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Unformatted text preview: AIAA JOURNAL Vol. 38, No. 12, December 2000 Response Surface Approximations: Noise, Error Repair, and Modeling Errors Melih Papila and Raphael T. Haftka University of Florida, Gainesville, Florida 32611-6250 In the past few years there has been interest in using response surface techniques to create surrogates to computer simulations. Response surface techniques allow detection and correction of errors as well as ltering out numerical noise, but these techniques introduce additional modeling errors. Methods of reducing both noise and modeling errors are explored. It is also demonstratedthat repairing designs with large errors is preferable to eliminatingthese designs from consideration. Response surface approximationsfor a high-speed civil transport wing weight equation created from the results of a large number of structural optimizations are used for demonstration. It is shown that the statistical tools available for response surface techniques are effective for error detection and for ltering out noise. Once the noise is reduced, modeling errors can also be reduced by increasing the order of the approximation. I. Introduction R ESPONSE surface techniques are becoming important tools in design optimization based on noisy computational simula- tions. In multidisciplinary optimization, numerical noise is often a problem in addition to the dif culty of coupling simulations from different disciplines. Response surface (RS) techniques lter out numerical noise, provide a convenient representation of data from one discipline to another, and provide for easy interface with an optimizer. For example, in preliminary aircraft design, structural weight equations 1 are often used to representstructuralweight in con gura- tionoptimization.Such equationscanbe generatedby RS techniques when new aircraft concepts are not modeled well by traditional weight equations. Balabanov et al. 2 developed quadratic RS for wing-bendingmaterialweight W b (structuralweight neededto resist bending) for a high-speed civil transport (HSCT) aircraft as a func- tion of 29 con guration design variables. They constructed the ap- proximationbased on structuraloptimizationsfor thousandsof con- gurations to improve on the ight optimization system (FLOPS) 3 general weight equations for transport aircraft. Numerical noise is an importantissue in RS construction.Numer- ical experiments may be noisy for several reasons, including dis- cretization errors, incomplete convergence of iterative procedures, and roundoff errors. Giunta et al. 4 used RS approximations to l- ter out the noise in aerodynamic simulationsin design optimization for HSCT. They reported improvement in designs obtained based on the smooth response surface compared to the original noisy simulations. Balabanov et al....
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.
- Spring '08