European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate, J. Périaux (Eds) © TU Delft, The Netherlands, 2006
MOO Methods for Multidisciplinary Design Using Parallel Evolutionary
Algorithms, Game Theory and Hierarchical Topology: Theoretical, numerical
and practical aspects
“Summary Report of a 2006 VKI Course on Optimization and Multidisciplinary Design ; Applications to Aeronautics and Turbomachinery”
Name Luis F. Gonzalez1, J. Periaux2, Eric J. Whitney1 and K. Srinivas1 Organization 1
AMME, The University of Sydney, Sydney,
2 CIMNE/UPC, Barcelona, Country 1 Australia, 2 Spain
e-mails {gonzalez,eric,ragh}@aeromech.usyd.edu.au , jperiaux@gmail.com
Keywords
Optimisation, Multidisciplinary Design, Conceptual and Detailed Design,Pareto and Nash Equilibrium Objectives
Three lecture notes were presented at the VKI Course on Optimization and Multidisciplinary Design ; Applications to Aeronautics and Turbomachinery. The lectures:
• Described the needs, theory and developments on the application of evolutionary design methods in aeronautics.
• Described the use and implementation of a framework in which mathematical as well as engineering optimisation problems can be analysed. Highlighted some of the recent applications of multi-objective and multidisciplinary design optimisation in aeronautical design using the framework
Theory
The foundations of the framework and algorithms described -Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEAs) - lie upon traditional evolution strategies and incorporate the concepts of a multi-objective optimisation, hierarchical topology, asynchronous evaluation of candidate solutions and parallel computing. In a step by step approach, the implementation of EAs and HAPEAs for solving multi criteria optimisation problems is conducted providing the reader with the knowledge to reproduce these hand on training in academic or industrial environment of the designer.
Applications
Mathematical , inverse and direct optimisation test cases were presented. Mathematical Test Case:
TNK: A constrained problem that has five discontinuous Pareto optimal fronts. The problem has two variables and two constraints.
Results: The algorithnm successfully captures the four Pareto fronts Conceptual Design:
Aerofoil Reconstruction: Two Aerofoils at Two Different Design Points.
Results: This example showed how the algorithm captures the correct Pareto front and geometries for an inverse problem
Air Superiority Unmanned Combat Air Vehicle (UCAV), a Pareto - Nash Optimisation Comparison
Luis F. Gonzalez, Jacques. Periaux, E.J. Whitney and K. Srinivas
Detailed Design
Two Dimensional Two Objective Aircraft High Lift System Design and Optimisation
Results: This example showed how the algorithm captures the correct Pareto front and geometries for an inverse problem
Two Objective UAV Aerofoil Section Optimisation ,
Results: The results obtained show the capabilities of the method to find optimal solutions and classical aerodynamic shapes for low drag.. The requirement of constraining the pitching moment during the evolution process is necessary to avoid obtaining an aerofoil with lower drag for some flight conditions but with undesirable pitching moment characteristics.
Pareto Front TNK Target and computed pressure distribution for multi-point aerofoil design.
Pareto front and Nash Equilibrium obtained for UCAV.
Pareto set planform shapes.
UCAV Wing Aerofoil Section/Planform Design Optimisation
A three objective problem where the main objectives are to maximise lift to drag ratio at two flight conditions and minimise frontal area.
Results: The results obtained show the capabilities of the method to find optimal solutions in three-dimensions, produce aerodynamic shapes with very good performance, a high lift-to-drag ratio and small frontal area.
Conclusion
