bearing opsignal → tableimport fullseye as fs; fs.ledger.envelope_spectrum(x, rate, low, high, order=4, n_peaks=5) (実装を直接呼ぶなら import acoustics; acoustics.envelope_spectrum(x, rate, low, high, order=4, n_peaks=5)、台帳から引くなら opsacoustics.get("envelope_spectrum"))Band-pass, demodulate, transform — where a bearing defect actually shows.
The three steps are each already available (dsp.bandpass,
dsp.envelope, numpy.fft); what is not available anywhere in
:mod:dsp is the composition, and the composition is the diagnostic. The
raw spectrum of a defective bearing shows a resonance at some kHz and
nothing at the defect rate; the envelope of that resonance band, transformed,
shows the defect rate as a clean line.
low / high are the demodulation band in Hz and are required,
not optional. Choosing the band is the analysis; a default would hide the
one decision that has to be made. :func:spectral_kurtosis finds a
candidate band when there is no prior knowledge of the resonance.
The envelope’s mean is removed before the transform (otherwise a large DC
line dominates every plot), amplitudes are single-sided (2/N), and DC is
excluded from peak picking.
Returns a dict: freqs, magnitude, peak_freq, peak_amplitude,
peak_freqs / peak_amplitudes (the n_peaks largest, descending),
band, envelope_mean, resolution_hz, plus two numbers that exist
because this operator always returns a peak frequency, including when
there is nothing there:
peak_prominence
the peak divided by the median of the whole magnitude spectrum.
Band-width dependent, and it inverts in a narrow band — see
local_prominence below and the table in :func:_local_prominence.
local_prominence / local_noise_floor
the peak divided by the median of its own neighbourhood (±50 Hz,
excluding ±5 Hz of the peak itself), and that median. Use this one to
decide whether a peak is real: measured over both a 2000-4000 Hz and a
2900-3100 Hz demodulation band, pure noise and a constant signal stay
at 2.2-3.3 while a real 107 Hz defect reaches 1558 (wide) and 33.9
(narrow). peak_prominence puts pure noise at 11375 in the
narrow band, above the real defect’s 9434 — the ordering is reversed,
which is why the number below the table in this docstring (“white
noise 365”) only holds at that one band width.
band_fraction
the RMS of the band-passed signal divided by the RMS of the input — how
much of the record actually lives in the demodulation band.
Found by adversarial audit and not repaired by an exception, because there
is nothing invalid to refuse: a constant signal band-passed over
100-2000 Hz has an envelope made of rounding error, and this operator dutifully
reported peak_freq = 8.0000 Hz. Nothing raised, nothing was NaN, and
8 Hz is a perfectly plausible number to write down. Measured, the four
cases separate on the returned numbers rather than on any invented
threshold:
================ ======== ========= =========== ============= input peak Hz peak amp prominence band_fraction ================ ======== ========= =========== ============= AM, defect 107 107.0000 4.997e-01 10018.6 9.999e-01 impulse + noise 107.0000 1.968e-01 9384.7 9.201e-01 white noise 128.0000 2.785e-02 365.2 3.745e-01 constant signal 8.0000 1.691e-12 173.0 1.995e-12 ================ ======== ========= =========== =============
No cut-off is imposed here: a defect that is genuinely 20 dB into the noise
is a real finding and refusing it would be worse than reporting it. The
numbers are returned so the caller can see the difference between row 1 and
row 4, which peak_freq alone does not show.
Measured on :func:synthesize_bearing_signal (25600 Hz, 1 s, 3 kHz carrier,
107 Hz defect, m = 0.5) demodulated over 2000-4000 Hz: peak_freq =
107.000000 Hz, peak_amplitude = 0.499677 — the modulation depth
itself, because the analytic envelope of that signal is exactly
1 + 0.5 cos(2 pi 107 t). The ordinary spectrum of the same signal has a
one-sided amplitude of 4.291662e-16 at 107 Hz: the defect rate is not
present as a frequency component at all, which is the entire point of the
operator.
That number needs a scaling step that used to be missing from this
sentence. dsp.spectrum returns the raw |rfft|, not an amplitude —
the raw value in that bin is 5.493328e-12, and the one-sided amplitude
above is mag * (2.0 / len(x)), here 2/25600 = 7.8125e-05. This
operator and :func:order_spectrum apply that 2/N internally and so
return amplitudes directly (carrier 3000 Hz: raw 12800, amplitude
1.000000; sidebands 2893 / 3107 Hz: raw 3200, amplitude 0.250000 = m/2).
The two conventions coexist in the library, so do not apply 2/N twice
when comparing a dsp spectrum against one of these.
Raises ValueError: everything :func:_as_signal and dsp.bandpass
refuse (non-finite, complex, masked, non-1-D, a band edge outside
(0, rate/2), a signal too short for zero-phase filtering), plus a
non-positive n_peaks.
py -3.11 examples/acoustic_condition_monitoring.pypy -3.11 examples/poc_bearing_diagnosis.pytable を入力に取れる)bearing)bearing_defect_frequencies · spectral_kurtosis · cepstrum
Provenance: acoustics.py — ACOUSTICS operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.