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University of SydneyE. J. Whitney

L. F. Gonzalez

K. Srinivas

Dassault AviationJ. Périaux

M. Sefrioui

Multi-objective Evolution Design for

UAV Aerodynamic Applications

UAV-MMNT03

Sydney, Australia    14-16 July 2003

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Overview

Evolution Algorithms (EAs). Hierarchical Topology-Multiple Models. Multi-Criteria Optimisation – Game

Theory. Parallel Computing and Asynchronous

Evaluation. Test Case Applications:

UAV aerofoil design for transit and loiter. UAV aerofoil design for transit and takeoff. UCAV whole aircraft conceptual design.

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The Problem…

Problems in aerodynamic optimisation: Modern aerodynamic design uses CFD (Computational

Fluid Dynamics) almost exclusively. CFD has matured enough to use for preliminary design and

optimisation. Most aerodynamic design problems will need to be stated

in multi-objective form. The internal workings of validated in-house solvers are

essentially inaccessible from a modification point of view (they are black-boxes).

Fitness 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.

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… The Solution

We apply an Evolution Algorithm (EA):EAs are able to explore large search spaces.They are robust towards noise and local minima.They are easy to parallelise, significantly

reducing computation time.EAs successively map multiple populations of

points, alowing solution diversity.They are capable of finding a number of solutions

in a Pareto set or calculating a robust Nash game.

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“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 ModelsModel 1

precise model

Model 2intermediate

model

Model 3approximate model

Exploration(large mutation span)

Exploitation(small

mutation span)

Interactions of the 3 layers: solutions go up and down the layers.

The best ones keep going up until they are completely refined.

No need for great precision during exploration.

Time-consuming solvers are used only for the most promising solutions.

Think of it as a kind of optimisation and population based multigrid.

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Parallel Computing and Asynchronous Evaluation

Evolution AlgorithmAsynchromous

Evaluator

1 individual

1 individual

Different Speeds

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Asynchronous Evaluation

Fitness functions are computed asynchronously. Only 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.

Solutions can be generated and returned out of order.

No need for synchronicity no possible wait-time bottleneck. No need for the different processors to be of similar speed. Processors can be added or deleted dynamically during the

execution. There is no practical upper limit on the number of processors

we can use. All desktop computers in an organisation are fair game.

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Multi-Criteria Problems

Aeronautical 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:

Drag at two different values of lift.

Drag and thickness.

Pitching 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.

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…..Multi--Criteria Optimisation

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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.

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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.

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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.

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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

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Applications

Case One: Aerofoil design, drag minimisation for high-speed transit and loiter conditions.

Case Two: Aerofoil design, drag minimisation for high-speed transit and takeoff conditions.

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:

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Case One

Problem Definition: 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:

Transit Loiter

Mach 0.60 0.15

Reynolds 14.0 x 106 3.5 x 106

cl 0.05 0.78

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Bounding Envelope of the Aerofoil Search Space and an Example Solution

Constraints:• Thickness > 12% x/c• Pitching moment > -0.065

Two Bezier curves representation.

•Four control points on the mean line.

•Five control points on the thickness distribution.

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The Mutants

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Solver

Panel method with coupled integral boundary layer (XFOIL), by M. Drela of MIT Aero-Astro.

The solver gives very good approximations of important flow features in the purely subsonic regime, including finite separation bubbles and thinly separated regions.

Free boundary layer transition is used.Any candidate which is found to have

supersonic flow regions (transonic aerofoil) is rejected immediately.

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Hierarchical Implementation

Model 1 119 Surface Panels

Model 299 Surface Panels

Model 379 Surface Panels

ExploitationPopulation size = 20

Exploration Population size = 10

Intermediate Population size = 20

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First Case Results

Three discontinuous regions

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First Case Results (2)

Objective Two Optimal

Objective One Optimal

Compromise

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First Case Results (3)

Objective One Optimal - Transit Condition

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First Case Results (4)

Compromise Solution - Transit Condition

Compromise Solution - Loiter Condition

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First Case Results (5)

Objective Two Optimal - Loiter Condition

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Case Two

Problem Definition: Again, 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:

Transit Takeoff

Mach 0.60 0.11

Reynolds 14.0 x 106 2.46 x 106

cl 0.05 1.40

Flap Up 30%, +10º deflection

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Implementation

Single population used, 139 surface panels. 6 control points on the mean line, 8 on the

thickness distribution. Run for 7,700 function evaluations. Thickness similarly constrained (> 12%), but

pitching moment only constrained for transit case.

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Second Case Results

Concave region

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Second Case Results (2)

Objective Two Optimal

Objective One Optimal

Compromise

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Second Case Results (3)

Objective One Optimal - Transit Condition

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Second Case Results (4)

Compromise Solution - Transit Condition

Compromise Solution - Takeoff Condition

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Second Case Results (5)

Objective Two Optimal - Takeoff Condition

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Case Three

Problem Definition: Find conceptual design parameters for a UCAV, to minimise two

objectives: Gross weight min(WG) Cruise efficiency min(1/[MCRUISE.L/DCRUISE])

We have six unknowns:

Lower Bound

Upper Bound

Aspect Ratio 3.1 5.3

Wing Area (sq ft)

600 1400

Wing Thickness 0.02 0.09

Wing Taper Ratio

0.15 0.55

Wing Sweep (deg)

22.0 47.0

Engine Thrust (lbf)

32000 37000

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Mission Definition

Cruise 40000 ft, Mach 0.9, 400 nm

Landing

Release Payload 1800 Lbs

Maneuvers at Mach 0.9

Accelerate Mach 1.5, 500 nm

20000 ft

Engine Start and warm up

Taxi

Takeoff

Climb

Descend

Release Payload 1500 Lbs

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Solver

The FLOPS (FLight OPtimisation System) solver developed by L. A. (Arnie) McCullers, NASA Langley Research Center was used for evaluating the aircraft configurations.

FLOPS is a workstation based code with capabilities for conceptual and preliminary design of advanced concepts.

FLOPS 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.

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Implementation

Solved via a Nash game. Two hierarchical trees, each with two

levels and population sizes of 10. Information exchanged (epoch) after 50

function evaluations. Variables split:

Player One: Aspect ratio, wing thickness and wing sweep; Maximises cruise efficiency.

Player Two: Wing area, engine thrust and wing taper; Minimises gross weight.

Run for 550 function evaluations, but converged after 250.

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Third Case Results

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Third Case Results (2)

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Third Case Results (3)

Lower Bound Nash Equlibrium

Upper Bound

Aspect Ratio 3.1 5.13 5.3

Wing Area (sq ft)

600 618 1400

Wing Thickness 0.02 0.021 0.09

Wing Taper Ratio

0.15 0.17 0.55

Wing Sweep (deg)

22.0 28 47.0

Engine Thrust (lbf)

32000 33356 37000

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Third Case Results (4)

Nash Equilibrium

Upper Bound

Lower Bound

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Conclusion

The multi-criteria HAPEA has shown itself to be promising for direct and inverse design optimisation problems.

No problem specific knowledge is required The method appears to be broadly applicable to black-box solvers.

A wide variety of optimisation problems including Multi-disciplinary Design Optimisation (MDO) problems can be solved.

The process finds traditional classical aerodynamic results for standard problems, as well as interesting compromise solutions.

The algorithm may attempt to circumvent convergence difficulties with the solver.

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Future

Work is in progress to apply the optimisation procedure to multidisciplinary problems. We intend to couple the aerodynamic optimisation with: Electromagnetics - Investigating the tradeoff between

efficient aerodynamic design and RCS issues. Structures - Especially in three dimensions means we

can investigate interesting tradeoffs that may provide weight improvements.

Acoustics - How to maintain efficiency while lowering detectability.

And others…

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Questions???