Chapter 9

Question 1

What is model validation?

Answer 1

Validation refers to the process of conforming that the actual model is applicable or useful by demonstrating an adequate correspondence between the computational results of the model and the actual data (if exists) or other theoretical data`.

Question 2

How are the various different aspects / techniques of model validation classified? (7)

Answer 2

1. Standard deviation of parameter estimates
2. Correlation Coefficients among the estimates
3. Confidence interval of the parameter estimates
4. Residual Analysis
5. Inverse Simulation
6. Plausibility of Estimates
7. Model Predictive Capability

Question 3

What is the confidence interval in model validation?

Answer 3

▪ Confidence interval measures the quality of parameter estimates.

▪ The smaller the confidence interval the more accurate the parameter estimates.

Question 4

What are criterion used in residual analysis? (3)

Answer 4

• Fit error and coefficient of Determination
• Theil’s Inequality
• Test for whiteness

Question 5

What is fit error?

Answer 5

▪ Fit error indicates how close the estimates 𝒚𝑘 are to the measured values
𝒛𝑘.

Question 6

What is inverse simulation?

Answer 6

▪ Process of calculating desired controls, for the given system and output/response.

Question 7

What are the principles of inverse simulation? (4)

Answer 7

• The measured control inputs are fed to the identified mathematical model.
• The computed response is compared with the measurement → produce residuals.
• The residual which contain the model deficiencies are fed back to the system using a feedback controller.
• For a sufficiently accurate model, the incremental control inputs ∆𝒖 will be small enough
  and centered about zero.

Question 8

What are some methods for checking plausibility of the model?

Answer 8

▪ Comparison with estimates obtained from other sources, for example comparison with data from wind-tunnel testing or with analytical estimates.

▪ Checking and interpreting the estimates from physical understanding of the system.

▪ Approximating the oscillatory motion by a simple spring-mass-damper system and to apply parameter estimation method to estimate the damping and period.

Question 9

What is model predictive capability?

Answer 9

▪ Determined by comparing the flight measured system responses with those
predicted by the model for the same (“identical“) control inputs.

▪ Also called “proof-of-match“ (POM)

▪ The principle of Model Predictive Capability is that a set of ‘complementary
data‘ is used to validate the model/estimated parameters.

▪ Complementary data refers to the data which are not used in the estimation.

▪ POM is an important part of flight simulator and acceptance.