Subsurface stormflow modeling with sensitivity analysis using a latin. Even with latin hypercube sampling, monte carlo analysis requires a huge number of sampling points. Sensitivity analysis of deterministic models through latin hypercube sampling. Uncertainty and sensitivity analysis results obtained with random and latin hypercube sampling are compared. The following methods are currently supported for generating the lhs. Both the direct and adjoint deterministic methods are described. A comparison of global sensitivity techniques and sampling. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of latin hypercube designs. Sensitivity analysis of deterministic models introduction to latin hypercube sampling john m.
Subsurface stormflow modeling with sensitivity analysis using. Using techniques such as design of experiments doe also referred to as experimental design, you can choose a parameter set for sensitivity. The purpose of this presentation is to use selected test problems from a recent book on sensitivity analysis 55 to illustrate sampling based methods for uncertainty and sensitivity analysis. The sensitivity of calculated dose estimates to various radtran 4 inputs is an available output for incidentfree analysis because the defining equations are linear and sensitivity to each variable can be calculated in closed mathematical form. Latin hypercube sampling in sensitivity analysis joseph c. Things you wanted to know about the latin hypercube design. Sensitivity analysis procedures can be used to identify which input variable uncertainties contribute most to uncertainty in the response variable. In this paper an uncertainty and a sensitivity analysis are described and applied. Latin hypercube sampling is generally recommended over simple random sampling when the model is complex or when time and resource constraints are an issue. Sample size requierement for monte carlo simulations using. Latin hypercube sampling lhs was used for sampling the parametric combina tions, which gave predictive uncertainty results directly without using surrogate models, and the impacts of different parametric distribution functions on the results were investigated. Sobol, latin hypercube,random sampling, global sensitivity analysis, variance based,total effectsestimator 22nd international congress on modelling and simulation, hobart, tasmania, australia, 3 to 8 december 2017. Applications of latin hypercube sampling scheme and partial.
Latin hypercube sampling with inequality constraints matthieu petelet bertrand iooss. A comparison of uncertainty and sensitivity analysis. Illustration of samplingbased methods for uncertainty and. Latin hypercube sampling simulated annealing random fields. The uncertainty analysis allowed for the derivation of a frequency distribution for r o and the assessment of the relative contribution each of the three components of r o made. In this article, a sensitivity study based on a latin hypercube lh sampling design is compared with a similar study using a full factorial ff, fixedpoint smaple. Applications of latin hypercube sampling scheme and.
Desirable features of monte carlo analysis in conjunction with latin hypercube sampling are described in discussions of. Latin hypercube sampling lhs is a statistical method for generating a nearrandom sample of parameter values from a multidimensional distribution. Random sampling tutorial 4 latin hypercube sampling. View the article pdf and any associated supplements and figures for a period of 48 hours. Latin hypercube sampling now we seek to use latin hypercube sampling to explore the 12dimensional parameter space. Contains an existing latin hypercube design with a number of rows equal to the points in the. Xihui liang introduction reliability analysis and sensitivity analysis should be. That happens because, in latin hypercube, samples are noncollapsing orthogonality of the.
Latin hypercube sampling is a widely used method to generate controlled random samples the basic idea is to make sampling point distribution close to probability density function pdf m. Sensitivity heat map may be used to determine the e ects of parameter interactions or direction of e ect for further reading. No attempt is made to present results for all test problems. A methodology for performing global uncertainty and.
Sensitivity analysis is an analysis that attempts to provide a ranking of the models input parameters with. The technique is used for both random variables and random fields. Latin hypercube sampling of gaussian random field for sobol global sensitivity analysis of models with spatial inputs and scalar output nathalie saintgeours, jeanstephane bailly, christian lavergne, frederic grelot to cite this version. The comparison uses results from a model for twophase fluid flow obtained with three independent random samples of size 100 each and three independent latin hypercube samples lhss of size 100 each. Illustration of samplingbased methods for uncertainty and sensitivity analysis j. A tutorial on latin hypercube design of experiments viana. Through sensitivity analysis, smi identified input parameters that most influenced the modeling results. Gwo environmental sciences division, oak ridge national laboratory, now at center for computational sciences, oak ridge national laboratory, p. Smi then quantified the uncertainties associated with the parameters and incorporated these into the modeling effort using the latin hypercube lhs sampling technique. Nov 25, 2015 this paper provides a tutorial on latin hypercube design of experiments, highlighting potential reasons of its widespread use.
Latin hypercube sampling lhs belongs to the mc class of sampling methods, and was introduced by mckay et al. Desirable features of monte carlo analysis in conjunction with latin hypercube sampling are described in. The first step for a successful surrogate modeling and statistical analysis is the planning of the input configuration that is used. Latin hypercube sampling and the sensitivity analysis of a. Lhs allows an unbiased estimate of the average model output, with the advantage that it requires fewer samples than simple random sampling to achieve the same accuracy mckay et al.
This chapter discusses the use of computer models for such diverse applications as safety assessments for geologic isolation of radioactive waste and for nuclear power plants. Another good reason for the latin hypercube popularity is flexibility. Survey of samplingbased methods for uncertainty and. Usage augmentlhslhs, m 1 arguments lhs the latin hypercube design to which points are to be added. Using techniques such as design of experiments doe also referred to as experimental design, you can choose a parameter set for sensitivity analysis.
The sampling method is often used to construct computer experiments or for monte carlo integration. Subsurface stormflow modeling with sensitivity analysis. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Storlied adepartment of mathematics and statistics, arizona state university, tempe, az 852871804 usa bprostat, mesa, az 852045326 usa csandia national laboratories, albuquerque, nm 87185. All the areas of the sample space are represented by input values. Sensitivity analysis of a waterquality model using latin hypercube sampling article pdf available in journal of water resources planning and. Small sample sensitivity analysis techniques for computer. More efficient and refined statistical techniques have been applied to sampling. Reliability sensitivity analysis using axis orthogonal. Latin hypercube sampling for uncertainty and sensitivity. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty.
However, the necessary linearity is not characteristic of the equations used in calculation of accident dose risk, making a similar tabulation of. Sensitivity analysis of a waterquality model using latin hypercube sampling article pdf available in journal of water resources planning and management 3 may 2004 with 184 reads. Jun 27, 2007 in this setting it is desired to perform sensitivity studies of the inputoutput relationships. This paper presents the technique of latin hypercube sampling, a structured, formal sampling process used in the sensitivity analysis procedure. Factorial sampling plans for preliminary computational experiments. To generate a sample size n from k variables xx 1, x 2. For the love of physics walter lewin may 16, 2011 duration. Design and analysis of computer experiments, latin hypercube sampling, spacefilling designs. Generate parameter samples for sensitivity analysis.
This topic shows how to generate parameter samples for sensitivity analysis. Specifically, this very large analysis was repeated with three replicated latin hypercube samples of size 300 from 392 epistemically uncertain analysis inputs. In this article, a combined use of latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is. Latin hypercube sampling, halton, axis orthogonal importance sampling, spurious correlation reduction, parameter sensitivity, structural reliability date received. A latin hypercube of size n is generated from the desired quantile distribution functions.
Sobol or latin hypercube sampling, although random designs can also be used, at the loss of some efficiency. A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program. For each parameter a probability density function is defined and. A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate samplingbased uncertainty and sensitivity analysis procedures. A model for the spread of ebola virus disease john m. Abstract the following techniques for uncertainty and sensitivity analysis are briefly summarized. Parametric uncertainty and sensitivity analysis of. Conover, a comparison of three methods for selecting values of input variables in the analysis of output from a. In this article, a combined use of latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is equivalently solved by reliability. Currently, the standard sampling technique employed is latin hypercube sampling and this was introduced to the field of disease modelling the field of our research by blower. Generate parameter samples for sensitivity analysis matlab.
Center for connected learning and computerbased modeling, northwestern university, evanston, il. You can perform global sensitivity analysis using simulink design optimization software. Global sensitivity analysis and effective dimensions. Comparison of latin hypercube andcomparison of latin. Latin hypercube sampling are described in discussions of the following topics. Latin hypercube sampling and the propagation of uncertainty. Illustration of samplinga based methods for uncertainty and. Nathalie saintgeours, jeanstephane bailly, christian lavergne, frederic grelot. Monte carlo analysis, differential analysis, response surface methodology, fourier amplitude sensitivity test, sobol variance decomposition, and fast probability integration. Sample size requierement for monte carlo simulations. Uncertainty results obtained with replicated random and latin hypercube samples are compared, with the latin hypercube samples tending to produce more stable results than the random samples.
Sobol sequences and their properties comparison of scomparison of sample distributions generated by different techniquesample distributions generated by different techniques do qmc methods loose their efficiency in higher dimensions. How to determine the sample size of a latin hypercube. Use of replicated latin hypercube sampling to estimate. First, use the lhs package to simulate a large number say, points in the 12dimensional unit cube. Latin hypercube sampling in sensitivity analysis pir. Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system numerical or otherwise can be divided and allocated to different sources of uncertainty in its inputs. Latin hypercube sampling of gaussian random field for sobol. Apr 07, 2016 for the love of physics walter lewin may 16, 2011 duration. Computer models are often used in sensitivity analysis, reliability assessment, design optimization and a number of other studies which tend to require many function evaluations. This paper presents the technique of latin hypercube sampling, a structured, formal sampling process used in. In this setting it is desired to perform sensitivity studies of the inputoutput relationships. A comparison of global sensitivity techniques and sampling method. Pdf sensitivity analysis of a waterquality model using. Augments an existing latin hypercube sample, adding points to the design, while maintaining the latin properties of the design.
Wound healing, latin hypercube sampling, partial rank correlation coe cient procedure, uncertainty, sensitivity analysis ii. Sensitivity analysis of deterministic models through latin. Latin hypercube sampling operates in the following. Material degradation is to ngi the hypercube sampling is utilized. This example is using netlogo flocking model wilensky, 1998 to demonstrate exploring parameter space with categorical evaluation and latin hypercube sampling lhs. Davis2 a sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate. Numerical methods for engineering design and optimization.
To include more model features and their interactions in a sensitivity study, while limiting computer utilization, various sampling methods have been suggested. Factorial sampling plans for preliminary computational. A comparison of uncertainty and sensitivity analysis results. A discrete, monte carlo model of epidemics of influenzavirus infections in a human community is used for illustrative purposes. Latin hypercube sampling with inequality constraints. Samplingbased methods for uncertainty and sensitivity analysis have become very popular. Hence, a judicious selection procedure for the choic of values of input variables is required, latin hypercube sampling has been shown to work well on this type of problem.
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