Development of an augmented centroidal Voronoi tessellation for utilization of scattered data

Abstract

DOE (Design of Experiment) is a way to plan how to conduct an experiment for a certain problem to be solved, how to collect and statistically analyze data to the full with the min. number of experiments. DOE may be divided to conventional DOE for actual experiments and space-filling DOE for computer-based experiments. In the area of design, computer-based experiments are drawing more attention than typical experiments. Outstanding examples of computer-based DOE include Centroidal Voronoi Tessellations (CVT), Latin Hypercube Designs (LHD), Optimal Latin Hypercube Designs (OLHD), Quasi-random sequences, etc. Although such types of DOE do not present the optimum, they are advantageous in that the designer can provide an appropriate design improvement within a limited time and thus are used commonly in industry. In the actual field of that industrial sector, however, the initial experiment plans are not likely to be considered. Rather, various interpretations throughout the empirical designing of users based on their know-how are applied. Actual experimental results or function interpretation results take a lot of time and cost a tremendous amount of money. Such precious data is not properly utilized but merely disposed among most business entities. Accordingly, this study is to develop DOE of high performance with the aim to produce useful design results based on collected data. Existing DOEs that utilize data sets that are scattered about include Augmented Latin Hypercube Design (ALHD), Augmented Maximin Sampling (AMS), etc. ALHD and AMS require global optimization and thus need a lot of time and expense while it is difficult to find out the global optimum. Hence, this study suggests DOE that overcomes such disadvantages. First of all, among computer-based DOEs, CVT was founded to be DOE of the best spatial space-filling properties, and thus Augmented Centroidal Voronoi Tessellations (ACVT) was developed to utilize existing data sets scattered about on the basis of CVT. The method suggested in this study was compared with other existing methods in terms of space-filling properties and based on the design variables and change in NEXP (Number of EXperimental Points). As a result, it has been verified that the method suggested in this study has superior space-filling properties than existing DOEs. In addition, although the suggested method was developed based on computer-based experiments, it is expected that this can be utilized both in computer-based and actual experiments.