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Optimisation: Getting More and Better for Less

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Liquefied Natural Gas (LNG)-powered Tupolev 156 (FF 18 January 1989) ... Design variables: out-of-plane coordinates and slopes at the keypoints (12 in total) ... – PowerPoint PPT presentation

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Title: Optimisation: Getting More and Better for Less


1
OptimisationGetting More and Better for Less
Faculty of Engineering
  • Inaugural Lecture
  • by Vassili Toropov
  • Professor of Aerospace and Structural Engineering
  • School of Civil Engineering
  • School of Mechanical Engineering

2
Why do we call it that way?
Opis Roman goddess of abundance and
fertility. Opis is said to be the wife of
Saturn. By her the Gods designated the earth,
because the earth distributes all goods to the
human gender. Festus Meanings of the
word "riches, goods, abundance, gifts,
munificence, plenty". The word optimus - the
best - was derived from her name.
3
Mathematical optimisation problem
A formal mathematical optimization problem to
find components of the vector x of design
variables
where F(x) is the objective function, gj(x) are
the constraint functions, the last set of
inequality conditions defines the side
constraints.
4
Choice of design variables
  • Design variables are selected to uniquely
    identify a design.
  • Typical examples
  • areas of cross section of bars in a truss
    structure
  • number of a specific steel section in a catalogue
    of UB sections
  • coordinates points defining the shape of an
    aerofoil
  • etc.

5
Example
  • Optimization of a steel structure where some of
    the members are described by 10 design variables.
    Each design variable represents a number of a UB
    section from a catalogue of 10 available
    sections.
  • One full structural analysis of each design takes
    1 second on a computer.
  • Question how much time would it take to check
    all the combinations of cross-sections in order
    to guarantee the optimum solution?

Answer 1010 seconds
317 years
6
Criteria of systems efficiency
MATHEMATICAL OPTIMIZATION PROBLEM
  • Criteria of systems efficiency are described by
    the objective function that is to be either
    minimised or maximised.
  • Typical examples
  • cost
  • weight
  • use of resources (fuel, etc.)
  • aerodynamic drag
  • return on investment
  • etc.

7
Typical constraints on systems behaviour
  • Constraints can be imposed on
  • cost
  • equivalent stress
  • critical buckling load
  • frequency of vibrations (can be several)
  • drag
  • lift
  • fatigue life
  • etc.

8
Multi-objective problems
A general multi-objective optimization problem
  • Pareto optimum set consists of the designs which
    cannot be improved with respect to all criteria
    at the same time.

Vilfredo Pareto (1848-1923)
9
Multi-objective problems
Example. You are a looking for a plumber in the
Yellow Pages and want the job done both quickly
and cheaply. You consider a particular plumber,
do your research and see that no other can do the
job cheaper as well as come sooner. It means
that this particular plumber is Pareto optimal
with respect to the cost and waiting time.
10
Multi-objective problems
  • Let f1 be cost and f2 waiting time so we are
    minimising both.
  • Point A corresponds to the plumber who is
    cheapest (minimum cost f1) and B to the one who
    is quickest (minimum waiting time f2).
  • Pareto optimum solutions correspond to the AB
    part of the contour, C might be a good choice.
  • Point D is not Pareto-optimal, it is both dearer
    and slower than, e.g., C.

Conclusion dont put up with D!
11
Do you always get what you pay for?
  • Not always, only if you are choosing from the
    Pareto optimum set of solutions
  • You need to optimise to get there!

12
How does optimisation relate to saving the
planet?
  • In a variety of ways
  • Reduction in the use of natural resources (oil,
    gas, metals, etc.)
  • Reduction of the environmental impact of various
    activities (production, travel, etc.)
  • Development of technologies for mitigation of
    natural and man-made disasters
  • Freeing up budgets for the use on environmental
    issues

Dont confuse optimisation with CATNAP!
Cheapest Available Technology Narrowly Avoiding
Prosecution
13
Climate change Observations and simulations
Natural only
Human activity only
A large part of the warming is likely to be
attributable to human activities
Natural and human activity
Met Office Hadley Centre for Climate Change
14
An unlikely Eco-warrior
Honda F1 goes green!
Honda F1 Earth Car
15
How big is aviation's contribution to climate
change?
  • Now direct emissions from aviation account for
    about 3 of the total greenhouse gas emissions in
    the EU and about 2 worldwide.
  • This does not include indirect warming effects,
    such as those from nitrogen oxides (NOx)
    emissions, contrails and cirrus cloud effects the
    contribute go the greenhouse effect.
  • The overall impact is about two to four times
    higher than of its CO2 emissions alone.

Condensation trails (contrails) Cirrus
clouds
16
How big is aviation's contribution to climate
change?
  • EU emissions from international aviation have
    increased by 87 since 1990 as air travel becomes
    cheaper. This is faster than in any other sector.
  • Someone flying from London to New York and back
    generates the same level of emissions as the
    average family by heating their home for a whole
    year.
  • By 2020, aviation emissions are forecast to more
    than double from present levels.

17
Air travel is cheaper than ever before
Greenpeace Binge flying
18
EU blueprint for aeronautics research
The Advisory Council for Aeronautics Research in
Europe (ACARE) includes EU aeronautics industry,
Member States, the Commission, Eurocontrol,
research centres, airlines, regulators and
European users. 11 November 2002 The Strategic
Research Agenda in Aeronautics fully endorsed. It
will serve as a blueprint in the planning of
national and EU research programmes.
19
EU Strategic Research Agenda in Aeronautics
  • The Strategic Research Agenda in Aeronautics
    aims, by the year 2020, to achieve
  • 50 cut in CO2 and 80 in NOx emission
  • Fivefold reductions in accidents
  • Reduction of noise by 50
  • Increased punctuality 99 of all flights
    arriving and departing within 15 minutes of
    schedule
  • ACARE The objectives are not achievable without
    important breakthroughs, in both technology and
    in concepts of operation - evolutions of current
    concepts will not be sufficient.

20
Progress in aeronautics 1903-2007
Wright brothers Flier, FF 17 December, 1903
21
Progress in aeronautics 1903-2007
Boeing 367-80, FF 15 July 1954
22
Progress in aeronautics 1903-2007
Airbus A-380, FF 27 April 2005
23
Progress in aeronautics 1903-2007
Boeing 367-80, 1954 Airbus A-380, 2005
24
Progress in aeronautics 1903-2007
Boeing 367-80, 1954 Airbus A-380, 2005
25
Still, things are changing
787-8
Other 5
Steel 10
Composites50
Misc. 9
CFRP 43
Titanium15
Aluminum20
Boeing 787, FF expected in 2007. Composite
primary structure
26
Back to the future?
  • Cryogenic (hydrogen as fuel) aircraft.

Tupolev 155 (FF 15 April 1988)
Starboard engine experimental hydrogenpowered
NK-88. Hydrogen tank of 17.5 m3 capacity in the
aft part of the fuselage.
27
Back to the future - II
Liquefied Natural Gas (LNG)-powered Tupolev 156
(FF 18 January 1989)
Starboard engine experimental LNGpowered NK-88.
Tupolev 156 has made over 100 test flights.
28
Current developments
Tupolev 205 (210 pass.)
Tupolev 334 (102 pass.)
Tupolev 136 (53 pass.)
Tupolev 330 (36 tonne cargo)
29
Recent developments
DASA-Tupolev Cryoplane concept based on A-310
(1990-1993)
EADS-Tupolev demonstrator aircraft based on
Do-328 (1995-1998)
30
Challenges
  • Alternative fuel advantages
  • Reduction of emissions, especially for H2
  • Alternative fuel challenges
  • Large volumes are necessary to store liquefied
    fuels (4 times more for H2)
  • Cryogenic tanks are heavier
  • Increase in drag of the airframe
  • Possible safety issues
  • Contrail increase
  • New infrastructure to be built

31
Breaking away from tube with wings?
  • Novel design concept Blended Wing Body (BWB)

X-48, Boeing and NASA Langley Research Center,
project cancelled
32
Breaking away from tube with wings?
Boeing X-48B 21-foot wingspan model UAV built by
Cranfield Aerospace. Tests started in February
2007 at Edwards AF Base.
33
Breaking away from tube with wings?
  • BWB advantages
  • Improved fuel economy
  • Reduced noise impact if engines placed above the
    wings
  • BWB challenges
  • More difficult to control
  • Greater strength needed to maintain internal
    pressure, compared to tube-shaped body
  • Most of the passengers will not be able to see a
    window
  • Passengers more affected by acceleration as a
    result of a steep turn
  • Emergency evacuation can be problematic

34
Grand challenges ahead
  • It is very likely that the pressure for a
    greener aircraft will result in a dramatic change
    of the aircraft design concept in near(-ish)
    future
  • Very likely that BWB concept will be seriously
    examined
  • Alternative fuels will bring new demands to the
    design concepts
  • Ever greater use of new materials
  • This will be a major challenge for
    multidisciplinary optimisation!

35
Grand challenges ahead
  • Possibly, the pressure for a greener aircraft
    would push the civil aviation development as hard
    as the stealth technology pushed the development
    of military aircraft.

Northrop Grumman B-2 Spirit Lockheed F-117
Nighthawk FF 17 July 1989 FF 18
June 1981
36
Can optimisation invent a new design concept?
  • If you only put in wax and wick optimisation
    wont get you a light bulb
  • Wolfram Stadler (19372001)

If you allow the problem to contain a novel
solution then you will get it as a result of
optimisation.
I saw the angel in the marble and carved until I
set him free. Michelangelo Buonarrotti
(1475-1564)
I choose a block of marble and chop off whatever
I don't need. Auguste Rodin (1840-1917)
37
An example topology optimisation
  • Define the design space
  • Apply loads
  • Specify how the structure should be fixed in
    space
  • Do topology optimisation by chopping off whatever
    material is not needed
  • Interpret the result

38
Topology optimisation
Example of topology optimisation
39
Package space accommodation
Original design space
Restricted design space
40
Airbus A-380 droop nose leading edge
AIRBUS UK RETURN ON INVESTMENT
  • Mass of the rib package has been reduced by 44
    saving over 500kg
  • Awarded Airbus Chairmans Gold Award for
    Innovation
  • Altairs optimisation technology is integrated
    into Airbus design process

41
Wing rib designs
Note that a truss-like wing rib structure has
been obtained that is different from a
traditional plate with openings
A discovery?
Let us look at some historic parallels
42
Supermarine Southampton, 1925
43
Wing rib designs
Later, the truss-like wing rib structures have
been mostly replaced by plates with openings and
only occasionally used, notably, in
Concorde.Topology optimisation produced a
truss-like structure again.
44
Genetic Algorithm mimicking natural evolution
45
Composite optimization
Example composite optimisation
Fibre optimised configuration
Baseline configuration
Fibre orientation
z
Optimized fibre design
Thickness optimized design
Number of plies
Optimized thickness
46
Genetic Algorithm basics
  • The fitness function defines how good a
    particular design is
  • Darwin's principle of survival of the fittest
    evolution is performed by breeding the population
    of individual designs over a number of
    generations
  • crossover combines good information from the
    parents
  • mutation prevents premature convergence

47
Selection
  • Randomised
  • Biased towards the fittest members of population

48
Reproduction
  • Mating
  • creating a new chromosome (child) from two
    current chromosomes (parents)

49
Mutation
A crucial change in the genetic make-up of an ape
that lived 2.5 million years ago turned a
small-brained, heavy-jawed primate into the
direct ancestor of modern humans. Nature, March
2004
50
Mutation why it is important?
51
Evolutionary mechanism of the Genetic Algorithm
52
Case StudiesF1 Jaguar Racing Wing
  • The wing was split into patches
  • Each patch was optimized for number of plies and
    ply orientation

53
Load Cases Applied
Aerodynamic loading
FIA 50kg point loading
54
Front Wing Optimization Results
  • Successfully optimized wing structure for ply
    orientation and number of plies
  • Final mass of front wing reduced to 4.9kg
  • Mass reduction of 15
  • Provided important ply orientation information to
    Jaguar Racing

5.9
5.7
5.5
Mass (Kg)
5.3
5.1
4.9
Generations
55
Can we afford not to optimise?
  • Not really, the pressures are too great

Optimise or else
56
If it is so good, why dont we all do it all the
time?
  • Because it is not easy!
  • There are serious issues to address.

57
What are the obstacles?
  • Real-life problems are hard
  • Responses are implicit and computationally
    expensive
  • Responses are noisy
  • Responses can be blurred even more by random
    inputs
  • Simulation software falls over every now and then
  • Number of variables can be large
  • Tools arent sharp enough
  • Insufficient education of graduates and engineers
  • Mostly, we are preaching to the choir rather than
    the congregation

58
Computationally expensive and noisy
59
  • The start Computers of the 1970-80s

BESM-6 (1965-1995) 1 Mflop, 32K word RAM, 48
bit word
60
Challenge
  • Linking an optimizer to a simulation model would
    take a prohibitive amount of computing time
  • Even if all the computing might is available,
    convergence of optimization could be affected by
    numerical noise and domain-dependent calculability

61
Stochastic analysis
  • High costs of failure need to know risks
  • Uncertainties always exist in real life
  • Material tolerances
  • Environment conditions
  • Production tolerances
  • Deterministic simulation has to be followed by
    extensive testing to account for uncertainties
  • Alternative include uncertainties in simulation

62
Doing something else?
  • If something's hard to do,
  • then it's not worth doing!
  • Homer Simpson

63
Use approximations!
  • If the problem as is is too hard, use an
    approximation (metamodel, surrogate model) of
    the given function by a function with required
    properties (smooth, cheaper to compute, etc.).
  • Check the approximation quality, if
    insufficient, refine.

64
Metamodelling for design optimization
  • Metamodels should allow to
  • minimize the number of response evaluations
  • reduce the effect of numerical noise recognise
    is it a trend?
  • Is it a blip?
  • If necessary, metamodels can be built in a
    smaller subregions of the whole design space
    (trust regions) that are panning and zooming onto
    the solution

65
Metamodelling for stochastic analysis
  • Similarly to design optimization, the following
    process for the stochastic analysis has been
    suggested
  • Build a metamodel
  • Check its quality on the independent data set, if
    quality is not acceptable then refine metamodel
  • Run Monte Carlo simulation of a sufficient
    sampling size on the metamodel

66
DOEs for metamodel building
  • Sampling according to some Designs of Experiments
    (DOEs) is needed
  • to build a metamodel
  • and also to check the metamodel

67
Metamodelling techniques
  • Response surface methodology
  • Linear (e.g. polynomial) regression
  • Nonlinear regression
  • Mechanistic models
  • Selection of the model structure, e.g. using
    Genetic Programming
  • Artificial neural networks
  • Radial basis functions
  • Kriging
  • Multivariate Adaptive Regression Splines (MARS)
  • Use of lower fidelity numerical models in
    metamodel building
  • Moving Lest Squares Method (MLSM)
  • etc.

68
Interaction of high- and low fidelity models
  • Sometimes two levels of models are available,
    e.g.
  • High-fidelity model detailed FE simulation with
    a fine mesh
  • Low-fidelity model a faster and simpler
    simulation approach, e.g.
  • FE simulation with a coarse mesh
  • Other simulation tool?

The basic idea is to do the bulk of optimization
using the low fidelity model only occasionally
calling the high fidelity model
69
Example Optimum blank design for deep drawing
process
Initial blank
Drawn box
Target shape
Waste
Trimming
Find optimum blank shape to minimise waste of
material
Hiroshima University and Mazda Corp.
70
Example of stamping simulation
71
High- and low-fidelity models
FEM PAM-STAMP
FEM PAM-QUIKSTAMP
High-fidelity model (Fine mesh) Elements
1100 Time 150 sec.
Low-fidelity model (Coarse mesh) Elements
120 Time 10 sec.
  • Result
  • high-fidelity model only 1040 min,
  • interaction with low-fidelity model 155 min.

72
Creation of analytical metamodels using Genetic
Programming
  • Similar to GA but more general data structure
    (programs)
  • Darwinian evolution of programs
  • Main applications AI, design of electric
    circuits, financial forecasting
  • Application to design optimization and problems
  • Creation of analytical metamodels
  • Program analytical metamodel
  • Program Tree structure composed of nodes
  • Terminal set optimization variables
  • Functional set mathematical operators

73
Genetic Programming
John Koza Genetic Programming
74
Genetic Programming
Example Tree structure for the expression
75
Genetic Programming
  • Genetic operators
  • Selection
  • Crossover
  • Mutation
  • Elite transfer

76
Genetic Programming
  • Crossover

77
Genetic Programming
  • Mutation

78
Empirical modelling of shear strength of RC deep
beams
  • Find normalised shear strength using
    experimental data
  • Variables
  • Shear span to depth ratio x1
  • Beam span to depth ratio x2
  • Smeared vertical web reinforcement ratio x3
  • Smeared horizontal web reinforcement ratio x4
  • Main longitudinal bottom reinforcement ratio x5
  • Main longitudinal top reinforcement ratio x6
  • The design of RC deep beams is not covered by BS
    8110 that states, for the design of deep beams,
    reference should be made to specialist
    literature.

79
Empirical modelling of shear strength of RC deep
beams
Normalised shear strength
Collaboration Dr Ashraf Ashour, Bradford
University
80
Application Small-scale CHP plant
  • BIO-STIRLING FP6 project
  • Small-scale CHP (combined heat and power) plant
    based on a hermetic four cylinder Stirling engine
    for biomass fuels
  • EC F6 Programme on Energy, Environment and
    Sustainable Development, 2000-2003
  • Objective
  • improvement of thermodynamic efficiency
  • Collaboration
  • Technical University of Denmark (lead partner)
  • Partners from Austria, Denmark, Germany

81
Application Optimisation of a shell
  • A shell loaded by a uniform load is defined by a
    square reference plan.
  • Design variables out-of-plane coordinates and
    slopes at the keypoints (12 in total)
  • Objective minimization of the maximum
    displacement
  • Constraint volume no greater than prescribes
    value
  • Collaboration
  • TU Delft

82
Optimisation of a shell
  • First design, normalized constraint equals 1.0

83
Optimisation of a shell
  • Second design, normalized constraint equals 1.0

84
Aerofoil optimisation
  • B-spline representation of the NACA 0012
    aerofoil. The B-spline poles are numbered from 1
    to 25.
  • Design variables x and y coordinates of 22
    B-spline poles (N 44).

W.A. Wright, C.M.E. Holden, Sowerby Research
Centre, BAE Systems (1998)
85
Aerofoil optimisation
  • Objective function (to be minimized) drag
    coefficient at Mach 0.73 and Mach 0.76
  • F0 (x) 2.0 Cd total (M0.73) 1.0 Cd total
    (M0.76)
  • Constraints on lift and other operational
    requirements (sufficient space for holding fuel,
    etc.)
  • Result drag reduction by 4
  • Carren M.E. Holden, Sowerby Research Centre, BAE
    Systems (1998)

86
Optimisation of structural steelwork
Objective cost minimisation Design variables
numbers of steel sections from a
catalogue Constraints defined by BS 5950
87
ExoMars space mission
  • ESA Aurora exploration programme
  • 240kg mobile robotic exo-biology laboratory
  • To search for extinct or extant microbial life on
    Mars
  • Supporting geology and meteorology experiments
  • Launch by Ariane 5 or Soyuz in 2013
  • Currently in Phase B mission planning and
    concept design phase

88
Airbags for space landers
  • Un-vented type (inflatable ball)
  • Multiple bounces
  • Established heritage (from Luna-9 in 1966)
  • High mass
  • Vulnerable to rupture

Luna 9 (USSR Space Program)
Mars Pathfinder (NASA/JPL)
Beagle 2 (Beagle 2)
89
Airbags for space landers
  • Vented Type
  • Active control
  • Single stroke
  • No space heritage
  • Low Mass
  • Vulnerable to over-turning

Kistler Booster (Irvin)
ExoMars (ESA)
90
Airbag landing design concept
  • Design concept considers vented (or Dead-Beat)
    airbag coming to rest on second bounce
  • Inflated with N2 during descent under main
    parachute
  • Stowed rover mounted to platform
  • Vent patches activated by pyrotechnic cutters
  • Simple reactive vent control system simultaneous
    all-vent trigger at 65g

91
Airbag configuration
  • Six identical vented chambers
  • One anti-bottoming un-vented toroidal

92
Study objectives
  • Develop methodology for optimisation and
    probabilistic reliability assessment of vented
    airbags
  • Key requirements
  • No overturning
  • Payload acceleration below 70g
  • No airbag rupture
  • Key questions
  • What is the mass of an optimized vented airbag?
  • What is the probability of a successful landing?
  • What is the sensitivity of landing reliability to
    changing landing scenarios?

93
Landing scenarios
  • Two landing scenarios Flat bottom and Inclined
    rock impacts
  • Mars environment
  • Gravity 3.7 m/s2 0.38g
  • Pressure 440Pa 0.4 of Earth air pressure at
    sea level
  • at 36.5 km altitude on Earth
  • Temperature 187K - 86º C

94
Baseline design Flat bottom impact
All requirements are satisfied by the baseline
design
95
Baseline design Inclined rock impact
Baseline design deceleration 980g (target lt70g)
96
ExoMars Lander LS-DYNA simulation
97
Optimisation results
  • Mass increased by 2.7
  • Flat Bottom Impact payload acceleration increased
    remained below 70g
  • Rock Impact payload acceleration reduced from
    980g to 69g

98
Reliability assessment of ExoMars lander
  • Reliability study gives the probability of a
    successful landing for a given design under a
    range of conditions of landing, such as
  • the wind speed
  • terrain roughness
  • pitch attitude at impact
  • pitch rate at impact

99
Wind speed probability distribution
European Mars Climate Database (EMCD) - general
circulation model 45?N to 45?S latitudes Season
12 Mars Global Surveyor dust loading scenario PDF
fit to EMCD model data Rayleigh distribution
100
Rock height probability distribution
NASA/JPL rock size distribution model Viking 1
2, MPF landing sites Earth analogues Landing
Site rock coverage ? 20 Overall rock coverage
from orbital thermal imaging Rock height 0.5 x
diameter Exponential PDF
Mars Pathfinder landing site panorama (NASA/JPL)
101
Pitch angle and pitch rate probability
distribution
Pendulum motion gust reaction under parachute
at landing Assumed to be random with independent
normal PDFs
Pitch Angle Mean 0 degs, 3? 30 degs
Pitch Rate Mean 0 deg/s, 3? 20 deg/s
102
Monte Carlo simulationcounting failures
Another one bites the dust!
103
Result of reliability assessment of ExoMars lander
  • The optimization study arrived at a design that
    satisfies the requirements with only a small
    increase in mass
  • Reliability analysis proved that the concept is
    viable
  • Reliability analysis uncovered failure modes that
    had not previously been considered
  • Further design improvements can be made

104
ExoMars Lander LS-DYNA simulation
105
Comment on the specific choice of optimization
technique
  • There is no truly universal optimisation
    technique that is best for each and every
    problem
  • There are camps in design optimisation
    evolutionists, classicists, and pragmatists
    practitioners tend to belong to the latter

versus
106
Challenges ahead
  • Curse of dimensionality
  • Problems with non-smooth response, e.g.
    crashworthiness
  • Problems of large-scale composite optimisation
  • Large scale structural engineering problems
  • CFD optimisation problems, e.g. flow control to
    reduce drag
  • Coupled problems, e.g. aeroelasticity
  • Multidisciplinary problems

107
Any questions?
  • ?
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