Variable-complexity response surface approximations for wing structural weight in HSCT design

Abstract

VARIABLE-COMPLEXITY RESPONSE SURFACE APPROXIMATIONS FOR WING STRUCTURAL WEIGHT IN HSCT DESIGN by Matthew Douglas Kaufman Committee Chairs: Bernard Grossman and Raphael T. Haftka Aerospace Engineering (Abstract) A procedure for generating and using a polynomial approximation to wing bending material weight of a High Speed Civil Transport (HSCT) is presented. Response surface methodology is used to fit a quadratic polynomial to data gathered from a series of structural optimizations. Several techniques are employed in order to minimize the number of required structural optimizations and to maintain accuracy. First, another weight function based on statistical data is used to identify a suitable model function for the response surface. In a similar manner, geometric and loading parameters that are likely to appear in the response surface model are also identified. Next, rudimentary analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur. The use of intervening variables along with analysis of variance reduce the number of polynomial terms in the response surface model function. Structural optimization is then performed by the program GENESIS on a 28-node Intel Paragon. Finally, optimizations of the HSCT are completed both with and without the response surface. ii Acknowledgements

Comparative studies of metamodeling techniques under multiple modeling criteria

“…The second order polynomial models have k = (n+1)(n+2)/2 coefficients for n design variables. Giunta, et al (1994) and Kaufman, et al (1996) found that 1.5k sample points for 5-10 variable problems to 4.5k sample points for 20-30 variable problems are necessary to obtain reasonably accurate second-order polynomial models. Therefore, for large-scale problems, 3k sample points are selected and are referred to as a large sample set.…”

Probability Collectives using Response Surface estimation

“…10. These coefficients are trained using the method of least squares [9]. That is to say, to construct a RS for input variables of N, at least N c samples should be attained and evaluated.…”

“…However, when applying RS to some practical problems, the problem of curse of dimensionality emerges [9]. That is, to maintain good accuracy of approximation, one needs to minimize estimations beyond the domain where analyses were performed.…”

A variable‐fidelity aerodynamic model using proper orthogonal decomposition

“…Another strategy presented by Kaufmann et al . entails the use of low‐fidelity models to reduce the region in the design space, and once this is reduced, a high‐fidelity response surface is constructed over this reduced space.…”