This work discusses an approach, rst-order approximationand model management optimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower-delity, cheaper models in iterative procedures with occasional, but systematic, recourse to higherdelity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is that it is globally convergent to a solution of the original, high-delity problem. Variants of AMMO based on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing optimization problem and a two-dimensionalairfoil optimizationproblem. Euler analysison meshes of varying degrees of re nement provides a suite of variable-delity models. Preliminary results indicate threefold savings in terms of high-delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem. Nomenclature C D = drag coef cient C L = lift coef cient C l = rolling moment coef cient C M = pitching moment coef cient c E = equality constraints c I = inequality constraints f = objective function M 1 = freestream Mach number S = semispan wing planform area x; x L ; x U = design variables and bounds ® = angle of attack 1 = trust-region radius

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a first-and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first-and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving firstorder sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

With the recent interest in novel control effectors there is a need to determine the stability and control derivatives of new aircraft configurations early in the design process. These derivatives are central to most control law design methods and would allow the determination of closed-loop control performance of the vehicle. Early determination of the static and dynamic behavior of an aircraft may permit significant improvement in configuration weight, cost, stealth, and performance through multidisciplinary design. The classical method of determining static stability and control derivatives-constructing and testing wind tunnel models-is expensive and requires a long lead time for the resultant data. Wind tunnel tests are also limited to the preselected control effectors of the model. To overcome these shortcomings, computational fluid

This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow sol\-er to compute deri\-ati\-es. These preliminary results with this augmented code suggest that: e\-en in its infancy: tlie automated adjoint code generator can accurately and efficiently deli\-er deri\-ati\-es for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design \-ariables.

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