Faculty of Engineering
Optimisation:
Getting More and Better for Less
Inaugural Lecture
by Vassili Toropov
Professor of Aerospace and Structural Engineering
School of Civil Engineering
School of Mechanical Engineering
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.
Mathematical optimisation problem
A formal mathematical optimization problem: to find components
of the vector x of design variables:
F ( x )  min (or max)
g j ( x )  0, j  1,..., M
Ai  xi  Bi ,
i  1,..., N
where F(x) is the objective function, gj(x) are the constraint
functions, the last set of inequality conditions defines the side
constraints.
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.
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
Criteria
of system’s
efficiency
MATHEMATICAL
OPTIMIZATION
PROBLEM
Criteria of system’s 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.
Typical constraints on system’s behaviour
Constraints can be imposed on:
• cost
• equivalent stress
• critical buckling load
• frequency of vibrations (can be several)
• drag
• lift
• fatigue life
• etc.
Multi-objective problems
A general multi-objective optimization problem
F ( x ) k  min,
G j ( x )  0,
Ai  xi  Bi ,
k  1,..., K
j  1,..., M
i  1,..., N
Pareto optimum set consists of the
designs which cannot be improved with
respect to all criteria at the same time.
Vilfredo Pareto
(1848-1923)
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.
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: don’t put up with D!
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!
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 manmade disasters
• Freeing up budgets for the use on environmental issues
Don’t confuse optimisation with CATNAP!
Cheapest Available Technology Narrowly Avoiding Prosecution
Climate change: Observations and
simulations
Natural only
Natural and human activity
Human activity only
‘A large part of the warming is
likely to be attributable to
human activities’
Met Office Hadley Centre
for Climate Change
An unlikely Eco-warrior
Honda F1 goes green!
Honda F1 “Earth Car”
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
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.
Air travel is cheaper than ever before
Greenpeace:
“Binge flying”
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.
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.
Progress in aeronautics 1903-2007
Wright brother’s Flier, FF: 17 December, 1903
Progress in aeronautics 1903-2007
Boeing 367-80, FF: 15 July 1954
Progress in aeronautics 1903-2007
Airbus A-380, FF: 27 April 2005
Progress in aeronautics 1903-2007
Boeing 367-80, 1954
Airbus A-380, 2005
Progress in aeronautics 1903-2007
Boeing 367-80, 1954
Airbus A-380, 2005
Still, things are changing…
787-8
Carbon laminate
Carbon sandwich
Other composites
Aluminum
Titanium
Other
Steel 5%
10% CFRP
Titanium
15%
43%
Aluminum
20%
Boeing 787, FF: expected in 2007. Composite primary structure
Composites
Misc.
50%
9%
Back to the future?
Cryogenic (hydrogen as fuel) aircraft.
Tupolev 155 (FF 15 April 1988)
Starboard engine: experimental hydrogen–powered NK-88.
Hydrogen tank of 17.5 m3 capacity in the aft part of the fuselage.
Back to the future - II
Liquefied Natural Gas
(LNG)-powered
Tupolev 156
(FF 18 January 1989)
Starboard engine: experimental LNG–powered NK-88. Tupolev 156 has
made over 100 test flights.
Current developments
Tupolev 205 (210 pass.)
Tupolev 136 (53 pass.)
Tupolev 334 (102 pass.)
Tupolev 330 (36 tonne cargo)
Recent developments
DASA-Tupolev Cryoplane
concept based on A-310
(1990-1993)
EADS-Tupolev demonstrator
aircraft based on Do-328
(1995-1998)
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
Breaking away from
tube with wings?
Novel design concept: Blended Wing Body (BWB)
X-48, Boeing and NASA Langley Research Center, project cancelled
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.
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
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!
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
FF: 17 July 1989
Lockheed F-117 Nighthawk
FF: 18 June 1981
Can optimisation invent
a new design concept?
If you only put in wax and wick optimisation won’t get you a light bulb
Wolfram Stadler (1937–2001)
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)
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
Topology optimisation
Design space
F1
F2
F3
Example of topology optimisation
Package space accommodation
Original design space
Restricted design space
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 Chairman’s Gold Award for Innovation
•Altair’s optimisation technology is integrated into Airbus design process
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
Supermarine Southampton, 1925
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.
Genetic Algorithm: mimicking
natural evolution
Example: composite optimisation
Fibre optimised
configuration
Baseline
configuration
Fibre
orientation
z
Composite optimization
Optimized fibre
design
Thickness
optimized design
Number
of plies
Optimized
thickness
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
Selection
Randomised
Biased towards the fittest members of population
Reproduction
Mating
• creating a new chromosome (child) from two
current chromosomes (parents)
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
Mutation – why it is important?
Evolutionary mechanism of
the Genetic Algorithm
Fitness
Mutation
Genetic
Search
Crossover
Selection
Reproduction
Case Studies
F1 Jaguar Racing Wing
• The wing was split into patches
• Each patch was optimized for number of plies and ply
orientation
patch 5
patch 15
patch 2
patch 3
patch 14 patch 4
patch 12 patch 13
patch 11
patch 1
Load Cases Applied
Aerodynamic loading
FIA 50kg point loading
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
Mass (Kg)
•
5.5
5.3
5.1
4.9
Generations
Can we afford not to optimise?
Not really, the pressures are too great
Optimise or else…
If it is so good, why don’t we all
do it all the time?
Because it is not easy!
There are serious issues to address.
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 aren’t sharp enough
• Insufficient education of graduates and engineers
• Mostly, we are preaching to the choir rather than the congregation
Computationally expensive and noisy
The start: Computers of the 1970-80s
BESM-6 (1965-1995): 1 Mflop, 32K word RAM, 48 bit word
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
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
Doing something else?
If something's hard to do,
then it's not worth doing!
Homer Simpson
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.
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
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
DOEs for metamodel building
Sampling according to some Designs of Experiments (DOEs) is needed:
• to build a metamodel
• and also to check the metamodel
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.
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
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.
Example of stamping simulation
High- and low-fidelity models
FEM: PAM-STAMP
High-fidelity model (Fine mesh)
Elements: 1100
Time: 150 sec.
FEM: PAM-QUIKSTAMP
Low-fidelity model (Coarse mesh)
Elements: 120
Time: 10 sec.
Result:
• high-fidelity model only: 1040 min,
• interaction with low-fidelity model: 155 min.
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
Genetic Programming
John Koza: Genetic Programming
Genetic Programming
Example: Tree structure for the expression
x

1

 x3 
x

 2

SQ
Unary Node
+
Binary Nodes
/
x1
x3
x2
Terminal Nodes
2
Genetic Programming
Genetic operators:
•Selection
•Crossover
•Mutation
•Elite transfer
Genetic Programming
Crossover
SQ
+
/
*
x1
x2
SQ
x2
+
SQ
SQ
x1
x1
PARENT 1
x2
PARENT 2
SQ
+
+
SQ
*
x2
/
x1
SQ
x1
x2
SQ
x2
x1
OFFSPRING 1
OFFSPRING 2
Genetic Programming
Mutation
SQ
SQ
{+
-
SQ
x1
x2
-
/
*
}
*
SQ
x1
x2
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’’.
Empirical modelling of shear
strength of RC deep beams
Normalised shear strength:
  Ax52  Bx 5  C
where
A  4.56  1.68 x1
B  2.45  0.1x12  1.16 x1  3.12 x6
C  0.3( x3  x4 )
Collaboration:
Dr Ashraf Ashour, Bradford University
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
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
Optimisation of a shell
First design, normalized constraint equals 1.0
Optimisation of a shell
Second design, normalized constraint equals 1.0
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)
Aerofoil optimisation
Objective function (to be minimized): drag coefficient at Mach
0.73 and Mach 0.76:
F0 (x) = 2.0 Cd total (M=0.73) + 1.0 Cd total (M=0.76)
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)
Optimisation of structural steelwork
Objective: cost
minimisation
Design variables:
numbers of steel
sections from a
catalogue
Constraints:
defined by BS 5950
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
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)
Airbags for space landers
Vented Type
• Active control
• Single stroke
• No space heritage
• Low Mass
Kistler Booster (Irvin)
• Vulnerable to over-turning
ExoMars (ESA)
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
Airbag configuration
Six identical vented chambers
One “anti-bottoming” un-vented toroidal
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?
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
Baseline design:
Flat bottom impact
All requirements are satisfied by the baseline design
Baseline design:
Inclined rock impact
Baseline design: deceleration 980g (target <70g)
ExoMars Lander: LS-DYNA simulation
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
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
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
Mean Resultant Wind Speed
1000
PDF fit to EMCD model data
900
800
Rayleigh distribution
700
500
400
300
200
100
.0
.0
29
.0
28
.0
27
.0
26
.0
25
.0
24
.0
23
.0
22
.0
21
.0
20
.0
19
.0
Wind Speed (m/s)
18
.0
17
.0
16
.0
15
0
.0
0
9.
14
0
8.
.0
0
7.
13
0
6.
.0
0
5.
12
0
4.
11
0
3.
.0
0
2.
10
0
1.
0
0.
Frequency
600
Rock height probability distribution
Probability Density Function f(H)
NASA/JPL rock size distribution
model
7.0
k = 10%
6.0
k = 20%
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
Probability Density (m^-1)
k = 30%
5.0
4.0
3.0
2.0
1.0
0.0
0.000
Exponential PDF
Mars Pathfinder landing site panorama (NASA/JPL)
0.200
0.400
0.600
0.800
Rock Height H (m)
1.000
1.200
1.400
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
Pitch Rate
Mean = 0 degs, 3 = 30 degs
Mean = 0 deg/s, 3 = 20 deg/s
Monte Carlo simulation:
counting failures…
Another
one bites
the dust!
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
ExoMars Lander:
LS-DYNA simulation
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
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
Any questions?
?