M4: Model uncertainty and sensitivity analysis

Question 1

How can systematic errors occur in models/systems?

Answer 1

• Result from a mis calibrated device e.g., very cold or hot steel ruler for measurement of length
• Result from flawed design of the experiment e.g., measurement of a non representative sample

Require careful design of experiment to avoid systematic errors.

Question 2

Where can random errors occur?

Answer 2

In data as uncertainties (parameter estimation, accuracy and precision of measurements.

Question 3

How can one deal with random errors?

Answer 3

By using statistics.

Question 4

Name the three ways of dealing with uncertainties teached in the course.

Answer 4

1. Sensitivity analysis
   - How sensitive are variables to changes in parameters?
2. Error propagation
   - How reliable are results?
   - What is the impact of uncertainties of parameters on variables?
   
   • ->analytical approach
   • -> numerical approach (Monte Carlo simulation)
3. Data reconciliation / flow adjustment
   - How can flows and their uncertainties be adjusted by making use of the mass balance principle?

Question 5

List the uses of sensitivity analysis:

Answer 5

1. Improve a model
   - Validate a model –> warn of unrealistic model behavior.
2. Improve the data
   - Identify key parameters/assumptions
   - Suggest necessary levels of accuracy for parameters
   - -> If model is sensitive to parameter change –> high accuracy required.
   - Suggest improved measurements –> guide data collection efforts.
   - Adjust numerical values of parameters.
3. Improve system understanding
   - Identify most effective ways to control system
   - Test the behavior of the model in extreme situations

In general sensitivity analysis helps to build confidence in the model by studying the uncertainties that are often associated with parameters in models.

Question 6

Explain absolute sensitivity and its uses

Answer 6

• calculate change in output due to change in input

- analyze when a parameter has its greatest effect

Question 7

Explain relative sensitivity and its uses

Answer 7

• Percentual changes in parameters and variables.
• compare parameters
• analyze which parameter has greatest effect