vibration.immission.train_categories

Railway vibration by category of train (E DIN 4150-2:2023-08, 6.5.3).

The draft of August 2023 that is to replace DIN 4150-2:1999-06 rewrites how a railway is assessed for the people in a building. The 1999 edition formed the clock maximum r.m.s. over the intervals a class of train occupied, raised the guide values by 1,5 for an urban line and left the upper value out of the railway’s verdict altogether. The draft keeps the two assessment quantities and changes what feeds them:

• every train passage counts as one clock interval, however long it lasts (6.5.3.2), so $K{B}_{FTm,Zug}$ of Formula (5) is the r.m.s. of one clock maximum per passage, with nothing set to zero below 0,1;
• $K{B}_{F\max }$ of a railway is not the largest clock maximum observed but 1,5 times $K{B}_{FTm,Zug}$ of each category and the largest of those (Formulae (7) and (8)), because a single passage with a flat spot on a wheel is not what the line is like;
• the assessment vibration severity of Formula (6) weights each category by the number of its trains in the period, out of the 1920 or 960 clock intervals of the day or the night, and by a weighting factor ${\alpha }_{Zug}$ of Table 2 for the kind of train and whether the line runs on the surface or underground: 0,7 for a tram on the surface, 1,3 for a freight train over 600 m anywhere. A category whose r.m.s. is at or below 0,1 enters Formula (6) as zero;
• a line to be built new is held at night to an upper value of its own (6.5.3.5): 0,6 on the surface in any area, and underground the Table 1 value in an industrial or commercial area and 0,3 elsewhere;
• an existing line that is altered or extended is judged by the change it brings (6.5.3.6): the planned case is first held to the guide values as any immission is, and where $A_o$ or $A_r$ is exceeded the requirement still counts as met if $K{B}_{F\max }$ or $K{B}_{FTr}$ grows by less than 25 % against the case without the project, which is the least increase a laboratory study found people to notice. The clause says the requirements are met if one of its conditions holds, and its own Example 9 sends a line whose $K{B}_{F\max }$ does not change at all to mitigation because $K{B}_{FTr}$ grows by more; every condition that applies has to hold here, as in the example, and the sentence is in docs/ERRATA.md.

E DIN 45672-3:2023-02, the draft prediction method for railways, takes the sum of Formula (6) as its Formula (11) and the same factors as its Annex E, though it prints the sum without the sentence that zeroes a category at or below 0,1, so the functions here serve both; the prediction chain that leads up to them is in phonometry.vibration.immission.railway_prediction.

Every example of Annex B that the draft works with these formulae is a conformance row: the 47 passages of Table B.1 and their eight derived values, and the four assessment severities of Example 9. The two night-time severities of those four are printed over 920 intervals where 6.5.3.2 fixes 960, and the day-time one of Example 8 is printed as 0,099 8 where its own four-decimal inputs give 0,099 7; both are registered in docs/ERRATA.md, and the rows run the standard’s own 960 and its own inputs.

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

assess_railway_change(
    *,
    kb_fmax_before: float,
    kb_fmax_after: float,
    kb_ftr_before: float,
    kb_ftr_after: float,
    guide: GuideValues,
    time_of_day: str = 'day',
) -> RailwayChange

Judge an altered or extended line by the change it brings (6.5.3.6).

The case without the project, the Prognosenullfall, is the existing line with its present or its forecast timetable; the planned case, the Prognoseplanfall, is the line with the project. The planned case is first held to the guide values in the order of 6.3: a $K{B}_{F\max }$ at or below $A_u$ meets the requirements on its own, and so does one at or below $A_o$ with a $K{B}_{FTr}$ at or below $A_r$, and then the change is beside the point. Where $K{B}_{F\max }$ exceeds $A_o$, or $K{B}_{FTr}$ exceeds $A_r$, the requirements still count as met if the quantity grows by less than 25 % against the case without the project; otherwise mitigation is to be looked into. Example 9 of Annex B finds a night-time $K{B}_{FTr}$ of 0,096 against 0,066 before, an increase of over 25 % above an $A_r$ of 0,07, and sends the project to mitigation although its $K{B}_{F\max }$ does not change, which is why every condition that applies has to hold here and not one of them, as the clause is printed.

Parameters

Returns: The verdict, as a RailwayChange.

Raises

Constant (float).

RAILWAY_CHANGE_TOLERANCE_PERCENT = 25.0

railway_guide_values(
    area: str,
    *,
    time_of_day: str = 'day',
    alignment: str = 'surface',
) -> GuideValues

The guide values a line to be built new is held to (6.5.3.5).

$A_u$ and $A_r$ are Table 1 of the draft, by day and by night, and $A_o$ is Table 1 by day. At night the upper value is the line’s own: 0,6 on the surface whatever the area; underground, the Table 1 value in an industrial or commercial area and 0,3 in a mixed, residential or sensitive one. The same values bound the planned case of an altered or extended line (6.5.3.6 b)).

Parameters

Returns: The three values, as a GuideValues of the 2023 edition.

Raises

railway_kb_fmax(kb_ftm_zug: ArrayLike) -> float

The $K{B}_{F\max }$ of a railway, Formula (8).

The largest $K{B}_{F\max ,Zug}$ of Formula (7) over the categories, which is what the draft compares with $A_u$ and $A_o$.

Parameters

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

Raises

Constant (mapping).

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

RailwayChange(
    complies: bool,
    kb_fmax_met: bool,
    kb_ftr_met: bool,
    kb_fmax_increase_percent: float,
    kb_ftr_increase_percent: float,
    guide: GuideValues,
    time_of_day: str,
)

The verdict of 6.5.3.6 on an altered or extended line.

Attributes

train_assessment_severity(
    kb_ftm_zug: ArrayLike,
    trains: ArrayLike,
    *,
    alpha: ArrayLike,
    time_of_day: str = 'day',
) -> float

The assessment vibration severity of a railway, Formula (6).

$K{B}_{FTr}=\sqrt{{\sum }_{Zug}\frac{n_{Zug}}{N_r}({\alpha }_{Zug}K{B}_{FTm,Zug}{)}^2}$: each category weighted by the trains it runs in the period, out of the $N_r$ = 1920 clock intervals of the day or 960 of the night, and by its factor of Table 2. A category whose r.m.s. is at or below 0,1 enters as zero. The rest hours of the day are not applied to a railway (6.5.3.2). E DIN 45672-3:2023-02 Formula (11) is the same sum, printed without the sentence on 0,1. The categories are at least one per track or direction and kind of train, and their trains are counted apart, so nothing bounds their sum by the intervals of the period: two tracks can each carry a train in the same interval.

Parameters

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

Raises

train_category_rms(kb_fti_zug: ArrayLike) -> float

The clock maximum r.m.s. of one category of train, Formula (5).

$K{B}_{FTm,Zug}=\sqrt{\frac{1}{Z}{\sum }_{i=1}^{Z}K{B}_{FTi,Zug}^2}$ over the $Z$ passages measured, one clock maximum per passage whatever the passage lasted. Unlike Formula (1) and the 1999 edition’s (A.1), a maximum at or below 0,1 enters as it is: the suppression is applied to the category’s r.m.s. in Formula (6), not to the passages (C.2), because $K{B}_{F\max }$ of Formula (7) is formed from this value.

Parameters

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

Raises

train_kb_fmax(kb_ftm_zug: ArrayLike) -> NDArray[np.float64]

The $K{B}_{F\max ,Zug}$ of each category, Formula (7).

$K{B}_{F\max ,Zug}=1,5\cdot K{B}_{FTm,Zug}$, the estimate the draft uses instead of the largest clock maximum observed, which a single passage with an out-of-round wheel would decide. Formed from the value before rounding: Table B.1 prints 0,851 for a category whose r.m.s. it prints as 0,568.

Parameters

Returns: $K{B}_{F\max ,Zug}$ of each, in the same order.

Raises

Constant (float).

TRAIN_KB_FMAX_FACTOR = 1.5

Constant (tuple).

TRAIN_KINDS = ('tram_metro', 's_bahn', 'passenger', 'freight', 'freight_long')

train_weighting_factor(kind: str, *, alignment: str = 'surface') -> float

The weighting factor ${\alpha }_{Zug}$ of Table 2 for one category.

Parameters

Returns: ${\alpha }_{Zug}$, dimensionless.

Raises

Constant (mapping).

TRAIN_WEIGHTING_FACTORS = {'tram_metro': {'surface': 0.7, 'underground': 1.0}, 's_bahn': {'surface': 0.8, 'underground': 1.0}, 'passenger': {'surface': 0.9, 'underground': 1.0}, 'freight': {'surface': 1.0, 'underground': 1.0}, 'freight_long': {'surface': 1.3, 'underground': 1.3}}