The claim to be tested
The question is not “did the spectrum change while the signal was playing?” but “after the drive is removed and temperature, mounting and environment are back at baseline, does an independent low-amplitude modal test show a repeatable change in frequency, damping or mode shape beyond the measurement uncertainty?” Only the second is a claim about the object itself.
Design: A1, B, A2
| Stage | What happens | Purpose |
|---|---|---|
| A1: baseline | Excitation-off, low-amplitude modal test: frequencies, damping, mode shapes, temperature, mount log. | Reference state of the object. |
| B: treatment | Playback, load, control loop or sham, at the planned level, with temperature logged throughout. | Apply the condition under test. Observed shifts here are not yet evidence of retuning. |
| A2: return | Wait for temperature and mounting to return to baseline, then repeat the A1 test. | Test for a lasting change. |
The comparison that matters is A2 against A1, in units of the repeatability measured beforehand. B is reported separately as a forced or closed-loop response.
Pre-specified outcomes
- Change in each tracked natural frequency, A2 minus A1, with uncertainty.
- Change in damping or Q.
- Modal assurance criterion between A1 and A2 mode shapes.
- Persistence after the control or drive is disabled.
- Replication across sessions and specimens.
- Effect size relative to calibration and environmental uncertainty.
The smallest effect of interest and the decision thresholds are fixed from phase-0 repeatability measurements and registered before confirmatory data are taken. This page deliberately contains no numeric threshold.
Controls
- Sham treatment. A phase-randomised surrogate with the same amplitude spectrum and power, so signal content is separated from energy and heating.
- Reference sphere. An identical object that is never treated and shares the temperature history.
- Re-seat control. Remove and replace the sphere without any treatment to measure mounting scatter.
- Position-only control. Move the stage with no drive change, with temperature logged.
- Blinded fitting. The analyst does not know which runs are treatment and which are sham.
- Amplitude sweep. Check whether peak frequency depends on drive level.
How to read the outcomes
| Pattern | Reading | Next step |
|---|---|---|
| A2 = A1 within uncertainty; B differs | A forced, nonlinear, thermal or closed-loop effect during treatment. The object was not retuned. | Report as such; attribute with the covariates. |
| A2 differs from A1 and the sham does too | The cause is energy, heating or handling, not signal content. | Investigate the artifact before anything else. |
| A2 differs from A1, sham and reference do not, and it replicates | A candidate lasting change, still under standard physics until a mechanism is identified. | Independent replication and mechanism search. |
| No difference anywhere, small uncertainty | A null result that bounds any lasting effect under the tested conditions. | Publish with the bounds. |
| Large scatter between A1 repeats | Inconclusive: the test cannot detect the effect. | Improve repeatability before treating. |
Environmental and mounting covariates
Temperature moves every frequency, drive heating can mimic a shift, and mounting changes the boundary conditions. Log temperature continuously, hold mounting fixed or characterise it, and fit temperature as a covariate rather than assuming it away. The magnitude of these effects is discussed in the record-and-replay article and the error budget.
Score reproduction in both domains
When a replay or control system is tested, report the error in the radiated sound pressure and in the surface velocity field separately. Success at one microphone is not success in reproducing the sphere's motion. See the four levels of reproduction in the record-and-replay article.
Comments wanted
Is an A/B/A design sufficient, and which further controls would you require? Which statistics would you pre-register? Send comments through the expert review request or the community design review.
Sources
- Zero mass loading: effect and compensation in vibration analysis, Polytec application note.
- Effect of Temperature Changes on the Experimental Modal Analysis of a Galvanized Steel Benchmark Structure, Tuhta, Koç and Günday, Buildings 16(5), 1069 (2026).