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

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.

Why do we call it that way?

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.

NiBxA

Mjg

F

iii

j

,...,1,

,...,1,0)(

max)or(min)(

x

x

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.

Choice of design variables

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?

Example

Answer: 1010 seconds = 317 years

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.

MATHEMATICAL OPTIMIZATION PROBLEMCriteria of system’s efficiency

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.

Pareto optimum set consists of the designs which cannot be improved with respect to all criteria at the same time.

NiBxA

MjG

KkF

iii

j

k

,...,1,

,...,1,0)(

,...,1min,)(

x

x

A general multi-objective optimization problem

Multi-objective problems

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 man-made disasters

• Freeing up budgets for the use on environmental issues

Don’t confuse optimisation with CATNAP!

Cheapest Available Technology Narrowly Avoiding Prosecution

‘A large part of the warming is likely to be attributable to human activities’

Natural only Human activity only

Climate change: Observations and simulations

Met Office Hadley Centre for Climate Change

Natural and human activity

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.

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

Progress in aeronautics 1903-2007

787-8

Carbon sandwich

Carbon laminate

Other composites

Aluminum

Titanium

CFRP 43%

Misc. 9%

Composites50%

Aluminum20%

Titanium15%

Steel10%

Other5%

Still, things are changing…

Boeing 787, FF: expected in 2007. Composite primary structure

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 334 (102 pass.)

Tupolev 136 (53 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 Lockheed F-117 Nighthawk

FF: 17 July 1989 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)

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)

If you allow the problem to contain a novel solution then you will get it as a result of optimisation.

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

Design space

F1 F2 F3

Topology optimisation

Example of topology optimisation

Package space accommodation

Original design space Restricted design space

• 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

AIRBUS UK RETURN ON INVESTMENT

Airbus A-380 droop nose leading edge

Note that a truss-like wing rib structure has been obtained that is different from a traditional plate with openings

Wing rib designs

A discovery?

Let us look at some historic parallels

Supermarine Southampton, 1925

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.

Wing rib designs

Genetic Algorithm: mimicking natural evolution

Fibre optimised Fibre optimised configurationconfiguration

Baseline Baseline configurationconfiguration

Fibre Fibre orientationorientation

z

OptimizedOptimizedthicknessthickness

Optimized fibreOptimized fibre designdesign

Thickness Thickness optimized designoptimized design

Number Number of pliesof plies

Composite optimization

Example: composite optimisation

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

Genetic Algorithm basics

Randomised

Biased towards the fittest members of population

Selection

Reproduction

Mating

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

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

Mutation – why it is important?

Evolutionary mechanism of the Genetic Algorithm

G eneticS earch

F itn ess

S e lec tio n

R ep ro d u c tio nC ro sso v e r

M u ta tio n

patch 1patch 2

patch 3

patch 5

patch 4

patch 11patch 12 patch 13

patch 14

patch 15

• The wing was split into patches

• Each patch was optimized for number of plies and ply orientation

Case StudiesF1 Jaguar Racing Wing

Aerodynamic loading FIA 50kg point loading

Load Cases Applied

• 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

4.9

5.1

5.3

5.5

5.7

5.9

Generations

Mas

s (K

g)

Front Wing Optimization Results

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.

• 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

What are the obstacles?

Computationally expensive and noisy

The start: Computers of the 1970-80s

BESM-6 (1965-1995): 1 Mflop, 32K word RAM, 48 bit word

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

Challenge

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

Stochastic analysis

If something's hard to do,

then it's not worth doing!

Homer Simpson

Doing something else?

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.

Use approximations!

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 design optimization

• 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

Metamodelling for stochastic analysis

Sampling according to some Designs of Experiments (DOEs) is needed:

• to build a metamodel

• and also to check the metamodel

DOEs for metamodel building

• 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.

Metamodelling techniques

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

Interaction of high- and low Interaction of high- and low fidelity modelsfidelity models

Initial blank Drawn box Target shape

Trimming

Find optimum blank shapeto minimise waste of material

Example: Optimum blank design for deep drawing process

Waste

Hiroshima University and Mazda Corp.

Example of stamping simulation

High-fidelity model (Fine mesh)Elements: 1100Time: 150 sec.

FEM: PAM-STAMP

Low-fidelity model (Coarse mesh)Elements: 120Time: 10 sec.

High- and low-fidelity models

FEM: PAM-QUIKSTAMP

Result:• high-fidelity model only: 1040 min, • interaction with low-fidelity model: 155 min.

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

Creation of analytical metamodels using Genetic Programming

John Koza: Genetic Programming

Genetic Programming

2

32

1

x

x

x

SQ

+

/

x1 x2

x3

Binary Nodes

Unary Node

Terminal Nodes

Example: Tree structure for the expression

Genetic Programming

Genetic operators:

•Selection

•Crossover

•Mutation

•Elite transfer

Genetic Programming

Crossover +

* /

SQ SQx1

x2

x2

x1

SQ

+

SQ x2

x1

+

*

SQx1

x2

SQ

x1

SQ

+

x2/

SQx2

x1

PARENT 1 PARENT 2

OFFSPRING 1 OFFSPRING 2

Genetic Programming

Mutation

-

SQ

-

SQ

x1

x2

SQ

*

SQ

x1

x2

*/+{ }

Genetic Programming

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:

)(3.0

12.316.11.045.2

68.156.4

43

6121

1

525

xxC

xxxB

xA

CBxAx

where

Collaboration:

Dr Ashraf Ashour, Bradford University

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: Small-scale CHP plant

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

Application: Optimisation of a shell

First design, normalized constraint equals 1.0

Optimisation of a shell

Second design, normalized constraint equals 1.0

Optimisation of a shell

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)

Aerofoil optimisation

Objective: cost minimisation

Design variables: numbers of steel sections from a catalogue

Constraints: defined by BS 5950

Optimisation of structural steelwork

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

ExoMars space mission

Un-vented type (inflatable ball)

• Multiple bounces

• Established heritage (from Luna-9 in 1966)

• High mass

• Vulnerable to rupture

Mars Pathfinder (NASA/JPL) Beagle 2 (Beagle 2)

Luna 9 (USSR Space Program)

Airbags for space landers

Vented Type

• Active control

• Single stroke

• No space heritage

• Low Mass

• Vulnerable to over-turning

ExoMars (ESA)

Kistler Booster (Irvin)

Airbags for space landers

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 landing design concept

Six identical vented chambers

One “anti-bottoming” un-vented toroidal

Airbag configuration

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?

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

Landing scenarios

All requirements are satisfied by the baseline design

Baseline design: Flat bottom impact

Baseline design: deceleration 980g (target <70g)

Baseline design: Inclined rock impact

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

European Mars Climate Database (EMCD) - general circulation model

45N to 45S latitudes

Season 12

Mars Global Surveyor dust loading scenario

PDF fit to EMCD model data

Rayleigh distribution

Mean Resultant Wind Speed

0

100

200

300

400

500

600

700

800

900

1000

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

16.0

17.0

18.0

19.0

20.0

21.0

22.0

23.0

24.0

25.0

26.0

27.0

28.0

29.0

Wind Speed (m/s)

Fre

qu

ency

Wind speed 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

Probability Density Function f(H)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400

Rock Height H (m)

Pro

bab

ility

Den

sity

(m

^-1

)

k = 10%

k = 20%

k = 30%

Mars Pathfinder landing site panorama (NASA/JPL)

Rock height 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

Pitch angle and pitch rate probability distribution

Another one bites the dust!

Monte Carlo simulation:counting failures…

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

• 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

Comment on the specific choice of optimization technique

• 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

Challenges ahead

?

Any questions?