Sobol or latin hypercube sampling, although random designs can also be used, at the loss of some efficiency. Material degradation is to ngi the hypercube sampling is utilized. Nathalie saintgeours, jeanstephane bailly, christian lavergne, frederic grelot. Sensitivity heat map may be used to determine the e ects of parameter interactions or direction of e ect for further reading. A latin hypercube of size n is generated from the desired quantile distribution functions. On the basis of replicated latin hypercube sampling, the authors performed an uncertainty and sensitivity analysis of the basic reproductive rate of tuberculosis tb. A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate sampling based uncertainty and sensitivity analysis procedures.
This topic shows how to generate parameter samples for sensitivity analysis. Apr 07, 2016 for the love of physics walter lewin may 16, 2011 duration. This example is using netlogo flocking model wilensky, 1998 to demonstrate exploring parameter space with categorical evaluation and latin hypercube sampling lhs. Latin hypercube sampling lhs is a statistical method for generating a nearrandom sample of parameter values from a multidimensional distribution. Parametric uncertainty and sensitivity analysis of. A discrete, monte carlo model of epidemics of influenzavirus infections in a human community is used for illustrative purposes. A model for transmission of hiv among homosexual men.
A methodology for performing global uncertainty and. Latin hypercube sampling with inequality constraints. Wound healing, latin hypercube sampling, partial rank correlation coe cient procedure, uncertainty, sensitivity analysis ii. A comparison of uncertainty and sensitivity analysis. Factorial sampling plans for preliminary computational experiments.
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. Contains an existing latin hypercube design with a number of rows equal to the points in the. Numerical methods for engineering design and optimization. Desirable features of monte carlo analysis in conjunction with latin hypercube sampling are described in discussions of. Uncertainty and sensitivity analysis results obtained with random and latin hypercube sampling are compared. Pdf sensitivity analysis of a waterquality model using. Samplingbased methods for uncertainty and sensitivity analysis have become very popular. View the article pdf and any associated supplements and figures for a period of 48 hours. Illustration of samplingbased methods for uncertainty and. 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. More efficient and refined statistical techniques have been applied to sampling. Through sensitivity analysis, smi identified input parameters that most influenced the modeling results. Small sample sensitivity analysis techniques for computer.
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. Factorial sampling plans for preliminary computational. 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. Using techniques such as design of experiments doe also referred to as experimental design, you can choose a parameter set for sensitivity. For the love of physics walter lewin may 16, 2011 duration. To generate a sample size n from k variables xx 1, x 2. Davis2 a sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate. A model for the spread of ebola virus disease john m. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Sample size requierement for monte carlo simulations. Latin hypercube sampling in sensitivity analysis pir. A comparison of global sensitivity techniques and sampling. Illustration of samplingbased methods for uncertainty and sensitivity analysis j.
Latin hypercube sampling simulated annealing random fields. Things you wanted to know about the latin hypercube design. How to determine the sample size of a latin hypercube. Latin hypercube sampling with inequality constraints matthieu petelet bertrand iooss. Desirable features of monte carlo analysis in conjunction with latin hypercube sampling are described in.
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. To include more model features and their interactions in a sensitivity study, while limiting computer utilization, various sampling methods have been suggested. Design and analysis of computer experiments, latin hypercube sampling, spacefilling designs. Subsurface stormflow modeling with sensitivity analysis using. 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. Sensitivity analysis of a waterquality model using latin hypercube sampling article pdf available in journal of water resources planning and. However, the necessary linearity is not characteristic of the equations used in calculation of accident dose risk, making a similar. However, the necessary linearity is not characteristic of the equations used in calculation of accident dose risk, making a similar tabulation of. Random sampling tutorial 4 latin hypercube sampling. 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. This paper presents the technique of latin hypercube sampling, a structured, formal sampling process used in the sensitivity analysis procedure. Latin hypercube sampling operates in the following.
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. Both the direct and adjoint deterministic methods are described. A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate samplingbased uncertainty and sensitivity analysis procedures. 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. The technique is used for both random variables and random fields. Kanipe, sandia national laboratories, albuquerque, nm abstract the sensitivity of calculated dose estimates to various radtran 4 inputs is an available output for. Application of latin hypercube sampling to radtran 4 truck. Subsurface stormflow modeling with sensitivity analysis. 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. 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. Applications of latin hypercube sampling scheme and partial. This paper presents the technique of latin hypercube sampling, a structured, formal sampling process used in. Xihui liang introduction reliability analysis and sensitivity analysis should be.
In this paper an uncertainty and a sensitivity analysis are described and applied. First, use the lhs package to simulate a large number say, points in the 12dimensional unit cube. 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. Applications of latin hypercube sampling scheme and. All the areas of the sample space are represented by input values.
Another good reason for the latin hypercube popularity is flexibility. Sensitivity analysis of deterministic models through latin. Latin hypercube sampling, halton, axis orthogonal importance sampling, spurious correlation reduction, parameter sensitivity, structural reliability date received. The following methods are currently supported for generating the lhs. Sensitivity analysis is an analysis that attempts to provide a ranking of the models input parameters with. For example, if few dimensions have to be dropped out, the resulting design is still a latin hypercube design maybe suboptimal, but a latin hypercube nevertheless.
A comparison of uncertainty and sensitivity analysis results. Conover, a comparison of three methods for selecting values of input variables in the analysis of output from a. You can perform global sensitivity analysis using simulink design optimization software. 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. 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. Abstract the following techniques for uncertainty and sensitivity analysis are briefly summarized. 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 lhs belongs to the mc class of sampling methods, and was introduced by mckay et al. Sensitivity analysis of deterministic models through latin hypercube sampling. Latin hypercube sampling for uncertainty and sensitivity. Storlied adepartment of mathematics and statistics, arizona state university, tempe, az 852871804 usa bprostat, mesa, az 852045326 usa csandia national laboratories, albuquerque, nm 87185. Smi then quantified the uncertainties associated with the parameters and incorporated these into the modeling effort using the latin hypercube lhs sampling technique. Monte carlo analysis, differential analysis, response surface methodology, fourier amplitude sensitivity test, sobol variance decomposition, and fast probability integration. A tutorial on latin hypercube design of experiments viana.
Using techniques such as design of experiments doe also referred to as experimental design, you can choose a parameter set for sensitivity analysis. 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. Center for connected learning and computerbased modeling, northwestern university, evanston, il. Generate parameter samples for sensitivity analysis. Latin hypercube sampling now we seek to use latin hypercube sampling to explore the 12dimensional parameter space. 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.
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. Augments an existing latin hypercube sample, adding points to the design, while maintaining the latin properties of the design. Latin hypercube sampling are described in discussions of the following topics. Use of replicated latin hypercube sampling to estimate.
Even with latin hypercube sampling, monte carlo analysis requires a huge number of sampling points. Latin hypercube sampling of gaussian random field for sobol. Usage augmentlhslhs, m 1 arguments lhs the latin hypercube design to which points are to be added. Sensitivity analysis of deterministic models introduction to latin hypercube sampling john m. Sensitivity analysis procedures can be used to identify which input variable uncertainties contribute most to uncertainty in the response variable.
Subsurface stormflow modeling with sensitivity analysis using a latin. Comparison of latin hypercube andcomparison of latin. 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. Generate parameter samples for sensitivity analysis matlab. Reliability sensitivity analysis using axis orthogonal. A comparison of global sensitivity techniques and sampling method. Summary the adjoint method can be classified as an analytic method while latin hypercube sampling is a special form of direct sampling used during monte carlo simulation.
In this setting it is desired to perform sensitivity studies of the inputoutput relationships. Gwo environmental sciences division, oak ridge national laboratory, now at center for computational sciences, oak ridge national laboratory, p. Latin hypercube sampling and the sensitivity analysis of a. Nov 25, 2015 this paper provides a tutorial on latin hypercube design of experiments, highlighting potential reasons of its widespread use. Global sensitivity analysis and effective dimensions. A tutorial on latin hypercube design of experiments. Latin hypercube sampling and the propagation of uncertainty. For each parameter a probability density function is defined and.
Latin hypercube sampling is generally recommended over simple random sampling when the model is complex or when time and resource constraints are an issue. Illustration of samplinga based methods for uncertainty and. Specifically, this very large analysis was repeated with three replicated latin hypercube samples of size 300 from 392 epistemically uncertain analysis inputs. Survey of samplingbased methods for uncertainty and. Jun 27, 2007 in this setting it is desired to perform sensitivity studies of the inputoutput relationships. That happens because, in latin hypercube, samples are noncollapsing orthogonality of the. Latin hypercube sampling of gaussian random field for. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty. 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. 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. Latin hypercube sampling in sensitivity analysis joseph c.
720 1016 960 1491 1442 1116 1202 1445 799 496 1123 138 911 139 467 1042 824 1363 1393 781 518 1126 395 844 3 825 1067 780 651 899 910 716 1061 753 1398 485