Design of Experiments - A- D- I- S-optimality
2010 (English)In: Proceedings of the 2nd International Conference on Engineering Optimization, 2010Conference paper (Refereed)
A metamodel approximates an original model with a model that is more efficient and yields information about the response. Response surfaces and Kriging approximations are such metamodels. A metamodel is based on evaluations of the original function at some design points, where the choice of design points is crucial. The design points constitute the design of experiments (DoE). There are many methodologies of how to chose the DoE. In this work A-, D-, I- and S-optimal DoEs are generated and evaluated. The optimal DoEs are obtained by solving the following mathematical optimization problems:
- A-otimality. Minimize the average variance of the model coefficient estimates.
- D-otimality. Minimize the generalized variance of the model coefficient estimates.
- I-otimality. Minimize the average of the expected variance (taken as an integral)over the region of prediction.
- S-otimality. Maximize the geometric mean of the distances between nearest neighborsof the design points.
The optimization problems are solved by a hybrid method which consists of a genetic algorithm and sequential linear programming. The different optimality criteria are evaluated for a number of test cases in order to show the characteristics of each criteria. Regular as well as non-regular design spaces are considered. Furthermore, Kriging approximations of the well known Rosenbrock’s banana function are generated to evaluate the accuracy of a resulting metamodel based on the different DoEs. Results from the test cases show that D-optimal DoEs tend to place more design points close to the boundary of the design space compared to A- and I-optimality. It is also shown that A- D- and I-optimal DoEs often include duplicate design points which is not beneficial for a deterministic response, but might be beneficial for non-deterministic responses. Concerning S-optimal DoEs the design points are evenly distributed over the entire design space and no duplicates occur. Furthermore, the S-optimal DoE generates the best fitted Kriging approximation of the Rosenbrock’s banana function.
Place, publisher, year, edition, pages
A- D- I- S-optimality, Design of experiments (DoE), Response surface, Kriging, Genetic algorithm, Sequential linear programming
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-72346OAI: oai:DiVA.org:liu-72346DiVA: diva2:459262
2nd International Conference on Engineering Optimization. September 6 - 9, Lisbon, Portugal