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University of SydneyL. Gonzalez

Evolution Algorithms and their application to Aeronautical

Design Problems

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Overview

PART 1 Background LFG

PART 2

Future

Research in Evolution Algorithms for Aeronautical Design Problems (EAs)PART 3

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Background

2002

2001

Software :

C++ , FORTRAN

Multidisciplinary

Optimisation

Bsc. Mech. Eng

Work Experience: Mech Design Company and Airline industry

UAV- Aircraft DesignEvolutionary

Algorithms

Dep. Activities:

Tutoring :Thermo2, Fluid Mechanics

 

Others : ICCFD2

CAD Solid Works,

Structural – FEA

CFD : Dr Armfield,

CFX, Srinivas, Nsc2ke

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Research in Evolution Algorithms for Aeronautical Design Problems (EAs)

Based on the Darwinian theory of evolution Populations of individuals evolve and reproduce by means of mutation and crossover operators and compete in a set environment for survival of the fittest.

Computers can be adapted to perform this evolution process.

EAs have been implemented in different applications ranging from sciences, arts and engineering .

What is EAs.

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Research in Evolution Algorithms for Aeronautical Design Problems (EAs)

EAs are able to explore large search spaces.

Robust towards noise and local minima.

Easy to parallelise.

EAs are known to handle approximations and noise well.

EAs evaluate multiple populations of points.

They are capable of finding a number of solutions in a Pareto set

Why EAs

The main drawback of EAs are that they are inherently slow as they require to perform hundred or thousand of evaluations of the objective function.

Why not EAs

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Hierarchical Topology-Multiple Models

Model 1precise 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 should be used only for the most promising solutions.

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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 bottleneck No need for the different processors to be of similar

speed Processors can be added or deleted dynamically

during the execution

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…..Parallel Computing and Asynchronous Evaluation

Optimisation was parallelised on a network of computers at the University of Sydney.

The system has eighteen machines with performances varying between 2.0 GHz and 266 MHz.

Master computer carries on the optimisation process and remote machines compute the solver code.

Message passing model used is the Parallel Virtual Machine (PVM).

Following Hansen and Ostermeier , the method uses a mutation operator and covariance matrix adaptation that gives second order estimation of the problem topology, which is related to most deterministic descent methods.

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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.

Best to let the designer choose after the optimisation phase.

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…..Multi--Criteria Optimisation

Nixi

f ,...1)(

A multi-criteria optimisation problem can be formulated as :Maximise- Minimise:

Subject to constraints:

Using the concept of Pareto optimality the objective is to find the Pareto set of of compromised individuals (i,.e. aerofoil, nozzles, wings) between a number of specified criteria.

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1 solution thecase thisIn*

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a vector thanlesspartially said is 1

a vector problem, onminimisatia For

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Applications

Problem Definition: Fitting of two different shapes to two converging-

diverging nozzles. Nozzle throat parameterisation:

Bezier splines (design variables=control points).Start from scratch and try to build via genetic

operators a nozzle whose wall pressure distribution matches that of the target.

Pressure distribution is computed using a quasi-steady two dimensional approximation for the flow.

Two Objective-Two Dimensional Nozzle Inverse Optimisation Problem

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Overview of the Reconstruction

Select two target nozzles. Build the corresponding Pressure Distribution. Rebuild from scratch the target nozzles by finding the

Pareto set of nozzles between the two pressure distributions that approximately fit the two target pressure distributions.

The fitness functions to be optimised are:

The wall shape distribution of the two target nozzles are:

iitiit PPPPN

fN

f 2122 1

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1

225.005575.017575.02

25.000500.010000.01

2

2

xxy

xxy

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Flow is treated as two dimensional, viscous and is calculated using the CUSP formulation. [Srinivas]

This equation is solved by an iterative technique on a stretched regular quadrilateral grid.

The computations stop when the 2-norm of the density residual falls below a prescribed limit, in this case

The exit conditions used for this problem were fixed at

B.C Exit: Static pressure fixed, other variables extrapolated. Inlet: Total pressure, enthalpy fixed, velocity extrapolated.

CFD Solver

10000Re7.0 M

310

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Implementation

Population size: 15Computational grid is 75 x

37 points equally spaced.

Single Population EA (EA SP)

Hierarchical Asynchronous Parallel EA (HAPEA)

Population size: 15

Population size: 15

Population size: 15

Viscous:

Grid 75 x 37

Viscous:

Grid 50 x 25

Viscous:

Grid 25 x 12

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Results

Pareto Set of Nozzles.

Pareto Member 1

Pareto Member 15

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….Results CPU Time Comparison

The resolution for the solver was set to 10-2

The precision of the solution is set to pres =10-3

Evaluations

CPU Time

EA SP 2311 224

152m20m

HAPEA 504 490(-78%)

48m 24m(-68%)

HAPEA is 3 times faster.

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Constrained Single Element Aerofoil Design.

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:

Property Flt. Cond. 1

Flt Cond.2

Mach 0.75 0.75

Reynolds 9 x 106 9 x 106

cl 0.65 0.715

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Bounding Envelope of the Aerofoil Search Space and a Selected Member of the Final Pareto Set

Constraints:• Thickness > 12.1% x/c (RAE 2822)• Max thickness position = 20% 55%

Two Bezier curves representation.

•Six control points on the mean line.

•Ten control points on the thickness distribution.

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CFD Solver

Euler + boundary layer interactive flow solver (MSES). [M Drela]. The solver is based on a structured quadrilateral

streamline mesh which is coupled to an integral boundary layer based on a multi layer velocity profile representation.

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Implementation Using HAPEA

Model 1 Grid= 215 x 36

Model 2Grid=99 x 16

Model 3Grid= 71 x 12

ExploitationPopulation size = 30

Exploration Population size = 15

Intermediate Population size = 20

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Results

Twelve hours to run on a heterogeneous network of eight machines with speeds, of 2.00 GHz and the master running at 266 MHz.

Run for 20000 functions evaluations of the head node.

Aerofoil cd

[cl = 0.65 ]

cd

[cl = 0.715 ]

RAE 0.0147 0.0185

Nadarajah [1] 0.0098 (-33.3%) 0.0130 (-29.7%)

HAPEA Opt. 0.0094 (-36.1%) 0.0108 (-41.6%) [1] Nadarajah, S.; Jameson, A, " Studies of the Continuous and Discrete Adjoint

Approaches to Viscous Automatic Aerodynamic Shape Optimization," AIAA 15th Computational Fluid Dynamics Conference, AIAA-2001-2530, Anaheim, CA, June 2001.

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Pareto Front Transonic Aerofoil Design Problem

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Pareto Set of Aerofoils

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Aerofoil Characteristics – M = 0.75

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Aerofoil Characteristics cl = 0.65

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Aerofoil Characteristics cl = 0.715

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Conclusions – Research in EAs for Aeronautical Design

HAPEA with multiple models: Lower the computational expense dilemma in an engineering environment (at least 3 times faster than similar approaches for EA)

The multi-criteria HAPEA is promising for direct and inverse design optimisation problems.

As developed, the evolution algorithm/solver coupling is easy to setup and requires only a few hours for the simplest cases.

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

The benefits of using parallel computing, hierarchical optimisation and evolution algorithms to provide solutions for multi-criteria problems has been demonstrated.

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Current Research

F3 Rear wing Aerodynamics

Tree element aerofoil Problem

Hover Optimiser

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Future

Apply Hierarchical EAs to CFD problems with different flow analysis solvers (cheap solvers for exploration and only expensive ones for refinement).

More complex CFD will be investigated in the future (Euler and Navier-Stokes), Multi-component aerofoil design, ship design and race car wing design problems.

Apply HAPEA to MDO problems.

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Proposed Research MDO + EAs

Automatic aircraft design tool for

UAV and micro AV.

Evolutionary techniques.

+

Multidisciplinary Design Optimisation.

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Needs

Competitive market –Robust and fast design tools. Alternative –no conventional options. Coupled problems in aeronautics and aeroelastic wing

deformations of smart structures. Case studies on MDO of UAVs and micro AV. Lack of robust numerical methods for problems in MDO of UAV and

micro AV.

Industry

Evolutionary algorithms – Alternate techniques.

Micro Aerial Design competition.

Case studies on UAV, micro AV

Academic.

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MDO + EAs for UAV and micro AV

Aerodynamics

Propulsion

Aero elasticity

Aero acoustics

MOM3: Takeoff weight

MOM3 . Purchase Price,

MOM2 ?????

Fight Controls

Sensors

UAV Automatic Redesign

Pareto optimal Surface of UAV , μUAV

Structures

Nomenclature

Dominated Individuals (UAV, μUAV

MOM : Measure of Merit

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Multidisciplinary Design Optimisation

Methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena.

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Numerical Optimisation

Numerical Optimiser

Design Variables Measure of Merit

Other Physical Models – aero-acoustics, electromagnetic

Structures Solver – Smart structures (compliant mechanismAnalytical Model - FEA Model

CFD Solver - Inviscid-viscous –Potential , Euler + Boundary Layer , Navier -Stokes

Mission

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Objectives

To review the current state of research in the field of evolutionary computation and its applications to MDO of UAV/microAV.

To identify the need for an evolutionary algorithm MDO tool that concentrates on the generation of generic UAV/micro AV designs, and provide an overview of existing evolutionary design algorithms for this purpose.

Contribution and presentation of an alternative numerical tool for conceptual design to the Australian UAV Special Interest Group and to help students with alternative configurations for the micro aerial vehicle design competition.

Contribute to a conforming database of graphic case studies, validation guidelines and computational results in UAV and microAV analysis and design.

Cooperative integration of the Evolution Algorithms (EAs) research group with other research groups at the School of Aerospace, Mechanical and Mechatronic Engineering.

Consolidation and continuation of the research group in Evolutionary Algorithms for problems in Aeronautics.

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Proposed Team for the Research

One Supervisor and Two Supervisors

Aircraft Design(UAV/microAV)

Aerodynamics (CFD)

Structures (FEA)

Dr K Srinivas. L. TongKC Wong,

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Conclusions

Single discipline analysis,-- interesting shapes in inverse cases, drag minimisation and shock free nozzles have been produced.

The benefits of using parallel computing, hierarchical optimisation and evolution algorithms to provide solutions for Multi-criteria problems have been demonstrated and proven to be useful for this research.

The results of the literature survey suggest that, while the research being conducted is original, it is well placed within a number of well established fields of research aircraft conceptual design, structures and aerodynamics. Meaning ideas and lessons can be learned and adapted from previous research in these areas.

Both automatic aircraft design and multidisciplinary optimisation in parallel is a too ambitious task to be fulfilled within the time available, but it is hard to see another way of reaching some of the stated objectives. The results of the software and algorithms developed so far show initial promise.

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Questions???

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