Stabilization Diagram

The stabilization diagram is the primary tool for distinguishing physical (structural) poles from computational (mathematical) poles. It plots identified poles across increasing model orders, allowing the analyst to observe which poles remain stable as the model complexity grows.

Reading the Diagram

The horizontal axis represents frequency (Hz) and the vertical axis represents model order. Each pole is shown as a letter marker whose color and symbol indicate its stability classification:

Pole Markers

Marker	Color	Label	Meaning
s	Green	Stable	Both frequency and damping are stable across consecutive model orders. This is the strongest indicator of a physical mode.
f	Blue	Frequency Stable	Frequency is stable but damping varies. May indicate a physical mode with uncertain damping or a mode at the edge of the analysis band.
o	Red	Not Stable	Neither frequency nor damping is stable. Likely a computational pole — typically ignored.
v	Amber	Selected	A pole that has been selected by the user (or by Auto AI) for inclusion in the final modal model.

Stability Criteria

A pole at model order n is classified as stable relative to order n-2 if:

Criterion	Default Tolerance	Description
Frequency stability	1.0%	\|f_n - f_n-2\| / f_n < tolerance
Damping stability	5.0%	\|ζ_n - ζ_n-2\| / ζ_n < tolerance
MAC stability	0.95	MAC between mode shapes at orders n and n-2 > threshold

Tip: Physical poles form vertical columns of green "s" markers. Computational poles appear scattered and do not persist across model orders.

Background Overlays

The stabilization diagram can display background curves to aid in identifying resonance locations:

FRF Sum

The summed FRF magnitude is displayed as a gray-filled curve behind the pole markers. Peaks in the FRF Sum correspond to expected resonance locations. Stable pole columns should align with these peaks.

CMIF (Complex Mode Indicator Function)

The CMIF is computed from the singular value decomposition (SVD) of the FRF matrix at each frequency line:

[H(ω)] = [U] [Σ] [V]^H

The singular values σ₁(ω), σ₂(ω), ... are plotted as separate curves. Each peak in a singular value curve indicates a mode. Multiple singular value curves help identify closely spaced or repeated modes that appear as peaks at the same frequency in different singular value curves.

Overlay	Toggle	When to Use
FRF Sum	Toolbar: Sum	Default view; quick resonance identification.
CMIF	Toolbar: CMIF	Closely spaced modes; repeated roots; MIMO data.
None	Toolbar: Off	Clean view of pole markers only.

Interactive Features

Selecting Poles

Action	How	Effect
Select single pole	Double-click a pole marker	The pole turns amber ("v") and is added to the selected modes table.
Deselect pole	Double-click a selected (amber) pole	The pole reverts to its stability color and is removed from the selected modes.
Select all stable at frequency	Right-click a pole > Select All Stable at This Frequency	All green "s" poles in the same frequency column are selected, and the best one (highest order, lowest damping variation) is used.

Right-Click Context Menu

Menu Item	Description
Select All Stable	Automatically select the best stable pole at every resonance frequency across the entire diagram.
Select All Stable in Range	Same as above, but limited to the current frequency cursor range.
Clear All Selections	Remove all pole selections and reset the selected modes table.
Set Frequency Range	Restrict the visible and analysis frequency range interactively.
Add Cursor	Place a vertical frequency cursor for reference.
Export Diagram	Save the stabilization diagram as a PNG image.

Frequency Cursors

Cursors are vertical lines that can be placed on the diagram for reference or to define a frequency sub-range:

Add: Right-click > Add Cursor, or press Insert.
Move: Click and drag the cursor line to a new frequency.
Remove: Right-click the cursor > Remove Cursor, or select and press Delete.
Readout: The exact frequency of each cursor is displayed at the top of the diagram.

Zoom and Navigation

Zoom frequency axis: Scroll the mouse wheel to zoom in/out horizontally.
Zoom model order axis: Hold Ctrl + scroll to zoom vertically.
Pan: Click and drag with the middle mouse button.
Reset view: Double-click the background area or press Home.
Zoom to selection: Hold Shift and drag a rectangle to zoom into a specific region.

Interpreting the Diagram

Physical Mode Indicators

Vertical column of green "s" markers persisting across many model orders.
Column aligns with a peak in the FRF Sum or CMIF overlay.
Damping ratio is positive and within a physically reasonable range (typically 0.1% to 10%).
MPC (Modal Phase Collinearity) value close to 1.0.

Computational Pole Indicators

Scattered red "o" markers that do not form vertical columns.
Negative or unrealistically high damping ratio.
No corresponding peak in the FRF Sum or CMIF.
Pole appears only at one or two model orders, then vanishes.

Important: Closely spaced modes may appear as a single broad peak in the FRF Sum but as two separate columns on the stabilization diagram. Always check the CMIF overlay for multi-mode regions.

Diagram Settings

Setting	Default	Description
Max Damping Display	10%	Poles with damping above this value are hidden (likely computational).
Min Damping Display	0.0%	Poles with negative damping below this value are hidden.
Marker Size	Medium	Size of pole markers (Small / Medium / Large).
Background Opacity	30%	Opacity of the FRF Sum / CMIF background overlay.

Troubleshooting

Problem	Possible Cause	Solution
Diagram is empty	Model order range too low or frequency range excludes all data.	Increase the maximum model order. Widen the frequency range.
No stable poles anywhere	Poor FRF data quality or incorrect FRF estimator.	Return to Step 2 and check coherence. Try a different FRF estimator (H1 vs H2).
Too many stable poles (cluttered)	Model order range too wide or stability tolerances too loose.	Tighten the frequency and damping stability criteria. Reduce the maximum model order.
Stable columns shift with model order	Closely spaced modes or nonlinear behavior.	Narrow the frequency range to isolate the region. Check for nonlinearity (amplitude-dependent frequency shifts).

Workflow

Run the analysis algorithm to populate the stabilization diagram.
Enable the FRF Sum or CMIF overlay for reference.
Identify vertical columns of green "s" markers aligned with resonance peaks.
Double-click to select poles, or use Select All Stable for a starting selection.
Review selected modes in the Mode Selection table.
Proceed to Validation to verify the extracted modal parameters.