Extension of Latin Hypercube samples while maintaining the correlation structure

Robin Schmidt, Matthias Voigt, Konrad Vogeler

Due to its variance reducing properties compared with random sampling, Latin Hypercube sampling (LHS) is frequently used in Monte Carlo methods for the probabilistic analysis of a system. An extension of the sample size is created in the case of the LHS only by doubling its size. Especially with large samples and the perpetuation of an existing correlation structure this can become a drawback of LHS. This paper presents an engineering approach to the multiple extension of a Latin Hypercube sample. The objective is to extent the sample size but to keep the number of realizations small. It is of particular importance that the present approach is able to maintain the correlations between the input variables in the probabilistic analysis. The quality of the statistical measures as well as the correlation setting is discussed and evaluated by means of simple example cases. By comparative analyses with LHS without modifications, a benchmark of the method is performed. Subsequently the method is applied to the sensitivity analysis of the aerodynamic performance of a two-stage high pressure compressor.

Schmidt, R., Voigt, M., Vogeler, K., 2014.
"Extension of Latin Hypercube samples while maintaining the correlation structure".
Proceedings of the 12th International Probabilistic Workshop, 2014.
(online version: doi: 10.1466/20141125.01)