Error-based Design Space Windowing

ERROR-BASED DESIGN SPACE WINDOWINGMelih Papila" (papila@aero.ufl.edu) Nilay U. Papila" (nilay@aero.ufl.edu)Wei Shyy _ (_,_wss_aero.ufl.edu) Raphael T. Haftka * (haftka@ufl.cdt_)Norman Fitz-Coy § (nfc@aero.ufl.edu)Department of Aerospace Engineering, Mechanics & Engineering ScienceUniversity of Florida, Gainesville, FL 32611ABSTRACTWindowing of design space is considered in order toreduce the bias errors due to low-order polynomialresponse surfaces (RS). Standard design space windowing(DSW) uses a region of interest by setting a requirement onresponse level and checks it by a global RS predictionsover the design space. This approach, however, isvulnerable since RS modeling errors may lead to the wrongregion to zoom on. The approach is modified byintroducing an eigenvalue error measure based on point-to-point mean squared error criterion. Two examples arepresented to demonstrate the benefit of the error-basedDSW.1. INTRODUCTIONThe popularity of response surface (RS) techniques indesign optimization studies has brought attention to waysof increasing the accuracy of RS approximations.Adequacy and accuracy of RS are mainly affected by thefollowing three factors:• Use of finite number of data points due to cost ofdata generation• Noise in the data• Inadequacy of the fitting modelWe are mainly focused in this paper on modelinadequacy or bias error due to use of low-orderpolynomials such as quadratic RS.An obvious way for reducing bias error is to use higherorder polynomials or more complex functions in RS.Cubic or even higher order polynomials were applied, forinstance, by Venter et al. [1] and by Papila (N) et al. [2].