Multidisciplinary Design Optimisation of Unmanned Multidisciplinary Design Optimisation of Unmanned Aerial Vehicles (UAV) using Multi-Criteria Aerial Vehicles (UAV) using Multi-Criteria

Evolutionary AlgorithmsEvolutionary Algorithms

Eleventh Australian International Aerospace Congress 13-17 March , Melbourne Convention Centre and Australian International Airshow 2005 at Avalon Airport Design November 15-19, 2004

L. F. González, E. J. Whitney, K. Srinivas, K.C Wong

The University of Sydney, Australia

J. PériauxDassault Aviation – Pole Scientifique, INRIA Sophia Antipolis, OPALE project associate

OUTLINE Introduction

Unmanned Aerial Vehicle (UAV/UCAV) Design Requirements

The need and requirements for a Multidisciplinary Design Optimsation Framework in Aeronautics

Theory Evolution Algorithms (EAs). Multidisciplinary –Multi-objective Design Hierarchical Asynchronous Evolutionary Algorithm (HAPEA).

Applications: UAV Design

Conclusions

OUTLINE

UAVDESIGN REQUIREMENTS

Use and development of UAV for military and civilian applications is rapidly increasing.

Similar to the manned aircraft the challenge is to develop trade-off studies of optimal configurations to produce a high performance aircraft that satisfy the mission requirements.

UAV systems are ever increasingly becoming important topics for aerospace research and industrial institutions.

There are difficulties in these new concepts because of the compromising nature of the missions to be performed, like high-- or medium--altitude surveillance, combat environments (UCAV) and many others.

Multi-missions

high–medium--altitude surveillance

High Performance

Complex –trade-offs

Optimization-Optimal Solution(S)

Pareto optimal Surface of UAV,

μUAV

MDO Complex Task - UAV -Example

Multiple Goals Minimise-Maximise

Purchase Price

Aerodynamic Performance

Takeoff weight

Multiple Disciplines

Structures

Fight Controls

Aero acoustics

Propulsion

Sensors

Aero elasticity

Aerodynamics

Search Space – Large Multimodal Non-Convex Discontinuous

Post-Processing Visualization tools

Multi-objective, trade-off

WHY A FRAMEWORK FOR MDO?WHY A FRAMEWORK FOR MDO?

in-house/ commercial solvers-inaccessible –modification

OptimisationMultiple Disciplines

Parallel Computing

► A software system to integrate and evaluate A software system to integrate and evaluate different complexities of MDO is required different complexities of MDO is required

REQUIREMENTS FOR A MO-MDO FRAMEWORK

Robust Optimisation methods (Global solutions, handle noise, complex

functions, ease of integration of legacy codes CFD-FEA- black-boxes).

Problem formulation and execution (Automatic movement of data, parallel

Processing heterogeneous computers).

Architectural design and information access (GUI, object oriented, no-overhead on

optimization, easily extended, database-management, post-processing, visualization capabilities, fault –tolerance mechanisms)

Data Data

GUI

Aerofoil Design

MSES, XFOIL NSC2ke

Wing Design

FLO22

CalculiX

Aircraft Design

FLOPS , ADA

Nozzle Design

HDASS

Mathematical

Test Functions

GUI

Design of Experiments

Optimisation

EA Optimiser

Gradient Based

Optimiser

Parallel ComputingMPI PVM

Analysis Modules

RSM KrigingPost-Processor

Propeller Design

…

Mesh generator

MDO FRAMEWORK

Traditional Gradient Based methods for MDO might fail if search space is:

Advanced Optimisation Tools:Advanced Optimisation Tools: Evolutionary OptimisationEvolutionary Optimisation

Crossover Mutation

Fittest

Evolution

ROBUST AND EFFICIENT OPTIMISATION TOOLS

► LargeLarge► MultimodalMultimodal► Non-Convex Non-Convex ► Many Local OptimumMany Local Optimum► DiscontinuousDiscontinuous

► Good for all of the aboveGood for all of the above► Easy to paralelliseEasy to paralellise► Robust towards noiseRobust towards noise► Explore larger search spacesExplore larger search spaces► Good for multi-objective problemsGood for multi-objective problems

EVOLUTION ALGORITHMS

What are EAs.

► There are many evolutionary methods and There are many evolutionary methods and algorithms.algorithms.

► The complex task of MDO requires ….The complex task of MDO requires ….

Crossover Mutation

Fittest

Evolution► BBased on the Darwinian theory of ased on the Darwinian theory of

evolution evolution populations of populations of individuals evolve and reproduce individuals evolve and reproduce by means of mutation and by means of mutation and crossover operators and compete crossover operators and compete in a set environment for survival in a set environment for survival of the fittest.of the fittest.

► A Robust and efficient evolutionary optimisation A Robust and efficient evolutionary optimisation method.method.

DRAWBACK OF EVOLUTIONARY ALGORITHMS

► A typical MDO problem relies on CFD and FEA for aerodynamic and structural analysis.

► CFD/FEA Computation are time consuming

► Our research addresses these issue in some detail

► Evolution process is time consuming/ high number of function evaluations are required.

Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEA)

ROBUST OPTIMISATION METHODS

► Multi-objective Parallel Evolutionary Multi-objective Parallel Evolutionary AlgorithmAlgorithm

► Hierarchical TopologyHierarchical Topology

► Asynchronous ApproachAsynchronous Approach

Features of the Method:

► Our Contribution…..Our Contribution…..

MULTI-OBJECTIVE OPTIMISATION (1)

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.

Best to let the designer choose after the optimisation phase.

Maximise/ Minimise

Subjected to constraints

► Objective functions, output (e.g. cruise efficiency). Objective functions, output (e.g. cruise efficiency).

► x:x: vector of design variables, inputs (e.g. aircraft/wing geometry) vector of design variables, inputs (e.g. aircraft/wing geometry)

► g(x)g(x) equality constraints and equality constraints and h(x)h(x) inequality constraints: (e.g. inequality constraints: (e.g. element von Mises stresses); in general these are nonlinear element von Mises stresses); in general these are nonlinear functions of the design variables.functions of the design variables.

Nixfi ...1

Kkxh

Njxg

k

i

...10

...10

xfi

MULTI-OBJECTIVE OPTIMISATION (2)

F2

F1Pareto Optimal Front

Non-Dominated

Dominated

Feasible region

Infeasible region

► A set of solutions that A set of solutions that are non-dominated w.r.t are non-dominated w.r.t all others points in the all others points in the search space, or that search space, or that they dominate every they dominate every other solution in the other solution in the search space except search space except fellow members of the fellow members of the Pareto optimal set.Pareto optimal set.

PARETO OPTIMAL SET

► EAs work on population EAs work on population based solutions …can based solutions …can find a optimal Pareto set find a optimal Pareto set in a single runin a single run

HIERARCHICAL TOPOLOGY-MULTIPLE MODELS

Model 1precise model

Model 2intermediate

model

Model 3approximate

model

Exploration

Exploitation

► We use a technique that finds optimum solutions by using many We use a technique that finds optimum solutions by using many different models, that greatly accelerates the optimisation process. different models, that greatly accelerates the optimisation process.

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

► Time-consuming solvers only for the most promising solutions.Time-consuming solvers only for the most promising solutions.

► Asynchronous Parallel ComputingAsynchronous Parallel Computing

Hierarchical Topology

ASYNCHRONOUS EVALUATIONASYNCHRONOUS EVALUATION

► Suspend the idea of generationSuspend the idea of generation

Solution can be generated in and out of orderSolution can be generated in and out of order

► Processors– Can be of different speedsProcessors– Can be of different speeds –– Added at randomAdded at random –– Any number of them possibleAny number of them possible

Methods of solutions to MO and MDO -> variable time to complete.

► Time to solve non-linear PDE - > Depends upon geometryTime to solve non-linear PDE - > Depends upon geometry

Why asynchronous??

How:How:

Evolution Algorithm Evaluator

PROBLEM FORMULATION AND EXECUTION

► The Method is applicable to integrated or distributed The Method is applicable to integrated or distributed MDO analysisMDO analysis

► Single or multi-objective problems can be analysed Single or multi-objective problems can be analysed

► EAs require no derivatives of the objective function EAs require no derivatives of the objective function

► The coupling of the algorithm with different analysis The coupling of the algorithm with different analysis codes is by simple function calls and input and output codes is by simple function calls and input and output data files.data files.

► Different programming languages C, C++, Fortran 90, Different programming languages C, C++, Fortran 90, and Fortran 77. and CFD and FEA software: FLO22 and Fortran 77. and CFD and FEA software: FLO22 FLOPS, ADA, XFOIL, MSES, CalculiXFLOPS, ADA, XFOIL, MSES, CalculiX

ARCHITECTURAL DESIGN AND INFORMATION ACCESS

Design Modules

Design of Experiments

Post-processing

Parallel Computing

Optimisation Tools

DESIGN AND OPTIMISATION MODULES

Wing Design Aircraft Design

RESULTS SO FAR…

Evaluations CPU Time

Traditional 2311 224 152m20m

New Technique

504 490

(-78%)

48m 24m

(-68%)

► The new technique is The new technique is approximately three times approximately three times faster than other similar faster than other similar EA methods.EA methods.

► We have successfully coupled the optimisation code to We have successfully coupled the optimisation code to different compressible and incompressible CFD codes different compressible and incompressible CFD codes and also to some aircraft design codes and also to some aircraft design codes

CFD CFD Aircraft DesignAircraft Design HDASS MSES XFOIL Flight Optimisation HDASS MSES XFOIL Flight Optimisation

Software Software (FLOPS)(FLOPS)

FLO22 Nsc2ke ADS (In house)FLO22 Nsc2ke ADS (In house)

► A testbench for single and multi-objective problems has A testbench for single and multi-objective problems has been developed and tested been developed and tested

Aircraft Conceptual Design and Multidisciplinary Optimisation

2D Nozzle Inverse Optimisation

Transonic Wing Design

UAV Aerofoil Design

Shock Control Bump Optimisation

CURRENT AND ONGOING OPTIMISED INDUSTRIAL APLICATIONS

Propeller Design

High Lift Aircraft System

Transonic aerofoil optimisation using Grid-free solvers

AF/A-18 Flutter

Model Validation

F3 Rear Wing Aerodynamics

M1.113891.069341.024780.9802270.9356710.8911150.846560.8020040.7574480.7128920.6683370.6237810.5792250.5346690.4901130.4455580.4010020.3564460.311890.2673350.2227790.1782230.1336670.08911150.0445558

CURRENT AND ONGOING OPTIMISED INDUSTRIAL APLICATIONS

MULTIDISCIPLINARY AND

MULTI-OBJECTIVE WING DESIGN

OPTIMISATION

Mach Number 0.69

Cruising Altitude 10000 ft

Cl 0.19

Wing Area 2.94 m2

MOO OF TRANSONIC WING DESIGN FORAN UNMANNED AERIAL VEHICLE (UAV)

Objective: Minimisation of wave drag and wing weight

min

min

2

1

weight

w

sparcap

d

totalf

cf

DESIGN VARIABLES

16 Design variables on three span wise aerofoils

9 Design variables on three span wise aerofoil

section

57 design variables, , ,

, , , ,rb bt l

rb bt r b t

ARw b

+

DescriptionLowerBound

UpperBound

Wing Aspect Ratio [AR] 3.50 15.00

Break to root Taper [λbr] 0.65 0.80

Break to tip Taper [λbt] 0.20 0.45

Wing 1/4 Chord inboard Sweep, deg [Λi] 10.00 25.00

Break Location, [bl] 0.30 0.45

DESIGN VARIABLES

Minimum thickness

Position of Maximum thickness

Fitness functions

CONSTRAINTS & OBJECTIVE FUNCTIONS

/ 14% ,12% int ,11% tipt c root ermediate

/20% 55%t cx

1

2

min( )

min

w

weight

f Cd

f totalsparcap

Approach one : Traditional EA with single population model

Computational Grid 96 x 12 x 16

Approach two : HAPEAExploitation

Population size = 30

Exploration Population size = 30

Intermediate Population size =

30

Grid size96 x 12 x 16

Grid size72 x 9 x 12

Grid size48 x 6 x 8

Six machines were used in all calculations

IMPLEMENTATION

The algorithm was run five times for 2000 function evaluations and took about six hours to compute

PARETO FRONTS AFTER 2000 FUNCTION EVALUATIONS

MULTIDISCIPLINARY WING DESIGN

Best for Objective One

Best for Objective Two

Pareto Solutions

RESULTS

Aerofoil Geometries at 0, 20 and 100% semispan

UAV DESIGN AND OPTIMISATION

Minimise two objectives:

Operational Fuel Weight min(OFW) Endurance min (1/E)

Subject to: Takeoff length < 1000 ft Alt Cruise > 40000 ftEndurance > 24 hrs

With respect to: External geometry of the aircraft

• Mach = 0.3• Endurance > 24 hrs • Cruise Altitude: 40000 ft

DESIGN VARIABLES

In total we have 29 design variables

Design Variable Lower

Bound

Upper

Bound

Wing Area (sq ft) 280 330

Aspect Ratio 18 25.2

Wing Sweep (deg) 0.0 8.0

Wing Taper Ratio 0.28 0.8

13 Configuration Design variables

Aerofoil-Wing Geometry

Win

g

16 Design variables for the aerofoil

+

DESIGN VARIABLES

Twist

Horizontal Tail Area (sq ft)

65.0 85.0

HT Aspect Ratio 3.0 15.0

HT Taper Ratio 0.2 0.55

HT Sweep (deg) 12.0 15.0

Vertical Tail Area (sq ft)

11.0 29.0

VT Aspect Ratio 1.0 3.2

VT Taper Ratio 0.28 0.62

VT Sweep (deg) 12.0 34.0

Fuselage Diameter 2.6 5.0

Tail

Fuselage

MISSION PROFILE

Structural & weight analysis

A compromise on fidelity modelsVortex induced drag: VLMpcViscous drag: friction.fAerofoil Design Xfoil

Evolutionary Algorithms (HAPEA)Optimisation

Aircraft designand analysis

Aerodynamic Analysis

Analytically by FLOPS

Flight Optimsation System(FLOPS) – NASA CODE

DESIGN TOOLS

IMPLEMENTATION

Population size: 20

Population size: 20

Population size: 20

Grid 141 x 74 x 36 on aerofoil, 20 x 6 on Vortex model

Grid 109 x 57 x 27 on aerofoil, 17 x 6 on Vortex model

Grid 99 x 52 x 25 on aerofoil, 15 x 6 on Vortex model

► Aircraft Design and Optimisation Module Aircraft Design and Optimisation Module

► Hierarchical TopologyHierarchical Topology

PARETO OPTIMAL REGION

Objective 1 optimal

Objective 2 optimal

Compromise

PARETO OPTIMAL CONFIGURATIONS

CAD-Model and Flight Simulation

OUTCOMES (1)

The new technique facilitates the process of conceptual and preliminary MDO studies

The new technique with multiple models: Lower the computational expense dilemma in an engineering environment (three times faster)

Direct and inverse design optimisation problems have been solved for one or many objectives.

Some Multidisciplinary Design Optimisation (MDO) problems have been solved.

OUTCOMES (2)

The algorithms find traditional classical results for standard problems, as well as interesting compromise solutions.

In doing all this work, no special hardware has been required – Desktop PCs networked together have been up to the task.

No problem specific knowledge is required The method appears to be broadly applicable to different analysis codes.

Work to be done on approximate techniques and use of higher fidelity models.

Acknowledgements

Mourad Sefrioui, Dassault Aviation for fruitful discussions on Hierarchical EAs and his contribution to the optimization procedure.

Steve Armfield and Patrick Morgan at the University of Sydney for providing the cluster of computing facilities.

We would like to thank Arnie McCullers at NASA LaRC who kindly provided the FLOPS software.

Questions…

Thank you for your attention

Additional Slides

Acknowledgements

Multidisciplinary design problems involve search space that are multi-modal, non-convex or discontinuous.

Traditional methods use deterministic approach and rely heavily on the use of iterative trade-off studies between conflicting requirements.

Problems in MDO (1)

Traditional optimisation methods will fail to find the real answer in most real engineering applications, (Noise, complex functions).

The internal workings of validated in-house/ commercial solvers are essentially inaccessible from a modification point of view (they are black-boxes).

Problems in MDO

The process of MDO is complex and involves several considerations as robust optimisation tools, problem formulations, parallel computing visualization tools. A software system or “framework” is desired”

Parallelization Module

Classification of our Model:

The algorithm can be classified as a hierarchical Hybrid pMOEA model [CantuPaz] uses a Master slave PMOEA but incorporate the concept of isolation and migration trough hierarchical topology binary tree structure where each level executes different MOEAs/parameters (heterogeneous)

The distribution of objective function evaluations over the salve processors is where each slake performs k objective function evaluations.

Parallel Processing system characteristics:

We use a Cluster of maximum 18 PCs with Heterogeneous CPUs, RAMs , caches, memory access times , storage capabilities and communication attributes.

Inter-processor communication:

Using the Parallel Virtual Machine (PVM)

EAs

• The selection operator is a novel approach to determine whether an individual x is to be accepted into the main population

• Create a tournament Q

Where B is the selection buffer.

Population

Tournament Q

Asynchronous Buffer

Evaluate x

If x not dominated

x

Pareto Tournament Selection

BnBBqqqQ n 2

1

6

1 ;...., 21

Evolutionary Algorithms

Explore large search spaces.

Robust towards noise and local minima

Easy to parallelise

Map multiple populations of points, allowing solution diversity.

A number of multi-objective solutions in a Pareto set or performing a robust Nash game.

UAV design

Pareto Optimal configurations

The Challenge

The use of higher fidelity models is still prohibitive, research on surrogate modeling/approximation techniques is required.

MDO is a challenging topic, the last few year have seen several approaches for Design and optimization using Evolutionary techniques but research indicate that it is problem dependent and it is still an open problem.

Access to Dell Linux Cluster is limited for benchmarking purposes. Use of higher fidelity models is still prohibitive.

Work in Progress

• Master of Engineering

Rotor Blade design and Optimisation using evolutionary Techniques

Adaptive Transonic Wing/Aerofoil Design and MDO using Evolutionary Techniques

Grid-less Algorithms for Design and optimisation in Aeronautics

• Undergraduate Projects

Transonic wing design using DACE (Design of Experiments-approximation Theories)

An empirical study on DSMC for within evolutionary Optimisation