Latin hypercube sampling with inequality constraints |
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Authors: | Matthieu Petelet Bertrand Iooss Olivier Asserin Alexandre Loredo |
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Institution: | (1) School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-2035, USA;(2) School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088, USA;(3) Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907-2032, USA;(4) Department of Basic Medical Sciences, Purdue University, West Lafayette, IN 47907-2032, USA |
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Abstract: | 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. |
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