1 University of Sydney E. J. Whitney L. F. Gonzalez K. Srinivas Dassault Aviation J. Périaux M. Sefrioui Multi-objective Evolution Design for UAV Aerodynamic Applications UAV-MMNT03 Sydney, Australia July 2003

2 Overview qEvolution Algorithms (EAs). qHierarchical Topology-Multiple Models. q Multi-Criteria Optimisation – Game Theory. qParallel Computing and Asynchronous Evaluation. qTest Case Applications: mUAV aerofoil design for transit and loiter. mUAV aerofoil design for transit and takeoff. mUCAV whole aircraft conceptual design.

3 The Problem… Problems in aerodynamic optimisation: qModern aerodynamic design uses CFD (Computational Fluid Dynamics) almost exclusively. qCFD has matured enough to use for preliminary design and optimisation. qMost aerodynamic design problems will need to be stated in multi- objective form. qThe internal workings of validated in-house solvers are essentially inaccessible from a modification point of view (they are black- boxes). qFitness functions of interest are generally multimodal with a number of local minima. Sometimes the optimum shape/s is not obvious to the designer. The fitness function will involve some numerical noise.

4 … The Solution We apply an Evolution Algorithm (EA): qEAs are able to explore large search spaces. qThey are robust towards noise and local minima. qThey are easy to parallelise, significantly reducing computation time. qEAs successively map multiple populations of points, alowing solution diversity. qThey are capable of finding a number of solutions in a Pareto set or calculating a robust Nash game.

5 “The Central Difficulty” Evolutionary techniques are … still … very … slow! (Often involving hundreds or thousands of separate flow computations) Therefore, we need to think about ways of speeding up the process…

Hierarchical Topology-Multiple Models Model 1 precise model Model 2 intermediate model Model 3 approximate model Exploration (large mutation span) Exploitation (small mutation span) q Interactions of the 3 layers: solutions go up and down the layers. q The best ones keep going up until they are completely refined. q No need for great precision during exploration. q Time-consuming solvers are used only for the most promising solutions. q Think of it as a kind of optimisation and population based multigrid.

7 Parallel Computing and Asynchronous Evaluation Evolution Algorithm Asynchromous Evaluator 1 individual Different Speeds

8 Asynchronous Evaluation qFitness functions are computed asynchronously. qOnly one candidate solution is generated at a time, and only one individual is incorporated at a time rather than an entire population at every generation as is traditional EAs. qSolutions can be generated and returned out of order. qNo need for synchronicity  no possible wait-time bottleneck. qNo need for the different processors to be of similar speed. qProcessors can be added or deleted dynamically during the execution. qThere is no practical upper limit on the number of processors we can use. qAll desktop computers in an organisation are fair game.

9 Multi-Criteria Problems qAeronautical design problems normally require a simultaneous optimisation of conflicting objectives and associated number of constraints. They occur when two or more objectives that cannot be combined rationally. For example: mDrag at two different values of lift. mDrag and thickness. mPitching moment and maximum lift.  Generation of a Pareto front allows the designer to choose after the optimisation phase; This allows selection amongst a wide range of potential solutions.

10 …..Multi--Criteria Optimisation A multi-criteria optimisation problem can be formulated as: Minimise: Subject to constraints: Using this concept, the objective of Pareto optimality is to find the non-dominated set of of optimum individuals (i.e. aerofoils, nozzles, wings) between a number of specified criteria.

11 Some More Examples Here our EA solves a two objective problem with two design variables. There are two possible Pareto optimal fronts; one obvious and concave, the other deceptive and convex.

12 Some More Examples (2) Again, we solve a two objective problem with two design variables however now the optimal Pareto front contains four discontinuous regions.

13 Nash Games A Nash optimisation can be viewed as a competitive game between two players that each greedily optimise their own objective at the expense of the other player. A Nash equilibrium is obtained when no player can improve his own objective at the expense of the other. Player 1 Player 2 Epoch Completed? Migrate and Exchange

14 Applications q Case One: Aerofoil design, drag minimisation for high- speed transit and loiter conditions. q Case Two: Aerofoil design, drag minimisation for high- speed transit and takeoff conditions. q Case Three: Whole aircraft conceptual design, gross weight minimisation and cruise efficiency maximisation. Now we present three UAV case studies. All have two objectives. These are:

15 Case One Problem Definition: qDual point design procedure is described here to find the Pareto set of aerofoils for minimum total drag at two design points. The flow conditions for the two points analyzed are: TransitLoiter Mach Reynolds14.0 x x 10 6 cl

16 Bounding Envelope of the Aerofoil Search Space and an Example Solution Constraints: Thickness > 12% x/c Pitching moment > Two Bezier curves representation. Four control points on the mean line. Five control points on the thickness distribution.

17 The Mutants

18 Solver qPanel method with coupled integral boundary layer (XFOIL), by M. Drela of MIT Aero-Astro. qThe solver gives very good approximations of important flow features in the purely subsonic regime, including finite separation bubbles and thinly separated regions. qFree boundary layer transition is used. qAny candidate which is found to have supersonic flow regions (transonic aerofoil) is rejected immediately.

19 Hierarchical Implementation Model Surface Panels Model 2 99 Surface Panels Model 3 79 Surface Panels Exploitation Population size = 20 Exploration Population size = 10 Intermediate Population size = 20

20 First Case Results Three discontinuous regions

21 First Case Results (2) Objective Two Optimal Objective One Optimal Compromise

22 First Case Results (3) Objective One Optimal - Transit Condition

23 First Case Results (4) Compromise Solution - Transit Condition Compromise Solution - Loiter Condition

24 First Case Results (5) Objective Two Optimal - Loiter Condition

25 Case Two Problem Definition: qAgain, a dual point design procedure is described here to find the Pareto set of aerofoils for minimum total drag at two design points. The flow conditions for the two points analyzed are: TransitTakeoff Mach Reynolds14.0 x x 10 6 cl FlapUp30%, +10º deflection

26 Implementation q Single population used, 139 surface panels. q 6 control points on the mean line, 8 on the thickness distribution. q Run for 7,700 function evaluations. q Thickness similarly constrained (> 12%), but pitching moment only constrained for transit case.

27 Second Case Results Concave region

28 Second Case Results (2) Objective Two Optimal Objective One Optimal Compromise

29 Second Case Results (3) Objective One Optimal - Transit Condition

30 Second Case Results (4) Compromise Solution - Transit Condition Compromise Solution - Takeoff Condition

31 Second Case Results (5) Objective Two Optimal - Takeoff Condition

32 Case Three Problem Definition: qFind conceptual design parameters for a UCAV, to minimise two objectives: mGross weight  min(W G ) mCruise efficiency  min(1/[M CRUISE.L/D CRUISE ]) qWe have six unknowns: Lower BoundUpper Bound Aspect Ratio Wing Area (sq ft) Wing Thickness Wing Taper Ratio Wing Sweep (deg) Engine Thrust (lbf)

33 Mission Definition Cruise ft, Mach 0.9, 400 nm Landing Release Payload 1800 Lbs Maneuvers at Mach 0.9 Accelerate Mach 1.5, 500 nm ft Engine Start and warm up Taxi Takeoff Climb Descend Release Payload 1500 Lbs

34 Solver qThe FLOPS ( FL ight OP timisation S ystem) solver developed by L. A. (Arnie) McCullers, NASA Langley Research Center was used for evaluating the aircraft configurations. qFLOPS is a workstation based code with capabilities for conceptual and preliminary design of advanced concepts. qFLOPS is multidisciplinary in nature and contains several analysis modules including: weights, aerodynamics, engine cycle analysis, propulsion, mission performance, takeoff and landing, noise footprint, cost analysis, and program control.

35 Implementation q Solved via a Nash game. q Two hierarchical trees, each with two levels and population sizes of 10. q Information exchanged (epoch) after 50 function evaluations. q Variables split: m Player One: Aspect ratio, wing thickness and wing sweep; Maximises cruise efficiency. m Player Two: Wing area, engine thrust and wing taper; Minimises gross weight. q Run for 550 function evaluations, but converged after 250.

36 Third Case Results

37 Third Case Results (2)

38 Third Case Results (3) Lower Bound Nash Equlibrium Upper Bound Aspect Ratio Wing Area (sq ft) Wing Thickness Wing Taper Ratio Wing Sweep (deg) Engine Thrust (lbf)

39 Third Case Results (4) Nash Equilibrium Upper Bound Lower Bound

40 Conclusion qThe multi-criteria HAPEA has shown itself to be promising for direct and inverse design optimisation problems. qNo problem specific knowledge is required  The method appears to be broadly applicable to black-box solvers. qA wide variety of optimisation problems including Multi- disciplinary Design Optimisation (MDO) problems can be solved. qThe process finds traditional classical aerodynamic results for standard problems, as well as interesting compromise solutions. qThe algorithm may attempt to circumvent convergence difficulties with the solver.

41 Future qWork is in progress to apply the optimisation procedure to multidisciplinary problems. We intend to couple the aerodynamic optimisation with: mElectromagnetics - Investigating the tradeoff between efficient aerodynamic design and RCS issues. mStructures - Especially in three dimensions means we can investigate interesting tradeoffs that may provide weight improvements. mAcoustics - How to maintain efficiency while lowering detectability. mAnd others…

42 Questions???