Parameter identification

Question 1

What are the approaches to modelling?

Answer 1

-Law of physics
-data driven approach

Question 2

How does the data driven approach work?

Answer 2

-Least squares to estimate parameters
-using linear regression

Question 3

Explain the data driven approach using Hooke’s law

Answer 3

-From experimental data, write each data point in terms of Hooke’s law equation
-Variables and parameters can be grouped into vectors
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Question 4

How can experimental results be written in an equation?

Answer 4

y = xø + r
y - collection of measured outputs
x - collection of measured variables
ø - are true parameters
r - collection of measurement error

Question 5

How can estimated outputs be expressed in an equation?

Answer 5

y = known variable x estimated parameter

Question 6

What is the residual error?

Answer 6

-error between measured and estimated
-e = measured experimental point - estimated output

Question 7

Define the cost function

Answer 7

A measure of overall error of all experimental points
- J = 0.5 x ∑(residual of each point)^2

Question 8

What are ways the fit of a model can be measured?

Answer 8

-Validate with standard inputs
-Visual observation
-Quantative Summary (root mean of error squared)
-Correlation (pmcc)
-R squared

Question 9

What is the purpose of effective data use?

Answer 9

For a model to be effective, the data must be effective as well

Question 10

How should experimental data be split?

Answer 10

-fitting data
-validation data
-testing data (largest sector)

Question 11

What is the approach for designing a Data driven model?

Answer 11

1. Specify different possible system structures
   * Different order systems
   * Different collection of variables
2. Use fitting data to obtain parameter identification for each
   possible structure
3. Compare each model to Validation data
   * Use combination of quality of fitting metrics vs. complexity of
   model to choose DD model
4. Use Test Data to validate DD model over full operational range