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A core Course on Modeling

This course explores fundamental questions in modeling that guide the creation of effective models. Participants will learn to identify choices in modeling, assess the necessity of numerical outputs, and determine the value or knowledge expected from a model. Through practical examples, such as analyzing the mechanics of a yoyo, learners will enhance their understanding of how to collect and organize data, verify model accuracy, and communicate findings. The course emphasizes critical thinking and decision-making in the modeling process, with an emphasis on real-world applications.

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A core Course on Modeling

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.3

  2. Three questions help tofind the purpose of a model 2 http://commons.wikimedia.org/wiki/File:Fairy_tale_castle.jpg

  3. Question1: Is theresomethingtochoose? Ifso, what? 3

  4. Question2: Do we neednumerical output? Ifso, what do these numbersmean? 4 http://commons.wikimedia.org/wiki/File:Sunset_with_railroad_signal.jpg

  5. Question3: Should the model yieldknowledge or value? Whatknowledge, or whatvalue? 5 http://commons.wikimedia.org/wiki/File:Academic_dress_Oxford_walking.jpg

  6. QUIZ ‘Value’ is not alwaysabout money. People sometimesuse money, however, as a way tocompare the value of things. How couldyouestimate the (negative) value of someonehavinginfluenza?

  7. Summary: • Is theresomethingtobechosen? Ifso, what? • Shouldtherebe a numericaloutcome? Ifso, what? • Should the model yieldvalue or knowledge? Whatvalue or knowledge?

  8. Examples • Whydoes a yoyo... • … climb the rope? • … go down slower than with 9.8 m/s2? • … attractsomuch fans? Explanation: why is something as it is?

  9. QUIZ Examples Whydoes a yoyoclimb the rope? • Whydoes a yoyo... • … climb the rope? • … go down slower than with 9.8 m/s2? • … attractsomuch fans? Explanation: why is something as it is?

  10. Examples 2. Whenwill the yoyo... • … reachitshighest point? • … stop yoyoing? • … get out of fashion? Prediction (1): at what time will X happen?

  11. Examples 3. Whatwill happen if... • … I pull up the yoyorope later? • … the diameter of the yoyoincreases? • … a new toy comesto the market? Prediction (2): whatwill happen if X?

  12. Examples 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

  13. Examples 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.

  14. Examples 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: howtocompactlyrepresent data? 2 4 6 8 10 • a = 2g / (2+r22/r12) a (m/s2) r2/r1 2 4 6 8 10

  15. Examples 5. Focus on what is important: • Is the shape important? • Is the ropequality important? • Is the brand important for the nr. soldyoyo’s? Abstraction: restricttoessentials

  16. Examples 6. Relatesimilarthings: • How does a yoyoresemble a bouncingball? • How does a yoyoresemble a hula hoop? • How does a yoyo hype resembleanyother hype? Unification: findcommonalitiesamong different things

  17. Examples 7. Investigate... • ... the changing force in the rope • ... the importance of friction • ... howyoyo-popularityvaries with the season Analysis: seek relations within the modeled system

  18. QUIZ At some point during the motion of a yoyo, the force in the rope is zero. When? Whatabout the rest of the time? Examples 7. Investigate... • ... the changing force in the rope • ... the importance of friction • ... howyoyo-popularityvaries with the season Analysis: seek relations within the modeled system

  19. Examples 8. Verify... • ... that the ropewillbe strong enough • ... that energy is conserved • ... that marketing lawsapplytoyoyosales Verification: ascertain the truth of something

  20. Examples 9. Informpeople... • ... how a yoyoworks • ... howto set up yoyoexperiments • ... howyoyo hype spreads Communication: givecomprehensible information

  21. Examples 10. What options existfor... • ... shapes of yoyo’s • ... tricks with yoyo’s • ... marketing strategiestospawn hypes Exploration: make inventory of options

  22. Examples 11. How todecide... • ... what diameters tomake yoyofall slower than ... m/s2 • ... whatmassto have a stableyoyo • ... what marketing priceto get turnover betterthan X Decision: whatinterventionneededtoachieve goal

  23. Examples 12. How tooptimize... • ... diameters to have yoyorise as far as possible • ... massto have yoyo as stable as possible • ... marketing priceto get turnover as large as possible Optimization: whatinterventiongivemaximalresult

  24. Examples 13. How toinstruct... • ... manufacturertoassemble a yoyo • ... yoyo kid toperform trick X • ... shop ownerto put yoyo’s on display Specification: ensuresomethingwillbe as itshould

  25. Examples 14. How to... • ... have a robot operate a yoyo • ... have an intelligent yoyostabilizeitself • ... have shop order yoyo’sdependent on market demand Control: adaptingbehaviortocircumstances

  26. Examples 15. How to... • ... have a yoyo simulator help learning tricks • ... have a hype simulator train sales people • ... Train: familarize trainees with a system

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