Construction of column-orthogonal designs for computer experiments

Abstract

Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.

Construction of orthogonal symmetric Latin hypercube designs

“…Designs with many levels are desirable, but it is not essential to keep the number of runs equal to the number of levels. These designs are quite suitable for practical use, and in addition, they can be viewed as stepping stones to space-filling design as a good space-filling design must be column-orthogonal or nearly so (Bingham, Sitter, and Tang (2009) ;Sun, Pang, and Liu (2011);Georgiou, Koukouvinos, and Liu (2014); Yuan, Lin, and Liu (2017)). …”

“…For given q and p, if there does not exist any OSLHD(q, p) as the design B in the proposed method, and/or there does not exist a column-orthogonal matrix T d , a nearly orthogonal LHD for B and a nearly column-orthogonal matrix for T d (cf., Sun, Pang, and Liu (2011)) can be used instead. For an n × m matrix X, the near orthogonality is usually assessed by ρ M (X) = max i<j |ρ ij (X)| and ρ Corollary 2.…”

Global sensitivity analysis using a Gaussian Radial Basis Function metamodel

“…To enhance the space filling and orthogonal performance, various approach have been developed [37,[39][40][41], including the Optimal Criteria and Optimal Algorithms. The widely used…”

Self-adaptive multi-objective teaching-learning-based optimization and its application in ethylene cracking furnace operation optimization

“…11, when the COP is allowed to vary from 1.5 to 1.9 bar, the yields of ethylene and propylene decrease while the yield of butadiene increases. Furthermore, in order to analyze the synergic effects of these control variables, we adopt the uniform design (UD) [54][55][56], which is a kind of space filling designs, to seek experimental points to be uniformly scattered in the experimental domain. The table of uniform design U 6 ⁎ (6 4 ) is used to get the experimental points.…”