Optimisation: Getting More and Better for Less

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# Optimisation: Getting More and Better for Less - PowerPoint PPT Presentation

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?.

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## Optimisation: Getting More and Better for Less

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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 vectorxof design variables:

whereF(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?
• = 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
• frequency of vibrations (can be several)
• drag
• lift
• fatigue life
• etc.
Multi-objective problems
• Pareto optimum set consists of the designs which cannot be improved with respect to all criteria at the same time.
• A general multi-objective optimization problem
• 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 f2waiting time so we are minimising both.
• Point A corresponds to the plumber who is cheapest (minimum costf1) and B to the one who is quickest (minimum waiting timef2).
• 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

Climate change: Observations and simulations

Natural only

Human activity only

Natural and human activity

‘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

Carbon laminate

Carbon sandwich

Other composites

Aluminum

Titanium

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

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

• 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?

• 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

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!

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
• 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
• 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

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

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.

Example: composite optimisation

Composite optimization

Fibre optimised configuration

Baseline configuration

Fibre orientation

z

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

patch 5

patch 15

patch 1

patch 2

patch 3

patch 4

patch 14

patch 12

patch 13

patch 11

Case StudiesF1 Jaguar Racing Wing

• The wing was split into patches
• Each patch was optimized for number of plies and ply orientation

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

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
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
• 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.

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.

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

Genetic Programming

• Genetic operators:
• Selection
• Crossover
• Mutation
• Elite transfer

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:

Collaboration:

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 Cdtotal (M=0.73) + 1.0 Cdtotal (M=0.76)
• Constraints: on liftand 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
• Vulnerable to over-turning
• Kistler Booster (Irvin)
• 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
• 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)

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
• PDF fit to EMCD model data
• Rayleigh distribution

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)

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

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

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