Sensitivity-based Multi-Fidelity Multidisciplinary Design Optimization with Illustrative Applications to Aircraft Design

Abstract

Efficient optimization algorithms are required to reduce the computational costs of Multidisciplinary Design Optimization (MDO), motivating the use of gradient-based algorithms. Gradient-based algorithms can efficiently find the nearest local optimum, provided that the computation of the required gradients itself is efficient. They are known to be more efficient than gradient-free algorithms and can deal with constraints, given that their gradients are obtainable. In gradient-based aero-structural optimization, the gradients of all objectives and constraints with respect to all design parameters are required throughout the optimization, as well as the gradients of the computational mesh with respect to the design parameters and the gradients that may need to be considered when the aircraft is to be trimmed for straight-and-level flight. If the gradients are not accurate, then theoretically the design can move closer to the optimum but most probably not reach it. Also, the optimization will be slower and will stall before obtaining the optimal design. The use of inaccurate gradients can give us the impression that we are stuck at a local optimum. In this lecture we first discuss how the gradients of the computational mesh with respect to the design parameters, i.e. the shape sensitivities, can efficiently be computed when a computer aided design (CAD) tool that is not differentiated is used to model the aircraft geometry by differentiating a reduced order model of a parametric CAD model of the aircraft geometry. Then, we discuss the effect of approximating the gradients of the objective function and constraints in gradient-based aero-structural optimization of a simplified aircraft configuration by comparing an optimization driven by approximate gradients to others driven by a full set of gradients, once for a complete set of constraints and once for an aggregated set of constraints. This will not only help understanding the cross disciplinary effects, but also shows the impact of approximation on the computational cost. Thereafter, we discuss the implications in terms of sensitivities of performing gradient-based aero-structural optimization of a realistic full aircraft configuration for its trimmed state. Finally, we briefly introduce a novel approach to dealing with complexity in collaborative MDO, called the Cybermatrix, which is a highly-parallel approach capable of dealing with many disciplines, and relate it to the trimming problem.