Anthony A. Giunta
PhD Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Aerospace and Ocean Engineering
May 1, 1997
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.
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