Aircraft Multidisciplinary Design Optimization using Design of Experiments Theory and Response Surface Modeling Methods

Design engineers often employ numerical optimization

techniques to assist in the evaluation and comparison of new

aircraft configurations. While the use of numerical

optimization methods is largely successful, the presence of

numerical noise in realistic engineering optimization problems

often inhibits the use of many gradient-based optimization

techniques. Numerical noise causes inaccurate gradient

calculations which in turn slows or prevents convergence

during optimization. The problems created by numerical

noise are particularly acute in aircraft design applications

where a single aerodynamic or structural analysis of a

realistic aircraft configuration may require tens of CPU

hours on a supercomputer. The computational expense of

the analyses coupled with the convergence difficulties

created by numerical noise are significant obstacles to

performing aircraft multidisciplinary design optimization. To

address these issues, a procedure has been developed to

create two types of noise-free mathematical models for use

in aircraft optimization studies. These two methods use

elements of statistical analysis and the overall procedure for

using the methods is made computationally affordable by the

application of parallel computing techniques. The first

modeling method, which has been the primary focus of this

work, employs classical statistical techniques in response

surface modeling and least squares surface fitting to yield

polynomial approximation models. The second method, in

which only a preliminary investigation has been performed,

uses Bayesian statistics and an adaptation of the Kriging

process in Geostatistics to create exponential

function-based interpolating models. The particular

application of this research involves modeling the subsonic

and supersonic aerodynamic performance of high-speed

civil transport (HSCT) aircraft configurations. The

aerodynamic models created using the two methods outlined

above are employed in HSCT optimization studies so that

the detrimental effects of numerical noise are reduced or

eliminated during optimization. Results from sample HSCT

optimization studies involving five and ten variables are

presented here to demonstrate the utility of the two

modeling methods.