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NOTES

EFDD — Enhanced FDD: IFFT the SV1 Spectrum Back to Time for Damping

On top of FDD, IFFT the SV1 spectrum around each modal peak back to time domain to obtain an SDOF free decay, then estimate damping via logarithmic decrement.

Intuition

How to Get Damping from Frequency Domain?

Damping is the rate at which vibration decays over time—a time-domain concept. EFDD's trick:

  1. FDD finds frequencies and shapes (frequency domain)
  2. Extract a narrow band of SV1 around each peak (bandpass filter)
  3. IFFT back to time → SDOF free decay curve
  4. Estimate damping from the decay curve's slope

Logarithmic Decrement

For SDOF free decay:

\[ \delta = \ln\left(\frac{y_i}{y_{i+1}}\right) = \frac{2\pi \zeta}{\sqrt{1-\zeta^2}} \approx 2\pi \zeta \quad (\zeta < 0.2) \]

Damping Quality

  • Heavily depends on: mode separation, data length, SNR
  • Typical error ~±30%, sufficient for SHM trend monitoring
  • Unreliable when modes are < 3 bins apart

Design Deep Dive

1. IFFT Bandwidth

EFDD extracts SV1[peak-3:peak+3] (7 bins) for SDOF autocorrelation. At seg_len=1024, 0.049 Hz resolution, this corresponds to ~0.15 Hz bandwidth—sufficient for civil structures with damping < 5%.

2. Damping Reliability

EFDD damping error ~±30% comes from: - Time-domain leakage from spectral truncation - Log-decrement sensitivity to noise - Limited peak pairs in short data

3. When EFDD Damping Fails

  • Mode spacing < 3 bins → adjacent mode leaks into IFFT
  • Data < 20s → insufficient autocorrelation length
  • Damping < 0.2% → decay too slow, log ratio ≈ 1