6533b7d7fe1ef96bd1268561

RESEARCH PRODUCT

Latin hypercube sampling with inequality constraints

Matthieu PeteletOlivier AsserinBertrand IoossA. Loredo

subject

Statistics and ProbabilityFOS: Computer and information sciencesEconomics and EconometricsMathematical optimizationDesign of Experiments020209 energyMonotonic functionSample (statistics)Mathematics - Statistics Theory02 engineering and technologyStatistics Theory (math.ST)01 natural sciencesStatistics - Computation010104 statistics & probabilityRobustness (computer science)[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Sampling design0202 electrical engineering electronic engineering information engineeringFOS: Mathematics[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsDependenceUncertainty analysisLatin hypercube samplingComputation (stat.CO)MathematicsApplied MathematicsComputer experimentFunction (mathematics)[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Computer experiment[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]Latin hypercube samplingModeling and SimulationUncertainty analysisSocial Sciences (miscellaneous)Analysis

description

International audience; 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.

yearjournalcountryeditionlanguage
2010-01-01
https://dx.doi.org/10.48550/arxiv.0909.0329