Sensitivity Analysis of Graphical Functions

1. Sensitivity Analysis of Graphical Functions Sibel Eker, Jill Slinger Workshop on Model Analysis Tools and Methods, Part II The 32nd International Conference of the System Dynamics Society 24 July 2014, Delft

2. Graphical / Table / LookupFunctions • Table functions: • nonlinear relationships between two variables • Point-by-point definition, e.g. • Analytic functions: • nonlinear relationships between two variables • Analyticaldefinition, e.g.

3. Aim of the Workshop • To demonstrate and practice the implementation of an automated method for sensitivity analysis of table functions • To discuss and evaluate the usefulness of this method • Paper forthcoming?

4. Outline Whysensitivity analysis of tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration in Vensim Exercise 3: Application to a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

5. Why sensitivity analysison table functions? • Subjective and uncertain formulation, unless based on physical laws • Multiple alternatives • Effects on the model output should be investigated

6. Outline Whysensitivity analysis on tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration on Vensim Exercise 3: Application on a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

7. Hearne’s distortion method • Based on the multiplication of a model function by another function • Parameterization of the model function using the parameters of the distortion function

8. EXERCISE 1a:Conceptualizing Distortions

9. EXERCISE 1a:Conceptualizing Distortions

10. EXERCISE 1a:Conceptualizing Distortions

11. EXERCISE 1b:Conceptualizing Distortions

12. EXERCISE 1b:Conceptualizing Distortions

13. EXERCISE 1b:Conceptualizing Distortions

14. Outline Whysensitivity analysis of tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration in Vensim Exercise 3: Application to a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

15. EXERCISE 2:Demonstration of Automated Distortions in Vensim h * Original Table Function if then else(x<=p :AND: x>=0, 1 + m * (x-alpha)/(p -alpha), 1 + m * (x-beta)/(p -beta))

16. EXERCISE 2:Demonstration of Automated Distortions in Vensim h * Original Table Function if then else(x<=p :AND: x>=0, 1 + m * (x-alpha)/(p -alpha), 1 + m * (x-beta)/(p -beta))

17. EXERCISE 2:Demonstration of Automated Distortions in Vensim

18. EXERCISE 2:Demonstration of Automated Distortions in Vensim

19. Outline Whysensitivity analysis of tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration in Vensim Exercise 3: Application to a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

20. Application to a Simple Model:

21. Application to a Simple Model:

22. Application to a Simple Model:

23. EXERCISE 3:Application to a Sample Model

24. EXERCISE 3:Application to a Sample Model

25. EXERCISE 3:Application to a Sample Model

26. Outline Whysensitivity analysis of tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration in Vensim Exercise 3: Application to a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

27. Extensions

28. Extensions

29. ExtensionsDouble Triangular Distortion Function with Static End Points

30. EXERCISE 4:Extensions to the Method = 3 h3 – Double-triangular distortion function

31. EXERCISE 4:Extensions to the Method

32. EXERCISE 4:Extensions to the Method

33. Outline Whysensitivity analysis on tablefunctions? Hearne’smethod Exercise 1: Concept Exercise 2: Demonstration on Vensim Exercise 3: Application on a Sample Model Exercise 4: Extensionsto the Method Discussion & Evaluation

34. Other approaches to sensitivity analysis of table functions • Trying out a number of possibilities manually • Multiplying the original table function by constant factors, like 0.9 and 1.1 • Distorting the table function point by point (Keloharju and Wolstenholme, 1988) • Using analytical functions instead of table functions defined by pairs of input and output values • Defining the function as a weighted average of two predetermined table functions (Gonçalves et al., 2005)

35. Discussion • Criteria for comparison • Automated application on the commercial software packages • Variety of alternative function forms created, different from the original shape • Control on the distortions, avoiding infeasible shapes • Ease of use (e.g. being based on a tabular form, ease of determination of parameter ranges)

36. Evaluation 1 2 3 4

37. References Eker S, Slinger J, Yucel G. 2011. Investigating an Automated Method for the Sensitivity Analysis of Functions In Proceedings of the 29th International Conference of the System Dynamics Society, edited by J. M. Lyneis and G. P. Richardson. Washington, D. C. Gonçalves P, Hines J, Sterman J. 2005. The impact of endogenous demand on push–pull production systems. System Dynamics Review 21 (3):187-216. Hearne J. 2010. An Automated Method for Extending Sensitivity Analysis to Model Functions. Natural Resource Modeling23 (2):107-120. Keloharju R, Wolstenholme E. 1988. The Basic Concepts of System Dynamics Optimisation. Systems Practice 1 (1).