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Probabilistic Simulation

Probabilistic Simulation. “Uncertainty is a sign of humility, and humility is just the ability or the willingness to learn .” - Charlie Sheen. Agenda. Definitions Defining s tochastic inputs Modeling Risk and Reliability. Uncertainty. Doubt, lack of certainty

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Probabilistic Simulation

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  1. Probabilistic Simulation “Uncertainty is a sign of humility, and humility is just the ability or the willingness to learn.” - Charlie Sheen

  2. Agenda • Definitions • Defining stochastic inputs • Modeling Risk and Reliability

  3. Uncertainty • Doubt, lack of certainty • State of having a limited knowledge • Impossible to exactly describe existing state or future outcome

  4. Error vs. Uncertainty • Error: Derived or assumed value  true value • Uncertainty represents a range of truepossibilities

  5. Types of Uncertainty • Parameter uncertainty • Roughness coefficient, infiltration parameter • Uncertainty in future events • Equipment failure • Accident • Population growth • Model uncertainty • Simplifications and approximations • Representations of a process • Time dependent

  6. Memory and Correlation • Streamflow • Climate uncertainty and environmental response

  7. Uncertainty in Model Input • Identify uncertainty components • Add components to the model? • Simplify? • Physically based vs. Empirical • Goal: Quantify combined effect of the components

  8. Validating Model Uncertainty • Best fit parametric distribution • Requires historic dataset (non-biased) • Tools: Excel, MatLab • User-defined distribution (non-parametric) • Subjective assessments and judgment • Expert elicitation (multi-disciplinary)

  9. Why Uncertainty Modeling? • Quantify risk associated with uncertainty • Quantify cost associated with the risk • Visualize a range of possibility • Correlate uncertain parameters • Explore combinations of possibilities • Propagation of uncertainty

  10. Quantifying Uncertainty A probability distribution is a mathematical representation of the relative likelihood of an uncertain variable having certain specific values. Height = probability density (integrate to get probability) PDFs:

  11. Probability Distribution Views • Probability density function (PDF) • Cumulative distribution function (CDF) • Complimentary cumulative distribution function (CCDF)

  12. Monte Carlo Simulation • Nuclear weapons project Los Alamos NL 1940’s • Random inputs from a prob. Distribution • Deterministic computation on each input • Aggregate results Random Inputs Computations Aggregate Results Iterate Computations on Random Inputs

  13. Risk vs. Reliability Modeling • Risk: • Predicting the probability of a (usually bad) outcome • Reliability: • Analyzing the ways that systems can fail (and be repaired) in order to increase their design life, and eliminate or reduce the likelihood of failures, downtime and safety risks.

  14. GoldSim Examples …switch to GoldSim…

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