Multidisciplinary Aircraft Conceptual Design

1
Multidisciplinary Aircraft Conceptual Design
Optimisation Using a Hierarchical
Asynchronous Parallel Evolutionary Algorithm
(HAPEA)

• University of Sydney
• L. F. Gonzalez
• E. J. Whitney
• K. Srinivas
• K.C Wong
• Pole Scientifique - Dassault Aviation-
• J. Périaux

Presented at the Sixth ADAPTIVE COMPUTING IN
DESIGN AND MANUFACTURE(ACDM 2004) APRIL 20th -
22nd, 2004 at ENGINEERS HOUSE, CLIFTON, BRISTOL,
UK
2
Overview
Multi-Objective Problems
PART 1
Research in Evolution Algorithms for Aeronautical
Design Problems (EAs)
PART 2
Test Cases and Applications .
PART 3
3
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.

4
..Multi--Criteria Optimisation
A multi-criteria optimisation problem can be
formulated as Minimise
Subject to constraints
Different Approaches Traditional aggregating
functions, and Pareto and Nash.
5
Pareto Optimality

• Formally, the Pareto optimal set can be defined
  as the set of solutions that are non-dominated
  with respect to all other points in the search
  space, or that they dominate every other solution
  in the search space except fellow members of the
  Pareto optimal set. For two solutions x and y (in
  minimisation form)

.

• For a problem in M objectives, this is called the
  'relationship' operator. In practice we compute
  an approximation to the continuous set, by
  assembling .or each player, as can be seen in
  Figure 2, whereby information is exchanged

6
Nash Games

• A Nash optimisation can be viewed as a
  competitive game between two players that each
  greedily optimise their own objective at the
  expense of the other player.

• A Nash equilibrium is obtained when no player can
  improve his own objective at the expense of the
  other.

Epoch Completed?
Player 2
Player 1
Migrate and Exchange
7
The Problem

• Problems in aeronautical design optimisation
• Traditional optimisation methods will fail to
  find the real answer in most real engineering
  applications.
• Fitness functions of interest are generally
  multimodal with a number of local minima.
  Sometimes the optimum shape/s is not obvious to
  the designer. The fitness function will involve
  some numerical noise.
• Most aerodynamic design problems will need to be
  stated in multi-objective form.
• Modern aeronautical design uses CFD
  (Computational Fluid Dynamics) and FEA almost
  exclusively.
• CFD has matured enough to use for preliminary
  design and optimisation.
• The internal workings of validated in-house
  solvers are essentially inaccessible from a
  modification point of view (they are black-boxes).

8
The Solution. Why Evolution?

• Techniques such as Evolution Algorithms can
  explore large variations in designs. They also
  handle errors and deceptive sub-optimal solutions
  with aplomb.
• They are extremely easy to parallelise,
  significantly reducing computation time.
• They can provide optimal solutions for single and
  multi-objective problems.
• EAs successively map multiple populations of
  points, allowing solution diversity.
• They are capable of finding a number of solutions
  in a Pareto set or calculating a robust Nash
  game.

9
What Are Evolution Algorithms?

• 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 perform this evolution process as a
  mathematical simplification.
• EAs move populations of solutions, rather than
  cut-and-try one to another.
• EAs applied to sciences, arts and engineering.
  Aerofoil and wing design, crew scheduling,
  control loops,etc.

10
Why EAs? Test Functions
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.
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The Central Difficulty
Evolutionary techniques are still very
slow!
(Often involving hundreds or thousands of
separate flow computations)
Therefore, we need to think about ways of
speeding up the process
12
Hierarchical Topology-Multiple Models
Model 1 precise model
Exploitation

• We use a technique that finds optimum solutions
  by using many different models, that greatly
  accelerates the optimisation process.
• Interactions of the layers solutions go up and
  down the layers.
• Time-consuming solvers only for the most
  promising solutions.
• Asynchronous Parallel Computing

Model 2 intermediate model
Model 3 approximate model
Exploration

Hierarchical Topology
Parallel Computing and Asynchronous Evaluation
13
Synchronous Evaluation
different speed

• Single population

• The whole population is passed to the evaluator.
• All the individuals of a given generation need to
  be evaluated before proceeding to the next
  generation

• Hierarchical populations

ES

• Each population has to go through a fixed number
  of generations before migration can take place
• Since migration is global, the different
  populations will have to wait for the slowest one
  before exchanging individuals

Sync
Sync
Sync
ES
ES
ES
ES
ES
ES
Sync
14
Asynchronous Evaluation
different speed

• Single population

• Individuals are evaluated one by one, and
  reintegrated in the population there is no
  notion of generation
• That means the ES can run on any number of
  processors (whereas for a synchronous approach, a
  population of 20 individuals can run on 20
  processors at the most)

1 individual
Evolution Strategy
Asynchromous Evaluator
1 individual

• Hierarchical populations

ES

• Since there is no generation, migration can take
  place anytime after a minimum number of
  evaluations have been performed
• There is no bottleneck

ES
ES
Async
ES
ES
ES
ES
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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.

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.Asynchronous Evaluation

• Offspring are not sent as a complete 'block' to
  the parallel machines.
• A candidate is generated at a time, and sent to
  any idle processor where it is evaluated at its
  own speed.
• After evaluation return to optimiser and check if
  accepted for insertion into the main population
  or rejected.
• New selector operator because offspring cannot
  now be compared one against the other, or even
  against the main population due to the
  variable-time evaluation.
• Recently evaluated offspring are compared to a
  previously established rolling-benchmark and if
  successful, we replace (according to some rule) a
  pre-existing individual in the population.
• A separate evaluation buffer, which provides a
  statistical 'background check' on the comparative
  fitness of the solution.  Buffer size 2 x PopSize
  
• We compare it with the selection buffer by
  assembling at random a small subset called the
  tournament Q q1,q2,q3,qn and check that the
  individual is not dominated by any member of Q.
• Q 1/2B (Strong selective pressure), Q 1/6B
  (weak selection pressure).
• Compare to past individuals (both accepted and
  rejected) -inserted or not  
• If accepted us strategy for replacement
  replace-worst-always method in this paper.

Generate candidate
Send to idle processor
If evaluation completed send back to optimiser
Assign fitness
Compare to a tournament and if successful replace
Compare to accepted and rejected individuals
insert into the population
17
Applications-Test Functions (1)
Here our EA solves a two objective problem with
two design variables. The optimal Pareto front
contains four discontinuous regions.
18
Applications-Test Functions (2) TNK
Again, we solve a two objective problem with two
design variables and one. The optimal Pareto
front contains four discontinuous regions and
constraints
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Asynchronous Test One Dimensional Nozzle
20
Synchronous, Single Population, Viscous model
Pop size 20 7 processors
45mn
21
Asynchronous, Multiple Models, Viscous only
Pop size 10 7 processors
12mn
22
CPU Times for HAPEA
23
Real world applications

• 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.

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Real world applications (2)

• AF/A-18 Flutter model validation.

• 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

25
Case Studies
Multidisciplinary Aircraft Conceptual Design Case
Studies.
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UCAV Conceptual Design.

• Problem Definition
• Find conceptual design parameters for a UCAV, to
  minimise two objectives
• Gross weight ? min(WG)
• Cruise efficiency ? min(1/MCRUISE.L/DCRUISE)
• We have six unknowns

27
Mission Definition
Engine Start and warm up
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Solver

• 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.

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Two Approaches

• Solved via
• Nash theory
• and
• Pareto Optimality.

30
Implementation
Epoch Completed?

• Nash Approach.
• -Two hierarchical trees, with two levels,
  population size of 40.

Player 2
Player 1
Migrate and Exchange
- Information exchanged (epoch) after 50 function
evaluations. Variables split -Player
One Aspect ratio, wing thickness and wing
sweep Maximises cruise efficiency. -Player
Two Wing area, engine thrust and wing taper
Minimises gross weight. - Run for 600 function
evaluations, but converged after 300.
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Nash Results
32
Nash Results (2)
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Nash Results (3)
34
Implementation

• Single population

• Pareto Optimality Approach
• - Single Population.
• - Population size of 40.
• - Parallel computations, run
  asynchronously.
• - Run for 600 function evaluations.

1 individual
Asynchromous Evaluator
1 individual
35
Pareto Optimality Results
36
Comparison Results
37
Comparison Results (2)
Upper Bound
Nash Equilibrium
Nash Design
Lower Bound
38
Subsonic Transport Design and Optimisation

• Problem Definition
• Find conceptual design parameters for a subsonic
  medium size transport aircraft .
• Gross weight ? min(WG)
• The aircraft has two wing-mounted engines, and
  the number of passengers and crew is fixed to 200
  and 8 respectively.
• The aircraft is designed to cruise at 40000 ft
  and Mach 0.8.
• We have six unknowns

39
Constraints and Implementation

• Constraints
• Constraints in this case are minimum takeoff
  distance, moment coefficient for stability and
  control and range required. Violation of these
  constraints is treated with an rejection
  criteria.

• Implementation
• The solution to this problem has been implemented
  using a single population and parallel
  asynchronous evaluation, with the optimiser only
  considering a single objective.
• After an empirical study, it was found that a
  small population size of 10 and buffer size of 30
  produced acceptable results.

40
Results

• The algorithm was allowed to run for 1500
  functions evaluations.
• Broyden-Fletcher-Goldfarb-Shano (BFGS) algorithm
  --- gt a 3.5 improvement
• Conjugate gradient (CG) based (Polak-Ribiere)
  algorithm -- gt 2.4 improvement

Description EA Best BFGS CG_____ Aspect Ratio
ARw 13.1 13.0 12.8 Engine Thrust T,
lbf 34,770 38,852 39,021 Wing Area Sw, sq
ft 1,929 2,142 2,218 Sweep ?w, deg
27.0 28.4 27.32 Thickness t/c 0.091 0.112
0.096 Taper Ratio ?w 0.267 0.267 0.267 ----
--------------------------------------------------
---------------------------------------------- Fue
l Weight Wf, lbs 34,337 37,342 36,092 Gross
Weight Wg , lbs 216,702 222,154 224,618
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Conclusion

• The new technique with multiple models Lower
  the computational expense dilemma in an
  engineering environment (three times faster)
• The multi-criteria HAPEA has shown itself to be
  promising for direct and inverse design
  optimisation problems.
• No problem specific knowledge is required ? The
  method appears to be broadly applicable to
  black-box solvers.
• As illustrated a variety of optimisation problems
  including Multi-disciplinary Design Optimisation
  (MDO) problems can be solved.
• The process finds traditional classical
  aerodynamic results for standard problems, as
  well as interesting compromise solutions.
• The algorithm may attempt to circumvent
  convergence difficulties with the solver.
• In doing all this work, no special hardware has
  been required Desktop PCs networked together
  have been up to the task.

42
What Are We Doing Now?

• A Hybrid EA - Deterministic optimiser.
• EA MDO Evolutionary Algorithms Architecture
  for Multidisciplinary Design Optimisation
• We intend to couple the aerodynamic
  optimisation with
• Aerodynamics Whole wing design using Euler
  codes.
• Electromagnetics - Investigating the tradeoff
  between efficient aerodynamic design and RCS
  issues.
• Structures - Especially in three dimensions
  means we can investigate interesting tradeoffs
  that may provide weight improvements.
• And others

Wing MDO using Potential flow and structural FEA.
43
Questions???
44
Results So Far

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

• 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)

45
Appendix-Applications
46
Publications

• ADVanced EvolutioN Team (ADVENT ) Selected
  Publications and Conference Papers
• 2003 E. Whitney, L. Gonzalez, K. Srinivas, J.
  Périaux Adaptive Evolution Design Without
  Problem Specific Knowledge , Proceedings (to
  appear) of  EUROGEN 2003, Barcelona, Spain.
• 2003 E. Whitney, A Modern Evolutionary Technique
  for Design and Optimisation in Aeronautics , PhD
  Thesis, School of Aerospace, Mechanical and
  Mechatronic Engineering, J07 University of
  Sydney, NSW, 2006 Australia 
• 2003 E. Whitney, L. Gonzalez,  J. Périaux, and
  K. Srinivas, Playing Games with Evolution
  Theory and Aeronautical Optimisation
  Applications,  ICIAM 2003 -- 5th International
  Congress on Industrial and Applied Mathematics,
  Sydney, Australia, July 2003. To appear. 
• 2002 E. Whitney, L. Gonzalez, K. Srinivas, J.
  Périaux Multi-Criteria Aerodynamic Shape
  Design Problems in CFD using a Modern
  Evolutionary Algorithm on Distributed Computers,
  Proceedings of the Second International
  Conference on Computational Fluid Dynamics,
  Sydney, Australia.  
• 2002 J. Périaux, M. Sefrioui, E. Whitney, L.
  Gonzalez, K. Srinivas, and J. Wang 
  Evolutionary Algorithms, Game Theory and
  Hierarchical Models in CFD, Proceedings of the
  Second International Conference on Computational
  Fluid Dynamics, Sydney, Australia.
• 2002 E. Whitney, M. Sefrioui, K. Srinivas, J.
  Périaux Advances in Hierarchical, Parallel
  Evolutionary Algorithms for Aerodynamic Shape
  Optimisation, JSME (Japan Society of Mechanical
  Engineers) International Journal, Vol. 45, No. 1.
  
• 2001 J. Périaux, M. Sefrioui, K. Srinivas, E.
  Whitney, J. Wang Recent Advances in
  Evolutionary Algorithms for Multicriteria Design
  Optimisation in Aeronautics, Kickoff Meeting,
  MACSI Working Group on Multidisciplinary
  Optimisation and Inverse Problems, Vienna,
  Austria.
• 2001 M. Sefrioui, E. Whitney, J. Périaux, K.
  Srinivas Evolutionary Algorithms for
  Multi-Objective Design Optimisation, Proceedings
  of Coupling of Fluids, Structures and Waves in
  Aeronautics (CFSWA), A French / Australian
  workshop, Melbourne, Australia.
• 2001 J. Périaux, M. Sefrioui, K. Srinivas, E.
  Whitney, J. Wang Advances in Hierarchical
  Parallel Genetic Algorithms and Game Decision
  Strategies for Design Optimisation in
  Aeronautics, Proceedings of the First French /
  Finnish Seminar on Innovative Methods for
  Advanced Technologies, Espoo, Finland.
• 2000 E. Whitney, K. Srinivas Non-Generational
  Multiobjective Evolution Strategy for Aerofoil
  Design and Optimisation Problems in CFD
  Proceedings of the First International Conference
  on Computational Fluid Dynamics, Kyoto, Japan

47
Hierarchical Topology-Multiple Models
Model 1 precise model
Exploitation
Model 2 intermediate model
Model 3 approximate model
Exploration

• 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 are used only for the
  most promising solutions.
• Think of it as a kind of optimisation and
  population based multigrid.

48
An Example Aerofoil Optimisation

• Constraints
• Thickness gt 12.1 x/c (RAE 2822)
• Max thickness position 20 55

To solve this and other problems standard
industrial flow solvers are being used.

• 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.

49
Aerofoil Characteristics cl 0.715
Aerofoil Optimisation (2)
Aerofoil Characteristics cl 0.65
Delayed drag divergence at high Cl
Delayed drag divergence at low Cl
Aerofoil Characteristics M 0.75
Delayed drag rise for increasing lift.
50
ZDT Test Cases
51
ZDT1
52
ZDT2
53
ZDT3
54
ZDT4
55
Constrained Test Cases
56
BNH
57
SRN
58
Two Bar Truss Design
A
B
59
Goal Programming- Test Problem P1
60
Results. Candidate and Target Geometries
61
Results Example of Convergence.
Mesh Adaptation Mesh 15