Optimisation: Getting More and Better for Less

1. 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

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 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.

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 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.

7. 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.

8. 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)

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 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!

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 • Don’t confuse optimisation with CATNAP! • Cheapest Available Technology Narrowly Avoiding Prosecution

13. 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

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 brother’s 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. 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

26. 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.

27. 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.

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 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)

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. Design space F1 F2 F3 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 Chairman’s Gold Award for Innovation • Altair’s 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. Example: composite optimisation Composite optimization 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?