environment.sources.statistical_pass_by

What a road surface adds to the noise of the traffic on it (ISO 11819-1:1997).

A road surface is not a source, but it changes how loud every tyre on it is, and the Statistical Pass-By (SPB) method is how that change is measured. A microphone stands 7,5 m from the centre of the lane and 1,2 m above it, and for each vehicle that passes on its own, the maximum A-weighted level with time weighting F and the speed are written down, together with the vehicle’s category: cars (1), dual-axle heavy vehicles (2a) or multi-axle heavy vehicles (2b). Other vehicles are not used (clause 4).

9.1 and 9.2, the vehicle sound level. For each category the levels are regressed on the logarithm of the speed by least squares,

and the ordinate of that line at the reference speed of Table 1 is the vehicle sound level $L_{\mathrm{veh}}$ of the category (pass_by_regression). The reference speed depends on the road speed category of 3.3 (low, medium, high) and is the same for the two heavy categories.

9.5, the index. The three vehicle sound levels are added on an energy basis, each weighted by the proportion $W_x$ of its category in a standard mix and the heavy ones by the ratio of the car reference speed to their own:

(statistical_pass_by_index). The index is for comparing surfaces, not for predicting a traffic noise level (9.5 NOTE), and the comparison clause 10 has in mind is a difference from a reference surface, of which Annex D gives an example built from seven dense bituminous surfaces (normalized_reference_levels, SPB_NORMALIZED_REFERENCE_DB).

The rounding chain. 9.2 ends “All levels shall be calculated to two decimal places and rounded to one decimal place”, and 9.5 defines the levels the index adds as “the Vehicle Sound Levels … according to 9.2”. The index is therefore the index of the three vehicle sound levels rounded to one decimal, the ones a report prints, which is what lets anyone recompute it from the report: 7.4 asks for “the sound levels Lveh and the SPBI calculated from them”, and 9.5 says the mandatory reporting of every $L_{\mathrm{veh}}$ allows the index to be recalculated with other weighting factors. The regressions are carried at full precision, each level is rounded once, and the index is rounded once when it is reported (the reported_ properties); both roundings are half up, a convention of this module, since 9.2 gives no rule for a level on the half. “Two decimal places” is read as the least precision of the calculation, not as a first rounding: rounded to 0,01 dB and then to 0,1 dB, 79,946 dB would print 80,0 dB. Temperature-corrected levels and a reference given as levels enter their indices rounded the same way.

The example of Annex E is reproduced by this chain: its levels 78,5, 81,1 and 83,8 dB give 79,946 dB, printed 79,9 dB. Carried at full precision from the coefficients Annex E prints, the same levels are 78,546, 81,114 and 83,838 dB, and their index, 79,985 dB, would print 80,0 dB (StatisticalPassByResult.full_precision_index_db). The printed coefficients are rounded too, so the page alone does not prove which chain the example was computed with: over every line that agrees with the intercept, slope, mean level, mean speed and vehicle sound level Annex E prints, to their last printed digit, the full-precision index spans 79,948 dB to 79,996 dB, and only the corner below 79,95 dB would also print 79,9 dB.

9.3 and 7.3, as warnings. The regression is only used to normalize to the reference speed if that speed lies within one standard deviation of the measured mean speed for the heavy vehicles and one and a half for the cars. The mean and the standard deviation are those of $\lg v$, the variable the line is fitted in; the speed printed in Annex E is marked “converted from the logarithm of speed”, and the mean it prints is $10^{\overline{\lg v}}$. For surface classification, 7.3 asks for at least 100 cars, 30 vehicles of each heavy category and 80 heavy vehicles in all. Both conditions are judged, kept on the result and, when they fail, emitted as StatisticalPassByWarning rather than raised: a before-and-after study (6.6) is still an SPB measurement.

9.4, temperature. The vehicle sound levels should be corrected to an air temperature of 20 °C, and the standard says a suitable method is under consideration. None is implemented here: temperature-corrected levels are an input (corrected_vehicle_sound_levels_db), and the index is then computed for both. Clause 13 lists the corrected levels and index as optional report items (26 and 28) beside the mandatory uncorrected ones (25 and 27).

9.6, the random errors. Table 2 gives the spread expected of individual vehicles about $L_{\mathrm{veh}}$ and the 95 % confidence interval that spread leaves on it for 100 cars and 40 heavy vehicles of each type (SPB_VEHICLE_STANDARD_DEVIATIONS_DB, SPB_CONFIDENCE_INTERVALS_DB). A regression also returns the confidence interval of its own line at the reference speed, from the Student distribution with $n-2$ degrees of freedom, and the result combines the three into an interval on the index with the sensitivity of the index to each level. The standard says the index error “will be a combination of these errors according to the chosen weighting factors” and gives no formula; the combination here assumes the three categories independent.

Read from BS EN ISO 11819-1:2001, which is identical to ISO 11819-1:1997 (its national foreword).

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

normalized_reference_levels(
    surface_levels_db: Mapping[str, Mapping[str, float]],
) -> Mapping[str, float]

The vehicle sound levels of a normalized reference surface, 10.2 and Annex D.

The normalized reference case is a fictitious surface whose $L_{\mathrm{veh}}$ are set by convention, “for instance … the average results of a great number of SPB measurements” on dense asphalt surfaces. Annex D builds one from seven surfaces (SPB_ANNEX_D_SURFACES_DB) and prints the average of each column, which is what this returns: the arithmetic mean, category by category.

The energetic mean would print the same row there (76,4, 81,0 and 84,0 dB either way), so the page does not decide between the two; the arithmetic mean is the plain reading of “average” for levels that are already averages.

Parameters

Returns: The mean level of each category, in decibels, unrounded.

Raises

pass_by_regression(
    speeds_kmh: ArrayLike,
    max_levels_db: ArrayLike,
    *,
    vehicle_category: str,
    road_speed_category: str,
) -> PassByRegression

Fit the level of one vehicle category against the logarithm of speed, 9.1 and 9.2.

The maximum A-weighted levels are regressed on $\lg (v/1km/h)$ by least squares, and the ordinate of the line at the Table 1 reference speed is the vehicle sound level $L_{\mathrm{veh}}$ of the category (PassByRegression.vehicle_sound_level_db).

Two conditions are judged on the way and emitted as StatisticalPassByWarning when they fail: the 7.3 minimum number of vehicles of the category for surface classification, and the 9.3 window the reference speed has to lie in for the line to be used at it. Both verdicts stay on the result.

Parameters

Returns: The line and its statistics, as a PassByRegression.

Raises

PassByRegression(
    vehicle_category: str,
    road_speed_category: str,
    speeds_kmh: NDArray[np.float64],
    max_levels_db: NDArray[np.float64],
    reference_speed_kmh: float,
    intercept_db: float,
    slope_db_per_decade: float,
    correlation: float,
    level_standard_deviation_db: float,
    residual_standard_deviation_db: float,
    lg_speed_standard_deviation: float,
)

The regression line of one vehicle category and what 9.2 reads off it.

The line is $L=a+b\lg (v/1km/h)$, fitted by least squares to the pass-bys of one category (9.1). Clause 13 item 29 asks for the slope and the intercept, the average and the standard deviation of the speeds and the standard deviation of the residuals. The spread of the speeds is given here as the standard deviation of $\lg v$, in decades, and not in km/h: the line is fitted in $\lg v$ and 9.3 is judged in it, and the standard gives no conversion. Annex E prints a spread in km/h “converted from the logarithm of speed” without saying how, and its three values do not agree with the slopes, correlations and level spreads printed beside them (the errata registry has the arithmetic).

Parameters

property

Half-width of the 95 % confidence interval of the line at the reference speed.

the textbook interval of a least-squares line, in decibels. It is the measured counterpart of the 0,3 dB and 0,7 dB Table 2 expects, and it widens as the reference speed moves away from the mean speed.

property

The mean of the measured levels, in decibels.

property

The mean speed $10^{\overline{\lg v}}$, in km/h.

The mean of the variable the line is fitted in, converted back, as Annex E prints it (“value converted from the logarithm of speed”). The line passes through it at mean_level_db.

property

Whether the category has the vehicles 7.3 asks for classification.

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

Draw the pass-bys, the fitted line, the 9.3 window and $L_{\mathrm{veh}}$.

Parameters

Returns: The axes drawn on.

property

Whether the reference speed lies inside speed_window_kmh (9.3).

property

$L_{\mathrm{veh}}$ rounded to one decimal, as 9.2 has it reported.

property

The speeds the reference speed must lie between, 9.3, in km/h.

$10^{\overline{\lg v}\pm ks}$ with $s$ the standard deviation of $\lg v$ and $k$ 1,5 for cars and 1 for heavy vehicles (SPB_SPEED_WINDOW_STANDARD_DEVIATIONS).

property

How many pass-bys the line was fitted through.

property

$L_{\mathrm{veh}}$, the line at the reference speed, unrounded (9.2).

Constant (mapping).

SPB_ANNEX_D_SURFACES_DB = {'A1': {'1': 76.6, '2a': 81.1, '2b': 84.1}, 'A2': {'1': 75.9, '2a': 80.0, '2b': 83.0}, 'A3': {'1': 76.4, '2a': 81.8, '2b': 84.0}, 'A4': {'1': 77.2, '2a': 81.5, '2b': 84.9}, 'B1': {'1': 76.1, '2a': 81.0, '2b': 84.4}, 'B2': {'1': 76.4, '2a': 80.4, '2b': 83.3}, 'B3': {'1': 76.4, '2a': 81.0, '2b': 84.1}}

Constant (mapping).

SPB_CONFIDENCE_INTERVALS_DB = {'1': 0.3, '2a': 0.7, '2b': 0.7}

Constant (mapping).

SPB_MINIMUM_VEHICLE_COUNTS = {'1': 100, '2a': 30, '2b': 30, '2': 80}

Constant (mapping).

SPB_NORMALIZED_REFERENCE_DB = {'1': 76.4, '2a': 81.0, '2b': 84.0}

Constant (float).

SPB_REFERENCE_AIR_TEMPERATURE_C = 20.0

Constant (mapping).

SPB_REFERENCE_SPEEDS_KMH = {'low': {'1': 50.0, '2a': 50.0, '2b': 50.0}, 'medium': {'1': 80.0, '2a': 70.0, '2b': 70.0}, 'high': {'1': 110.0, '2a': 85.0, '2b': 85.0}}

Constant (tuple).

SPB_ROAD_SPEED_CATEGORIES = ('low', 'medium', 'high')

Constant (mapping).

SPB_SPEED_WINDOW_STANDARD_DEVIATIONS = {'1': 1.5, '2a': 1.0, '2b': 1.0}

Constant (tuple).

SPB_VEHICLE_CATEGORIES = ('1', '2a', '2b')

Constant (mapping).

SPB_VEHICLE_STANDARD_DEVIATIONS_DB = {'1': 1.5, '2a': 2.0, '2b': 2.0}

Constant (mapping).

SPB_WEIGHTING_FACTORS = {'low': {'1': 0.9, '2a': 0.075, '2b': 0.025}, 'medium': {'1': 0.8, '2a': 0.1, '2b': 0.1}, 'high': {'1': 0.7, '2a': 0.075, '2b': 0.225}}

statistical_pass_by(
    vehicle_categories: ArrayLike,
    speeds_kmh: ArrayLike,
    max_levels_db: ArrayLike,
    *,
    road_speed_category: str,
    corrected_vehicle_sound_levels_db: Mapping[str, float] | None = None,
    reference_db: float | Mapping[str, float] | None = None,
    weighting_factors: Mapping[str, float] | None = None,
) -> StatisticalPassByResult

The Statistical Pass-By method of ISO 11819-1 from a list of pass-bys.

One row per vehicle that passed on its own: its category, its speed and its maximum A-weighted level. The rows are split by category, a line is fitted through each (pass_by_regression), and each line is read at its Table 1 reference speed. The three vehicle sound levels are rounded to one decimal, as 9.2 has them reported, and combined into the index (statistical_pass_by_index), so that the index is the one anyone recomputes from the reported levels (9.5). The unrounded levels and their index stay on the result (StatisticalPassByResult.full_precision_index_db).

The 7.3 counts (the two heavy categories together included) and the 9.3 speed windows are judged, kept on the result and emitted as StatisticalPassByWarning when they fail.

Parameters

Returns: The regressions, the levels and the index, as a StatisticalPassByResult.

Raises

statistical_pass_by_index(
    vehicle_sound_levels_db: Mapping[str, float],
    *,
    road_speed_category: str,
    weighting_factors: Mapping[str, float] | None = None,
) -> float

The Statistical Pass-By Index of three vehicle sound levels, 9.5.

with the reference speeds and the weighting factors of Table 1 for the road speed category. The heavy terms carry the ratio of the car reference speed to their own because a vehicle that goes slower is heard for longer: the ratio weights each category by the time its vehicles take to pass, so that a difference in SPBI between two surfaces is the difference in equivalent level for the reference speeds and proportions of Table 1 (9.5). The index itself is not an equivalent level of traffic noise (9.5 NOTE).

Whatever levels are handed in are used as they are. Handed the three levels a report prints to one decimal, this is the index a third party computes from the report, which 9.5 anticipates, and the index statistical_pass_by reports, which rounds its levels that way before calling this.

Parameters

Returns: The index, in decibels, unrounded.

Raises

StatisticalPassByResult(
    road_speed_category: str,
    regressions: Mapping[str, PassByRegression],
    weighting_factors: Mapping[str, float],
    vehicle_sound_levels_db: Mapping[str, float],
    index_db: float,
    corrected_vehicle_sound_levels_db: Mapping[str, float] | None = None,
    corrected_index_db: float | None = None,
    reference_index_db: float | None = None,
)

The vehicle sound levels and the index of one road surface (ISO 11819-1).

Parameters

property

The temperature-corrected SPBI less the reference one, or None.

property

The SPBI less that of the reference surface, in decibels, or None.

Positive for a surface louder than the reference. Unrounded; 9.5 says that in many cases the main use of the index is this difference.

property

The SPBI of the unrounded $L_{\mathrm{veh}}$, in decibels.

Not the index the standard reports, which adds the levels of 9.2 as they are reported, to one decimal (index_db). The two never differ by more than 0,05 dB, the most a level moves when it is rounded, but that can be enough to move the reported digit: for the lines Annex E prints, this is 79,985 dB, which would print 80,0 dB, where the annex prints 79,9 dB.

property

Dual-axle and multi-axle heavy vehicles together, as 7.3 counts them.

property

Half-width of the 95 % interval the three line intervals leave on the index.

with $W_x^{\prime }$ the weighting factor times the speed ratio of 9.5, $L_x$ the reported levels the index adds and ${\Delta }_x$ each category’s PassByRegression.confidence_interval_db. The three categories are measured on different vehicles and are taken as independent.

property

Whether every count of 7.3 is met, the heavy vehicles together included.

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

Draw the three clouds of pass-bys, their lines and $L_{\mathrm{veh}}$.

Parameters

Returns: The axes drawn on.

property

Whether every reference speed lies inside its 9.3 window.

property

The Table 1 reference speeds the levels are normalized to, in km/h.

property

The temperature-corrected SPBI rounded to one decimal, or None.

property

The temperature-corrected levels rounded to one decimal, or None.

property

The SPBI rounded to one decimal (9.2).

property

$L_{\mathrm{veh}}$ of each category rounded to one decimal (9.2).

The levels the index is computed from, and the ones a report prints.

A pass-by data set falls short of a condition ISO 11819-1 states.