投影均匀分片拉丁超立方体设计

空间填充设计是有效的计算机试验设计,比如均匀设计、最大最小距离拉丁超立方体设计等.虽然这些设计在整个试验空间中有较好的均匀性,但其低维投影均匀性可能并不理想.对于因子是定量的计算机试验,已有文献构造了诸如最大投影设计、均匀投影设计等相适应的设计;而对于同时含有定性因子和定量因子的计算机试验,尚未有投影均匀设计的相关文献.文章提出了综合投影均匀准则,利用门限接受算法构造了投影均匀的分片拉丁超立方体设计.在新构造设计中,整体设计与每一片设计均具有良好的投影均匀性.模拟结果显示,与随机分片拉丁超立方体设计相比,利用新构造设计进行试验而拟合的高斯过程模型具有更小的均方根预测误差.

Uniform Projection Sliced Latin Hypercube Designs

Space-filling designs are efficient computer experimental designs,such as uniform designs,maximin distance Latin hypercube designs,and so on.Although these designs have good uniformity in the entire experimental space,the low-dimensional projection properties may be unsatisfying.For computer experiments with only quantitative factors,there has been literature constructing appropriate designs,for example,maximum projection designs,and uniform projection designs.However,for computer experiments with both quantitative and qualitative factors,there has been no literature studying projection unform designs.In this paper,we propose a combined projection uniformity criterion,and construct uniform projection sliced Latin hypercube designs using threshold accepting algorithm.In the new obtained designs,not only the whole designs but also the slices have good uniform projection properties.The simulated example shows that the new designs have smaller root mean squared prediction error when fitting Gaussian process models,compared with random sliced Latin hypercube designs.