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A Core Course on Modeling

A Core Course on Modeling. 1. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 AUD 3 Kees van Overveld c.w.a.m.v.overveld@tue.nl AUD 6 Tijn Borghuis v.a.j.borghuis@tue.nl. A Core Course on Modeling. 2. What is the mathematical model of a yoyo?. A Core Course on Modeling. 3.

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A Core Course on Modeling

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  1. A Core Course on Modeling 1 Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 AUD 3 Kees van Overveld c.w.a.m.v.overveld@tue.nl AUD 6 Tijn Borghuis v.a.j.borghuis@tue.nl

  2. A Core Course on Modeling 2 What is the mathematical model of a yoyo?

  3. A Core Course on Modeling 3 What is the mathematical model of a yoyo? Answer: JJ=2D+T

  4. A Core Course on Modeling Week 1- No Model Without a Purpose 4 Lesson 1 no model without a purpose

  5. A Core Course on Modeling Week 1- No Model Without a Purpose 5 Two types of purposes: • I want to know something • I want to achieve something

  6. A Core Course on Modeling Week 1- No Model Without a Purpose 6 Two types of purposes: • I want to know something: research • I want to achieve something: design

  7. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  7

  8. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  8 1. Why does a yoyo ... • … climb the rope? • … go down slower than with 9.8 m/s2? • … attract so much fans? Explanation: why is something as it is?

  9. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  9 2. When will the yoyo ... • … reach its highest point? • … stop yoyoing? • … get out of fashion? Prediction (1): at what time will X happen?

  10. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  10 3. What will happen if ... • … I pull up the rope later? • … the diameter of the yoyo increases? • … a new toy comes to the market? Prediction (2): what will happen if X?

  11. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  11 4. How can I organize data? r1(cm) r2(cm) m(kg) a(m/s2) 2.5  0.1 5  0.2 0.2  0.05 3.3  0.2 2.0  0.1 8  0.1 0.3  0.05 1.4  0.5 2.5  0.05 5.10.1 0.5  0.02 3.2  0.1 3.0  0.2 6  0.1 0.3  0.05 3.2  0.4 1.0  0.1 10  0.2 0.6  0.05 0.2  0.05 5  0.1 1  0.1 0.1  0.05 9.8  0.3 4  0.2 4  0.2 0.3  0.05 7.4  0.2 .... r2 r1

  12. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  12 4. How can I organize data? r1(cm) r2(cm) m(kg) a(m/s2) r2/r1 2.5  0.1 5  0.2 0.2  0.05 3.3  0.2 2 2.0  0.1 8  0.1 0.3  0.05 1.4  0.5 4 2.5  0.05 5.10.1 0.5  0.02 3.2  0.1 2 3.0  0.2 6  0.1 0.3  0.05 3.2  0.4 2 1.0  0.1 10  0.2 0.6  0.05 0.2  0.05 10 5  0.1 1  0.1 0.1  0.05 9.8  0.3 0.2 4  0.2 4  0.2 0.3  0.05 7.4  0.2 1 ....

  13. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  13 4. How can I organize data? a(m/s2) r2/r1 3.3  0.2 2 1.4  0.5 4 3.2  0.1 2 3.2  0.4 2 0.2  0.05 10 9.8  0.3 0.2 7.4  0.2 1 Compression: how to compactly represent data? a (m/s2) 2 4 6 8 10 a = 2g / (2+r22/r12) r2/r1 2 4 6 8 10

  14. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  14 5. Focus on what is important: • Is the shape important? • Is the rope quality important? • Is the brand important for the nr. sold yoyo’s? Abstraction: restrict to essentials

  15. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  15 6. Relate similar things: • In what respect does a yoyo resemble a bouncing ball? • In what respect does a yoyo resemble a hula hoop? • In what respect does a yoyo hype resemble any other hype? Unification: find commonalities among different things

  16. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  16 7. Investigate ... • ... the changing force in the rope • ... the importance of friction • ... how yoyo-popularity varies with the season Analysis: seek relations within the modeled system

  17. lin. height lin. velocity lin. acceleration ang. velocity () ang. rotation () tijd A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  17 7. Investigate ... Analysis: seek relations within the modeled system

  18. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  18 8. Verify ... • ... that the rope will be strong enough • ... that energy is conserved • ... that marketing laws apply to yoyo sales Verification: ascertain the truth of something

  19. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to research  19 9. Inform people ... • ... how a yoyo works • ... how to set up yoyo experiments • ... how yoyo hype spreads Communication: give comprehensible information

  20. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  20

  21. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  21 1. What options exist for ... • ... shapes of yoyo’s • ... tricks with yoyo’s • ... marketing strategies to spawn hypes Exploration: make inventory of options

  22. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  22 2. How to decide ... • ... what diameters to have yoyo rise more than 1 m • ... what mass to have a stable yoyo • ... what marketing price to get turnover better than X Decision: what intervention needed to achieve goal

  23. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  23 3. How to optimize ... • ... diameters to have yoyo rise as far as possible • ... mass to have yoyo as stable as possible • ... marketing price to get turnover as large as possible Optimization: what intervention give maximal result

  24. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  24 4. How to instruct ... • ... manufacturer to assemble a yoyo • ... yoyo kid to perform trick X • ... shop owner to put yoyo’s on display Specification: ensure something will be as it should

  25. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  25 5. How to ... • ... have a robot operate a yoyo • ... have an intelligent yoyo stabilize itself • ... have shop order yoyo’s dependent on market demand Control: adapting behavior to circumstances

  26. A Core Course on Modeling Week 1- No Model Without a Purpose    Purposes related to design  26 6. How to ... • ... have a yoyo simulator help learning tricks • ... have a hype simulator train sales people • ... Train: familarize trainees with a system

  27. A Core Course on Modeling Week 1- No Model Without a Purpose    Various Kinds of Modeling Purposes  27 Purposes from research • Explanation • Prediction (2) • Compression • Abstraction • Unification • Analysis • Verification • Communication (Documentation)

  28. A Core Course on Modeling Week 1- No Model Without a Purpose    Various Kinds of Modeling Purposes  28 Purposes from design: • Exploration • Decision • Optimization • Specification • Steering and Control • Training

  29. A Core Course on Modeling Week 1- No Model Without a Purpose    Various Kinds of Modeling Purposes  29 Q: Why is purpose important for the modeler? A: The answer to almost any question in modeling will be: ‘check your purpose’

  30. A Core Course on Modeling Week 1- No Model Without a Purpose    How models work  30 • Question • Data, Measurements • Calculations, Approximations • Conclusion • Consequences • Question • Data, Measurements • Calculations, Approximations • Conclusion • Consequences

  31. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: material / immaterial  31 19th centurybrain model, Boerhaave Museum 20th centurybrain model (Wang & Chiew, UofCalgary, 2010)

  32. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: static / dynamic  32

  33. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: continuous / discrete  33

  34. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: numerical / symbolic  34 3 x 5 + 3 x 6 = 3 x (5+6) = 33 a x b + a x c = a x (b+c) = ?

  35. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: geometric / non geometric  35

  36. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: deterministic / stochastic 36

  37. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: calculating / reasoning  37

  38. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: black box/ glass box  38

  39. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches - overview  39 Material – Immaterial Static – Dynamic Continuous – Discrete Numerical – Symbolic Geometric – Non-geometric Deterministic – Stochastic Calculating – Reasoning Black box – Glass box typically, several of these dimensions are relevant for any given model

  40. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches - overview  40 dynamical systems data modeling process modeling modling from scratch Material – Immaterial Static – Dynamic Continuous – Discrete Numerical – Symbolic Geometric – Non-geometric Deterministic – Stochastic Calculating – Reasoning Black box – Glass box M Im StDy CoDi NuSy GeoNg DetSto CalRea BbGb M Im StDy CoDi NuSy GeoNg DetSto CalRea BbGb M Im StDy CoDi NuSy GeoNg DetSto CalRea BbGb M Im StDy CoDi NuSy GeoNg DetSto CalRea BbGb

  41. A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  41 http://www.visade.nl/nieuws/2008/mailing__de_verkeerde_volgorde

  42. define conceptualize initial problem  conceptual model formalize conceptual model  formal model execute formal model  result conclude result  resolve initial problem? A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  42 context  initial problem

  43. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  43 sometimes, all modeling phases may be skipped

  44. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  44 sometimes, the formal phases may be skipped

  45. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  45 formulate purpose

  46. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  46 formulate purpose identify entities choose relations

  47. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  47 formulate purpose identify entities choose relations obtain values formalize relations

  48. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  48 formulate purpose identify entities choose relations obtain values formalize relations operate model obtain result

  49. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  49 formulate purpose identify entities choose relations obtain values formalize relations operate model obtain result present result interpret result

  50. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  50 formulate purpose identify entities choose relations obtain values formalize relations r e f l e c t i n g operate model obtain result present result interpret result

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