Quasi-LHD sequential sampling method for computer experiments

Space-filling and projective properties are desired features in design of computer experiments to create global metamodels to replace of expensive computer simulations in engineering design. Our goal in this paper is to develop an efficient and effective sequential Quasi-LHD (Latin Hypercube Design) sampling method to maintain and balance the two aforementioned properties. The sequential sampling is formulated as an optimization problem, with the objective being the Maximin distance, a space-filling criterion, and the constraints based on a set of pre-specified minimum one-dimensional distances to achieve the approximate one-dimensional projective (Quasi-LHD) property. Through comparative studies on sampling property and metamodel accuracy, the new approach is shown to outperform other sequential sampling methods for global metamodeling and is comparable to the one-stage sampling method while providing more flexibility in a sequential metamodeling procedure.