Lecture Slides: Lecture Evaluation

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The lecture slides of lecture Evaluation of the Modelling Course of Industrial Design of the TU Delft

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Lecture Slides: Lecture Evaluation

  1. 1. G-L-4: Evaluation Prof. Dr. Christos Spitas Dr. Y. Song (Wolf) Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 1
  2. 2. Contents 1 Why evaluation? 2 Define the evaluation criteria 3 Sensitivity analysis • of the simulation • of the system 4 What did we learn today? Challenge the future 2
  3. 3. Evaluation in the modelling cycle what are you studying? Case brief ‘touch’ your thoughts choices what exactly...? what do you foresee? Build abstract model System choices choices what does your model foresee? Thought simulation Experience Solve/ simulate choices Compare did you both agree? everything you did/ saw/ felt/ remember to be true... Finish! Acceptable ? Revisit choices do you need more insights/ data? Experiment Courtesy of centech.com.pl and http://www.clipsahoy.com/webgraphics4/as5814.htm Challenge the future 3
  4. 4. Evaluation Identify, choose Learn Modelling System Solve Evaluation Evaluation is systematic determination of merit, worth, and significance of something or someone using metrics against a set of quantified expectations Challenge the future 4
  5. 5. A case study: Heat the house 1 °C in  3 min Design brief •Specify the areas of radiators  and the hot water temperature  for the boiler in a house in order  to raise the room temperature 1  degree in 3 minutes Courtesy of http://www.daalderop.nl/verwarming-en-koeling/twee-cv-zone-systeem/ Challenge the future 5
  6. 6. Components Boiler House Water Radiator Air Courtesy of http://www.daalderop.nl/verwarming-en-koeling/twee-cv-zone-systeem/ Challenge the future 6
  7. 7. Cause - effect Boiler Water The house is heated Radiator Air Challenge the future 7
  8. 8. Choice Neglect the heat capacity of radiator Heat transfer from radiator to air is uniform Model Adiabatic house And many more… Challenge the future 8
  9. 9. Modelling Air temperature Hot water temperature from the heater Heat capacity of air mair cair Mass of air Twater  Tair (t ) d Tair (t )  1 dt hAradiator Heat transfer coefficient The surface area of radiator We choose The initial temperature of room is 10°C The specific heat capacity of air is 1012 J/(kg*K) The volume of the house is 350 m3 The density of air 1.024 kg/m3 The heat transfer coefficient is 10 W/m2 Challenge the future 9
  10. 10. Define the evaluation criteria Challenge the future 10
  11. 11. Define the evaluation criteria – The metric Input 1 Input 2 … Parameter 1 … Input: any intended or unintended excitation of the system Parameter 1 Parameter: design parameter, chosen by designer System Metric function Usually from design brief Output 1 Output 2 … Output: system response (state) Challenge the future 11
  12. 12. What is the metric in this system? An output (against expectations) Part of an output (against expectations) Combined (parts of) outputs Combined (parts of) inputs / parameters / outputs Courtesy of http://www.daalderop.nl/verwarming-en-koeling/twee-cv-zone-systeem/ Challenge the future 12
  13. 13. The metric and the criteria Criterion is the metric for judging (satisfaction)  t M  T  M 1ºC Time to raise the temperature by 1ºC Part of the criterion  1C The metric Tair (t   t  M )  Tair (t )   T  M where  t  M  f (Twater , Aradiator ) Part of the criterion 180 seconds Challenge the future 13
  14. 14. Sensitivity analysis Challenge the future 14
  15. 15. We cannot always explore every possible solution An example - Drop an cup on the floor Simulate from 0 to 0.00125 second Only one step Computation time: 48 hours on Pentium 4 3.6 GHZ CPU Challenge the future 15
  16. 16. Sensitivity analysis one parameter vs one metric Input /parameter1 Metric System Derivative of the metric (f) w.r.t. input / parameter(p) d f ( p) dp Challenge the future 16
  17. 17. Sensitivity analysis multiple parameters vs one metric Input /parameter1 Input /parameter 2 System Metric Input /parameter… Gradient of the metric (f) w.r.t. inputs / parameters (p1,p2...,pn) f  (    f ( p1 , p2 ,... pn ), f ( p1 , p2 ,... pn ),, f ( p1 , p2 ,... pn )) p1 p2 pn Challenge the future 17
  18. 18. Sensitivity analysis: An Example x f ( x, y )  xe  x2  y2 f ( x, y ) y f(x, y) Challenge the future 18
  19. 19. Sensitivity analysis: An Example x f ( x, y )  xe  x2  y 2 f ( x, y ) y Sensitive f ( x, y )  ( Insensitive  ( f ( x, y )  ( f ( x , y ) , ) x y Challenge the future 19
  20. 20. Numerical approach of partial differences f ( p1   p , p 2 ,... p n )  f ( p1 , p 2 ,... p n )  f ( p1 , p 2 ,... p n )   p1 p Example: f ( x, y )  xe  x2  y2  f ( x, y ) x x 0  (0  x)e e  ( 0  x ) 2  y 2  0e 02  y 2 x  x 2  y 2 Challenge the future 20
  21. 21. Sensitivity analysis of the simulation Challenge the future 21
  22. 22. Sensitivity analysis in simulation Suppose the temperature of house is 10°, the water is 55° and the surface area of radiators is 5m2, the model is d T (t )  0.0129 - 0.000234T (t ) dt Euler method: d y (t ) t y (t  t )  y (t )  dt Using Euler method to solve differential equation over the interval t=0 .. 5000 seconds. d y (t ) y (t  t )  y (t )  lim t  0 dt t Challenge the future 22
  23. 23. Euler method in detail Euler method: y (t  t )  y (t )  d y (t ) t dt Challenge the future 23
  24. 24. Sensitivity analysis in simulation 1 step Errors 3 steps 6 steps 12 steps Steps in Euler method Challenge the future 24
  25. 25. Sensitivity analysis of the system Challenge the future 25
  26. 26. Evaluations – the metric w.r.t initial temperature Time to raise the temperature by 1°C 180 seconds Choice Choice Initial room temperature Challenge the future 26
  27. 27. Evaluations – the metric w.r.t. surface area & water temperature mair cair Time needed to raise the temperature by 1°C Area of radiator (m2) Twater  Tair (t ) d Tair (t )  1 dt hAradiator Water temperature (ºC) Challenge the future 27
  28. 28. Evaluations 1ºC@180 s 1ºC@220 s 1ºC@240 s Safe zone 1ºC@260 s 1ºC@280 s Area of radiator (m2) Water temperature (ºC) Challenge the future 28
  29. 29. Recall: A more complicate case Simulate from 0 to 0.00125 second Only one step Computation time: 48 hours on Pentium 4 3.6 GHZ CPU Challenge the future 29
  30. 30. Evaluation of the results: Sensitivity analysis 1 2 3 How much do we trust our model? (sensitivity to solution parameters) Think smart, not hard: Substitutes calculationintensive ‘blind’ searches of the solutions space Design for ‘insensitivity’/ toleranceinsensitive, wide tolerances Challenge the future 30
  31. 31. What did we learn today? How to establish metric(s) (functions) Proper adjustment of design parameters leads to better designs Parameters play different roles in both modelling and simulation Challenge the future 31
  32. 32. Success! Prof. Dr. Christos Spitas Dr. Y. Song (Wolf) Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 32

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