vibration.immission.people

Vibration and the people in a building (DIN 4150-2:1999-06).

DIN 4150-2 is the assessment the DIN 45669-1 meter exists for. The meter produces two numbers for a record, the maximum weighted vibration severity $K{B}_{F\max }$ and the clock maximum r.m.s. $K{B}_{FTm}$, and this standard says what they may be for the people who live or work where the vibration arrives: a table of guide values by kind of area and time of day, a procedure that reads them in a fixed order, and the special rules for the sources that most often bring vibration into a house.

The two assessment quantities (Clause 6.1). $K{B}_{F\max }$ is what the vibration felt like at its worst. The assessment vibration severity $K{B}_{FTr}$ of Formulae (4a), (4b) and (5) is what it added up to over the whole assessment period, 16 h by day and 8 h by night: the clock maximum r.m.s. of each stretch of exposure, weighted by its share of the period, and doubled in weight where the stretch falls in the rest hours of the day. The largest of the three directions is the one assessed.

The procedure (Clause 6.2, Figure 2). If $K{B}_{F\max }$ is at or below the lower guide value $A_u$, the requirement is met and the question is over. If it is above the upper guide value $A_o$, it is not met. In between, rare and short events are accepted as they are, and everything else is decided by $K{B}_{FTr}$ against $A_r$. The guide values of Table 1 are not to be applied mechanically, the standard says, and Example 3 of its Annex C shows what it means: 0,17 against an $A_u$ of 0,15 is inside the 15 % a measurement of $K{B}_F$ is uncertain by, and the requirement “can as a rule still be regarded as met”.

The sources (Clause 6.5). Up to three short events a day, blasting among them, are judged on $A_o$ alone, and quarry blasting by day in a mixed or residential area, under the conditions of 6.5.1, on the $A_o$ of an industrial one. Road traffic uses the procedure without the rest-time factor. A railway is judged on $A_u$ and $A_r$ only, with the factor 1,5 on both for an urban surface line; $A_o$ is not a verdict for it, and 6.5.3.5 sets its own night-time thresholds, 0,6 on a surface line and 0,3 underground, above which a single clock maximum is a reason to look into the cause. A construction site has its own Table 2, by how many working days it shakes the neighbours and how far the operator is prepared to go, with the values for two to six days interpolated as Figure 3 draws them.

A railway, in detail (Annex A). The trains of one class occupy a few clock intervals each, so their $K{B}_{FTm}$ is formed over the occupied intervals alone (Formula (A.1)), a standard deviation is put on its square (Formula (A.2)), and the assessment severity weights each class by the intervals it occupies in the period, 1920 by day and 960 by night (Formula (A.3)). Figure D.1 turns that around: how many trains an hour a class may run before $K{B}_{FTr}$ reaches $A_r$.

From a velocity record (Clause 7). Where only an unweighted record exists, Formula (6) turns its peak and its frequency into a KB value and Formula (7) scales that by an empirical factor of Table 3 to an estimate of $K{B}_{F\max }$, marked with an asterisk in the standard because it is one.

A formula printed wrong. Formula (A.1b) equates $K{B}_{FTm,j}$ to a mean of squares with no root over it; Formula (A.1a) beside it, Formula (A.2) and the worked Example 8 all take the root. Registered in docs/ERRATA.md.

The draft of 2023. E DIN 4150-2:2023-08 is to replace the 1999 edition, and edition="2023" reads it: Table 1 with one cell changed, the night $A_u$ of a mixed area down from 0,15 to 0,1; no shortcut for a $K{B}_{F\max }$ within the 15 % above $A_u$, which its Example 3 sends on to $A_r$ and fails; a railway compared with $A_o$ like any other source, its $K{B}_{F\max }$ and $K{B}_{FTr}$ formed by category of train in phonometry.vibration.immission.train_categories; an existing road whose neighbours must put up with $A_u$ and $A_r$ exceeded by up to 50 % (6.5.2); and an induced seismic event, held by day and by night to the daytime $A_o$ (6.5.1.3). The rest of the numbers are the same, and the draft’s Table 3 prints the days two to six that the 1999 Figure 3 made one read off a curve, cell for cell what the interpolation gives.

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

admissible_exposure_s(
    kb_ftm: float,
    a_r: float,
    *,
    time_of_day: str = 'day',
) -> float

How long a source may act before $K{B}_{FTr}$ reaches $A_r$.

Formula (4b) turned around, as Example 2 of Annex C does it: $T_e=(A_r/K{B}_{FTm}{)}^2{T}_r$. Longer than the period means the source may run all day and still keep to $A_r$.

Parameters

Returns: The exposure, in seconds.

Raises

admissible_trains_per_hour(kb_ftm: float, a_r: float) -> float

How many trains an hour keep $K{B}_{FTr}$ at $A_r$ (Figure D.1).

With one class of train and each train occupying one clock interval, Formula (A.4) reads $K{B}_{FTr}=K{B}_{FTm}\sqrt{n/120}$ for $n$ trains an hour, so the most an hour may carry is $120(A_r/K{B}_{FTm}{)}^2$. Annex D reads the figure at 7 trains for an $A_r$ of 0,05 and 14 for 0,07, both at a $K{B}_{FTm}$ of 0,2.

Parameters

Returns: Trains per hour, not rounded; the standard rounds down.

Raises

assess_people_in_buildings(
    kb_fmax: float,
    guide: GuideValues,
    *,
    kb_ftr: float | None = None,
    source: str = 'general',
    rare_short_events: bool = False,
    edition: str | None = None,
) -> PeopleAssessment

Read the guide values in the order of Clause 6.2 (Figure 2).

$K{B}_{F\max }$ at or below $A_u$ meets the requirement, and so, as a rule, does one above it by less than the 15 % of 5.4 that a measurement of $K{B}_F$ is uncertain by, which is how the standard’s own Example 3 concludes on 0,17 against an $A_u$ of 0,15; the verdict says so in within_uncertainty. Above $A_o$ it is not met, unless the source is a railway, which 6.5.3.1 judges on $A_u$ and $A_r$ alone. Between the two, up to three short events a day are met as they are (6.5.1), and anything else is decided by $K{B}_{FTr}$ against $A_r$, which has to be supplied then: it is formed from the record by assessment_vibration_severity or, for a railway, by railway_assessment_severity. The note to 6.2 says when that is not worth doing: a steady vibration acting for much longer than 4 h by day or 2 h by night keeps to $A_r$ only if it keeps to $A_u$.

Each comparison is made at the decimals the guide value is printed with, which is how Example 4 reads a $K{B}_{FTr}$ of 0,154 as meeting an $A_r$ of 0,15; and the standard says the values are not to be applied mechanically in any case.

The draft of 2023 reads the same order (its 6.3 and Figure 2) with three differences: a $K{B}_{F\max }$ within the 15 % above $A_u$ goes on to $A_r$ like any other, which is how its Example 3 fails 0,114 against 0,10; a railway is compared with $A_o$ as well, its $K{B}_{F\max }$ being the 1,5 times $K{B}_{FTm,Zug}$ of railway_kb_fmax and its $K{B}_{FTr}$ that of train_assessment_severity; and a road is not, by night, its 6.5.2 saying that a rare exceedance of the night-time $A_o$ does not fail the requirement, with ROAD_NIGHT_INVESTIGATION_KB in its place as a reason to look into the cause. An induced seismic event is a rare short event by definition (6.5.1.3). The edition is the one the guide values were read from, and asking for the other is refused: the values of one edition under the rules of the other is not an assessment of either.

Parameters

Returns: The verdict, as a PeopleAssessment.

Raises

Constant (mapping).

ASSESSMENT_PERIOD_S = {'day': 57600.0, 'night': 28800.0}

Constant (mapping).

ASSESSMENT_TAKT_COUNT = {'day': 1920, 'night': 960}

assessment_vibration_severity(
    kb_ftm: ArrayLike,
    exposure_s: ArrayLike,
    *,
    time_of_day: str = 'day',
    in_rest_time: ArrayLike | None = None,
) -> float

The assessment vibration severity $K{B}_{FTr}$, Formulae (4) and (5).

$K{B}_{FTr}=\sqrt{\frac{1}{T_r}{\sum }_j{w}_j{T}_{e,j}K{B}_{FTm,j}^2}$: the clock maximum r.m.s. of each stretch of exposure, weighted by the share of the assessment period it lasts for. One stretch is Formula (4b), several are Formula (4a), and a stretch in the rest hours of the day carries the weight 2 of Formula (5), which 6.5.2 and 6.5.3.1 say is not applied to road or rail traffic.

Parameters

Returns: $K{B}_{FTr}$, dimensionless.

Raises

Constant (float).

BLASTING_EXCEPTION_KB_FMAX = 8.0

Constant (int).

BLASTING_MAX_PER_WEEK = 15

Constant (float).

CONSTRUCTION_BLASTING_A_O = 8.0

Constant (mapping).

CONSTRUCTION_GUIDE_VALUES = {'I': {1: GuideValues(a_u=0.8, a_o=5.0, a_r=0.4, time_of_day='day', edition='1999'), 26: GuideValues(a_u=0.4, a_o=5.0, a_r=0.3, time_of_day='day', edition='1999'), 78: GuideValues(a_u=0.3, a_o=5.0, a_r=0.2, time_of_day='day', edition='1999')}, 'II': {1: GuideValues(a_u=1.2, a_o=5.0, a_r=0.8, time_of_day='day', edition='1999'), 26: GuideValues(a_u=0.8, a_o=5.0, a_r=0.6, time_of_day='day', edition='1999'), 78: GuideValues(a_u=0.6, a_o=5.0, a_r=0.4, time_of_day='day', edition='1999')}, 'III': {1: GuideValues(a_u=1.6, a_o=5.0, a_r=1.2, time_of_day='day', edition='1999'), 26: GuideValues(a_u=1.2, a_o=5.0, a_r=1.0, time_of_day='day', edition='1999'), 78: GuideValues(a_u=0.8, a_o=5.0, a_r=0.6, time_of_day='day', edition='1999')}}

construction_guide_values(
    duration_days: int,
    *,
    stage: str = 'I',
    area: str = 'residential',
) -> GuideValues

The daytime guide values of Table 2 for a construction site (6.5.4.2).

The duration is the number of working days on which the site actually shakes the neighbours, not how long it stands. A duration of two to six days takes the values Figure 3 interpolates between the one-day column and the column that starts at seven days, and a duration over 78 days is outside the table. Vibration at night is judged by Table 1 instead, and the site’s blasting by CONSTRUCTION_BLASTING_A_O alone. Table 2 is not applicable to an especially sensitive area, a hospital for one; 6.5.4.2 sends those to their own investigation and agreement.

Parameters

Returns: The three values, as a GuideValues.

Raises

Constant (tuple).

CONSTRUCTION_STAGES = ('I', 'II', 'III')

Constant (float).

DAY_REST_TIME_S = 14400.0

Constant (mapping).

GUIDE_VALUES = {'industrial': {'day': GuideValues(a_u=0.4, a_o=6.0, a_r=0.2, time_of_day='day', edition='1999'), 'night': GuideValues(a_u=0.3, a_o=0.6, a_r=0.15, time_of_day='night', edition='1999')}, 'commercial': {'day': GuideValues(a_u=0.3, a_o=6.0, a_r=0.15, time_of_day='day', edition='1999'), 'night': GuideValues(a_u=0.2, a_o=0.4, a_r=0.1, time_of_day='night', edition='1999')}, 'mixed': {'day': GuideValues(a_u=0.2, a_o=5.0, a_r=0.1, time_of_day='day', edition='1999'), 'night': GuideValues(a_u=0.15, a_o=0.3, a_r=0.07, time_of_day='night', edition='1999')}, 'residential': {'day': GuideValues(a_u=0.15, a_o=3.0, a_r=0.07, time_of_day='day', edition='1999'), 'night': GuideValues(a_u=0.1, a_o=0.2, a_r=0.05, time_of_day='night', edition='1999')}, 'sensitive': {'day': GuideValues(a_u=0.1, a_o=3.0, a_r=0.05, time_of_day='day', edition='1999'), 'night': GuideValues(a_u=0.1, a_o=0.15, a_r=0.05, time_of_day='night', edition='1999')}}

guide_values(
    area: str,
    *,
    time_of_day: str = 'day',
    source: str = 'general',
    edition: str = '1999',
) -> GuideValues

The guide values of Table 1 for one area, time of day and kind of source.

Parameters

Returns: The three values, as a GuideValues.

Raises

Constant (mapping).

GUIDE_VALUES_2023 = {'industrial': {'day': GuideValues(a_u=0.4, a_o=6.0, a_r=0.2, time_of_day='day', edition='2023'), 'night': GuideValues(a_u=0.3, a_o=0.6, a_r=0.15, time_of_day='night', edition='2023')}, 'commercial': {'day': GuideValues(a_u=0.3, a_o=6.0, a_r=0.15, time_of_day='day', edition='2023'), 'night': GuideValues(a_u=0.2, a_o=0.4, a_r=0.1, time_of_day='night', edition='2023')}, 'mixed': {'day': GuideValues(a_u=0.2, a_o=5.0, a_r=0.1, time_of_day='day', edition='2023'), 'night': GuideValues(a_u=0.1, a_o=0.3, a_r=0.07, time_of_day='night', edition='2023')}, 'residential': {'day': GuideValues(a_u=0.15, a_o=3.0, a_r=0.07, time_of_day='day', edition='2023'), 'night': GuideValues(a_u=0.1, a_o=0.2, a_r=0.05, time_of_day='night', edition='2023')}, 'sensitive': {'day': GuideValues(a_u=0.1, a_o=3.0, a_r=0.05, time_of_day='day', edition='2023'), 'night': GuideValues(a_u=0.1, a_o=0.15, a_r=0.05, time_of_day='night', edition='2023')}}

GuideValues(
    a_u: float,
    a_o: float,
    a_r: float,
    time_of_day: str = 'day',
    edition: str = '1999',
)

One row of Table 1 or Table 2 for one period: the three guide values.

Attributes

induced_seismic_kb_fmax(peak_velocity_mm_s: float) -> float

The $K{B}_{F\max }$ of an induced seismic event, E DIN 4150-2:2023-08 6.5.1.3.

$K{B}_{F\max }=0,44v_{\max }$, the simplified estimate the draft gives for an event of a few seconds with its energy below 15 Hz, which is held by day and by night to the daytime $A_o$ alone; $K{B}_{FTr}$ is not formed for it.

Parameters

Returns: $K{B}_{F\max }$.

Raises

Constant (float).

INDUCED_SEISMIC_PEAK_FACTOR = 0.44

kb_fmax_from_peak_velocity(
    peak_velocity_mm_s: float,
    frequency_hz: float,
    *,
    kind: str,
) -> float

An estimate of $K{B}_{F\max }$ from an unweighted record, Formula (7).

$K{B}_{F\max }^{\ast }=KB\cdot c_F$, Formula (6) scaled by the factor of Table 3 for the kind of vibration. An estimate, which is what the asterisk marks: Table 3 puts its factors at about 15 % either way.

Parameters

Returns: $K{B}_{F\max }^{\ast }$.

Raises

kb_from_peak_velocity(
    peak_velocity_mm_s: float,
    frequency_hz: float,
) -> float

The KB value of a peak velocity at a frequency, Formula (6).

$KB=\frac{1}{\sqrt{2}}\frac{v_{\max }}{\sqrt{1+(f_o/f{)}^2}}$ with $f_o$ = 5,6 Hz, the corner of the KB weighting: the value the weighted severity settles at for a sine of that peak and frequency, which the note under the formula says is the KB of the 1975 edition.

Parameters

Returns: $KB$, dimensionless.

Raises

Constant (float).

KB_UNCERTAINTY_PERCENT = 15.0

Constant (mapping).

PEAK_TO_KB_FACTORS = {'harmonic': 0.9, 'harmonic_distorted': 0.8, 'stochastic_resonant': 0.8, 'stochastic': 0.7, 'single_event_resonant': 0.8, 'single_event': 0.6}

PeopleAssessment(
    complies: bool,
    criterion: str,
    kb_fmax: float,
    kb_ftr: float | None,
    guide: GuideValues,
    source: str,
    within_uncertainty: bool,
)

The verdict of Clause 6.2 on one immission, and how it was reached.

Attributes

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

Draw the two assessment quantities against the three guide values.

Requires matplotlib (pip install phonometry[plot]).

Parameters

Returns: The Axes.

railway_assessment_severity(
    kb_ftm: ArrayLike,
    occupied_takte: ArrayLike,
    *,
    time_of_day: str = 'day',
    spread: ArrayLike | None = None,
) -> RailwayAssessment

The assessment vibration severity of a railway, Formulae (A.3) and (A.4).

$K{B}_{FTr}=\sqrt{\frac{1}{N_r}{\sum }_j{M}_{j}K{B}_{FTm,j}^2}$: each class of train weighted by the clock intervals it occupies in the period, out of the 1920 of a day or the 960 of a night. With one class that is Formula (A.4). Given the spread of Formula (A.2) for each class, the same sum is formed with each mean square one spread up and one down, which is how Example 8 reports $0,325_{-0,073}^{+0,059}$.

Parameters

Returns: The severity and, with a spread, its interval, as a RailwayAssessment.

Raises

Constant (mapping).

RAILWAY_NIGHT_INVESTIGATION_KB = {'surface': 0.6, 'underground': 0.3}

railway_takt_maximum_rms(kb_fti: ArrayLike) -> float

The clock maximum r.m.s. of one class of train, Formula (A.1).

The root of the mean square of the clock maxima the trains of the class occupied, $Z_j$ of them, with nothing counted for the intervals between trains: Formula (A.1b), with the root Formula (A.1a) and the worked Example 8 carry and the print of (A.1b) lost. The rule of Formula (3) that a maximum at or below 0,1 enters as zero applies here as well.

Parameters

Returns: $K{B}_{FTm,j}$.

Raises

railway_takt_spread(kb_fti: ArrayLike) -> float

The standard deviation of the square of the clock maxima, Formula (A.2).

$s(K{B}_{FTm,j}^2)=\sqrt{\frac{1}{Z_j-1}{\sum }_i(K{B}_{FTi,j}^2-K{B}_{FTm,j}^2{)}^2}$, on the square because it is the square that Formula (A.3) averages, so the spread of $K{B}_{FTr}$ follows from it by adding and subtracting it there. The maxima enter as they enter railway_takt_maximum_rms, a value at or below 0,1 as zero, so the spread is about the mean square that function returns.

Parameters

Returns: $s(K{B}_{FTm,j}^2)$.

Raises

RailwayAssessment(
    kb_ftr: float,
    kb_ftm: NDArray[np.float64],
    occupied_takte: NDArray[np.int64],
    lower: float | None,
    upper: float | None,
    time_of_day: str,
)

The assessment vibration severity of a railway, Formula (A.3).

Attributes

Constant (int).

RARE_EVENTS_PER_DAY = 3

Constant (float).

REST_TIME_WEIGHT = 2.0

Constant (float).

ROAD_EXISTING_TOLERANCE_FACTOR = 1.5

Constant (float).

ROAD_NIGHT_INVESTIGATION_KB = 0.6

Constant (float).

URBAN_RAILWAY_FACTOR = 1.5