By Andras Sobester, Alexander I J Forrester
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Extra info for Aircraft Aerodynamic. Design Geometry and Optimization
S´obester). as they naturally admit the embedding of such rules, though most interactive geometry engines also have some features geared towards this type of design thinking. 2 Fuselage Cross-Section Optimization: An Illustrative Example Let us now test the flexibility of the formulations discussed above on a simple optimization problem. To enable the reader to experiment with variations on this design case study (for which the code is provided in the toolkit accompanying this book) we shall use an objective function that is based simply on geometrical calculations, and it is thus very quick to compute.
Local search methods may still be deployed at this stage, but they require multiple restarts from a range of starting geometries. These starting geometries should fill the design space relatively uniformly, increasing the probability that we exploit the neighbourhoods of all radically different designs. If the cost of computing the objective function is relatively low and the number of design variables is high, evolutionary optimization methods can make very efficient global optimizers. A large range of such methods is available, all sharing the fundamental philosophy of imitating the mechanics of natural evolution.
The Pareto front of this cloud of points (coloured according to the camber of the aerofoils) is the top-left boundary, as we are aiming to maximize thickness and minimize cd . The Pareto optimal, or non-dominated subset of this large set of designs is highlighted by black circles. This set is selected such that any other selection that would lead to an improvement against one objective, would lead to a deterioration against another. The designs highlighted with black circles (we have also plotted the corresponding aerofoil alongside some of them) are therefore all optimal in the Pareto sense and we need another objective or some design constraint to pick the final design.
Aircraft Aerodynamic. Design Geometry and Optimization by Andras Sobester, Alexander I J Forrester