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CS 351/ IT 351 Lecture 05

Explore sources of errors in modelling and simulation technologies, including input values, machine inaccuracies, algorithm errors, and measurement granularity. Learn how errors impact results and how to control and predict their effects.

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CS 351/ IT 351 Lecture 05

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  1. Modelling and Simulation Technologies Dr. Jim Holten CS 351/ IT 351Lecture 05

  2. CS 351/ IT 351 Errors • Sources of Errors • Characterizing Errors • Using Error Bounds • Interpreting Error Implications

  3. CS 351/ IT 351 Sources of Errors • Input Values (measurements) • Machine Inaccuracies • Algorithm Inaccuracies • Bad models

  4. CS 351/ IT 351 Measurement Errors • Measurement granularity • Accuracy ==> Error intervals • Types of measurements

  5. CS 351/ IT 351 Machine Errors: Representation • Float: 7 decimal places, E+/-38, or subnormal E-45 • Double – 16 decimal places, E +/-308, or subnormal E-324

  6. CS 351/ IT 351 Machine Errors: Representation • Equality comparisons • Overflow • Underflow

  7. CS 351/ IT 351 Machine Errors • Divide by zero, or divide zero by zero • Propagate “bad” values • Worst-case scenarios, not seen as errors • Near zero results of add or subtract • Near zero denominator

  8. CS 351/ IT 351 Algorithm Sources of Errors • Inaccurate representation of real world • Inaccurate representation of ideal world • Computational errors

  9. CS 351/ IT 351 Real World to Ideal Model • Math Models are Idealistic • Real world has many perturbations • Statistical estimates are only “best fit” • Results in inaccurate ideal model

  10. CS 351/ IT 351 Ideal Model to Implementation • Machine errors in number representations • Machine errors in arithmetic calculations • Results in even worse implementation model values

  11. CS 351/ IT 351 Computational Errors • Numerical calculation of math functions • Numerical Integration • Numerical differentiation • Techniques used determine the error behavior

  12. CS 351/ IT 351 Controllable Errors • Understanding sources and behavior of errors empowers you to control them and predict their effects on the results. • Identifying sources and effects of errors allows you to better judge the quality of models.

  13. CS 351/ IT 351 Bad Models • Wrong equations • Wrong numerical methods • Details gone awry • All irrationally affect results.

  14. CS 351/ IT 351 Characterizing Errors • Error Forms • Error propagation effects on error forms • Limitations versus needs

  15. CS 351/ IT 351 Error Forms • Error probability distributions • The normal distribution • Error bounds • Generalized error estimation functions

  16. CS 351/ IT 351 Error Probability Distributions • Measurement error characteristics • Calculation error characteristics • Introduced algorithmic error terms

  17. CS 351/ IT 351 Measurement ErrorCharacteristics • Discrete sample on a number line • Spacing determines “range” for each measurement point • Actual value may be anywhere in that range

  18. CS 351/ IT 351 Calculation ErrorCharacteristics • Round-off • Divide by near-zero • Divide by zero • Algorithm inaccuracies

  19. CS 351/ IT 351 Algorithmic ErrorCharacteristics • Depends on the algorithms/solvers used • Depends on the problem size • Depends on inter-submodel data sharing patterns and volume

  20. CS 351/ IT 351 Error Normal Distributions • Easy to characterize • Propagates nicely through linear stages • Useless for nonlinearities, special conditions • Not always a good fit

  21. CS 351/ IT 351 Error Bounds • Not commonly used • Easy to represent (+/-error magnitude) • Can be propagated through nonlinear calculations • Still awkward for some calculations

  22. CS 351/ IT 351 Generalized Distributions • Not commonly used • Easy to represent (histograms) • Propagated through nonlinear calculations • Awkward, histograms for each variable

  23. CS 351/ IT 351 Propagating an Error Distribution • Highly dependent on the distribution and the calculations being performed. • Generally only linear operations give easily predictable algebraic results.

  24. CS 351/ IT 351 Error Bounds • Expected value, +/-error magnitude • Propagation Through Calculations • More complex forms may be needed

  25. CS 351/ IT 351 Unhandled Error Implications • Misinterpretation of results • Misplaced confidences • “Chicken Little” and “The Boy Who Cried 'Wolf'”

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