Transcript Document

MULTIDISCIPLINARY AIRCRAFT DESIGN AND
OPTIMISATION USING A ROBUST EVOLUTIONARY
TECHNIQUE WITH VARIABLE FIDELITY MODELS
The University of Sydney
L. F. Gonzalez
E. J. Whitney
K. Srinivas
Pole Scientifique
J. Périaux
10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York,USA, 30 Aug - 1 Sep 2004,
Outline
•
Introduction
– Problems in aeronautical design and optimisation
– The need for Evolutionary algorithms
• Theory
– Evolution Algorithms (EAs).
– Multidisciplinary –Multi-objective Design
– Hierarchical Asynchronous Evolutionary Algorithm
(HAPEA).
• Application
- Mathematical Test functions
- Two real world examples
• Conclusions
Multidisciplinary aircraft design
and optimisation
• Aircraft Deign is multidisciplinary in nature and
there is a strong interaction between the
different multi-physics involved (aerodynamics
, structures , propulsion)
• A tradeoff between aerodynamic performance
and other objectives becomes necessary.
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 many real
engineering applications,
(Noise, complex functions).
•Commercial solvers are essentially inaccessible
from a modification point of view (they are blackboxes).
•Question- High Fidelity model? Or a thorough
search with a Low Fidelity Model?
Why Evolution?
• Evolution Algorithms can explore large
variations in designs.
• Robust towards noise and local minima
and easy to to parallelise, reducing
computation time.
• Provide optimal solutions for single and
multi-objective problems or calculating a
robust Nash game
• EAs successively map multiple
populations of points, allowing solution
diversity.
Evolution Algorithms
What are 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.
Evolution
Crossover
Mutation
Fittest
• Computers can be adapted to perform this evolution process.
Introduction to MultiObjective 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.
Introduction to Multi-Objective
Optimisation (2)
Maximise/ Minimise
Subjected to
constraints
•
f1 x  i  1...N
gi x   0
j  1...N
hk x   0 k  1...K
f i x  objective functions, output (e.g. cruise efficiency).
• x: vector of design variables, inputs (e.g. aircraft geometry ) with
upper and lower bounds;
• g(x) equality constraints and h(x) inequality constraints: (e.g.
element von Mises stresses); in general these are nonlinear
functions of the design variables.
Pareto Optimal Set
• A set of solutions that
are non-dominated
w.r.t all others points
in the search space,
or that they dominate
every other solution
in the search space
except fellow
members of the
Pareto optimal set.
Our Approach:
Hierarchical Asynchronous Parallel
Evolutionary Algorithms (HAPEA)
• Parallel Computing and Asynchronous Evaluation
• Pareto Tournament Selection
• Hierarchical Population Topology
Parallel Computing and Asynchronous
Evaluation
Different Speeds
1 individual
Evolution Algorithm
Asynchronous
Evaluator
1 individual
Asynchronous Evaluation
Why asynchronous
Methods of solutions to MO and MDO -> variable time to complete.
Time to solve non-linear PDE - > Depends upon geometry
How:
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
Asynchronous Evaluation
Methods of solutions to MO and MDO -> variable time to complete.
Time TO SOLVE NON-linear pfF - > DEPENDS UPON GEOMETRY
Traditional EAs
-> create an unnecessary bottleneck when used on parallel
computers;
-> i.e processors that have already completed their
solutions will remain idle until all processors have completed their
work.
Pareto Tournament Selection
• The selection operator is a
novel approach to
determine whether an
individual x is to be
accepted into the main
population
Population
Asynchronous Buffer
• Create a tournament
Tournament Q
Q   q1 , q2 ,...qn   B ;
Evaluate x
x
If x not dominated
1
1
Bn B
6
2
Where B is the selection buffer.
Hierarchical Population Topology
Exploitation
(small
mutation span)
Model 1
precise model
Model 2
intermediate
model
Exploration
(large mutation span)
Model 3
approximate model
Optimisation of Analytical Test
Functions
• Ackley
• MOEAs Examples
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
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 :
Evolved Aerofoils
Evolved Wings
Evolved Aircrafts (in progress)
Two Representative Examples
• Three Element Aerofoil Euler
Reconstruction.
• Multidisciplinary UAV 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 nbv 2500
Hierarchical Asynchronous Parallel EA (HAPEA)
Population size: 40
Viscous:
Grid nbv 2500
Population size: 40
Viscous:
Grid nbv 2000
Population size: 40
Viscous:
Grid nbv 1500
Pressure Distribution
Candidate and Target Geometries
Example of Convergence
History.
A better solution in lower
computing time
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 distance <1000 ft,
Alt Cr > 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
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
Conclusions
•
The results indicate that aircraft design optimisation and shape
optimisation problem can be resolved with an evolutionary
approach using a hierarchical topology.
•
The new method contributes to the development of numerical tools
required for the complex task of MDO and aircraft design.
•
A practical design of a long endurance high altitude UAV was
studied and realistic designs were obtained.
•
No problem specific knowledge is required  The method appears
to be broadly applicable to different analysis codes
•
A family of Pareto optimal configurations was obtained giving the
designer a restricted search space to proceed into more details
phases of design.
Acknowledgements
•
The authors would like to thank Arnie McCullers at NASA LARC
for providing the FLOPS code.
•
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 Professor M. Drela for
providing the MSES code
•
Also to Professor K. Deb for discussions on developments and
applications of MOEA during his visit to The University of
Sydney in 2003.
Questions…
ADDITIONAL SLIDES
CFD Solver
• Flow is treated as two dimensional, inviscid
and is calculated using B. Mohammadi code
NSC2ke
• The solver uses unstructured mesh which are
generated using Bamg.
• The computations stop when the 2-norm
of the
3
10
residual falls below a prescribed limit,
in this
case
Optimization Methods
•
Guess /Intuition: decreases as the increasing
dimensionality.
•
Nonlinear simplex: simple and robust but
inefficient for more than a few design variables.
•
Grid or random search: the cost of searching
the design space increases rapidly with the
number of design variables.
•
Gradient-based: it is most efficient for a large
number of design variables; assumes the
objective function is “well-behaved”.
•
Evolution algorithms: good for discrete design
variables and very robust; but infeasible when
using a large number of design variables.

Asynchronous Evaluation (1)
•
Different Speeds
•
1 individual
•
Evolution Algorithm
Asynchronous
Evaluator
1 individual
•
Ignores the concept of
generation-based solution.
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.
Asynchronous Evaluation (2)
•
Different Speeds
1 individual
Evolution Algorithm
Asynchronous
Evaluator
1 individual
•
•
•
•
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.
Need for Asynchronous
Evaluation
cases used in engineering today may take
different times to complete their operations
Time taken for solutions of non-linear partial
differential equations will strongly depend
upon the geometry.
Generation –based approach used by evolutionary algorithm,
traditional genetic algorithms and evolution strategy create an
unnecessary bottleneck when used on parallel computers , i.e.,
the processors that have already completed their solutions will
remain idle until all processors have completed their work
Methods of solutions to MO and MDO -> VARIABLE TIME TO
COMPLETE.
Time TO SOLVE NON-linear pfF - > DEPENDS UPON GEOMETRY
Traditional EAs -> create an unnecessary bottleneck when used
on parallel computers;
-> I.E processors that have already completed their solutions
will remain idle until all processors have completed their work.
Multi-Objective EAs (MOEAs) and
parallel (pEAs)
Why MOEAs:
• MOEA have been studied intensively in the last 8 years and show
to be promising and effective for different non -linear problems.
• In Multi-objective optimisation we seek to find a set of Pareto
optimal solutions which are better those other
solutions in
all objectives.
• The two main desirable characteristics a MOEA (DEb
2003) are:
-- Convergence to true Pareto optimal set
-- Good Diversity among the solutions on the optimal set
pMOEA
• In general “..a pMOEA seeks to find as good or better MOP
solutions in less time than its serial MOEA counterpart, use less
resources, and /or search
more of the solution space , i.e. ,
increased efficiency and
effectiveness [Veldhuizen et al 2003]
pMOEAs
Components of pEA optimisation
Optimisation Method
Flow analysis method
Geometry
Representation
Implementation
Traditional EA techniques,
hierarchical methods ,
deterministic and EAs
Navier Stokes computationally
expensive but accurate) –panel
methods ( fast but could be
unstable)
Bezier , Splines, depending on the
problem
Parallelization strategy
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
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.
Conclusions
•
The proper use of evolutionary techniques for MDO can reduce
weight and improve endurance of an aircraft concept by minor
changes in the design variables.
•
The results obtained for the aircraft design optimisation are
encouraging and promote application of the method with higher
fidelity solvers and approximation techniques.
Evolutionary Design Optimisation
Problem Definition
HAPEA Optimiser Setup
Create and evaluate
initial population
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)
Do While Convergence
not reached
Compute Objective Functions
Generate and evaluate
new candidates
Evolve/ modify design variables on
optimiser until stopping criteria is met.
Aerodynamic Analysis
Control Points
Sample of Pareto Optimal
configurations
AR =24.30
AR =23.77
SW =321.2 ft2
SW = 321.74 ft2
SWEEP =2.77 deg
FW = 3148 Lbs
SWEEP = 4.87
FW =3486 Lbs
TR = 0.45
ENDR = 1846 min
TR = 0.48
ENDR= 2184 min
ARHT = 5.61
ARHT = 5.43
SWPWT = 5.79
SWPWT = 10.74
Pareto Member 0
TRHT = 0.43
Pareto Member 16
AR = 24.14
AR = 18.9
SW = 301.2 ft2
TRHT = 0.40
SW = 305 ft2
FW =3337 Lbs
SWEEP =2.01 deg
FW =2978 Lbs
SWEEP = 7.07
ENDR= 1533 min
TR = 0.70
TR = 0.62
ARHT = 3.43
ARHT = 4.9
SWPWT = 3.48
SWPWT = 6.55
Pareto Member 14
TRHT = 0.33
ENDR= 2008 min
Pareto Member 19
TRHT = 0.44
Convergence history for
objective one