Transcript Document

Developments in
Evolutionary Algorithms
and
Multi Disciplinary Optimisation
A University of Sydney
Perspective
The Team
Dr. K Srinivas - Leader
Prof. J. Périaux – Advisor
Prof. S W Armfield
Dr. E. J. Whitney
Mr. L. F. Gonzalez
Mr. S. Nagarathinam
Mr. D. S. Lee
Dr. M Sefrioui
Overview
General aspects of the program
K. Srinivas
Discussion of specific examples
Mr. Luis Felipe Gonzalez
Motivation
Multi Disciplinary
Search Space – Large
Multimodal
Non-Convex
Discontinuous
Traditional Methods- Trade off between
Conflicting Requirements
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.
Multi-Objective Optimisation
Maximise/ Minimise
Subjected to constraints
f i ( x), i  1,......, N
g j ( x)  0, j  1,......, J
hk ( x)  0, k  1,......., K
Pareto Front
Drawback of EAs
A typical aerodynamic optimisation relies on CFD
and FEA on structures
CFD Computation is time consuming
Our research addresses this issue in some detail
Our Contribution
Parallel Computing
Asynchronous Evaluation
Hierarchical Population Topology
Hierarchical Asynchronous Parallel
Evolutionary Algorithms (HAPEA)
Parallel Computing and Asynchronous
Evaluation
Different Speeds
1 individual
Evolution Algorithm
Asynchronous
Evaluator
1 individual
Asynchronous Evaluation
Suspend the idea of generation
Solution can be generated in and out of order
Processors – Can be of different speeds
Added at random
Any number of them possible
Pareto Tournament Selection
Create a tournament
Q   q1 , q2 ,...qn   B ;
Where
1
1
Bn B
6
2
B is the selection buffer.
If the new individual x is not dominated any other in the tournament
(Q), then it is immediately accepted and inserted into the main
population according to the replacement rules.
Hierarchical Population Topology
Exploitation
(small
mutation span)
Exploration
(large mutation span)
Model 1
precise model
Model 2
intermediate
model
Model 3
approximate model
Problems in Aerodynamic
Optimisation (1)
• 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 Aerodynamic
Optimisation (2)
• 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).
NASA and US Air force and EAs
•[1] N. Madavan, Turbomachinary airfoil Design
Optimization using Differential Evolution,
•[2] Thomas A. Zang and Lawrence L. Green,
Multidisciplinary Design Optimisation Techniques:
Implications and opportunities for Fluid Dynamics
Research.
•[3] Illinois Genetic Algorithms Laboratory, U.S. Air
Force Office of Scientific Research, F49620-97-10050..
Optimisation of Analytical Test
Functions
• Ackley
• MOEAs Examples
• Asynchronous Test Case –
Sphere Function
Test Functions: Ackley
N
f  N  e  Ne
0.2
1
N
 xi2
i 1
N
e
1
N
 cos( 2 xi
i 1
Increasing
number of
variables
Asynchronous Test Case –
Sphere Function
• Solved on a single population
• Asynchronous:
Assign a small fictitious delay to
each function evaluation. This will
vary uniformly between two values
fastest and lowest. Evaluate
asynchronously.
• Synchronous:
Assign the same delay to all
individuals in advance. Wait until the
slowest evaluation is completed, as
it will occur in practice on a cluster
of computers.
• Four unknowns=4), Stopping
Condition = 0.0001, 25 runs.
Configurations up to tslowest
/tfastest = 5
MOEA 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
MOEA Examples
• Again, we solve a two objective problem with two
design variables however now the optimal Pareto front
contains four discontinuous regions
Results So Far…
• The new technique is
approximately three times
faster than other similar EA
methods.
Evaluations
CPU Time
Traditional
2311 ± 224
152m ± 20m
New
Technique
504 ± 490
(-78%)
48m ± 24m
(-68%)
• A testbench for single and multiobjective problems has been
developed and tested
• We have successfully coupled the optimisation code to
different compressible and incompressible CFD codes and
also to some aircraft design codes
CFD
Aircraft Design
HDASS
MSES XFOIL
Flight Optimisation
Software
(FLOPS)
FLO22
Nsc2ke
ADS (In house)
Applications So Far… (1)
• Constrained aerofoil design for transonic
transport aircraft  3% Drag reduction
• UAV aerofoil design
-Drag minimisation for high-speed
transit and loiter conditions.
-Drag minimisation for high-speed
transit and takeoff conditions.
• Exhaust nozzle design for minimum
losses.
Applications So Far… (2)
• Three element aerofoil reconstruction
from surface pressure data.
•
UCAV MDO
Whole aircraft multidisciplinary design.
Gross weight minimisation and cruise
efficiency Maximisation. Coupling with NASA
code FLOPS
2 % improvement in Takeoff GW and Cruise
Efficiency
AF/A-18 Flutter model validation.
Applications So Far… (3)
• Transonic wing design Two Objectives
•
UAV Wing Design
• Wind Tunnel Test on :
Evolved Aerofoils
Evolved Wings (in progress)
Evolved Aircrafts (in progress)
Capabilities
• We are now confident of our ability to
optimise real industrial/Aeronautical
cases, which could be threedimensional, having multi-objective
criteria or related to multidisciplinary
Design Optimisation (MDO).
Technical Resources: Parallel
Computing
Computer resources
• Access to a Dell Linux Cluster (Scalable
Parallel)
Theoretical Peak Performance: 1860 Gflops
(or 1.82 Tflops)
• Sustain Performance Achieved: 1095 Gflops
(or 1.07 Tflops) - using LINPACK
measurement
Technical Resources Analysis
Tools
Aerodynamics/CFD
•
•
•
•
•
FLUENT
FLO22 (NASA Langley)
HDASS (In house Navier-Stokes
Solver)
(2D Gridless solver)
VLMpc ( Vortex lattice method)
Structural Analysis
•
Finite Element Analysis : Strand
7 Nastran
CAD
•Solid Works, Autocad
Aircraft Design
•FLight Optimisation
System (FLOPS)
NASA Langley
• AAA (DART
corporation)
•
ADS (In House)
Four Representative
Examples
• Three Element Aerofoil Euler
Reconstruction.
• Aerofoil Optimisation
• Multidisciplinary UAV Design Optimisation
• Multidisciplinary Wing Design
Optimisation
Three Element Aerofoil Euler
Reconstruction.
Problem Definition:
• Rebuild from scratch the
pressure distributions that
approximately fit the target
pressure distributions of a three
element aerofoil set.
• Flow Conditions
-Mach 0.2,
- Angle of Attack 17 deg
- Euler Flow, unstructured
mesh
Multi-element aerofoil
reconstruction problem
Design variables
The design variables are the position
And
rotation 
 x, y 
of the slat and flap
Upper and lower bounds of position and rotation
are  x, y   0.05
and   30 respectively
Fitness Function
The fitness function is the RMS error of the surface
pressure coefficients on all the three elements

 N
 1

  Cpcandidate  CpT arg et
F  min 

 N elements  i 1






2






Implementation
Single Population EA (EA SP)
Population size: 40
Grid n x 2500
Hierarchical Asynchronous Parallel EA (HAPEA)
Population size: 40
Viscous:
Grid n x 2500
Population size: 40
Viscous:
Grid n x 2000
Population size: 40
Viscous:
Grid n x 1500
Pressure Distribution
Candidate and Target Geometries
Example of Convergence
History.
A better solution in lower
computing time
Aerofoil Optimisation
Problem Definition:
• Find the Pareto set of aerofoils for minimum total drag at
two design points,
• Compare to Nadarajah and RAE 2822.
Property
Mach
Reynolds
Lift
Flt. Cond.
1
Flt Cond.2
0.75
0.75
9 x 106
9 x 106
0.65
0.715
Design Variables: Bounding Envelope of the
Aerofoil Search Space
Two Bezier curves
representation:
16 Design variables
for the aerofoil
Six control points on the mean line.
Constraints:
Ten control points on the thickness
• Thickness > 12% x/c
distribution.
• Pitching moment > -0.065
Implementation
Hierarchical Asynchronous Parallel EA (HAPEA)
Exploitation
Population size = 30
Model 1
Grid= 215 x 36
Intermediate
Population size = 20
Model 2
Grid=99 x 16
Exploration
Population size = 15
Model 3
Grid= 71 x 12
To solve this and other problems standard industrial flow solvers
are being used. In This case MSES (Euler+BL ) M. Drela
Flight Condition 1
Pareto Front Transonic
Aerofoil Design Problem
Compromise
Flight Condition 1
Aerofoil Optimisation Results
Aerofoil
cd
[cl = 0.65 ]
Traditional Aerofoil
RAE2822
0.0147
0.0185
0.0098
(-33.3%)
0.0130
(-29.7%)
0.0094
(-36.1%)
0.0108
(-41.6%)
Conventional
Optimiser
[Nadarajah [1]]
New Technique

cd
[cl = 0.715 ]
 For a typical
400,000 lb airliner,
flying 1,400
hrs/year:
 3% drag reduction
corresponds to
580,000 lbs
(330,000 L) less
fuel burned.
[1] Nadarajah, S.; Jameson, A, " Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape
Optimisation," AIAA 15th Computational Fluid Dynamics Conference, AIAA-2001-2530, Anaheim, CA, June 2001.
UAV Conceptual Design
Optimisation Problem
Minimise two objectives:
•
•
•
Mach = 0.3
Endurance > 24
hrs
Cruise Altitude:
40000 ft
Gross weight  min(WG)
Endurance
 min (1/E)
Subject to:
Takeoff lenght < 1000 ft,
Alt Cruise > 40000
ROC > 1000 fpm,
Endurance > 24 hrs
With respect to:
external geometry of the aircraft
Design Variables
In total we have 29 design variables
13 Configuration Design variables
Design Variable
Camber
Lower
Bound
Upper
Bound
280
330
Aspect Ratio S
18
25.2
Wing Sweep
(deg)
0.0
8.0
0.28
0.8
Twist
Wing
Wing Area (sq ft)
Wing Taper Ratio
Design Variables
Horizontal Tail
Area (sq ft)
Camber
Tail
Twist
Fuselage
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
2.6
5.0
Fuselage
Diameter
Design Variables: Bounding Envelope of the
Aerofoil Search Space
Two Bezier curves
representation:
16 Design variables
for the aerofoil
Six control points on the mean line.
Constraints:
Ten control points on the thickness
• Thickness > 12% x/c
distribution.
• Pitching moment > -0.065
Mission profile
Design Tools
Optimisation
pMOEA (HAPEA)
Aircraft design
and analysis
FLOPS (Modified to accept
user computed
aerodynamic data)
Aerodynamics
Structural &
weight analysis
A compromise on fidelity models
Vortex induced drag: VLMpc
Viscous drag: friction
Aerofoil Design Xfoil
FLOPS
Implementation
Population size: 20
Population size: 20
Population size: 20
Grid 141x 74x 36
on aerofoil, 20 x 6
on Vortex model
Grid 109x 57x 27
on aerofoil, 17 x 6
on Vortex model
Grid 99x 52x 25 on
aerofoil, 15 x 6 on
Vortex model
Convergence history for
objective one
Pareto optimal region
Objective 1 optimal
Compromise
Objective 2 optimal
Sample of Pareto Optimal
configurations
Pareto Member 0
Pareto Member 14
Pareto Member 16
Pareto Member 19
MOO of transonic wing design for an
Unmanned Aerial Vehicle (UAV)
Minimisation of wave drag and wing weight
Mach Number
0.69
Cruising Altitude 10000
ft
Cl
0.19
Wing Area
2.94
m2
Procedure
Aerodynamics
 Potential Flow Solver (FLO22)
Structural Analysis
Wing Weight
approximated as the sum of
 the span-wise cap weight to
resist the bending moment
• Lift distribution is replaced by concentrated loads
• The local stress has to be less than the ultimate
shear stress. In this case for Aluminum Alloy
Design Variables
16 Design variables on
three span wise aerofoils
+
9 Design variables on
three span wise aerofoil
section
ARw, rb , bt , bl
 rb ,  bt ,  r , b , t
57 design variables
Constraints & Objective
Functions
Minimum thickness
t / c  14% root,12% int ermediate,11% tip
Position of Maximum
thickness
Fitness functions
 20%  xt / c  55%
f1  min(Cd w )
f 2  min  totalsparcapweight 
Implementation
Approach one : Traditional EA with single population model
Computational Grid 96 x 12 x 16
Approach two : HAPEA
Exploitation
Population size = 30
Grid size
96 x 12 x 16
Intermediate
Population size =
30
Grid size
72 x 9 x 12
Exploration
Population size = 30
Grid size
48 x 6 x 8
Six machines were used in all calculations
Pareto fronts after 2000
function evaluations
The algorithm was run five times for 2000 function evaluations and took
about six hours to compute
HAPEA approach
Single population approach
Convergence history for
objective one
Results
Aerofoil sections for Pareto
Top view of wings on
Member 0 12, 20
Pareto set
Aerofoil sections for Pareto
member ten (PM10)
Wing span pressure coefficient
distribution
Aspect Ratio = 3.5
MACH
= 0.69
YAW
= 0.0
ALPHA
= 0.920
L.E Sweep
= 10.2 deg
L.E Sweep 2 = -1.9 deg
CD
= 0.0013
Pareto Member 10
Top and side view Pareto Wing 10
Top View
Side View
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
The Challenge
• The use of higher fidelity models is till 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.
Long term vision
•
A robust framework for Aeronautical MDO
Optimiser Set
Higher Fidelity
Models
(EAS, gradient hybrid)
Conceptual design
Approximation
Techniques
(RSM….?),
Preliminary design
Database of
Case Studies)
CAD Integration
Detailed Design
Multidisciplinary
Analysis
Parallelization
Strategies
Limitations
• Higher fidelity analysis codes
• Funding
• Limited access to Dell Linux Cluster for
benchmarking purposes. Use of higher
fidelity models is still prohibitive.
Outcomes (1)
• 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 Multi-disciplinary Design Optimisation (MDO) problems
have been solved.
• 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.
Outcomes (2)
•
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
•
The authors would like to acknowledge Professor Steve
Armfield and Dr Patrick Morgan at The University of Sydney for
providing the facilities on using the cluster of computers.
•
The authors would like to thank Arnie McCullers at NASA LARC
for providing the FLOPS code.
•
The authors would like to thank Professor M. Drela, B.
Mohammadi and NASA for providing the MSES, Nsc2ke and
FLO22 codes respectively.
•
Also to Professor K. Deb for discussions on developments and
applications of MOEA during his visit to The University of
Sydney in 2003.
•
The authors would like also acknowledge contribution of MER
students S. Nagarathinam and D.S. Lee, with some of the slides
and figures for this presentation.
Questions…
ADDITIONAL SLIDES
Funding Sought
DIRECT COSTS
Personnel
Postgraduate Student (PhD) / Research Associate
$20,000.00
$20,000.00
$20,000.00
$21,000.00
$4,000.00
$0.00
$4,000.00
$0.00
$2,500.00
$2,500.00
Total Travel (c)
$2,500.00
$2,500.00
TOTAL DIRECT COSTS (e)
$26,500.00
$23,500.00
$2,000.00
$5,000.00
TOTAL INDIRECT COSTS (f)
$2,000.00
$2,000.00
TOTAL COSTS (h)
$28,500.00
$25,500.00
Total Personnel (a)
Equipment
Computer Resources
Total Equipment (b)
Travel
Two trips to AIAA and US conferences sites.
INDIRECT COSTS
PIs and any researcher Level A or above x multiplier
The University of Sydney
Justification of Funding
Requested
•
Personnel: A postgraduate student stipend. Experimental work at the
University labs.
The intellectual content makes it suitable as a twoyear project for a PhD student and the successful candidate will be
required to be proficient in a wide range of CFD and optimisation
techniques.
•
Equipment: Provision of a PC, that will be put in place at the university
labs, the requirements of this PC are for high performance parallel
computing resources.
These characteristics are essential in order to compute high fidelity
models on the CFD and structural analysis.
•
Travel: Travel expenses, including airfare, accommodation and meals to
attend to AIAA conferences in the US. The U.S. Air force is asked to
contribute half the cost of producing journal papers and registration to
conferences.
•
Indirect Costs: Indirect Costs have been calculated for The University
of Sydney and using the standard multiplier for laboratory research
(1.25).
USYD and AFRL
• Possible areas of collaboration
within AFRL divisions:
Computational Fluid
Dynamics
Aerodynamics
• AFRL/VAA: Aeronautical Science
Division
VAAA: The Aerodynamic
Configuration Branch
VAAC: The Computational
Sciences Branch
VAAI: Aerospace Vehicles
Integration and Demonstration
Branch
• VAS: Structures Division
AFRL/VASD: Design and
analysis methods branch
Aero thermodynamics
Airframe-Propulsion
Integration
Airframe-Weapons
Integration
Stability and Control
Flight Vehicle Performance
Flow Diagnostics
Aero Configuration
Integration
Evolutionary Design Optimisation
Problem Definition
HAPEA Optimser Setup
Create and evaluate
initial population
Do While Convergence
not reached
Evaluation of Candidates
Compute the flow around the aerofoil
sections and obtain a Cdo estimate
for the wing
Create drag polar on the candidate
geometry Satisfying trim conditions.
Analyze each configuration using FLOPS)
Compute Objective Functions
Generate and evaluate
new candidates
Evolve/ modify design variables on
optimiser until stopping criteria is met.
Aircraft Design and Analysis
• 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.
• FLOPS has capabilities for optimisation but in this case was
used only for analysis.
• Drag is computed using Empirical Drag Estimation Technique
(EDET) - Different hierarchical models are being adapted for
drag build up using higher fidelity models.
Aerodynamic Analysis
Control Points
Design Variables: Bounding Envelope of the
Aerofoil Search Space
16 Design variables
for the aerofoil
Two Bezier curves
representation:
•Six control points on the
mean line.
•Ten control points on the
thickness distribution.
Constraints:
• Thickness > 12% x/c
• Pitching moment > -0.065
Aerofoil Optimisation (2)
Aerofoil Characteristics cl = 0.715
Delayed drag divergence at high Cl
Aerofoil Characteristics cl = 0.65
Delayed drag divergence at low Cl
Aerofoil Optimisation (2)
Aerofoil Characteristics
M = 0.75
Delayed drag rise for increasing lift.
Design Variables
Description
Lower Bound
Upper Bound
Wing Aspect Ratio
3.50
7.00
Break to root taper
0.65
0.80
1
Break 4to
0.20
0.45
Wing Chord inboard
1
Sweep,
4 deg
10.00
20.00
Wing Chord outboard
Sweep, deg
-20.00
0.00
Twist at root, deg
0.00
3.00
Twist at Break, deg
-1.00
0.00
Twist at Tip, deg
-1.00
0.00
Break location
0.20
0.35
tip taper