Latin hypercube sampling with inequality constraints

Matthieu Petelet (1) , Bertrand Iooss (2, 3) , Olivier Asserin (1) , Alexandre Loredo (4)

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
2 LCFR - Laboratoire de Conduite et Fiabilité des Réacteurs
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 DRIVE - Département de Recherche en Ingéniérie des Véhicules pour l'Environnement

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.

Mots clés: Computer experiment; Latin hypercube sampling; Design of Experiments; Uncertainty analysis; Dependence

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Matthieu Petelet, Bertrand Iooss, Olivier Asserin, Alexandre Loredo. Latin hypercube sampling with inequality constraints. 2009. ⟨hal-00412235v1⟩