An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models
2009 (English)In: Reliability Engineering and System Safety, ISSN 0951-8320, Vol. 94, no 7, 1173-1182 p.Article in journal (Other academic) Published
Response surface methodologies can reveal important features of complex computer code models and thereby provide a basis for developing user-friendly decision support tools. Here, we suggest experimental designs and interpolation methods for extracting nonlinear response surfaces whose nonlinearity or roughness varies substantially over the input domain. A sequential design algorithm for cuboid domains is initiated by selecting an extended corner/centre point design for the entire domain. Additional design points are then generated by decomposing this domain into disjoint cuboids and taking the corners and centre of these cuboids as new design points. A roughness criterion based on local polynomial approximation of the response surface is used to control the domain decomposition so that the design becomes space-filling and the coverage is particularly good in the parts of the input domain where the response surface is strongly nonlinear. Finally, the model output at untried inputs is predicted by carefully selecting a local neighbourhood of each new point in the input space and fitting a full quadratic polynomial to the data points in that neighbourhood. Test runs with different types of nonlinear response surfaces showed that our sequential design algorithm automatically adapts to the nonlinear features of the model output. Moreover, we found that our design and interpolation technique is particularly useful for extracting nonlinear response surfaces from computer code models with two to seven input variables. A simple modification of the outlined algorithm enables adequate handling of non-cuboid input domains.
Place, publisher, year, edition, pages
2009. Vol. 94, no 7, 1173-1182 p.
Computer experiments, emulator, exeperimental design, response surface, interpolation
IdentifiersURN: urn:nbn:se:liu:diva-17111DOI: 10.1016/j.ress.2008.10.013OAI: oai:DiVA.org:liu-17111DiVA: diva2:201974