vibration.human.signal_burst

The saw-tooth signal burst of ISO 8041-1:2017, 5.9, and what a meter reads.

Clause 5.9 is the one place where ISO 8041-1 prints an oracle instead of a requirement. It defines a test signal in Table 6 (folio 17), and then prints in Tables 7, 8 and 9 (folios 17, 18 and 19) the 228 indications a conforming human-vibration meter has to show when that signal is applied, each with the tolerance it is judged against. The standard says where those numbers come from: “NOTE 1 The response to the saw-tooth signal burst is determined by digital simulation of the filter characteristics” (folio 16). They are arithmetic, so a library that implements the weightings and the four indication quantities can reproduce them, and this module does.

The signal. Figure 3 (folio 17) draws it: a bipolar saw-tooth of amplitude 1 m/s2 from zero to peak, a linear rising ramp and a vertical fall, with every burst starting at an upward zero crossing and ending at one. That geometry is load-bearing rather than decorative: a burst started at the peak reads 28 % high on the single-cycle row of Table 8, four times its tolerance. Table 6 supplies the rest, per application: the angular frequency, the start time of the first burst, the burst lengths (1, 2, 4, 8 and 16 cycles, plus a continuous row), the repeat time and the measurement duration. Six bursts fit in the printed duration in all three applications.

Three conventions the tables do not print, each fixed here by measuring which reading reproduces the page:

1. The continuous row starts at t = 0 and fills the printed duration; it does not start at the Table 6 start time. Read from zero, the band-limiting continuous cell of Table 7 comes out 0,564 9 against the 0,565 printed; started at 0,2 s it comes out 0,560 1.
2. The filtering is zero state. apply_weighting multiplies in the frequency domain without padding, which is a circular convolution, and its own docstring says so. In the continuous row that wraps the tail of the record onto its front and erases the switch-on transient the linear MTVV is built to catch: filtered circularly, four continuous cells of Table 8 sit at Wc -0,81 %, Wm -1,10 %, Wd -3,24 % and We -5,19 %; filtered from rest they sit at -0,17 %, -0,31 %, -0,36 % and -0,52 %. This module therefore pads the record with zeros before applying the response and keeps the first samples back, which is a filter switched on at t = 0 with nothing stored in it. The default behaviour of apply_weighting is deliberately left alone: the choice belongs to this test, not to every weighted signal.
3. The MTVV integration time is 1 s (ISO 2631-1 6.3.1, and the constant Annex D of this standard is written around). With any other constant the two MTVV columns stop lining up. It is also why the continuous row of the linear MTVV repeats the 16-cycle value for whole-body vibration: 16 cycles at 15,915 Hz last 1,005 s, so the burst already fills the window.

Which band limiting the band-limiting row is. 5.6.6 (folio 14) makes the band-limiting response a graded quantity of its own, and Tables 7 to 9 give it 18 of their 72 rows. Six of the seven whole-body weightings share the corner pair 0,4 Hz and 100 Hz of Table 3 and Wm does not, so the whole-body row had to be decided by measurement as well: with the shared pair the 24 printed cells reproduce to -0,25 % at worst, with the Wm pair to +0,67 %. The hand-arm and low-frequency rows have only one candidate each, Wh and Wf.

What the reproduction is worth. At the sampling rates recommended per application, all 228 printed cells come out within 2,3 %, against printed tolerances of 10 % and 12 %. The three widest are the 2-cycle row of Wf and the 8-cycle row of We, cells the page prints to three significant figures and whose weightings attenuate hardest.

What a pass means. The signal-burst response is one clause of a standard that also grades indication, linearity, overload, timing and environmental behaviour. A verdict here says the time response of the weighting chain matches the printed table, and nothing else.

The personal meter of Part 2. ISO 8041-2:2021 5.9 (folio 11) repeats this clause for personal vibration exposure meters, and its 12.13 (folio 31) repeats the acceptance test with the same maximum expanded uncertainty of 3 %. Its Table 6 (folio 12) is this Table 6 row for row, and its Tables 7, 8 and 9 (folios 12 to 14) are these tables cell for cell: read off the Part 2 pages and compared with SIGNAL_BURST_RESPONSE, all 228 indications and all 228 tolerances beside them are the same numbers. One implementation therefore covers both parts, and a verdict here is a verdict against either.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

Constant (str).

BAND_LIMITING = 'band-limiting'

Constant (mapping).

BURST_TOLERANCE_PERCENT = {'rms': 10.0, 'vdv': 12.0, 'mtvv_linear': 10.0, 'mtvv_exponential': 10.0, 'msdv': 10.0}

sawtooth_burst(
    application: str,
    cycles: int | None,
    *,
    fs: float | None = None,
    amplitude_m_s2: float = 1.0,
) -> NDArray[np.float64]

The saw-tooth burst record of ISO 8041-1 Table 6 (folio 17).

The full measurement record: zero everywhere except during the bursts, which start at start_time_s and repeat every repeat_time_s until the printed duration runs out (six bursts, in all three applications). Each burst is cycles whole saw-tooth periods, rising linearly from an upward zero crossing to +amplitude_m_s2, falling vertically to -amplitude_m_s2 and ending back at zero, which is the waveform of Figure 3.

cycles=None returns the continuous row of Tables 7 to 9 instead: an unbroken saw-tooth from t = 0 to the end of the printed duration. The start time does not apply to it, and the reason is measured rather than printed: read from zero, the band-limiting continuous cell of Table 7 comes out 0,564 9 against the 0,565 printed, and read from the start time it comes out 0,560 1.

The fall is vertical, as Figure 3 draws it. 12.13 (folio 36) allows a real generator a fall time of up to 1/(5 f2), which is SawtoothBurstTest.max_fall_time_s, and that allowance describes the laboratory rig, not this record.

Parameters

Returns: The record, in m/s2, round(duration_s * fs) samples long.

Raises

Constant (mapping).

SAWTOOTH_BURST_TESTS = {'hand-arm': SawtoothBurstTest(application='hand-arm', weightings=('Wh',), band_limiting_weighting='Wh', angular_frequency_rad_s=500.0, start_time_s=0.2, cycle_counts=(1, 2, 4, 8, 16), repeat_time_s=2.0, duration_s=12.0, max_fall_time_s=0.00015886564694485628, recommended_sampling_rate_hz=200000.0), 'whole-body': SawtoothBurstTest(application='whole-body', weightings=('Wb', 'Wc', 'Wd', 'We', 'Wj', 'Wk', 'Wm'), band_limiting_weighting='Wb', angular_frequency_rad_s=100.0, start_time_s=1.0, cycle_counts=(1, 2, 4, 8, 16), repeat_time_s=10.0, duration_s=60.0, max_fall_time_s=0.002, recommended_sampling_rate_hz=20000.0), 'low-frequency-whole-body': SawtoothBurstTest(application='low-frequency-whole-body', weightings=('Wf',), band_limiting_weighting='Wf', angular_frequency_rad_s=2.5, start_time_s=40.0, cycle_counts=(1, 2, 4, 8, 16), repeat_time_s=400.0, duration_s=2400.0, max_fall_time_s=0.31746031746031744, recommended_sampling_rate_hz=200.0)}

SawtoothBurstTest(
    application: str,
    weightings: tuple[str, ...],
    band_limiting_weighting: str,
    angular_frequency_rad_s: float,
    start_time_s: float,
    cycle_counts: tuple[int, ...],
    repeat_time_s: float,
    duration_s: float,
    max_fall_time_s: float,
    recommended_sampling_rate_hz: float,
)

One application’s row of ISO 8041-1 Table 6 (folio 17).

Attributes

property

How many bursts the printed duration holds at the repeat time.

property

The saw-tooth frequency, in hertz.

Table 6 prints it beside the angular frequency (79,58 Hz, 15,915 Hz and 0,397 9 Hz); this is the division, not the rounded decimal.

signal_burst_indications(
    application: str,
    name: str,
    cycles: int | None,
    *,
    fs: float | None = None,
) -> dict[str, float]

What a conforming meter indicates for one row of Tables 7 to 9.

Runs the library chain the standard describes: the burst of sawtooth_burst, the weighting (or the band-limiting response) of ISO 8041-1 Table 3 applied from rest, and then the indication quantities the table for that application prints, over the whole measurement duration. The MTVV columns are the maximum of the running r.m.s. of ISO 2631-1 Eq. (4) with the 1 s integration time this clause implies, in the linear and the exponential average of Annex D.

Parameters

Returns: The indications for a 1 m/s2 amplitude burst, keyed by the printed column names of that application’s table ("rms", "vdv", "mtvv_linear", "mtvv_exponential", "msdv"), in the units of each quantity.

Raises

Constant (mapping).

SignalBurstVerification(
    application: str,
    weighting: str,
    amplitude_m_s2: float,
    cycle_counts: tuple[int | None, ...],
    quantities: tuple[str, ...],
    measured: NDArray[np.float64],
    printed: NDArray[np.float64],
    deviation_percent: NDArray[np.float64],
    tolerance_percent: NDArray[np.float64],
    within_tolerance: NDArray[np.bool_],
)

A meter’s signal-burst indications against ISO 8041-1 Tables 7 to 9.

Attributes

property

Whether every graded cell is inside its printed tolerance.

True says the time response of this weighting chain matches the printed table. Clause 5.9 is one of the clauses a meter is graded on, and the others are hardware measurements this cannot stand in for.

SignalBurstVerification.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the deviations against the printed tolerance band.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

Returns: The axes.

property

The largest deviation in magnitude, signed as it was measured.

verify_signal_burst_response(
    application: str,
    name: str,
    measured: Mapping[int | None, Mapping[str, float]],
    *,
    amplitude_m_s2: float = 1.0,
) -> SignalBurstVerification

Verify measured burst indications against ISO 8041-1 Tables 7 to 9.

The acceptance test of 12.13 (folio 36): “The vibration values indicated in response to the signal bursts, relative to the values of the vibration amplitude of the input signal, shall be as specified in Table 7, 8 or 9”, within the tolerance printed beside each column. A personal vibration exposure meter is graded by the same sentence, ISO 8041-2:2021 12.13 (folio 31), against Tables 7 to 9 of that document, which print the same cells.

5.9 (folio 16) says the printed responses “are relative to a 1 m/s2 amplitude signal and shall be multiplied by the amplitude of the actual test signal”, and every one of the five quantities is homogeneous of degree one in the signal, so amplitude_m_s2 scales the printed side exactly.

Parameters

Returns: The verdict, as a SignalBurstVerification.

Raises