Anthony A. Giunta

Variable-Complexity Response Surface Approximations for Wing Structural Weight in HSCT Design

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, simple 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.

Response surface models combining linear and Euler aerodynamics for supersonic transport design

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 75MHz IP21 processor of a Silicon Graphics, Inc. Power Challenge.

A Coarse-Grained Parallel Variable-Complexity Multidisciplinary Optimization Paradigm

Modem aerospace vehicle design requires the interac tion of multiple disciplines, traditionally processed in a sequential order. Multidisciplinary optimization (MDO), a formal methodology for the integration of these disci plines, is evolving toward methods capable of replacing the traditional sequential methodology of aerospace vehi cle design by concurrent algorithms, with both an overall gain in product performance and a decrease in design time. A parallel MDO paradigm using variable-complexity modeling and multipoint response surface approxima tions is presented here for the particular instance of the design of a high-speed civil transport (HSCT). This para digm interleaves the disciplines at one level of complexity and processes them hierarchically at another level of complexity, achieving parallelism within disciplines rather than across disciplines. A master-slave paradigm manages a coarse-grained parallelism of the analysis and optimization codes required by the disciplines showing reasonable speedups and efficiencies on an Intel Paragon.

Dependence of optimal structural weight on aerodynamic shape for a High Speed Civil Transport

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. Connguration optimization of the HSCT employing customized weight functions with diierent response surfaces are compared.

Variable-complexity response surface aerodynamic design of an HSCT wing

A design methodology which uses a variable-complexity modeling approach in conjunction with response surface approximation methods has successfully been developed. This technique is applied to an example problem of wing design for a High Speed Civil Transport (HSCT) aircraft involving a subset of four HSCT wing design variables. The wing design methodology is applied using a simple algebraic model for the wing weight. The applicability of the methodology for the multidisciplinary design of an HSCT is discussed.

HSCT configuration design using response surface approximations of supersonic Euler aerodynamics

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 ∗Graduate Research Assistant, Dept. of Aerospace and Ocean Engineering. Current Position: Postdoctoral Research Associate, Dept. of Aeronautics and Astronautics, University of Washington, Seattle, WA, Member AIAA. †Postdoctoral Research Associate, National Research Council/NASA Langley Research Center, Hampton, VA, Member AIAA. ‡Graduate Research Assistant, Dept. of Aerospace and Ocean Engineering, Student Member AIAA. §Professor and Dept. Head of Aerospace and Ocean Engineering, Associate Fellow AIAA. ¶Professor of Aerospace and Ocean Engineering, Associate Fellow AIAA. ‖Professor of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL, Fellow AIAA ∗∗Professor of Computer Science and Mathematics twenty variable HSCT 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, 11 hour, 47 hour, 115 hour, and 255 hour savings in CPU time on a single 75 MHz IP21 processor of a SGI Power Challenge are obtained for the five, ten, fifteen, and twenty variable design problems, respectively. Errors in the RS model cruise drag predictions, based on actual Euler calculations, for the optimal designs range from 0.1 counts to 0.8 counts for the twenty variable optimum.

Variable-Complexity Multidisciplinary Design Optimization Using Parallel Computers

The use of multidisciplinary optimization techniques in aerospace vehicle design often is limited because of the significant computational expense incurred in the analysis of the vehicle and its many systems. In response to this difficulty, a variable-complexity modeling approach, involving the use of refined and computationally expensive models together with simple and computationally inexpensive models has been developed [1]. This variable-complexity technique has been previously applied to the combined aerodynamic-structural optimization of subsonic transport aircraft wings and the aerodynamic-structural optimization of the High Speed Civil Transport (HSCT) [2]–[4].

Developing customized weight function by structural optimization on parallel computers

A procedure for generating a customized weight function for wing bending material weight of the High Speed Civil Transport (HSCT) is described. Response surface methodology is used to fit a quadratic polynomial to data gathered from a large number of structural optimizations. Coarsegrained parallelization of structural optimization is achieved by a master-slave processor arrangement on an Intel Paragon computer. Noisy behavior of the structural optimization results is discussed, and it is shown that the response surface filters out this noise. Several techniques are employed in order to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT. Intervening variables and analysis of variance are employed to reduce the number of polynomial terms in the response surface model function. Overall optimizations of the HSCT are compared to optimizations with a more general weight function.

Parallel multipoint variable-complexity approximations for multidisciplinary optimization

The design of modern aerospace vehicles involves multidisciplinary interactions and presents a formidable challenge to the designer in a competitive marketplace. Multidisciplinary optimization technology is a major tool for addressing this need, but its current use in the design process is limited by its enormous computational burden. Even refined models for recent applications such as the High Speed Civil Transport fall short of the level of complexity required for realistic designs. The goal of the research is to apply the power of emerging parallel computation systems to permit a level of model refinement that would produce realistic designs. We propose a new variable-complexity approximation strategy that will take maximum advantage of parallel computation capabilities.<<ETX>>