Modification of the Audze–Eglājs criterion to achieve a uniform distribution of sampling points

Abstract

The Audze–Eglājs (AE) criterion was developed to achieve a uniform distribution of experimental points in a hypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of the boundaries of the hypercube. We propose a simple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion are demonstrated using simple numerical examples focused on (i) the uniformity of sampling density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate the statistical parameters of functions of random variables. An engineering example of reliability calculation is presented, too.