Source: https://jmrplens.github.io/phonometry/environment/sources/road-surface-pass-by/ # Road-surface noise: the statistical pass-by method (ISO 11819-1) A road surface makes no noise of its own, yet the same traffic can be up to 15 dB louder on one surface than on another (the Introduction of ISO 11819-1). The Statistical Pass-By method measures that influence without choosing any vehicles: it records the traffic that uses the road, one isolated vehicle at a time, and lets a regression take the vehicles out. The implemented text is ISO 11819-1:1997, read from BS EN ISO 11819-1:2001, which is identical to it. ## 1. What is measured, and on which vehicles Each vehicle is put in one of three categories (3.4): **cars (1)**, **dual-axle heavy vehicles (2a)** and **multi-axle heavy vehicles (2b)**. Vans, cars with trailers and motorcycles are not used (clause 4). The road is put in one of three speed categories by the average speed of its traffic (3.3): low (45 km/h to 64 km/h), medium (65 km/h to 99 km/h) and high (cars at 100 km/h or more). Table 1 gives, for each, the reference speed every level is brought to and the weighting factor $W_x$ each category gets in the index: | Vehicle category | Low: speed | Low: $W_x$ | Medium: speed | Medium: $W_x$ | High: speed | High: $W_x$ | | :--- | ---: | ---: | ---: | ---: | ---: | ---: | | Cars (1) | 50 km/h | 0,900 | 80 km/h | 0,800 | 110 km/h | 0,700 | | Dual-axle heavy (2a) | 50 km/h | 0,075 | 70 km/h | 0,100 | 85 km/h | 0,075 | | Multi-axle heavy (2b) | 50 km/h | 0,025 | 70 km/h | 0,100 | 85 km/h | 0,225 | ## How the measurement goes | Requirement | Value | Clause | | :--- | :--- | :--- | | Microphone | 7,5 m ± 0,1 m from the centre of the test lane, 1,2 m ± 0,1 m above it | 8.1 | | Level | Maximum A-weighted level, time weighting F; type 1 meter; calibration drift over 0,5 dB invalidates the series | 5.1, 5.3, 8.2 | | Speed | As the vehicle midpoint passes the microphone, standard uncertainty under 3 % | 5.4, 8.4 | | Which pass-bys | The level at least 6 dB lower just before and after; no overtaking or opposing traffic at the peak; constant speed | 7.2 | | How many | 100 cars, 30 dual-axle, 30 multi-axle and 80 heavy vehicles together, for classification | 7.3 | | Site and weather | Level and straight over 30 m each side (50 m on a high-speed road); wind at most 5 m/s; air 5 °C to 30 °C; road 5 °C to 50 °C; dry | 6, 11 | | Background | At least 10 dB under the quietest pass-by | 12 | ## 2. The vehicle sound level For each category the pass-bys are fitted by least squares with $L_{\mathrm{AFmax}} = a + b \lg(v / 1\ \mathrm{km/h})$ (9.1), and the line read at the reference speed is the **vehicle sound level** $L_\mathrm{veh}$ (9.2). ```python import numpy as np from phonometry import environment rng = np.random.default_rng(11819) site = { # pass-bys, mean speed (km/h), spread of lg v, line and scatter (dB) "1": (120, 88.0, 0.055, 16.6, 32.6, 1.4), "2a": (40, 76.0, 0.050, 46.5, 18.8, 2.0), "2b": (50, 74.0, 0.045, 34.5, 26.7, 2.0), } categories, speeds, levels = [], [], [] for category, (n, mean_kmh, spread, a, b, scatter) in site.items(): lg_v = np.log10(mean_kmh) + spread * rng.standard_normal(n) categories += [category] * n speeds += (10.0**lg_v).tolist() levels += (a + b * lg_v + scatter * rng.standard_normal(n)).tolist() result = environment.statistical_pass_by( categories, speeds, levels, road_speed_category="medium", reference_db=environment.SPB_NORMALIZED_REFERENCE_DB, ) print(dict(result.reported_vehicle_sound_levels_db)) # {'1': 78.9, '2a': 81.0, '2b': 83.7} print(result.reported_index_db) # 80.1 dB print(round(result.difference_db, 2)) # 1.22 dB above Annex D ``` Each regression reports what clause 13 item 29 asks for (the slope, the intercept, the mean speed $10^{\overline{\lg v}}$ and the spread of the speeds, the spread of the residuals) and the correlation Annex E prints beside them. Clause 9.3 asks the reference speed to lie within one standard deviation of the mean speed for heavy vehicles and one and a half for cars; the window is judged in $\lg v$, the variable of the fit. The 9.3 window and the 7.3 counts are kept on the result and, when they fail, emitted as `StatisticalPassByWarning` rather than raised. ## 3. The index and the reference surface The **Statistical Pass-By Index** adds the three levels on an energy basis (9.5): $$ \mathrm{SPBI} = 10 \lg \left[ W_1 \, 10^{L_1/10} + W_{2a} \frac{v_1}{v_{2a}} 10^{L_{2a}/10} + W_{2b} \frac{v_1}{v_{2b}} 10^{L_{2b}/10} \right] \ \mathrm{dB}. $$ It adds the vehicle sound levels as 9.2 reports them, to one decimal: 9.5 defines its $L_1$, $L_{2a}$ and $L_{2b}$ as the vehicle sound levels "according to 9.2", which has every level "calculated to two decimal places and rounded to one decimal place". The index of the unrounded levels stays on the result as `full_precision_index_db` (80,153 dB for the site above). The index compares surfaces under a standard mix and is not an equivalent level of any traffic (9.5 NOTE). In many cases it is used as a difference from a reference surface (clause 10): a real dense asphalt concrete (10.1), a normalized case set by convention (10.2, with the Annex D example of seven dense bituminous surfaces as `SPB_ANNEX_D_SURFACES_DB` and its average `SPB_NORMALIZED_REFERENCE_DB`), the same surface at the same age (10.3) or any surface chosen (10.4). The standard gives no temperature correction (9.4): corrected levels are an input, `corrected_vehicle_sound_levels_db`, and the index is computed for them too, from the levels rounded to one decimal. Clause 13 lists the corrected levels and index as optional report items (26 and 28). ## 4. How precise it is Table 2 expects individual vehicles to scatter by 1,5 dB (cars) and 2,0 dB (heavy) about $L_\mathrm{veh}$, which leaves 0,3 dB and 0,7 dB of 95 % confidence interval for 100 cars and 40 heavy vehicles of each type. Each regression also gives its own interval at the reference speed (`confidence_interval_db`, Student $t$ with $n - 2$ degrees of freedom), and the result combines the three into an interval on the index through the sensitivity of the index to each level, taking the categories as independent. ## 5. The example of Annex E, and its rounding Annex E prints $L_\mathrm{veh}$ = 78,5, 81,1 and 83,8 dB and an index of 79,9 dB, which is the index of those three levels, 79,946 dB, rounded once. That is the chain 9.2 and 9.5 require, and the one the library runs: from pass-bys placed on the printed regression lines, `index_db` is 79,946 dB and `reported_index_db` 79,9 dB, and the conformance row pins that value. Carried unrounded from the printed lines, the levels would be 78,546, 81,114 and 83,838 dB and their index 79,985 dB (`full_precision_index_db`), which would print 80,0. The printed coefficients are themselves rounded, so the lines alone do not decide between the two: over every line consistent with the printed intercept, slope, mean level, mean speed and vehicle sound level, the unrounded index spans 79,948 dB to 79,996 dB. The corrected index (80,1 dB) and the temperature-corrected 2,8 dB difference from the 77,3 dB reference are pinned the same way. The 77,3 dB reference is described as seven surfaces of the same composition as Annex D, whose levels index to 78,92 dB with the same weights; the standard does not say they are one database. The speed spreads of Annex E do not fit its own regression; see the [errata registry](https://jmrplens.github.io/phonometry/reference/errata/). ## What this page does not cover The measurement itself (classifying vehicles, screening pass-bys for the 6 dB dips of 7.2, the site and weather checks), a temperature correction the standard does not give, and the Close-Proximity method of ISO 11819-2. Later editions of ISO 11819-1 were not consulted. ## See also - [CNOSSOS-EU road traffic source emission](https://jmrplens.github.io/phonometry/environment/sources/cnossos-road-emission/): the prediction side, where a surface is a correction per vehicle category. - [In-situ road-surface absorption](https://jmrplens.github.io/phonometry/materials/surfaces/road-absorption/): the ISO 13472 absorption of the surface itself. - [Errata in published sources](https://jmrplens.github.io/phonometry/reference/errata/): the two ISO 11819-1 entries. - API reference: [`environment.sources.statistical_pass_by`](https://jmrplens.github.io/phonometry/reference/api/environment/statistical-pass-by/).