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Review for Final

Review for Final. Fall 2010 James R. Burns. Dimensionless Ratios. What do we use them for?? What impact do they have on dimensional consistency of an equation? Why do they make sense?. Dimensionless Ratios. How is the dimensionless ratio used in the natural gas model?.

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Review for Final

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  1. Review for Final Fall 2010 James R. Burns

  2. Dimensionless Ratios • What do we use them for?? • What impact do they have on dimensional consistency of an equation? • Why do they make sense?

  3. Dimensionless Ratios • How is the dimensionless ratio used in the natural gas model?

  4. Construct equations for this model

  5. What kind of behavior is this?

  6. Dimensionality Considerations • Rigorously, all models must be ________ _______ • What ever units you use for stocks, the associated rates must have those units divided by ______ • Explain what the SYNTHESIM tool does in VENSIM

  7. What if Dimensionless Ratios Don’t give us the effect we want? • Is there another way to pull in information? • Let’s look at the Forrester World Model

  8. What we see here is the use of table functions—Dimensionless Multipliers • Birth Rate = Birth Rate Normal * Population * Births Material Multiplier * Births Pollution Multiplier * Births Food Multiplier * Births Crowding Multiplier The last four multipliers are dimensionless table functions

  9. Establishing units for unquantified variables • How did Forrester do this in his world model?

  10. More ratios • Food ratio = Food/ Food normal • Again, Food normal is the amount of food available in the year 1970, in Food units • Crowding ratio = Population density normal/Population density • again, Population density normal is the population density in the year 1970, say

  11. Explain this picture

  12. What does it take to create a table lookup function in VENSIM? • Do table lookups ever have connectors (arrows) directed toward them? • What point do we generally expect to see on a table lookup function? • Why? • How is the table lookup used in the function it impacts?

  13. More about table lookups • Table lookups use _____ ______ between data points, by default

  14. Comment about Table Lookups • To find the ordinate value corresponding to a particular abscissa value that is given, let b = ordinate desired, a given abscissa. Then b = bi + (a – ai)*(bi+1 – bi) / (ai+1 – ai) Where a has been determined to lie between abscissas ai and ai+1

  15. Delays • Where do they appear? • Name some delays • aging populations, mail delays, perception delays, shipping delays, appearance delays, adjustment delays, scheduling delays and queue delays • Name two delay types

  16. Why 3rd-order exponential delays? • Why 1st-order exponential delays?

  17. Some Flow Delays that we’ve already looked at

  18. Comment about delays The modeler must ask… How do physical processes in the actual system create lagged behavior? How much disaggregation is necessary to represent the delay accurately

  19. Simulation Time Step • Should be between .5 and .25 of the shortest time constant (delay) in the model • Look at all of the time constants • Adjustment time • Perception time • Delivery delay time • Construction time • Lifetime • Find smallest • Set simulation time step appropriately

  20. Integration Method • Euler for models with discrete events • RK4 for models with oscillation

  21. Dynamic Test Inputs • Purpose • Reveal inherent behavior • Create extreme conditions • Examples • Pulse • Step • Ramp—one we didn’t look at • Exponential growth • Noise—randomness

  22. Extreme Conditions • Purpose • Reveal weaknesses • Generate insight • Methods • Remove contents of stock with PULSE function • Cut off inflows or outflows • Artificially force variables to 0 or to infinity

  23. Partial Model Testing • Purpose • Divide and Conquer • Develop understanding of subsystems • Test response of subsystems to driving data • Methods • Cut & paste structures into a new model • Use data variables or test inputs to drive behavior

  24. Feedback Elimination • Purpose • Identify feedback loops that are causing behavior • Methods • Sever flow connections • Replace variables with constants or test inputs • Insert 0*… in equations • Flatten lookups

  25. Parameter Sensitivity Analysis • Purpose • Link behavior to feedback loop structure • Identify leverage points • Search for equilibria • Methods • Vary parameters and initial conditions • Stretch and shift lookup table shapes

  26. Types of Sensitivity • Insensitive • Pendulum always comes to rest at bottom • Numerical • Numerical values change, but behavior “looks” the same • Behavior mode • Shift from s-shaped growth to oscillation • Policy • Policy conclusions change

  27. Policy Evaluation • Purpose • Develop effective policies • Identify conditions for effectiveness • Identify weakness in formulation of existing policies • Tools • Sensitivity Analysis • Optimization • Gaming

  28. Integration • What does RK4 assume in terms of step size? • Does RK4 like small step sizes? • What is the problem with small step sizes?

  29. Global Warming • How much warming is likely over the next century? • What changes in climate patterns, rainfall, growing season, storm incidence and severity, and sea level might ensue? • How much damage would these changes cause to humanity?

  30. All the models show the climate system to possess enormous inertia • The implication here is that if we had shut off all GHG emissions in the year 2000, TEMPERATURES WOULD CONTINUE TO RISE FOR ANOTHER 25 YEARS and then fall very slowly • This was an extreme condition test, of the type we talked about yesterday

  31. Would you describe the global warming system as…. • STABLE • UNSTABLE Why??

  32. Warming reduces the winter snow cover and shrinks the highly reflective polar ice caps, thus increasing heat absorption and leading to further melting, less snow cover and still greater absorption. This positive loop will cause much greater warming at the poles than in the tropics and more warming in the winter than summer

  33. This, in turn releases more methane and carbon dioxide into the atmosphere from decayed biomass in the frozen tundra, resulting in still another positive feedback loop ALL THE MODELS AGREE THAT STABILIZING THE GHG EMISSIONS WILL NOT STABILIZE TEMPERATURES OR THE CLIMATE ANYTIME SOON

  34. Barry Richmond’s Terrorism Model • Name some characteristic archetypes

  35. In addition to the escalation archetype, what other archetype comes to mind when you consider Barry Richmond’s model of terrorism

  36. Maturity • Contrast the concept of Maturity with the Senge concept of learning • Who created the capability maturity model? • What are the five levels of the capability maturity model? • How long does it take to go from one level to the next?

  37. The Five levels of the CMM • INITIAL • REPEATABLE • DEFINED • MANAGED • OPTIMIZING

  38. Goldratt’s Thinking process • What three questions does it address? • What are the five steps in Goldratt’s TOC?

  39. THEORY OF CONSTRAINTS: GOLDRATT 1. Identify the system constraints 2. Decide how to exploit the system constraints 3. Subordinate everything else to that decision 4. Elevate the system constraints 5. When this creates new constraints, go back to step 1

  40. What to change? • Team constructs a current reality tree (CRT) • Team starts by listing all undesirable effects (UDE’s) • Team inter-relates these by use of a tree, called a CRT • In the current reality tree, the team traces UDE’s back to a core problem (CP)

  41. Symptoms, Root Causes & a Core Problem • Rather than reacting to symptoms, we should be finding root causes • We consider undesirable effects to be symptoms • We look for a “common cause” that is the source for most of the undesirable effects

  42. Trees and such • Which tree do we use to address the question What to change??

  43. How do we read and interpret the following structure? Software Development Projects take too long • How are these structures different from CLD’s Fixing changes takes time There are many late- breaking changes to requirements

  44. Evaporating Cloud [EC] • The EC is used to address what question? • How does it work? • What is an injection? • What do we do next?

  45. The Future Reality Tree • How do we construct it? • What is it used for?

  46. The last question is… How to cause the change?? • What trees do we use to address this question?

  47. The prerequisite tree • The Transition tree

  48. The Prerequisite Tree • Place INJECTIONS at the top • List the obstacles that are expected • For each obstacle that is overcome, an intermediate objective is achieved • Each obstacle gives rise to an intermediate objective • The intermediate objectives need to be sequenced • The prerequisite tree does the sequencing

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