A Sequential Maximin Latin Hypercube Sampling Method And Its Application to Aircraft Design

Abstract

Space-filling and projective properties of design of computer experiments (DoCE) methods are desired features for metamodeling. To pursue good performance in the aforementioned properties, this article presents a novel deterministic sequential maximin Latin Hypercube design (LHD) method using successive local enumeration, notated as sequential-SLE (S-SLE). First, a mesh-mapping algorithm is proposed to map the positions of existing points into the new hyper chessboard to ensure the projective property. According to maximin distance criterion, new sequential samples are then generated through successive local enumeration iterations to improve the space-filling uniformity. A number of comparative studies are conducted to test the performance of S-SLE. Several appealing merits of S-SLE are demonstrated. i) S-SLE outperforms several existing LHD methods in terms of quality of sequential samples; ii) it is flexible and robust to produce high quality multiple-stages sequential samples; iii)The proposed method can improve the overall performance of sequential metamodel-based optimization algorithms. Final, S-SLE is successfully applied to solve an airfoil stealth optimization problem in order to demonstrate its effectiveness for aircraft design optimization problems using expensive simulations.