A Group-Based Space-Filling Design of Experiments Algorithm

Computer-aided engineering (CAE) is an important tool routinely used to simulate complex engineering systems. Virtual simulations enhance engineering insight into prospective designs and potential design issues and can limit the need for expensive engineering prototypes. For complex engineering systems, however, the effectiveness of virtual simulations is often hindered by excessive computational cost. To minimize the cost of running expensive computer simulations, approximate models of the original model (often called surrogate models or metamodels) can provide sufficient accuracy at a lower computing overhead compared to repeated runs of a full simulation. Metamodel accuracy improves if constructed using space-filling designs of experiments (DOEs). The latter provide a collection of sample points in the design space preferably covering the entire space. In this article, an algorithm is presented to create groups of space-filling multidimensional designs with uniform projections in one and two dimensions. In addition to each group having space-filling properties itself, unions of groups also have space-filling properties. This allows the designer to sequentially add points without damaging the space-filling property of the previous design. Thus, accurate metamodels can be created iteratively by adding points until interpolation error targets are met. This methodology avoids building an entirely new, larger space-filling DOE, requiring extensive new simulation runs. Instead, well-chosen points are added to an existing DOE so that additional simulation runs are required only for the added sample points. The proposed approach to constructing these DOEs uses Sobol quasi-random sequences in one dimension, a maxi-min distance criterion, a new optimality criterion based on the spread of the minimum distance of each point with all others, and a column-wise element exchange algorithm to efficiently produce a space-filling design.