Transcript No Slide Title

Evolution Algorithms
and their application to Aeronautical
Design Problems
University of Sydney
L. Gonzalez
@
1
Overview
PART 1
Background LFG
PART 2
Research in Evolution
Algorithms for
Aeronautical Design
Problems (EAs)
PART 3
Future
2
Background
2001
 Bsc. Mech. Eng
 Work Experience: Mech Design Company and Airline industry
2002
Multidisciplinary
Evolutionary
Optimisation
Algorithms
UAV- Aircraft Design
CFD : Dr Armfield,
CAD Solid Works,
Software :
CFX, Srinivas, Nsc2ke
Structural – FEA
C++ ,
FORTRAN
Dep. Activities:
Others : ICCFD2
Tutoring :Thermo2,
Fluid Mechanics
3
Research in Evolution Algorithms for Aeronautical
Design Problems (EAs)
What is 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 .
4
Research in Evolution Algorithms for
Aeronautical Design Problems (EAs)
Why 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 not 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.
5
Hierarchical Topology-Multiple Models
Exploitation
(small
mutation span)
Model 1
precise model
Model 2
intermediate
model
Exploration
(large mutation span)
Model 3
approximate model
 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.
6
Parallel Computing and Asynchronous
Evaluation
different speeds
1 individual
Evolution Algorithm
Asynchromous
Evaluator
1 individual
7
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
8
…..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.
9
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.
10
…..Multi--Criteria Optimisation
A multi-criteria optimisation problem can be formulated as :
Maximise- Minimise: f ( x )
i  1,... N
i
Subject to constraints:
g ( x)  0
j
j  1,.... M
h ( x)  0
k
k  1,.... M
For a minimisati on problem, a vector x is said partially less than a vector x if :
1
2

f (x )  f (x )
i
i 1
i 2
* In this case the solution x dominates the solution x
1
2
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.
11
Applications
Two Objective-Two Dimensional Nozzle Inverse
Optimisation Problem
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.
12
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:
f 
1
1
2
 Pit1  Pi 
N
f 
2
1
2
 Pit 2  Pi 
N
 The wall shape distribution of the two target nozzles
are:
y  0.10000 x 2  0.00500 x  0.25
1
y  0.17575 x 2  0.05575 x  0.225
2
13
CFD Solver
 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 103
 The exit conditions used for this problem were fixed at
M  0.7 Re  10000
 B.C Exit: Static pressure fixed, other variables
extrapolated. Inlet: Total pressure, enthalpy fixed,
velocity extrapolated.
14
Implementation
Single Population EA (EA SP)
Population size: 15
Computational grid is 75 x 37
points equally spaced.
Hierarchical Asynchronous Parallel EA (HAPEA)
Viscous:
Grid 75 x 37
Viscous:
Grid 50 x 25
Population size: 15
Population size: 15
Viscous:
Grid 25 x 12
Population size: 15
15
Results
Pareto Set of Nozzles.
Pareto Member 15
Pareto Member 1
16
….Results CPU Time Comparison
Evaluations
CPU Time
EA SP
2311  224
152m  20m
HAPEA
504  490
(-78%)
48m  24m
(-68%)
The resolution for the solver was set to 10-2
The precision of the solution is set to pres =10-3
HAPEA is 3 times faster.
17
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
Mach
Reynolds
cl
Flt. Cond. 1
Flt Cond.2
0.75
0.75
9 x 106
9 x 106
0.65
0.715
18
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.
19
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.
20
Implementation Using HAPEA
Model 1
Grid= 215 x 36
Exploitation
Population size = 30
Model 2
Grid=99 x 16
Intermediate
Population size = 20
Model 3
Grid= 71 x 12
Exploration
Population size = 15
21
Results
 Run for 20000 functions evaluations of the head node.
 Twelve hours to run on a heterogeneous network of eight
machines with speeds, of 2.00 GHz and the master
running at 266 MHz.
Aerofoil
RAE
Nadarajah [1]
HAPEA Opt.

cd
[cl = 0.65 ]
0.0147
0.0098 (-33.3%)
0.0094 (-36.1%)
cd
[cl = 0.715 ]
0.0185
0.0130 (-29.7%)
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.
22
Pareto Front Transonic Aerofoil
Design Problem
23
Pareto Set of Aerofoils
24
Aerofoil Characteristics – M = 0.75
25
Aerofoil Characteristics cl = 0.65
26
Aerofoil Characteristics cl = 0.715
27
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.
28
Current Research
F3 Rear wing
Aerodynamics
Tree element aerofoil
Problem
Hover Optimiser
29
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.
30
Proposed Research MDO + EAs
Multidisciplinary Design Optimisation.
+
Evolutionary techniques.
Automatic aircraft design tool for
UAV and micro AV.
31
Needs
Industry
 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.
Academic.
Evolutionary algorithms – Alternate techniques.
Micro Aerial Design competition.
Case studies on UAV, micro AV
32
MDO + EAs for UAV and micro AV
Aerodynamics
Structures
UAV Automatic Redesign
Pareto optimal Surface
of UAV , μUAV
MOM2 ?????
Fight Controls
Aero elasticity
MOM3: Takeoff weight
MOM3 . Purchase Price,
Sensors
Nomenclature
Propulsion
Dominated Individuals (UAV, μUAV
MOM : Measure of Merit
33
Aero acoustics
Multidisciplinary Design Optimisation
Methodology for the design of complex
engineering systems and subsystems that
coherently exploits the synergism of
mutually interacting phenomena.
34
Numerical Optimisation
Numerical Optimiser
Design Variables
Measure of Merit
Mission
CFD Solver - Inviscid-viscous –
Potential , Euler + Boundary
Layer , Navier -Stokes
Structures Solver – Smart
structures (compliant mechanism
Analytical Model - FEA Model
Other Physical Models – aeroacoustics, electromagnetic
35
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.
36
Proposed Team for the Research
One Supervisor and Two Supervisors
Aircraft Design
(UAV/microAV)
KC Wong,
Aerodynamics
(CFD)
Dr K Srinivas.
37
Structures
(FEA)
L. Tong
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.
38
Questions???
39
40