Efficient design of experiments for structural optimization using significance screening

When performing structural optimization of large scale engineering problems, the choice of experiment design is important. However, classical experiment designs are developed to deal with undesired but inevitable scatter and are thus not ideal for sampling of deterministic computational responses. In this paper, a novel screening and design of computer experiments algorithm is presented. It is based on the concept of orthogonal design variable significances and is applicable for problems where design variables do not simultaneously have a significant influence on any of the constraints. The algorithm presented uses significance orthogonality to combine several one-factor-at-a-time experiments in one several-factors-at-a-time experiment. The procedure results in a reduced experiment design matrix. In the reduced experiment design, each variable is varied exactly once but several variables may be varied simultaneously, if their significances with respect to the constraints are orthogonal. Moreover, a measure of influence, as well as an influence significance threshold, is defined. In applications, the value of the threshold is left up to the engineer. To assist in this choice, a relation between model simplification, expressed in terms of the significance threshold, and computational cost is established in a screening. The relation between efficiency and loss of accuracy for the proposed approach is discussed and demonstrated. For two solid mechanics type problems studied herein, the necessary number of simulations could be reduced by 25% and 64%, respectively, with negligible losses in accuracy.