materials.absorbers.uncertainty

Measurement uncertainty for sound absorption (ISO 12999-2:2020).

Companion of the sound-insulation uncertainty of phonometry.building.measurement.uncertainty (ISO 12999-1). This part gives the standard uncertainty u of the quantities produced by a reverberation-room absorption measurement and its ratings:

• the sound absorption coefficient αs and the equivalent sound absorption area AT measured according to ISO 354, in one-third-octave bands (Clause 5, Table 1);
• the practical sound absorption coefficient αp determined according to ISO 11654, in octave bands (Clause 6, Table 2);
• the single-number weighted sound absorption coefficient αw (ISO 11654) and single-number rating DLα,NRD (EN 1793-1) (Clause 7).

The standard uncertainty is estimated by the reproducibility standard deviation σR (different laboratories) or the repeatability standard deviation σr (same location, operator and equipment), both derived from inter-laboratory tests to ISO 5725. Where specimen-specific uncertainty data exist they take precedence (Clause 4).

Band formulae (Clause 5-6). For the absorption coefficient ${\sigma }_{\mathrm{R}}=m\alpha +n$ (Formula (1)/(4)); for the equivalent area ${\sigma }_{\mathrm{R}}=m{A}_{\mathrm{T}}+nS$ with $S=10{\text{m}}^2$ (Formula (2)); the repeatability value is ${\sigma }_{\mathrm{r}}=0.6{\sigma }_{\mathrm{R}}$ (Formula (3)/(5)). m and n are the frequency-dependent constants of Table 1 (one-third-octave, 63-5000 Hz) and Table 2 (octave, 250-4000 Hz).

Single numbers (Clause 7). αw: ${\sigma }_{\mathrm{R}}=0.035$ (Formula (6)), ${\sigma }_{\mathrm{r}}=0.020$ (Formula (7)). DLα,NRD: ${\sigma }_{\mathrm{R}}=0.10D_{L\alpha ,\mathrm{NRD}}$ (Formula (8)), ${\sigma }_{\mathrm{r}}=0.02D_{L\alpha ,\mathrm{NRD}}$ (Formula (9)).

Reporting (Clause 8). The expanded uncertainty is $U=ku$ (Formula (10)) with the coverage factor k of Table 3 (Gaussian assumption). The reported U is rounded to two decimal digits for absorption coefficients and one decimal digit for the equivalent area and DLα,NRD; the code keeps the exact U and exposes the rounded view through AbsorptionUncertaintyResult.reported_expanded_uncertainty.

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

absorption_coverage_factor(confidence: float = 0.95) -> float

Return the coverage factor k for a confidence level (Table 3).

Parameters

Raises

AbsorptionUncertaintyResult(
    quantity: str,
    condition: str,
    frequencies: np.ndarray,
    values: np.ndarray,
    standard_uncertainty: np.ndarray,
    coverage_factor: float,
    expanded_uncertainty: np.ndarray,
)

Standard and expanded uncertainty of an absorption quantity (ISO 12999-2).

For the single-number quantities (αw, DLα,NRD) it is the frequency array alone that is empty; the value and the two uncertainty arrays each hold a single element. That empty frequencies is what marks a single-number result apart, and what plot refuses on.

Attributes

property

Lower interval bound value − U (exact U).

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

Plot the quantity with its ±U uncertainty ribbon (band quantities).

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

property

U rounded for reporting (Clause 8): two decimals for absorption coefficients, one decimal for the equivalent area and DLα,NRD.

property

Upper interval bound value + U (exact U).

equivalent_area_uncertainty(
    area: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 354 equivalent sound absorption area AT (Clause 5).

${\sigma }_{\mathrm{R}}=m{A}_{\mathrm{T}}+nS$ with $S=10{\text{m}}^2$ (Formula (2)) per one-third-octave band; ${\sigma }_{\mathrm{r}}=0.6{\sigma }_{\mathrm{R}}$ (Formula (3)).

Parameters

Raises

practical_coefficient_uncertainty(
    alpha_p: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 11654 practical absorption coefficient αp (Clause 6).

${\sigma }_{\mathrm{R}}=m{\alpha }_{\mathrm{p}}+n$ (Formula (4)) per octave band; ${\sigma }_{\mathrm{r}}=0.6{\sigma }_{\mathrm{R}}$ (Formula (5)).

Parameters

Raises

single_number_rating_uncertainty(
    dl_alpha: float,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the EN 1793-1 single-number rating DLα,NRD (Clause 7).

${\sigma }_{\mathrm{R}}=0.10D_{L\alpha ,\mathrm{NRD}}$ (Formula (8)), ${\sigma }_{\mathrm{r}}=0.02D_{L\alpha ,\mathrm{NRD}}$ (Formula (9)).

Parameters

Raises

sound_absorption_coefficient_uncertainty(
    alpha: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 354 sound absorption coefficient αs (Clause 5).

${\sigma }_{\mathrm{R}}=m{\alpha }_{\mathrm{s}}+n$ (Formula (1)) per one-third-octave band; ${\sigma }_{\mathrm{r}}=0.6{\sigma }_{\mathrm{R}}$ (Formula (3)).

Parameters

Raises

weighted_coefficient_uncertainty(
    alpha_w: float = 0.0,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 11654 weighted absorption coefficient αw (Clause 7).

The standard uncertainty is a constant: ${\sigma }_{\mathrm{R}}=0.035$ (Formula (6)), ${\sigma }_{\mathrm{r}}=0.020$ (Formula (7)), independent of the value.

Parameters

Raises