1 / 17

Assessing Modelling Uncertainty

4th IMPACT Workshop. Assessing Modelling Uncertainty. A. Betâmio de Almeida Instituto Superior Técnico November 2004 Zaragoza, Spain. Risk Assessment Level. Level 0 → Identification hazard Level 1 → “Worst-case” approach Level 2 → “Quasi-worst-case” – plausible upper bounds

kellie-hinton
Download Presentation

Assessing Modelling Uncertainty

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. 4th IMPACT Workshop Assessing Modelling Uncertainty A. Betâmio de Almeida Instituto Superior Técnico November 2004 Zaragoza, Spain A. Betâmio de Almeida

  2. A. Betâmio de Almeida

  3. Risk Assessment Level • Level 0 → Identification hazard • Level 1 → “Worst-case” approach • Level 2 → “Quasi-worst-case” – plausible upper bounds • Level 3 → “Best estimate”, central value • Level 4 → Probabilistic risk assessment Probabilistic uncertainty management • Level 5 → Separation of different types of uncertainty Single risk distribution Uncertainty management A. Betâmio de Almeida

  4. Phase 1 A. Betâmio de Almeida

  5. Reference System for Uncertainty Management A. Betâmio de Almeida

  6. Monte Carlo Method of Simulation (L.H.S.) Uncertainty propagation scheme A. Betâmio de Almeida

  7. Monte Carlo Method of Simulation (L.H.S.) 1 - Generation of random number [0,1] – two tipes of sets • Type 1→ for generation of samples size N for each input / parameter of the model (susbsystem) • Type 2→ one set for L.H.S. Special procedure A. Betâmio de Almeida

  8. Latin Hypercube Sampling (L.H.S.) 2 – Latin Hypercube Sampling (L.H.S.) Justification – It is a refinement of the classical (standard) Monte Carlo Sampling. In general, it produces substantial variance reductions over standard Monte Carlo in Risk Analysis applications • Each (input/parameter) probability distribuition is divided into N intervals of equal probability (N ≡ sample size). Each strata is identified (1≤n≤N) • Each random number of set 1 [X] is renormalized according to each strata number of order → transformed matrix [X’] • Input samples of size N are generated based on [X’] and the inverse transform of each input/parameter distribution A. Betâmio de Almeida

  9. Latin Hypercube Sampling (L.H.S.) A. Betâmio de Almeida

  10. Monte Carlo simulation procedure A. Betâmio de Almeida

  11. Example: RoDaB Model(Franca and Almeida 2004) • 1) • 2) • with • 3) • 4) • 5) • 6) Initial conditions and model parameters 7 input/parameter for uncertainty analysis (Exner Equation) A. Betâmio de Almeida

  12. Example LHS (shuffling) • Size of each sample: N=1000 N≡number of strata • Number of variables: k=7 Sample matrix The vectors are correlated In order to break this correlation, we use the random number matrix [Y] k-1 samples will be randomly shuffled Induced sort sort A. Betâmio de Almeida

  13. Parameter Analysis Input Output Sensivity Analysis Output Comparative analysis of all parameters A. Betâmio de Almeida

  14. Integrated Monte Carlo Analysis A. Betâmio de Almeida

  15. Upper and Lower Bounds of the Outflow Hydrographs obtained through Monte Carlo Simulation A. Betâmio de Almeida

  16. Example of hydrographs obtained from the Monte Carlo Iterations A. Betâmio de Almeida

  17. A. Betâmio de Almeida

More Related