simultaneously SS and LHS. The LSS method is equivalent to an Orthogonal Array based LHS under certain conditions but is easier to obtain. Utilizing an LSS on the subspaces of a PSS provides a sampling strategy that reduces variance associated with both main effects and variable interactions and can be designed specially to minimize variance for a given problem. Several high-dimensional numerical examples highlight the strengths and limitations of the method. The Latinized partially stratified sampling method is then applied to identify the best sample strategy for uncertainty quantification on a plate buckling problem.; Comment: 31 pages...

Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal sampling: connections between Populations of Models and Experimental Designs

Donovan, Diane; Burrage, Kevin; Burrage, Pamela; McCourt, Thomas A; Thompson, Harold Bevan; Yazici, Emine Sule
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/10/2015 Português
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In this paper we use counting arguments to prove that the expected percentage coverage of a $d$ dimensional parameter space of size $n$ when performing $k$ trials with either Latin Hypercube sampling or Orthogonal sampling (when $n=p^d$) is the same. We then extend these results to an experimental design setting by projecting onto a 2 dimensional subspace. In this case the coverage is equivalent to the Orthogonal sampling setting when the dimension of the parameter space is two. These results are confirmed by simulations. The ideas presented here have particular relevance when attempting to perform uncertainty quantification or when building populations of models.; Comment: 15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1502.06559

Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques

Kucherenko, Sergei; Albrecht, Daniel; Saltelli, Andrea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/05/2015 Português
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Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling, and Quasi Monte Carlo with sampling based on Sobol sequences. Generally results show superior performance of the Quasi Monte Carlo approach based on Sobol sequences in line with theoretical predictions. Latin Hypercube Sampling can be more efficient than both Monte Carlo method and Quasi Monte Carlo method but the latter inequality holds for a reduced set of function typology and at small number of sampled points. In conclusion Quasi Monte Carlo method would appear the safest bet when integrating functions of unknown typology.

Space-filling Latin Hypercube Designs based on Randomization Restrictions in Factorial Experiments

Ranjan, Pritam; Spencer, Neil
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Latin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation among factors, maximin interpoint distance, and orthogonality among the factors via orthogonal arrays (OAs). Projective geometric structures like spreads, covers and stars of PG(p-1,q) can be used to characterize the randomization restriction of multistage factorial experiments. These geometric structures can also be used for constructing OAs and nearly OAs (NOAs). In this paper, we present a new class of space-filling LHDs based on NOAs derived from stars of PG(p-1, 2).; Comment: 16 pages (accepted in SPL)

Populations of models, Experimental Designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

Burrage, Kevin; Burrage, Pamela; Donovan, Diane; Thompson, Bevan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/02/2015 Português
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In this paper we have used simulations to make a conjecture about the coverage of a $t$ dimensional subspace of a $d$ dimensional parameter space of size $n$ when performing $k$ trials of Latin Hypercube sampling. This takes the form $P(k,n,d,t)=1-e^{-k/n^{t-1}}$. We suggest that this coverage formula is independent of $d$ and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the $t$ dimensional subspace at the sub-block size level.; Comment: 9 pages, 5 figures

Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques

KUCHERENKO Sergei; ALBRECHT Daniel; SALTELLI ANDREA
Fonte: arXiv - University of Cornell (USA) Publicador: arXiv - University of Cornell (USA)
Tipo: Articles in periodicals and books Formato: Online
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Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random and Latin Hypercube Sampling and the Quasi Monte Carlo method with sampling based on Sobol’ sequences. Generally, results show superior performance of the Quasi Monte Carlo approach based on Sobol’ sequences in line with theoretical predictions. There are also some types of functions for which Latin Hypercube Sampling can be more efficient than the Monte Carlo method. For the same functions types it can be more efficient than the Quasi Monte Carlo method at small number of sampled points.; JRC.DDG.01-Econometrics and applied statistics

Convergence analysis for Latin-hypercube lattice-sample selection strategies for 3D correlated random hydraulic-conductivity fields

Simuta-Champo,R.; Herrera-Zamarrón,G. S.
Fonte: Instituto de Geofísica, UNAM Publicador: Instituto de Geofísica, UNAM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2010 Português
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The Monte Carlo technique provides a natural method for evaluating uncertainties. The uncertainty is represented by a probability distribution or by related quantities such as statistical moments. When the groundwater flow and transport governing equations are solved and the hydraulic conductivity field is treated as a random spatial function, the hydraulic head, velocities and concentrations also become random spatial functions. When that is the case, for the stochastic simulation of groundwater flow and transport it is necessary to obtain realizations of the hydraulic conductivity. For this reason, the next question arises, how many hydraulic conductivity realizations are necessary to get a good representation of the quantities relevant in a given problem? Different methods require different number of realizations and it is relevant to work with the one that reduces the computational effort the most. Zhang and Pinder (2003) proposed a specific case of the latin hypercube sampling (LHS) method called the lattice sampling technique for the generation of Monte Carlo realizations that resulted in a reduction in the computational effort required to achieve a reliable random field simulation of groundwater flow and transport. They compared the LHS method with three other random field generation algorithms: sequential Gaussian simulation...