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An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
2009 (English)In: Reliability Engineering and System Safety, ISSN 0951-8320, Vol. 94, no 7, 1173-1182 p.Article in journal (Other academic) Published
Abstract [en]

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.
Keyword [en]
Computer experiments, emulator, exeperimental design, response surface, interpolation
National Category
Computer Science
Identifiers
URN: urn:nbn:se:liu:diva-17111DOI: 10.1016/j.ress.2008.10.013OAI: oai:DiVA.org:liu-17111DiVA: diva2:201974
Available from: 2009-03-06 Created: 2009-03-06 Last updated: 2009-06-08Bibliographically approved
In thesis
1. Computer Experiments Designed to Explore and Approximate Complex Deterministic Models
Open this publication in new window or tab >>Computer Experiments Designed to Explore and Approximate Complex Deterministic Models
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Computer experiments are widely used to investigate how technical, economic, and ecological systems respond to changes in inputs or driving forces. This thesis is focused on design of computer experiments that can help us better understand the output from complex computer code models. The major part of our work was devoted to experiments involving derivation and application of computationally cheaper surrogate models of a given computer code model. We developed an adaptive sequential design algorithm that efficiently reveals nonlinearities in the model output, and we integrated this algorithm with methods for predicting model outputs at untried inputs. Compared to the methods currently in use, our sequential design has the advantage of not requiring any prior information about the response of the investigated model output to changes in the inputs. Of special interest, we found that our algorithm works satisfactorily even if the curvature of the response surface varies strongly over the input domain. Variance-based sensitivity analysis is a well-established technique to elucidate model outputs, but it can become prohibitively expensive to implement because it requires numerous model runs. Surrogate models can facilitate such analysis, and if our sequential design algorithm is utilized, it can supply useful information about both linear and nonlinear responses to model inputs. Experiments involving repeated runs of a model of the flow of water and nitrogen through a river basin showed that our approach can be applied to extract the essence of complex deterministic models. In addition, our research showed that computationally inexpensive surrogate models offer an ideal basis for interactive decision support tools and learning processes, because they can provide almost immediate responses to user-defined model inputs.

Abstract [sv]

Datorexperiment används allmänt för att undersöka hur tekniska, ekonomiska och ekologiska system reagerar på förändringar i tillförsel eller drivkrafter. Denna avhandling är inriktad på datorexperiment som kan hjälpa oss att bättre förstå beräkningar baserade på komplicerade numeriska modeller som bara är definierade av en datorkod. Huvuddelen av vårt arbete ägnades åt experiment som innefattar härledning och tillämpning av beräkningsmässigt billiga s.k. surrogatmodeller som ger nästan samma resultat som ursprungsmodellen. Vi utvecklade en adaptiv sekventiell designalgoritm som effektivt avslöjar icke-linjära reaktioner på ändrad input till modellen, och vi integrerade denna algoritm med metoder för att prediktera modellens output för nya indata. Jämfört med de metoder som nu används har vår algoritm fördelen att den inte ställer några krav på förhandsinformation om modellens struktur. Speciellt noterade vi att den fungerar tillfredsställande även om olika delar av modellens responsyta har helt olika statistiska egenskaper. Varians-baserad känslighetsanalys är en väl etablerad teknik för att belysa modellers output, men den kan leda till höga datorkostnader eftersom den kräver många modellkörningar. Surrogatmodeller kan i sådana fall underlätta analysen. Om vår sekventiella designalgoritm utnyttjas, kan man desutom få viktig information om både linjära och icke-linjära effekter av förändringar i modellens indata. Experiment som innefattade upprepade körningar av en model för flödet av vatten och kväve genom ett avrinningsområde visade att man kan klarlägga det centrala i stora komplexa modeller. Dessutom visade vår forskning att beräkningsmässigt billiga surrogatmodeller erbjuder en idealisk grund för beslutstöd och lärandeprocesser, eftersom de kan ge en nästan omedelbar respons på de data som användaren matar in i modellen.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2008. 58 + papers 1-4 p.
Series
Linköping Studies in Arts and Science, ISSN 0282-9800 ; 423Linköping Studies in Statistics, ISSN 1651-1700 ; 9
National Category
Computer and Information Science
Identifiers
urn:nbn:se:liu:diva-17115 (URN)978-91-7393-976-8 (ISBN)
Public defence
2008-02-29, Alan Turing, hus E, Campus Valla, Linköpings universitet, Linköping, 13:00 (English)
Opponent
Supervisors
Available from: 2009-03-06 Created: 2009-03-06 Last updated: 2014-09-23Bibliographically approved

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Shahsavani, DavoodGrimvall, Anders

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