NOTES¶

OMA Theory — What Are Modes? Why Output-Only Works?

Operational Modal Analysis (OMA) identifies modal parameters using only structural vibration responses (outputs), without measuring input excitation.

Every structure (bridge, building, wind turbine) has natural vibration patterns called modes. Each mode has three parameters:

Frequency¶

Structures "like" to vibrate at certain frequencies. A bridge might sway at 2.9 Hz front-to-back and twist at 9.3 Hz. These are natural frequencies.

Damping¶

If you strike a bell, the sound doesn't last forever—it decays. That decay rate is the damping ratio. High damping → vibration stops quickly. Low damping → it rings for a long time.

Mode Shape¶

Different parts of a structure vibrate with different amplitudes. A cantilever beam's root barely moves while the tip swings wide. The relative amplitudes form the mode shape.

OMA vs EMA¶

	EMA (Experimental)	OMA (Operational)
Excitation	Impact hammer / shaker	Ambient (wind, traffic)
Input measured	Yes	No
Best for	Lab, small structures	Real structures (bridges, buildings)
Equipment	Requires excitation gear	Accelerometers only

Core Assumption¶

OMA assumes ambient excitation is stationary white noise—random in time, covering all frequencies in the spectrum. The structure's response is then entirely determined by its own modes.

Six Methods in One Sentence¶

Method	One sentence
PP	Find peaks in averaged PSD—fastest, can't separate close modes
FDD	SVD at each frequency bin—noise is automatically separated
EFDD	FDD + IFFT for damping—approximate but useful
ITD	AR models on channel pairs—catches very weak modes
ERA	Big Hankel matrix + SVD—most accurate overall
SSI	Toeplitz matrix + cross-order voting—best damping