building.measurement.structure_borne_power

Structure-borne sound power of building equipment (EN 15657:2018; ISO 9611).

Building service equipment (pumps, fans, boilers, sanitary appliances) injects structure-borne sound power into the building structure it is fixed to. EN 15657 measures it with the reception-plate method: the source is mounted on a plate of known mass per unit area m and area S whose structural loss factor eta is known, and the spatial-average vibratory velocity level of the plate is measured.

The power a resonant plate dissipates equals $P=\omega \eta (mS)⟨v^2⟩$, so the power injected into that reception plate is, in one-third-octave bands (Formula 14):

$$L_{W\mathrm{s}}=10{\log }_{10}\frac{2\pi f\eta mS}{f_0{m}_0{S}_0}+L_v-60\text{dB re 1 pW}$$

with the references $f_0=1$ Hz, $m_0=1$ kg (printed as 1 kg; the quantity it normalises is a mass per unit area, so the reference is 1 kg/m² — see docs/ERRATA.md), $S_0=1$ m²; the fixed -60 dB term is $10{\log }_{10}(v_0^2/P_0)$ for the EN 15657 velocity reference $v_0=10^{-9}$ m/s and $P_0=1$ pW. The spatial mean velocity level is the energetic average over the N plate positions (Formula 12):

$$L_v=10{\log }_{10}\left(\frac{1}{N}\sum 10^{L_{v,i}/10}\right)$$

and the plate loss factor follows from its structural reverberation time Ts (Formula 13, identical to the ISO 10848 total loss factor):

$$\eta =\frac{2.2}{f{T}_s}$$

Formula (14) is plate-specific, not a source descriptor. The same source injects a different power into a different receiver; feeding L_Ws directly into EN 12354-5 as a characteristic level mis-states the receiving-room level by up to ~20 dB. EN 15657 derives the plate-independent source quantities from two test plates: a low-mobility plate (its point mobility and loss factor are unchanged by the source) and a high-mobility plate (loaded by the source):

• the equivalent blocked force level (Formula 15, dB re $F_0=10^{-6}$ N): $L_{F\mathrm{b},\mathrm{eq}}=L_{Ws,low}-10{\log }_{10}(\mathrm{Re}\{Y_{R,low,eq}\}/Y_0)$ with the measured low-mobility-plate mobility and $Y_0=1$ m/(N.s);
• the characteristic reception-plate power level used by EN 12354-5 (Formula 17), referred to the standard 10 cm concrete plate of characteristic mobility $Y_{R,\infty ,low}=5\cdot 10^{-6}$ m/(N.s) (clause 7.2.4): $L_{Wsn}=L_{F\mathrm{b},\mathrm{eq}}+10{\log }_{10}(Y_{R,\infty ,low}/Y_0)$;
• the equivalent free velocity level (Formula 18, dB re 1e-9 m/s) from the high-mobility plate, and the source mobility from both (Formula 19). L_Wsn plus the mobility corrections of EN 12354-5 Annex I (see phonometry.building.prediction.installed_structure_borne) close the EN 15657 -> EN 12354-5 chain.

The source-side free velocity of ISO 9611:1996 is the direct-measurement counterpart: velocity levels re $v_0=5\cdot 10^{-8}$ m/s (clause 7), averaged over positions with the energy mean of its equation (9), implemented by mean_free_velocity_level.

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

characteristic_reception_plate_power

characteristic_reception_plate_power(
    blocked_force_level: ArrayLike,
    *,
    characteristic_mobility: float = 5e-06,
) -> np.ndarray

Characteristic reception-plate power level (EN 15657:2018, Formula 17).

$L_{Wsn}=L_{F\mathrm{b},\mathrm{eq}}+10{\log }_{10}(|Y_{R,\infty ,low}|/Y_0)$ with the characteristic mobility of the standard 10 cm concrete reception plate $Y_{R,\infty ,low}=5\cdot 10^{-6}$ m/(N.s) (clause 7.2.4) and $Y_0=1$ m/(N.s). This is the plate-independent source power level L_Ws,n that EN 12354-5 consumes (its Annex I mobility correction phonometry.installed_power_from_reception_plate then refers it to the actual receiver).

Parameters

Name	Description
blocked_force_level	Equivalent blocked force level L_Fb,eq (per band), in dB re 1e-6 N (see equivalent_blocked_force_level).
characteristic_mobility	Y_R,inf,low, in m/(N.s) (Default: 5e-6, clause 7.2.4).

Returns: The characteristic power level L_Wsn, in dB re 1 pW.

Raises

Exception	When
ValueError	for a non-positive characteristic mobility.

equivalent_blocked_force_level

equivalent_blocked_force_level(
    power_level: ArrayLike,
    plate_mobility: ArrayLike,
) -> np.ndarray

Equivalent blocked force level, squared (EN 15657:2018, Formula 15).

$L_{F\mathrm{b},\mathrm{eq}}=L_{Ws,low}-10{\log }_{10}(\mathrm{Re}\{Y_{R,low,eq}\}/Y_0)$ in dB re $F_0=10^{-6}$ N, from the power injected into the low-mobility reception plate (Formula 14) and the equivalent point mobility of that plate (the arithmetic mean of Re{Y} over the contact points, Formula 16).

Parameters

Name	Description
power_level	Injected power level L_Ws,low (per band), in dB re 1 pW (see structure_borne_power_level).
plate_mobility	Equivalent plate mobility Y_R,low,eq (per band), in m/(N.s); complex values use their real part (Formula 16).

Returns: The equivalent blocked force level L_Fb,eq, in dB re 1e-6 N.

Raises

Exception	When
ValueError	if Re{plate_mobility} is not positive and finite.

equivalent_free_velocity_level

equivalent_free_velocity_level(
    power_level: ArrayLike,
    plate_mobility: ArrayLike,
) -> np.ndarray

Equivalent free velocity level of the source (EN 15657:2018, Formula 18).

$L_{vf,eq}=L_{Ws,high}+10{\log }_{10}\left(|Y_{R,high,eq}{|}^2/(\mathrm{Re}\{Y_{R,high,eq}\}{Y}_0)\right)+60\text{dB}$ in dB re 1e-9 m/s, from the power injected into the high-mobility reception plate and its equivalent (complex) point mobility. The plus sign follows the printed formula and the physics ($v_f^2=P|Y{|}^2/\mathrm{Re}\{Y\}$); it is what makes Formulae (15) and (18) combine through Formula (19) into $|Y_{S,eq}|=v_f/F_b$.

Parameters

Name	Description
power_level	Injected power level L_Ws,high (per band), in dB re 1 pW.
plate_mobility	Equivalent plate mobility Y_R,high,eq (per band, complex), in m/(N.s).

Returns: The equivalent free velocity level L_vf,eq, in dB re 1e-9 m/s.

Raises

Exception	When
ValueError	if Re{plate_mobility} is not positive and finite.

mean_free_velocity_level

mean_free_velocity_level(levels: ArrayLike) -> float

Mean free velocity level over positions (ISO 9611:1996, equation (9)).

${\overline{L}}_{vx}=10{\log }_{10}\left[\frac{1}{N}\sum 10^{L_{vxi}/10}\right]$, the energy mean of the free-velocity levels measured at the N contact/attachment points of one direction x, each in dB re the ISO 9611 free-velocity reference $v_0=5\cdot 10^{-8}$ m/s (clause 7). The arithmetic is the energetic average (identical to EN 15657 Formula 12, spatial_mean_velocity_level); only the reference differs.

Parameters

Name	Description
levels	Free velocity levels Lvxi at the N positions, in dB re 5e-8 m/s.

Returns: The mean free velocity level, in dB re 5e-8 m/s.

plate_loss_factor

plate_loss_factor(
    frequency: ArrayLike,
    reverberation_time: ArrayLike,
) -> np.ndarray

Plate loss factor $\eta =2.2/(f{T}_s)$ (EN 15657, Formula 13).

Estimated from the plate’s structural reverberation time; identical to the ISO 10848 total loss factor.

Parameters

Name	Description
frequency	Band centre frequency f, in hertz (per band).
reverberation_time	Structural reverberation time Ts, in s.

Returns: The loss factor eta (dimensionless) per band.

reception_plate_power

reception_plate_power(
    velocity_level: ArrayLike,
    frequency: ArrayLike,
    mass_per_area: float,
    area: float,
    *,
    loss_factor: ArrayLike | None = None,
    reverberation_time: ArrayLike | None = None,
) -> StructureBornePowerResult

Reception-plate injected structure-borne sound power (EN 15657, clause 7).

Provide the plate loss factor directly, or its structural reverberation time Ts (from which $\eta =2.2/(f{T}_s)$ is computed, Formula 13). The result is the power injected into this plate (Formula 14); see the module docstring for the conversion chain to the EN 12354-5 source quantities.

Parameters

Name	Description
velocity_level	Spatial mean plate velocity level L_v (per band), in dB re 1e-9 m/s (see spatial_mean_velocity_level).
frequency	Band centre frequencies f, in hertz.
mass_per_area	Plate mass per unit area m, in kg/m^2 (> 0).
area	Plate area S, in m^2 (> 0).
loss_factor	Plate loss factor eta (per band), or None to derive it from reverberation_time.
reverberation_time	Structural reverberation time Ts, in s, used when loss_factor is None.

Returns: The StructureBornePowerResult.

Raises

Exception	When
ValueError	if neither loss_factor nor reverberation_time is given.

source_mobility_from_levels

source_mobility_from_levels(
    free_velocity_level: ArrayLike,
    blocked_force_level: ArrayLike,
) -> np.ndarray

Equivalent source mobility magnitude (EN 15657:2018, Formula 19).

$|Y_{S,eq}{|}^2/Y_0^2=10^{(L_{vf,eq}-L_{F\mathrm{b},\mathrm{eq}})/10}\cdot 10^{-6}$, the ratio of the free-velocity (re 1e-9 m/s) and blocked-force (re 1e-6 N) references makes the constant $(10^{-9}/10^{-6}{)}^2=10^{-6}$.

Parameters

Name	Description
free_velocity_level	Equivalent free velocity level L_vf,eq (per band), in dB re 1e-9 m/s (Formula 10 or 18).
blocked_force_level	Equivalent blocked force level L_Fb,eq (per band), in dB re 1e-6 N (Formula 15).

Returns: The source mobility magnitude |Y_S,eq|, in m/(N.s).

spatial_mean_velocity_level

spatial_mean_velocity_level(levels: ArrayLike) -> float

Spatial-average velocity level over the plate (EN 15657, Formula 12).

$L_v=10{\log }_{10}\left(\frac{1}{N}\sum 10^{L_{v,i}/10}\right)$ — the energetic average of the per-position velocity levels.

Parameters

Name	Description
levels	Velocity levels L_v,i at the N positions, in dB.

Returns: The spatial mean velocity level, in dB.

structure_borne_power_level

structure_borne_power_level(
    velocity_level: ArrayLike,
    frequency: ArrayLike,
    mass_per_area: float,
    area: float,
    loss_factor: ArrayLike,
    *,
    reference_velocity: float = 1e-09,
) -> np.ndarray

Structure-borne power injected into the reception plate (EN 15657, Formula 14).

The power a resonant reception plate dissipates, expressed as a level re 1 pW:

$$L_{W\mathrm{s}}=10{\log }_{10}\frac{2\pi f\eta mS}{f_0{m}_0{S}_0}+L_v+10{\log }_{10}\frac{v_0^2}{P_0}$$

With the EN 15657 reference $v_0=10^{-9}$ m/s the last term is -60 dB.

Note

This is the power injected into this particular plate, not a source descriptor: do not feed it into EN 12354-5 as the characteristic level L_Ws,c. Convert it first via equivalent_blocked_force_level (Formula 15) and characteristic_reception_plate_power (Formula 17), then apply the EN 12354-5 Annex I mobility correction (phonometry.installed_power_from_reception_plate).

Parameters

Name	Description
velocity_level	Spatial mean plate velocity level L_v (scalar or per band), in dB re v0.
frequency	Band centre frequency f, in hertz.
mass_per_area	Plate mass per unit area m, in kg/m^2 (> 0).
area	Plate area S, in m^2 (> 0).
loss_factor	Plate loss factor eta (scalar or per band, > 0).
reference_velocity	Velocity reference v0 (Default: 1e-9 m/s).

Returns: The structure-borne sound power level L_Ws, in dB re 1 pW.

Raises

Exception	When
ValueError	for a non-positive mass, area, reference, frequency or loss factor.

StructureBornePowerResult

StructureBornePowerResult(
    power_level: np.ndarray,
    velocity_level: np.ndarray,
    loss_factor: np.ndarray,
    mass_per_area: float,
    area: float,
    frequencies: np.ndarray | None = None,
)

Structure-borne sound power injected into a reception plate (EN 15657).

The power level is specific to the measured plate; derive the plate-independent source quantities with equivalent_blocked_force_level and characteristic_reception_plate_power before using EN 12354-5.

Attributes

Name	Description
frequencies	Band centre frequencies, in hertz, or None.
power_level	Reception-plate injected power level L_Ws per band, in dB re 1 pW (Formula 14).
velocity_level	Spatial mean plate velocity level L_v per band, dB.
loss_factor	Plate loss factor eta per band.
mass_per_area	Plate mass per unit area m, in kg/m^2.
area	Plate area S, in m^2.

StructureBornePowerResult.plot()

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

Plot the characteristic structure-borne power level per band.

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

StructureBornePowerResult.report()

StructureBornePowerResult.report(
    path: str,
    *,
    metadata: ReportMetadata | None = None,
    engine: str = 'reportlab',
    verbose: bool = False,
    language: str = 'en',
) -> str

Render an EN 15657 structure-borne sound power fiche to path.

Writes a one-page reception-plate characterization sheet: the standard-basis line naming the EN 15657:2018 reception-plate method (Formula 14), an optional metadata header (client, source equipment, test environment, instrumentation, climate, date), a per-band table (nominal octave/one-third-octave frequency, the spatial mean plate velocity level Lv and the injected structure-borne sound power level L_Ws), the L_Ws(f) spectrum with a nominal band axis, the boxed band-summed total L_Ws (dB re 1 pW) with the plate mass per area m and area S, an optional verdict row against a declared limit, and a basis strip stating Formula 14 and the conversion to the plate-independent source quantities (Formulae 15/17) required before EN 12354-5.

Parameters

Name	Description
path	Destination path of the PDF file.
metadata	Optional ReportMetadata supplying the header (client, specimen the source equipment, test_room the test environment, instrumentation, temperature, relative_humidity, pressure, test_date), the footer identity (laboratory, operator, report_id, notes) and, via requirement, a declared upper limit on the total L_Ws (lower is better). The plate mass and area come from the result itself.
engine	Rendering back end; only "reportlab" is supported.
verbose	When True the per-band table adds the plate loss factor eta column.
language	Fiche language: "en" (default) or "es".

Returns: The written path as a str.

Raises

Exception	When
ValueError	If engine is not "reportlab" or language is unknown.
ImportError	If reportlab (or, for the figure, matplotlib) is not installed (pip install phonometry[report]).

StructureBornePowerResult.total_level

property

Band-summed power level $10{\log }_{10}(\sum 10^{0.1L_{W\mathrm{s}}})$, in dB.