Keywords: design of experiments, space-filling, orthogonality, latin hypercube sampling, sampling-based sensitivity analysis.

Nowadays, numerical models of real-world structures are more precise, more complex and of course also more time-consuming to evaluate. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. Sensitivity analysis is a basic tool for investigating the sensitivity of the model with respect to its inputs. One widely used strategy to assess the sensitivity is sampling-based sensitivity analysis [1], which is based on a finite set of simulations for given sets of input parameters. An estimate of the sensitivity can be then obtained by computing correlations between the input parameters and the chosen response of the model. The accuracy of the sensitivity prediction depends on the choice of the input parameter sets called the design of experiments (DOE). This paper reviews and compares available criteria assessing the quality of the design of experiments.

In particular, we examine the suitability of eight criteria which can be organized into two groups: (i) four criteria evaluating mainly the space-filling properties of a DOE: the Audze-Eglais objective function [2]; the Euclidean maximum distance [3]; the modified L2 discrepancy [4]; the D-optimality criterion [5] and (ii) four well-known criteria preferring the orthogonality of a DOE: the conditional number; the Pearson product-moment; Spearman's rank and the Kendall tau rank correlation coefficients. The quality of these criteria is evaluated in terms of ease of their optimization, their mutual qualities and their suitability for usage in sampling-based sensitivity analysis.

The overall results revealed the superiority of the D-optimal criterion. However, its practical use is complicated by the need of an interactive tuning. In addition very good results were achieved using the latin hypercube designs optimized with Pearson's coefficient. This method can be recommended for an immediate use as a result of its implementation in engineering software [6].

1

J.C. Helton, J.D. Johnson, C.J. Sallaberry, C.B. Storlie, "Survey of sampling-based methods for uncertainty and sensitivity analysis", Reliab Eng Syst Safe, 91(10-11), 1175-1209, 2006. doi:10.1016/j.ress.2005.11.017

2

P. Audze, V. Eglais, "New approach for planning out of experiments", Problems of Dynamics and Strengths, Zinatne Publishing House, 35, 104-107, 1977.

3

M. Johnson, L. Moore, D. Ylvisaker, "Minimax and maximin distance designs", Journal of Statistical Planning and Inference, 26(2), 131-148, 1990. doi:10.1016/0378-3758(90)90122-B

4

K.T. Fang, Y. Wang, "Number-theoretic Methods in Statistics", Chapman & Hall, London, 1994. doi:10.1214/ss/1177010392

5

M. Hofwing, N. Strömberg, "D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method", Structural and Multidisciplinary Optimization, 42(1), 73-88, 2010. doi:10.1007/s00158-009-0464-3

6

J. Novák, "Generator of optimal LHS designs SPERM v. 2.0", Centre for Integrated Design of Advanced Structures (CIDEAS), Czech Technical University in Prague, 2011. http://www.cideas.cz/ke_stazeni/sperm/

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