Response Surface Models Combining Linear and Euler Aerodynamics for Supersonic Transport Design

Abstract

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

Optimization using surrogate models and partially converged computational fluid dynamics simulations

“…Mason et al (1998) present a review of work on the conceptual design of a high speed civil transport (HSCT) aircraft, in which DoE, variable complexity analysis using the 'reasonable design space' approach (Balabanov et al 1999), and polynomial response surface modelling are used to incorporate high-fidelity analysis into conceptual design. Knill et al (1999) make use of the same HSCT problem to investigate using a low-fidelity model to decrease the number of terms used to build a polynomial RSM and so reduce the number of high-fidelity simulations required. The University of Southampton multi-level wing design environment (Keane & Petruzzelli 2000) attempts to combine the merits of varying fidelity computer models in the conceptual design of a commercial airliner wing.…”

Sampling strategies for mining in data-scarce domains

“…This fundamentally differs from DACE (Design and Analysis of Computer Experiments), 12 polynomial response surface approximations, 13 and other approaches in geostatistics where the goal is accuracy of functional prediction at untested data points. Here, we trade accuracy of estimation for the ability to mine pockets.…”

Control System Optimization Design and Simulation for BBT Missile Based on Kriging Meta-model

“…The Latin Hypercube design which is based on random numbers is adopted. Many different surrogate models, including polynomial response model [4][5], radial basis function [6,7], and Kriging model [8][9][10], have been widely used in engineering applications. In this paper, Kriging model is adopted, which is an unbiased estimation model based on least estimation of variance and fits with the original model better in the whole design space.…”