A procedure for generating a customized weight function for wing bending material weight of the High Speed Civil Transport (HSCT) is described. The weight function is based on the shape parameters. A response surface methodology is used to t a quadratic polynomial to data gathered from a large number of structural optimizations. The results of the structural optimization are noisy. Noise reduction in the structural optimization results is discussed. Several techniques are used to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to nd regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT, while the response surfaces themselves are created employing detailed analysis methods. Intervening variables and analysis of variance are used to reduce the number of polynomial terms in the response surface model functions. Minimum variance and minimum bias procedures for creation of response surfaces are compared. Con guration optimization of the HSCT employing customized weight functions with di erent response surfaces are compared.

A method has been developed to efficiently implement supersonic aerodynamic predictions from Euler solutions into a highly constrained, muItidisciplinary design optimization of a High-Speed Civil Transport. The method alleviates the large computational burden associated with performing computational fluid dynamics analyses through the use of variable-complexity modeling techniques, response surface (RS) methodologies, and coarse-grained parallel computing. Using information gained from lower-fidelity aerodynamic models, reduced-term RS models representing a correction to the linear theory RS model predictions are constructed using Euler solutions. Studies into 5-, 10-, 15-, and 20-variable design problems show that accurate results can be obtained with the reduced-term models at a fraction of the cost of creating the full-term quadratic RS models. Specifically, a savings of 255 CPU hours out of 392 CPU hours required to create the full-term RS model is obtained for the 20-variable problem on a single 75-MHz IP21 processor of a Silicon Graphics, Inc. Power Challenge. Nomenclaturec jk -response surface model coefficients g(x) = vector of optimization constraint values K = drag polar shape parameter m = number of design variables N = number of points used to evaluate response surface model error n = number of terms in the response surface model n p -number of processors used on a parallel computer Design Center for Advanced Vehicles. p = number of experimental design points q = number of candidate sample sites R LE = leading-edge radius parameter ffus, = fuselage radius at /th axial location 5 LE/ = inboard leading-edge length s TEj = inboard trailing-edge length (//c)break = thickness-to-chord ratio at leading-edge break (tlc\ ool = thickness-to-chord ratio at wing root 0/c) tip = thickness-to-chord ratio at wing tip WC-TOGW = corrected takeoff gross weight Wfue, = fuel weight WTOGW = takeoff gross weight Wwing = wing weight x = ra-dimensional vector of design variable values (*/c)max-r = chordwise location of maximum thickness Xj = jth design variable *max = vector of upper bounds on design variable values *min = vector of lower bounds on design variable values v = observed response value y = predicted response value Vnac = spanwise location of inboard nacelle AC Do = correction to linear theory value of the drag polar shape parameter A^f = correction to linear theory value of the drag polar shape parameter AW^i = correction to fuel weight A;y nac = distance between nacelles A LE/ = inboard leading-edge sweep angle ALE O = outboard leading-edge sweep angle A T E 7 = inboard trailing-edge sweep angle

A method has been developed to efficiently implement supersonic aerodynamic predictions from Euler solutions into a highly constrained, multidisciplinary design optimization of a High-Speed Civil Transport (HSCT) configuration. The method alleviates the large computational burden associated with performing CFD analyses and eliminates the numerical noise present in the analyses through the use of response surface (RS) methodologies, a variation of the variable-complexity modeling (VCM) technique, and coarse grained parallel computing. Variablecomplexity modeling techniques allow one to take advantage of information gained from inexpensive lower fidelity models while maintaining the accuracy of the more expensive high fidelity methods. In this research, simple conceptual level aerodynamic models provide the functional form of the drag polar. Response surface models are therefore created for the intervening functions (drag polar shape parameters) revealed by the simple models instead of for the drag itself. Optimization results using linear theory RS models are used to select the allowable ranges of the design variables. Stepwise regression analysis, performed using data from linear theory aerodynamic results, provides information on the relative importance of each term in the polynomial RS models. With this information, reduced term RS models representing a correction to the linear theory RS model predictions are constructed using fewer Euler evaluations. Studies into five, ten, fifteen, and

The applied aerodynamics community is struggling to develop a means of incorporating computational fluid dynamics (CFD) into the early stages of aircraft systems design, where it can have the greatest impact on vehicle design. This paper describes developments in computational design methodology arising from research into multidisciplinary design optimization (MDO) done recently by the authors that addresses this problem. The premise is that advanced CFD should be used to precompute a database of solutions which is then interpolated during the design process. Design of experiments theory is used to select the "conditions" or "design points" used to populate the database, and statistical methods are then used to develop a mathematical model of the CFD solutions which is used to "interpolate" the database. The specific models we use, called "response surface models" are quadratic least squares fits to functions of the CFD results. Populating the database is made possible through the use of coarse grained parallel computing. We demonstrate the method using a recent example from our MDO work.

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