1 / 22

Lesson 11: Go over take-home + miscellaneous topics

Lesson 11: Go over take-home + miscellaneous topics. This class is scheduled to be a catch-up, so we will go after the following: Discussion of the final exam ( takehome ) Point flux estimator FOM as measure of convergence of deep penetration shielding problem MCNP 10 statistical checks.

zinna
Download Presentation

Lesson 11: Go over take-home + miscellaneous topics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lesson 11: Go over take-home + miscellaneous topics • This class is scheduled to be a catch-up, so we will go after the following: • Discussion of the final exam (takehome) • Point flux estimator • FOM as measure of convergence of deep penetration shielding problem • MCNP 10 statistical checks

  2. Takehome test

  3. Takehome test (2)

  4. Takehome test (3)

  5. Takehome test (4)

  6. Point Flux Estimators • It is impossible to determine the flux at a point using traditional Monte Carlo: • For collision estimator, a collision would have to occur AT the point desired • For path length estimator, the particle would have to pass THROUGH the point • Both are impossible • Furthermore, tallies have to be integrals • Therefore: We must reduce the point flux to an integral based on the collision rate variable • We treat an emerging particle like an point, monoenergetic, anisotropic beam source

  7. Point Flux Estimators (2) • The c(...) represents “emerging particles”, which includes both original source particles and particles coming out of a scattering collision • Basically this means that we estimate the

  8. Point Flux Estimators (2) = • The c(...) represents “emerging particles”, which includes both original source particles and particles coming out of a scattering collision • Basically this means that we estimate the flux at a new point from particles emerging ANYWHERE else in the problem • In practice, we do this AFTER we have chosen the source point and new energy, but BEFORE we have chosen the new direction

  9. Figure of Merit (FOM) • Of practical significance beyond considerations of variance is the idea of Figure of Merit (FOM) which gives us a relative measure of Monte Carlo efficiency • Theoretical basis: where T=computer time • Of practical concern: • We invert this (so that bigger is better):

  10. Use of FOM In our previous (brief) discussion of FOM, I mentioned two uses: • Relative metric to compare two computers or new version of code vs. old version, etc. • Relative metric of gain from a “variance reduction” process There is actually a third: • Good measure of whether a problem has reached statistical stability (i.e., is delivering the right answer)

  11. MCNP 10 statistical checks

  12. MCNP 10 statistical checks

  13. MCNP 10 statistical check #1 • Coding of an “eyeball” trick that confirms that the answers—as time goes by—are really bouncing around a central value and not trending up or down (or both)

  14. MCNP 10 statistical check #2 • Biggest problem of interpreting the answer for a deep penetration—long running—MCNP calculation: • You are so hungry for an answer after hours (or days) of waiting for a solution that you believe MCNP when it tells you (for example) that it knows the answer within 20% or 40% • This is a complete fiction: An error of 100% (1.00) means that ONE particle has scored. • So this translates into needing at least 100 contributing particles before we “believe”

  15. MCNP 10 statistical check #3 • Translates into the requirement that no high-scoring “rogue” particle has disrupted the answer during the last half of the problem • Too much “settling down” is going on in the first half to apply this rule of thumbding at least 100 contributing particles before we “believe”

  16. MCNP 10 statistical check #4 • We know theoretically that the “inverse square root of N” rule applies to a stable statistical process • Meaning that we are sampling meaningful particles often enough that we should not expect future surprises

  17. MCNP 10 statistical check #5 • This is the equivalent of the 0.1 for the answer itself • “Variance of the variance” is just a mind-bending expression that says our ESTIMATE of the variance (and then the standard deviation) itself settles into an answer in time.

  18. MCNP 10 statistical check #6 • Equivalent to #3 for the variance (standard deviation)

  19. MCNP 10 statistical check #7 • Equivalent to #4 for the variance. Notice that it converges as 1/N instead of 1/sqrt(N) • This means, of course, that we know it better sooner

  20. MCNP 10 statistical check #8 • FOM (as discussed earlier) is supposed to be a constant for a statistically stable process being sampled. • This is just a measure that the problem is not “drifting”

  21. MCNP 10 statistical check #9 • This goes a little beyond the previous measure, as another coding of the “eyeballing” of drift in your solution

  22. MCNP 10 statistical check #10 • This is the hardest to grasp of the 10 • It has to do with the “upper end” of the distribution of your scores • The idea is that your MC process viewed as a whole is sampling of a distribution. • This is a guess of whether the distribution we are sampling actually HAS a mean or not • What is magic about the slope of 3 (actually -3)?

More Related