©GoldSim Technology Group LLC., 2004 Probabilistic Simulation “Uncertainty is a sign of humility, and humility is just the ability or the willingness to

©GoldSim Technology Group LLC., 2004

Probabilistic Simulation

“Uncertainty is a sign of humility, and humility is just the ability or the willingness to learn.”

- Charlie Sheen


Agenda

Definitions

Defining stochastic inputs

Modeling Risk and Reliability


Uncertainty

Doubt, lack of certainty

State of having a limited knowledge

Impossible to exactly describe existing state or future outcome


Error vs. Uncertainty

Error: Derived or assumed value true value

Uncertainty represents a range of true possibilities


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


Memory and Correlation

Streamflow Climate uncertainty and environmental response


Uncertainty in Model Input

Identify uncertainty components

– Add components to the model?

– Simplify?

– Physically based vs. Empirical

Goal: Quantify combined effect of the components


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)


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


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:


Probability Distribution Views

Probability density function (PDF)

Cumulative distribution function (CDF)

Complimentary cumulative distribution function (CCDF)

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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


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.


GoldSim Examples

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Documents

©GoldSim Technology Group LLC., 2004 Probabilistic Simulation “Uncertainty is a sign of humility, and humility is just the ability or the willingness to