Glossary term
Stabilization Diagram
Modal-identification validation display that tracks poles across model orders to separate stable structural modes from numerical or noise poles.
Definition
methodA stabilization diagram is a modal-identification plot that shows how estimated poles change with model order so that stable structural modes can be distinguished from numerical, noise or forcing-related poles.
In operational modal analysis and curve-fitted experimental modal analysis, a stabilization diagram plots candidate modal poles across increasing model orders. A pole is usually considered stable only if its frequency, damping and mode shape remain sufficiently consistent between adjacent or repeated orders. The diagram supports engineering judgement; it does not replace physical validation.
A stabilization diagram is a validation display used in modal identification. It shows candidate poles across increasing model orders so the engineer can separate repeatable structural modes from numerical artifacts, noise poles, harmonic forcing and overfitted model dynamics.
For each model order n, an identification method such as stochastic subspace identification estimates poles. Each pole can be converted into:
where f_n is modal frequency, \zeta_n is damping ratio and \boldsymbol{\phi}_n is the mode shape. A pole is usually marked as stable only if these quantities remain close enough to a corresponding pole at a neighbouring or previous model order.
Engineering Role
Stabilization diagrams are central to defensible OMA and high-order modal curve fitting because increasing model order creates both physical and nonphysical poles. A structural mode should persist as the model order changes. A noise pole or numerical pole often appears, disappears or moves significantly.
Typical stabilization checks include:
- frequency stability between adjacent orders;
- damping stability and realistic damping magnitude;
- mode-shape consistency using modal assurance criterion;
- repeated appearance over several model orders;
- agreement with frequency-domain decomposition peaks or FRF evidence;
- absence of obvious harmonic operating-order behaviour;
- physical plausibility relative to the structure and sensor layout.
The acceptance limits are engineering choices. A civil OMA review may use tight frequency stability but more cautious damping tolerance. An aerospace ground test may use stricter mode-shape and reciprocity evidence because the result can affect flight-clearance decisions.
Worked Example: Classify Stable and Unstable Poles
An SSI analysis is run over several model orders. A candidate mode near 3\ \text{Hz} appears as:
| Model order | Frequency | Damping | MAC with previous shape |
|---|---|---|---|
| 20 | 3.00\ \text{Hz} | 0.78\% | 0.96 |
| 24 | 3.02\ \text{Hz} | 0.82\% | 0.97 |
| 28 | 3.03\ \text{Hz} | 0.84\% | 0.98 |
Use the order 24 pole as the reference and compare the order 28 frequency:
The damping change from order 24 to 28 is:
The MAC value is:
Engineering comment: if the project criteria are frequency change below 1\%, damping change below 0.2 percentage points and MAC above 0.95, this pole is stable between orders 24 and 28. The same check from order 20 to 24 is also acceptable:
and the damping change is:
Now consider another candidate:
| Model order | Frequency | Damping | MAC with previous shape |
|---|---|---|---|
| 24 | 4.70\ \text{Hz} | 3.4\% | 0.58 |
| 28 | 5.15\ \text{Hz} | 0.9\% | 0.52 |
The frequency change is:
Engineering comment: this second candidate should not be accepted as a stable structural mode. Its frequency shifts strongly, damping changes substantially and mode-shape correlation is poor. It may be a noise pole, an overfit artifact, a local nonstationary response or a harmonic forcing feature.
Distinction from Related Terms
A stabilization diagram is not stochastic subspace identification. SSI is an identification method; the stabilization diagram is a review display used to select credible poles from repeated model orders.
A stabilization diagram is not modal assurance criterion. MAC is one numerical comparison used inside the stability decision. The diagram combines frequency, damping, mode-shape and persistence evidence.
A stabilization diagram is not a mode shape. It helps decide whether an identified mode shape is repeatable enough to report.
A stabilization diagram is not a frequency response function or frequency-domain decomposition plot. Those show spectral or response evidence. A stabilization diagram shows identified poles as model order changes.
A stabilization diagram is not proof of validation by itself. Stable numerical poles still need physical plausibility, sensor-layout review, environmental checks and comparison with independent evidence.
Validation and Common Mistakes
A defensible stabilization diagram states the identification method, model-order range, pole-matching rules, frequency tolerance, damping tolerance, MAC threshold, damping limits, data segments, preprocessing, sensor set, operating condition and final pole-selection rationale.
Common mistakes include:
- accepting every visually vertical pole column without checking mode shapes;
- using the same tolerance for all structures and frequency bands;
- accepting negative damping, excessive damping or unstable discrete poles without explanation;
- ignoring harmonic forcing that can create repeatable but nonstructural poles;
- hiding rejected poles instead of documenting selection criteria;
- using model order as a tuning knob until the desired result appears;
- reporting stable poles without independent physical or experimental validation.