A modern evolutionary technique for design and optimisation in aeronautics

Abstract

This thesis presents a modern evolutionary technique for design and optimisation in aeronautics, with particular focus on aerodynamics. The purpose for developing a contemporary algorithm for this purpose is the difficult design and optimisation environment in which practicing engineers are forced to work. Most aerodynamic optimisation problems are multimodal, meaning they have many separate solutions which would satisfy by a conventional optimiser. Often the flowfield solvers used to compute these solutions are proprietary, calibrated and difficult to modify, unlike the situation that prevails in a research institu— tion, and so they must be treated as black boxes. The results returned by these solvers are subject to roundoff error and uncertainty. Generally a number of different types of solver are available for the same problem, modeling different physical laws and providing differing levels of fidelity. Modern aerodynamic design also increasingly requires the consideration of a number of separate design ob jectives, such as weight, performance, cost and emissions.

Responding to this requirement, a single evolutionary algorithm is developed that has the capacity to successfully solve problems of this type. Evolutionary methods are known for their capacity to be robust to noise, handle multiple local minima, and be easily implemented on parallel computers. We use the Evolution Strategy (ES) as a starting point, and extensions to improve the efficiency, robustness and applicability of the algorithm are developed. Asyn— chronous function evaluation is introduced to allow the solution of problems on a cheap parallel computer composed of a heterogeneous cluster of desktop computers. In addition, this allows the more efficient use of solvers which take a varying time to execute, a feature typical of Computational Fluid Dynamics (CFD) methods. Hierarchical populations are used to accelerate the solution process, by allowing the use of many types of solver simultaneously. These can include solvers that solve different physical models (such as the Euler and Navier—Stokes equations) as well as solvers of varying fidelity (the case with multiple mesh densities). A mechanism for using popular mutation methods from both Evolution Strategies and Genetic Algorithms is given, showing that the efficiency of the first and the robustness of the second can be combined into a single algorithm. We then give a technique for handling multiobjective problems in an identical manner to single objective problems, which requires no additional parameters and as its result gives a complete and evenly distributed set of compromise solutions between the given problem objectives. We then test the performance of the algorithm on a number of purely mathematical test functions, to determine expected performance levels. These functions are unimodal and multimodal as well as single and multiobjective. In the single objective case, we measure the performance of the algorithm with varying numbers of problem unknowns, on non—symmetric cases, with the addition of noise, and the intentional mis-scaling and rotation of problem axes. In two ob— jectives we examine the convergence of the algorithm to a discontinuous solution as well as a deceptive problem.

Practical cases that are representative of preliminary design in aerodynamics are then presented. These include a one dimensional internal flow case with inverse optimisation of one prescribed Mach number distribution, a two dimen— sional internal flow case with inverse optimisation of two prescribed pressure distributions, two cases of subsonic aerofoil design for an Unmanned Aerial Vehicle (UAV) with two objectives, and finally a transonic aerofoil design for a transport category aircraft with two objectives.

Finally, a conclusion is given that summaries the results obtained, and gives direction for possible topics of future research.