Operational Modal Analysis (OMA)

Operational Modal Analysis extracts modal parameters from output-only vibration measurements, without requiring knowledge of or control over the excitation forces. OMA is used when the structure is excited by ambient or operational forces that cannot be measured directly.

When to Use OMA

OMA is the appropriate choice when:

The structure cannot be artificially excited (e.g., large civil structures, offshore platforms, operating machinery).
Stopping or modifying normal operation is impractical or too costly.
The excitation forces cannot be measured (wind, traffic, internal combustion).
You want to capture the actual operating conditions, including load-dependent effects.
The structure is too large for practical impact hammer or shaker testing.

Key Assumption: All OMA methods assume that the unmeasured excitation is broadband random (white noise). If the excitation contains strong harmonic components (e.g., rotating machinery), these harmonics may be misidentified as structural modes. Use harmonic detection tools to identify and exclude such components.

Differences from EMA

Aspect	EMA	OMA
Input measurement	Required (force signal)	Not required
Excitation	Controlled, measured	Ambient, unmeasured
FRF computation	Yes (input/output ratio)	No (output spectra / correlations only)
Mode shape scaling	Absolute (mass-normalized)	Relative only
Damping	Structural damping only	Total damping (structural + aerodynamic + operational)
Harmonic sensitivity	Low (controlled input)	High (harmonics may appear as spurious modes)
Typical structure size	Small to medium	Medium to very large

Data Requirements

OMA requires output-only vibration measurements. The following guidelines ensure reliable results:

Requirement	Guideline	Rationale
Number of channels	Minimum 3; recommended 10+	More channels provide better spatial resolution for mode shapes.
Recording duration	At least 1000 × longest expected period	Sufficient data length ensures statistical convergence of spectral estimates.
Sampling rate	At least 2.5 × highest frequency of interest	Adequate anti-aliasing margin above the Nyquist frequency.
Stationarity	Operating conditions should remain approximately constant	Non-stationary loads violate the white-noise assumption and degrade results.
Sensor placement	Cover all expected mode shapes; avoid nodal lines	Sensors at nodal points will not capture the corresponding mode.

Important: OMA mode shapes are unscaled (relative amplitudes only). If absolute scaling is needed for structural modification prediction or FE model updating, use the mass-change method or combine with EMA data.

OMA Algorithms

V-Listen provides three OMA engines. All three share the same stabilization criteria reverse-engineered from LMS PolyMAX Plus — frequency + damping + participation/mode-shape MAC — together with a cluster-median representative, so physical-mode frequencies stay stable across model order (no drift). Running two or more of them and keeping the modes they agree on is the recommended validation strategy.

OPolyProMax (Operational PolyMAX) — recommended

OPolyProMax is V-Listen's operational counterpart of the EMA PolyProMax engine and the recommended OMA method. It turns the output responses into cross-power half-spectra and feeds them into the very same verified poly-reference LSCF solver and three-criterion stabilization used for EMA — the half-spectrum obeys the same common-denominator (pole) model as an FRF.

Step	Description
1. Half-spectra	Welch-averaged cross-power Y_o·conj(Y_r) → IFFT → keep the positive-lag (causal) correlation → FFT. Averaging suppresses the random excitation and yields clean structural peaks.
2. PolyMAX solve	Per-order independent poly-reference LSCF on the half-spectra → companion eigenvalues = poles, participation vectors = mode shapes.
3. Stabilization	Frequency + damping + participation-vector MAC three-criterion clustering across orders; representative frequency = cluster median.

Why it does not drift: each model order builds its equations independently (no shared maximum-order approximation), and the participation-vector MAC separates physical modes from mathematical poles. Mode frequencies are stable to a fraction of a Hz across model order.

SSI-COV (Covariance-Driven Stochastic Subspace Identification)

The time-domain engine that cross-validates OPolyProMax. It builds output cross-correlation matrices (Welch-averaged cross-PSD → IFFT), assembles a block Hankel matrix, and recovers the state-space system by subspace projection.

Step / Parameter	Description
Cross-correlation R(τ)	Output × reference correlation matrices (the cross terms carry the mode-shape information — an auto-spectrum-only estimate cannot).
Block Hankel → SVD	One SVD of the block Hankel; each model order truncates it (drift-free stabilization diagram). Observability matrix O → system matrices (A, C).
Poles & shapes	Eigenvalues of A = poles; C·φ = mode shapes → same frequency + damping + shape-MAC stabilization.
Block rows / Max order	Default i = 40 block rows, max order 80.

Note: SSI stabilization diagrams naturally contain more mathematical (spurious) poles than the frequency-domain methods; the shape-MAC criterion and minimum-stable-count filter remove most of them. OPolyProMax usually gives the cleaner mode set.

EFDD (Enhanced Frequency Domain Decomposition)

A singular-value method on the output cross-PSD matrix. The "Enhanced" part is the MAC-based SDOF bell, which isolates a single mode and lets the natural frequency and damping be refined from its free-decay correlation.

Step	Description
1. Cross-PSD matrix	Welch-averaged G(ω) = ⟨Y·Y^H⟩ (n×n, full rank). Sufficient averaging (long records) is essential for a clean first-singular-value curve.
2. SVD per line	SVD of G(ω) at every line → first singular value SV1 (CMIF) and first singular vector u₁.
3. Peak picking	Local maxima of SV1 with a prominence gate and minimum-separation suppression.
4. MAC SDOF bell	The contiguous lines around each peak where MAC(u₁(f), u₁(peak)) ≥ threshold — this isolates the single mode (a too-narrow bell is rejected as spurious).
5. SDOF refinement	IFFT of the SDOF bell → free-decay correlation → refined natural frequency (zero-crossing spacing) and damping (log-decrement regression on the correlation extrema).

Tip: EFDD is intuitive and works well for well-separated modes. It needs a long record (many Welch averages) for a smooth SV1 curve; short records produce extra noise peaks. For closely-spaced modes prefer OPolyProMax or SSI-COV.

Algorithm Comparison

Criterion	OPolyProMax	SSI-COV	EFDD
Domain	Frequency (half-spectra)	Time (correlation)	Frequency (cross-PSD SVD)
Closely spaced modes	Excellent	Good	Limited
Damping accuracy	Good	Good	Good (SDOF refinement)
Spurious (math) poles	Few	More (SSI-typical)	Few (long records)
Drift across model order	None (median)	None (median)	n/a (single order)
Stabilization diagram	Yes	Yes	No (SV1 peak plot)
Mode shape MAC criterion	Yes	Yes	Yes (SDOF bell)
Role	Recommended / main	Time-domain cross-check	Quick look

Harmonic Detection

Operational data often contains harmonic components from rotating machinery (engine orders, pump frequencies, electrical interference). These harmonics must be identified and excluded to avoid misidentification as structural modes.

Harmonics appear as extremely narrow peaks with very low damping (<0.05%) on the stabilization diagram.
Their frequency is exactly proportional to the operating speed (RPM).
V-Listen flags potential harmonics with a warning symbol on the stabilization diagram when damping is below a configurable threshold.

Best Practices

Record data for at least 10–15 minutes for structures with natural frequencies below 5 Hz. Shorter records may not provide sufficient averaging for reliable spectral estimates.
Use multiple reference sensors (fixed during roving measurements) to maintain phase coherence across all measurement runs.
Run at least two different OMA algorithms (e.g., EFDD + SSI-COV) and compare results. Modes that appear consistently across methods are more likely to be physical.
Monitor operating conditions (RPM, temperature, load) during the measurement. Changes in these conditions can cause time-varying modal parameters.
Apply the harmonic detection filter before selecting modes to avoid including engine orders or electrical interference as structural modes.

Caution: OMA damping estimates include all sources of energy dissipation present during operation (structural damping, aerodynamic damping, friction at joints). These values will generally be higher than EMA damping estimates obtained under controlled laboratory conditions.

OMA Workflow

Import geometry (same as EMA — see Import Geometry).
Import output-only time-domain data (HDF or WAV).
Select the OMA algorithm (OPolyProMax, SSI-COV, or EFDD).
Configure parameters and run the analysis.
Select modes from the stabilization diagram (OPolyProMax / SSI-COV) or the singular-value plot (EFDD).
Validate using mode shape animation and Auto-MAC.
Export results.