Convergence diiculties were encountered in our recent eeorts toward a combined aerodynamic-structural optimization of the High Speed Civil Transport (HS-CT). The underlying causes of the convergence problems were traced to numerical noise in the calculation of aerodynamic drag components for the aircraft. Two techniques were developed to circumvent the obstacles to convergence. The rst technique employed a sequential approximate optimization method which used large initial move limits on the design variables. This helped dislodge the optimizer out of the local minima in the design space created by the noisy drag data. The second method utilized response surface methods to construct smooth approximations to the noisy data. The response surfaces were formed by analyzing several individual HSCT conngurations and then tting polynomial functions to selected objective function data. A simpliied example design problem was used to demonstrate the response surface technique and to investigate various other issues relating to the construction of the response surfaces.

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.

A design methodology which uses a variable-complexity modeling approach in conjunction with response surface approximation methods has successfully been developed. This approach uses simple models to improve the accuracy of the response surface and reduce the number of analyses based on complex models required for constructing the surface. Simple models are rst used to eliminate \nonsense" portions of the design space. Then a response surface based on the simple models is used to reduce the number of unknown coeecients that deene the response surface. This approach 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.

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.

Convergence difficulties were encountered in our recent efforts towards a combined aerodynamic-structural optimization of the High Speed Civil Transport (HSCT). The underlying causes of the convergence problems were traced to numerical noise in the calculation of aerodynamic drag components for obstacles to convergence. The first technique employed a sequential approximation optimization method which used large initial move limits on the design variables. This helped dislodge the optimizer out of the local minima in the design space created by the noisy drag data. The second method utilized the aircraft. Two techniques were developed to circumvent the response surface methods to construct smooth approximations to the noisy data. The response surfaces were formed by analyzing several individual HSCT configuration and then fitting polynomial functions to selected objective function data. A simplified example design problem was used to demonstrate the response surface technique and to investigate various other issues relating to the construction of the response surfaces.

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities which closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the presence of the shock in the discretized flow field. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. These t...