ENGN 8101 Modelling and Optimisation

1. ENGN 8101Modelling and Optimisation Professor Qinghua Qin Email :Qinghua.Qin@anu.edu.au Tel: 6125 8274 Office: Room R228 Ian Ross Building

2. MODELLING OF ENGINEERING SYSTEMS Engineering? “Profession in which knowledge of maths & natural science gained by study and practice is used with judgment to develop ways to utilise economically, material and forces of nature for the benefit of mankind” Definition by : ABET ENGN8101 Modelling and Optimization

3. Design? “Process of converting customer requirements into detailed plans (drawings and specifications) from which the product, process or system can be put together” Product/process/system must meet all customer requirements and be best with respect to chosen goodness measure(s). ENGN8101 Modelling and Optimization

4. DESIGN OPTIMIZATION Selecting the “best” design within the available means What is our criterion for “best”design? Objective function What are the available means? Constraints (design requirements) How do we describe different designs? Design Variables ENGN8101 Modelling and Optimization

5. Optimization? Minimise f(x); f  l; x  nObjectives Subject to : h(x) = 0; h  m Equality Constraints g(x)  0; g  p Inequality constraints xL  x  xUSide constraints ENGN8101 Modelling and Optimization

6. Subjective? Heuristic? Objective? Optimum design? Generic Approach • Choose an initial design • Identify design variables, X • Assign values to X • Assess system for acceptance • Modify X to improve design • Iterate till design is acceptable ENGN8101 Modelling and Optimization

7. Issues? • Problem statement. Identify • Design variables • Constraints • Objectives • Choose validated analysis for function evaluation • Optimization • Solution procedure: Golden Section Method/ Conjugate Gradient Method… • Sensitivity • Surrogate building • Software integration ENGN8101 Modelling and Optimization

8. System engineering in PracticeDesign of Boeing 777 • Program launched in Oct 29,1990 • First flight on June 1994 • 777 has 132,500 engineered, unique parts and a total of three million+ total parts ENGN8101 Modelling and Optimization

9. System engineering in practice Design of the Boeing 777 • Program launched in • October 29, 1990 • First flight on June • 1994 • 777 has 132,500 • engineered, unique • parts and a total of • three million + total • parts ENGN8101 Modelling and Optimization

10. ENGN8101 Modelling and Optimization

11. Text Books • “Optimization concepts and applications in engineering”- A.D. Belegundu & T.R. Chandrupatla - Required • “Engineering Methods for Robust Product Design” – W.Y. Fowlkes & C. M. Creveling – Strongly Recommeded • Available at ANU Bookshop ENGN8101 Modelling and Optimization

12. Course Schdule • Lecturers : Monday 1-3 Tuesday 1-3 • Lab ENGN8101 Modelling and Optimization

13. Assessment • Problem sets(20%) • modelling and optimization problems • EXTEND DES + design assignment – 20% • Experimental design exercise – 20% • Final Exam(40%) ENGN8101 Modelling and Optimization

14. Expectations • Every student to master all fundamental concepts • You must spend time with the material • It will be worth it in the future! • I promise to do my best to provide a robust learning environment ENGN8101 Modelling and Optimization

15. Academic Honesty • Personal and corporate integrity is an essential element of any quality organization. Accordingly, I expect every student to avoid even the appearance of cheating, and to claim credit only for his or her own work. • I promise the same level of personal integrity that I expect. Cheating of any kind simply will not be tolerated! ENGN8101 Modelling and Optimization

16. MODELLING OF ENGINEERING SYSTEMS “Real phenomena that are subject to uncertainty can be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated” Barry Nelson 1995 i.e. whose state varies with time i.e. dynamic phenomena e.g. an engineering system What is a system? - not for now! ENGN8101 Modelling and Optimization

17. “Real phenomena that are subject to uncertainty can be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated” i.e. convert system into smaller entities whose state can be modelled using a probability distribution e.g. what is the probability that after an hour, a machine is still working? ENGN8101 Modelling and Optimization

18. “Real phenomena that are subject to uncertaintycan be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated” Take actual readings of variables and plug them into the probabilistic model to generate key performance characteristics ENGN8101 Modelling and Optimization

19. “Real phenomena that are subject to uncertaintycan be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated” come up with statistically robust estimates of future system behaviour ENGN8101 Modelling and Optimization

20. Furthermore: “Investigate how parametric design affects key parts of the system” i.e. obtain combinations of parameters that give maximum desirability in a key performance measure i.e. OPTIMIZATION ENGN8101 Modelling and Optimization

21. Good engineering practice…… Take a system and use modelling and optimization techniques to present a theoretically robust design NEVER design using trial and error! ENGN8101 Modelling and Optimization

22. Brief example: Probability that a light bulb breaks States = ‘working’ or ‘not working’ over a time ‘x’ When x=0 + δx – the light bulb has just been switched on Can be modelled as an exponential distribution Often used in failure analysis Light bulb most likely to fail when switched on! ENGN8101 Modelling and Optimization

23. Purpose of modelling – “to deduce statements about the performance of a real or conceptual engineering system” i.e. Dynamic systems that are subject to uncertainty Models = 100% predictable Systems = never! ENGN8101 Modelling and Optimization

24. Key to successful modelling of a system…. Scale down into manageable entities then model behaviour through probabilistic/statistical techniques i.e. Discrete Event Modelling An example of numerical modelling ENGN8101 Modelling and Optimization

25. EXTEND – typical DE modelling software ENGN8101 Modelling and Optimization

26. Also – simple analytical modelling i.e. analytical solutions to linear, differential and partial differential equations ENGN8101 Modelling and Optimization

27. Numerical Modeling • Finite Element Models, Matlab, EXTEND ENGN8101 Modelling and Optimization

28. Also - Structural/Numerical Modelling ENGN8101 Modelling and Optimization

29. Some Modelling Issues… • Most analytical and numerical models tend to be discipline • specific (exceptions include multi-body physics models) • Some of these modelling techniques need expert training • There are several practical applications where • analytical/numerical modelling techniques are not effective • (cost, time, expert training or limitations in coping with the • complexity of the problem) ENGN8101 Modelling and Optimization

30. MAJOR FOCUS OF ENGN8101 How to model and thus optimize an engineering system to improve it ‘Improve’ could mean ‘enhance the quality of the output’ In terms of quality – Possible to model a system without formally optimizing it Also – may have to optimize a system without a model Data generation not always possible ENGN8101 Modelling and Optimization

31. Special note on Taguchi Methods • These are methods that use quality as a performance measure • They are not limited to any specific discipline area • Often used when analytical and numerical modelling are ineffective • Often used in synergy with other modelling strategies • Widely used in industrial settings • More like a philosophy than a technique ENGN8101 Modelling and Optimization

32. The course in a nutshell…. • Introduction • Discrete Event Modelling • Review of the nature of statistics • Basic probability • Statistical models in simulation • Modelling of queueing processes • Quality Engineering • Introduction to quality engineering • Design of experiments (orthogonals, factorial, interactions) • Parametric design (S/N ratios, 2-step optimization) • Importance of loss functions • Classical Optimization • Philosophical issues • Mathematical foundations • Unconstrained optimization • Constrained optimization ENGN8101 Modelling and Optimization

33. A first modelling exercise….. • What is “best”? • Which option “best”? • 100% of the time? – neither will be! Dynamic system with variables (customer type etc.) One option best x% of the time One option best y% of the time If x»y – find the first option and live with the uncertainty Uncertainty = randomness = stochastic ENGN8101 Modelling and Optimization

34. Essential first step…… collect data! What is this data giving us? CASE STUDY 1 The general office of a large company has as one of its responsibilities, the photocopying area. Currently, they have one photocopying machine and one operator. Employees needing some copying work wait in a single line until called by the operator. Some jobs involve mere copying, whereas others are more complicated, requiring collation, stapling etc. Employees are now complaining that they are waiting too long, so the office is considering expanding its photocopying service. There are two options. The first is to purchase another copier and a second operator, and the second option is to have a second copier for self-service jobs only (i.e. no operator). Which option is best? To assist with the task, the following data were collected on one morning period: ENGN8101 Modelling and Optimization

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36. Or in a more meaningful structure…… i.e. a queueing scenario a very common system model ENGN8101 Modelling and Optimization

37. Data presentation methods…..Histogram • Graphically visualize the data spread and hint at any pattern • Divide data set into classes (ranges of values) • sample size = n – no. of classes = √n i.e. 100 observations of the inside diameter of a metal sleeve 20 samples of 5 specimens To create a histogram… ENGN8101 Modelling and Optimization

38. 49.90 49.92 49.94 49.96 49.98 50.00 50.02 50.04 50.06 50.08 50.10 ENGN8101 Modelling and Optimization

39. % Service time (minute) ENGN8101 Modelling and Optimization

40. Conclusions… • Look at the average service times: full service = 7 • self service = 3 • all service = 4.6 •  problem?  make second copier a self-service? • - not yet! • Service time = wrong variable to base decisions on • most likely – 2nd copier will have no effect on service times Need to differentiate between variables under the customer’s control & variables under the company’s control Uncontrollable v. controllable factors! ENGN8101 Modelling and Optimization

41. More appropriate to use a controllable factor • e.g. delay (time waiting in queue) • data – lead to sample paths • 2 parts: • Customer characteristics (arrival times, service times) • Company characteristics (one-at-a-time, FCFS) • =system inputsb) =system logic • Concentrate on logic – not inputs CASE STUDY 1 ENGN8101 Modelling and Optimization

42. Sample path method – a graphical system model SAMPLE PATH – record of the time-dependent behaviour of a system SAMPLE PATH DECOMPOSITION – represents a sample path as inputs and logic SIMULATION – generates new sample paths without building a new system SAMPLE PATH ANALYSIS – extracts system performance measures from sample paths ENGN8101 Modelling and Optimization

43. 2-copier system alternatives: Full-service + self-service 2 x Full-service Self-service system: - define the system logic… 2 queues – 1 for full-service, 1 for self-service no swapping of queues Customers always join appropriate queue Service times – same as before (uncontrollable (noise) factor ENGN8101 Modelling and Optimization

44. Performance measure – waiting time i.e. Delay 3 system events: • customer arrival • customer finish (full-service) • customer finish (self-service) CASE STUDY 1 Now – let’s run a simulation based on the previous data….. ENGN8101 Modelling and Optimization

45. First four events: system starts customer 1 arrives customer 2 arrives customer 2 finishes etc… ENGN8101 Modelling and Optimization

46. Dear students……. Continue this analysis on the sheets on the table – then answer the following: The first non-zero delay is at t = ? It occurs for customer number ? It is a delay of ? minutes At t = ? two events occur simultaneously The simulation ends at t = ? Which customers experience delays? How big are these delays? answers 45 7 1 76 129 7&13 1&7 ENGN8101 Modelling and Optimization

47. Dear students…….answers! Continue this analysis on the sheets on the table – then answer the following: The first non-zero delay is at t =45 It occurs for customer number7 It is a delay of1minutes At t =76two events occur simultaneously The simulation ends at t =129 Which customers experience delays?7&13 How big are these delays1&7 ENGN8101 Modelling and Optimization

48. How does this compare to the alternative? i.e. 2 copiers, both full-service System logic: 1 queue – service delivered as FCFS 3 system events: • customer arrival • customer finish (left-hand machine) • customer finish (right-hand machine) • i.e. ENGN8101 Modelling and Optimization

49. RESULTS (do it for yourself…?) 1 2 Simulation end time 129 124 Delayed customers 7,13 7,13,20 Delays 1,7 1,5,1 Total delay 8 7 Not much in it – but second model appears quicker Unexpected?? Need to consider the “goodness” of the data set (the sample ) ENGN8101 Modelling and Optimization

50. DATA QUALITY Must ensure the data is reliable i.e. statistically realistic and representative Sample size? Sample time? etc.. The statistics of sampling – sampling theory Also – relationship between sample and population ENGN8101 Modelling and Optimization