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Examples

The examples/ folder contains eight self-contained scripts. Each one generates a multi-panel matplotlib figure you can run directly:

python examples/example_spectral.py
python examples/example_filters_utils.py
python examples/example_timefreq.py
python examples/example_instantaneous.py
python examples/example_emd.py
python examples/example_peaks_indicators.py
python examples/example_fdd.py
python examples/example_multisensor_stats.py

example_spectral.py

2DOF spectral analysis.

Simulates 60 s of 2DOF acceleration under white noise, then shows:

  • Time signal (first 2 s), both channels
  • FFT amplitude spectrum (semi-log)
  • Welch PSD of both channels
  • Magnitude-squared coherence between channels
  • Autocorrelation with 95 % confidence bands

example_filters_utils.py

Filtering, decimation, signal metrics.

Adds 50 Hz mains hum to the 2DOF signal, then demonstrates:

  • Bandpass filter to isolate mode 1
  • Notch filter to remove the 50 Hz tone
  • Decimation from 1 kHz → 100 Hz with anti-aliasing
  • Numerical integration: acceleration → velocity → displacement
  • Bar chart of RMS, peak, and crest factor across signal variants

example_timefreq.py

Time-frequency comparison on a chirp and a 2DOF segment.

Runs four TF methods side by side (chirp on the left, 2DOF on the right):

Row Method Notes
0 STFT 128-sample window, 94 % overlap
1 CWT (Morlet) Log frequency axis, 80 analysis frequencies
2 Wigner-Ville Cross-terms visible, N = 1000
3 Smoothed Pseudo WVD Hann lag + time smoothing reduce cross-terms

example_instantaneous.py

Hilbert transform on three signal types.

Three rows, three columns (waveform + envelope, instantaneous frequency, instantaneous phase):

  1. AM sine at 100 Hz — envelope recovers the 3 Hz modulation exactly
  2. Linear chirp 10 → 200 Hz — instantaneous frequency tracks the sweep
  3. 2DOF ring-down, mode 1 isolated — log-envelope gives damping ratio ζ

example_emd.py

EMD and Hilbert-Huang Transform on 20 s of 2DOF acceleration.

  • Figure 1 — IMF waterfall: each IMF plotted with its Hilbert envelope
  • Figure 2 — HHT analysis:
    • Time-frequency scatter coloured by instantaneous energy
    • Marginal spectrum vs Welch PSD
    • Log-envelope fit → damping ratio per modal IMF

example_peaks_indicators.py

Peak detection and SHM indicators on a 2DOF system.

  • Figure 1 — Peak Detection:

    • FFT peak detection with prominence filtering
    • PSD peak detection in dB
    • Peak bandwidth and Q-factor estimation
    • Harmonic series identification (f0 = 25 Hz)

  • Figure 2 — SHM Indicators:

    • Scalar indicators: spectral entropy, kurtosis, skewness
    • RMS variation over time (10 s segments)
    • Energy variation over time
    • Dominant frequency tracking
    • Spectral entropy evolution

example_fdd.py

Frequency Domain Decomposition (FDD) on a 2DOF system.

Full OMA workflow:

  • Singular values of the PSD matrix (peak picking)
  • Natural frequency identification
  • Mode shape extraction and visualisation
  • Enhanced FDD (EFDD) damping estimation

example_multisensor_stats.py

Multi-sensor analysis and probability statistics.

  • Figure 1 — Multi-Sensor:

    • Correlation matrix heatmap
    • Coherence between channels vs frequency
    • PSD matrix singular values (FDD-style)
    • Covariance matrix

  • Figure 2 — Probability Statistics:

    • PDF estimation (KDE + histogram) for each channel
    • Joint distribution (2D histogram)
    • Mahalanobis distance for outlier detection