CA09 exercise · Validation and model-updating exercise
Fit stiffness and damping from a synthetic frequency-response function, compute MAC/FRAC-style agreement measures and prepare a validation statement.
Aim
This exercise turns the validation lecture into a practical workflow: identify an oscillator from FRF data, compute MAC for mode-shape comparison and write a short validation statement.
Verification asks whether the implementation solves the chosen equations correctly. Validation asks whether the model is adequate for the real problem and intended use. Parameter identification updates uncertain parameters using reference data.
Which statement best describes validation?
For the synthetic vectors used in the MAC code, the similar mode has MAC ≈ 0.9987.
Python exercise
The code fits natural frequency and loss factor to a synthetic measured FRF magnitude.
Expected observation
The identified natural frequency should be close to 120 Hz and the loss factor close to 0.045.
Teaching note
The example uses synthetic data so students can focus on the inverse-modelling workflow.
Python exercise
The code computes a MAC value between a reference mode and two simulated candidates.
Expected observation
The similar vector should have a MAC close to 1, while the different vector should have a much lower MAC.
Teaching note
MAC is insensitive to global sign but sensitive to mode-shape mismatch.
Written submission
Write a validation conclusion
Write a short conclusion explaining whether the identified FRF model is acceptable and what independent check you would still perform.
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