Sub-design Selection For Orthogonal Latin Hypercube Design

The research on experimental design is getting deeper and deeper with the development of industrial and agricultural production,the progress of the medical and health industry,and the analysis of massive information data.With the further improvement of computer technology,computer experiments are also booming.Computer experiments are more used to study complex systems than traditional experimental designs.For computer experiments,the general design approach is to find design points to fill the design area as evenly as possible.Representative designs include the Latin hypercube design and its improved design.However,the randomly generated Latin hypercubes are designed in many ways.The two criteria commonly used to select such designs are the orthogonality criterion and the distance criterion.Given an orthogonal Latin hypercube design,its sub-designs are also column-orthogonal,but sub-designs of different choices may vary greatly under distance criteria.This paper studies how to select the sub-design of orthogonal Latin hypercube design under the distance criterion.First,in the case of deleting one column and two columns,we get some conclusions and suggestions.Then,when the number of deleted columns is large,we select the optimal sub-design under the maximin distance criteria based on the improved PSO algorithm.Finally,we study the effectiveness of the proposed method through numerical simulation.The simulation found that the proposed design has a smaller prediction error,which illustrates the rationality of using the PSO algorithm to select the optimal sub-design of the orthogonal Latin hypercube design.