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papila-aaiaa-journal-2000

papila-aaiaa-journal-2000 - AIAA JOURNAL Vol 38 No 12...

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AIAA J OURNAL 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 yearsthere hasbeen interest in usingresponse 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 designswith largeerrors is preferable to eliminatingthese designsfrom consideration.Response surface approximationsfora high-speedcivil transportwing weight equation created from the results of a large number of structural optimizationsare 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, modelingerrors 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 computationalsimula- tions. In multidisciplinaryoptimization, 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 representationof 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 oftenusedto representstructuralweightin con gura- tionoptimization.SuchequationscanbegeneratedbyRS 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 (structuralweightneededto resist bending) for a high-speed civil transport(HSCT) aircraft as a func- tion of 29 con guration design variables. They constructedthe ap- proximationbased on structuraloptimizationsfor thousandsof con- gurations to improve on the ight optimization system (FLOPS) 3 general weight equations for transport aircraft. Numericalnoiseis an importantissuein 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 aerodynamicsimulationsin 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. 5 investigated the noisy behavior of wing-bending material weight of HSCT designs. They found that a large portion of the noise was due to incomplete optimization of the wing camber that affects the wing-bending material weight via the aerodynamicloads. Much of the remaining numerical noise was due to the structural optimization process itself. Venter and
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