Railway rolling-stock noise: the ISO 3095 type test

A train passing a microphone is two sources at once: the vehicle, with its wheels, its traction equipment and its bodywork, and the track it runs on, whose rails are rough and whose response to a wheel spreads the vibration along them. ISO 3095 is the type test of rolling stock, the method a vehicle is measured by so that the result says something about the vehicle. It fixes where the microphones stand, what they record and how the runs are averaged, and for the test at constant speed it fixes the track too: a vehicle measured on a rough, lively track is louder than the same vehicle on a smooth, well damped one, and the result is only comparable between sites whose tracks are alike. That second half is two more standards, EN 15610 for the roughness of the rails and EN 15461 for how fast vibration decays along them, and this page covers all three.

One pass-by: the level history, the interval the unit takes to pass, and the two numbers read from it.

ISO 3095:2013 has four tests. Each has its own microphone positions and its own measured quantity, and all of them take at least three runs per position, which are valid when they lie within 3 dB of each other (9.3).

Only the constant-speed test needs a reference track. The starting and braking tests ask for a track without joints or visible defects (7.3, 8.2), but only at constant speed does the rolling noise the track shares in dominate the result, and only there does the standard limit the rail roughness and the decay rates (6.2), both printed as numbers. A vehicle can still be measured on a track that misses either limit, but its result then belongs to that site.

The microphones of the constant-speed test and the area around them that has to be free.

The quantity of the constant-speed test is the A-weighted equivalent level over a measurement interval $T$ from $T_1$ to $T_2$ (3.14),

and for a multiple unit or a fixed formation the interval is the pass-by time of the whole unit, from its front to its rear, $T_p=l/v$ (6.6.3). Inside a train the interval runs from the centre of the first unit under test to the centre of the last. pass_by_measurement A-weights a pressure record, keeps the level history $L_{p\mathrm{AF}}(t)$ with time weighting F, and reads the equivalent level and the maximum within the interval it is given:

import numpy as np
from phonometry import environment

fs = 16000
length_m, speed_kmh, distance_m = 100.0, 80.0, 7.5
tp = environment.pass_by_time(length_m, speed_kmh=speed_kmh)
t = np.arange(int(14.0 * fs)) / fs
front_s = 4.0                                  # the front passes the microphone at 4 s
x_front = speed_kmh / 3.6 * (t - front_s)      # metres the front is past the microphone
# The unit as an incoherent line source of its own length: the mean square at
# the microphone follows the angle the unit subtends there.
angle = np.arctan(x_front / distance_m) - np.arctan((x_front - length_m) / distance_m)
rng = np.random.default_rng(3095)
p = 0.25 * np.sqrt(angle / np.pi + 1e-4) * rng.standard_normal(t.size)

passby = environment.pass_by_measurement(p, fs, start_s=front_s, end_s=front_s + tp)
print(round(tp, 2), round(passby.equivalent_level_db, 1), round(passby.max_level_db, 1))
# 4.5 81.3 81.9   T_p in s, L_pAeq,Tp and L_pAFmax in dB

6.6.3 also asks that the record itself start at least 10 dB below the level when the front is opposite the microphone and end 10 dB below the level when the rear is. Given when the front and the rear pass, the result keeps both margins and says whether they are enough.

The 2005 edition of the standard defined one more quantity, the transit exposure level: the energy of the whole passage, measured over an interval long enough to hold all of it, spread over the pass-by time alone (ISO 3095:2005, 3.14, Formulae 8 to 10),

The 2013 edition dropped it, but it is still quoted, and its form survives in Formula B.1, where a single trailer at the end of a train is measured from its centre onwards and the energy spread over the pass-by time of half the unit. Pass the pass-by time to pass_by_measurement and the result carries the energy of its interval spread over it:

whole = environment.pass_by_measurement(
    p, fs, start_s=0.0, end_s=14.0, pass_by_time_s=tp,
    front_passing_s=front_s, rear_passing_s=front_s + tp,
)
print(round(whole.start_margin_db, 1), round(whole.end_margin_db, 1), whole.recording_interval_sufficient)
# 14.0 17.8 True
print(round(whole.equivalent_level_db, 1), round(whole.normalized_level_db, 1))
# 77.1 82.0   L_pAeq,T over the whole 14 s record, and TEL

The transit exposure level is 0,7 dB above the pass-by level here because it also counts the energy of the approach and the departure, which the pass-by level leaves out. transit_exposure_level is Formula 10 on its own, for a level and two durations already known.

Every test ends the same way: the runs of each position are averaged arithmetically, the mean is rounded to the nearest integer decibel, and the result is the highest of those means, the louder side at constant speed and the loudest position when starting or braking (6.7.1, 7.5.4, 7.6.4, 8.7). rolling_stock_test does it for any of the four methods, and says whether the runs of every position lie within the 3 dB of 9.3:

test = environment.rolling_stock_test(
    {"left": [81.3, 82.1, 81.6], "right": [80.4, 80.9, 81.2]}
)
print(dict(test.reported_levels_db), test.final_level_db, test.valid)
# {'left': 82.0, 'right': 81.0} 82.0 True

The standard rounds to the nearest integer without a rule for a value that falls on the half; the library rounds a half up, and says so in the result’s documentation. A speed normalisation, where one is asked for, goes on the runs before this (6.7.1).

The clauses around the test are small rules the library states as functions: the type-test speeds of 6.6.2, 80 km/h and the maximum speed or the maximum alone up to 80 km/h; the smallest curve radius of 6.2.2; and the positions of the maximum level starting test, 10 m ahead of the unit, 10 m ahead of its middle when it is longer than 50 m, and evenly between them when those two are more than 50 m apart (7.5.1.1, Figure 10):

print(environment.type_test_speeds(160.0), environment.minimum_curve_radius(160.0))
# (80.0, 160.0) 5000.0
print(environment.acceleration_test_positions(108.0))
# [-10.  17.  44.]   metres behind the front of the unit, as Figure 10 draws them

The stationary test averages the positions of a set on energy, weighting each by the length of the unit it stands for, $(\pi /2)\times 7,5$ m for the positions off the ends (5.8.1, Formulae 1 and 2), and reports the mean of three sets rounded to the integer:

# A 20 m locomotive: four 5 m areas a side, and two positions off each end.
side = [66.0, 68.5, 70.0, 67.0]
ends = [64.0, 63.5]
mesh = np.array(side + side + ends + ends)
sets = mesh + np.array([[0.0], [0.4], [-0.3]])  # three sets, one row each
lengths = [5.0] * 8 + [environment.STATIONARY_END_POSITION_LENGTH_M] * 4
standing = environment.stationary_test(sets, lengths)
print(standing.set_levels_db.round(2), standing.reported_level_db)
# [66.31 66.71 66.01] 66.0

A rail’s acoustic roughness is the height of its running surface along it, measured with a probe on a line along the rail head (EN 15610, 3.1). The record is processed in three stages before its spectrum is taken (7.1). The joints, welds and defects are edited out by the operator. Narrow upward spikes, from grains of dirt under the probe, are removed: a spike is where the second derivative falls below $-10^7\mu m/{\mathrm{m}}^2$ and the first derivative changes sign, its edges are where the slope falls below $5\times 10^3\mu m/m$, and it is replaced by a straight line when its height is more than $w^2/a$ with $a=3$ m, so a narrow peak goes and a broad one, which a wheel does feel, stays (7.2). Every point is then raised to where a wheel of 0,375 m radius would rest on it, because the probe reaches into pits a wheel rolls over (7.3).

Method A of 7.4.2 then cuts the record into segments at least 1 m long overlapping by half, removes the trend of each, applies a Hanning window and averages their spectra; the one-third octave band value is the energy of the lines inside the band, the two lines that straddle an edge counted for the part of their width inside it (Annex C). The level is $L_r=10\lg (r_{\mathrm{RMS}}^2/r_0^2)$ dB with $r_0=1\mu \mathrm{m}$ (3.3), and a segment resolves wavelengths up to a quarter of its length (7.5), so a 1 m segment reports from the 0,25 m band down.

limit = environment.REFERENCE_TRACK_ROUGHNESS_LIMIT_DB
x = np.arange(0.0, 20.0, 1.0e-3)               # 20 m of rail, one sample per millimetre

def rail(offsets_db, seed):
    """A record whose bands sit 3 dB under the limit, or where offsets_db says."""
    rng = np.random.default_rng(seed)
    r = np.zeros_like(x)
    for wavelength, level in limit.items():
        target = level + offsets_db.get(wavelength, -3.0)
        k = 10.0 ** np.linspace(-0.045, 0.045, 10) / wavelength  # ten lines across the band
        amplitude = np.sqrt(2.0 * 10.0 ** (target / 10.0) / k.size)
        for kk in k:
            r += amplitude * np.cos(2.0 * np.pi * kk * x + rng.uniform(0.0, 2.0 * np.pi))
    return r

# Rail 1 a little corrugated from 5 cm to 2,5 cm, rail 2 at 4 cm and 3,15 cm.
left = rail({0.05: -1.0, 0.04: 2.0, 0.0315: 2.5, 0.025: 0.5}, seed=1)
right = rail({0.04: 1.0, 0.0315: 1.5}, seed=2)
left[7300] += 25.0                             # a grain of dirt under the probe
spectra = [
    environment.acoustic_roughness_spectrum(r, sample_spacing_m=1.0e-3)
    for r in (left, right)
]
print(spectra[0].segment_count, spectra[0].wavelengths_m[0], spectra[0].wavelengths_m[-1])
# 39 0.25 0.0025
print(round(spectra[0].level_at(0.0315), 1), round(spectra[1].level_at(0.0315), 1), limit[0.0315])
# -2.6 -3.6 -5.0   dB re 1 um: both rails over the limit in the 3,15 cm band

The limit is ISO 3095’s Figure 2, and the figure prints its value beside every point, twenty-two of them from 0,4 m to 3,15 mm, so the library reads the numbers rather than a curve (REFERENCE_TRACK_ROUGHNESS_LIMIT_DB). The Annex B listing of EN 15610 types the same twenty-two values as its “2007 TSI limit”, a second printing the conformance suite checks the first against. Up to 190 km/h the roughness has to be known from 0,003 m to 0,10 m, and above it to 0,25 m (6.2.5). The spectra of the records of one line are averaged on their mean squares (average_roughness_spectra, 7.6), and 6.4.3 sets how many lines a rail is measured on by the width of its running band (roughness_measurement_lines).

The two rails against the limit of Figure 2: under it everywhere but at 4 cm and 3,15 cm, where both exceed it, and at 2,5 cm, where one does. The track passes only through Annex C (section 4.4), and the title says so.

Method B, filters along the rail (7.4.3). The other way to the same spectrum runs the processed record through digital one-third octave band filters and takes the mean square of what comes out of each. A filter starts from rest at the head of the record and rings for a while, so 2 m of every output are discarded at either end; a record needs 5 m to leave the 1 m a spectrum needs (NOTE 1), and the records of one line need at least 15 m analysed in total once those ends are gone. The filters “shall comply with EN 61260”, the 1995 edition EN 15610 dates in its references. The bank here is the library’s own filters.OctaveFilterBank, run at the record’s samples per metre, so that its frequencies are wavenumbers and its bands are the base-ten bands Method A reports (roughness_filter_bank). Graded by filters.verify_filter_class against that edition, it is class 0, the tightest, and its integrated response (4.5.3) and the sum of its outputs (4.9) are within class 0 as well. Every band runs at the record’s own rate, without the band-by-band decimation the library’s banks use by default. 4.8 asks the anti-alias filters of a sampled-data system to keep the wavenumbers that fold onto a band within Table 1; undecimated, a band has no alias at all, and the grade reaches the Nyquist wavenumber of the record and covers exactly what a record goes through.

The bank is of order 4, the lowest that is class 0, for a reason the standard leaves unsaid: a filter’s ringing lasts longer the longer the wavelength of its band, and 7.4.3 allows 2 m whatever the band. A band is reported only when, over the length analysed, its filter has built up to within 0,15 dB of its steady output, the class 0 tolerance of 4.5.3; a 5 m record therefore reports from the 0,25 m band, the quarter of the metre it analyses (7.5), and the 20 m records here from the 0,5 m band. The listing of Annex B runs its filters forward and back with filtfilt, which squares their response and takes them out of every class of EN 61260 (section 7).

from phonometry import filters

bank = environment.roughness_filter_bank(sample_spacing_m=1.0e-3)
print(bank.order, bank.num_bands, filters.verify_filter_class(bank, edition="1995").overall_class)
# 4 24 0   order, bands from 0,5 m to 2,5 mm, class of EN 61260:1995
filtered = [
    environment.filtered_roughness_spectrum(r, sample_spacing_m=1.0e-3)
    for r in (left, right)
]
print(filtered[0].method, filtered[0].record_length_m, filtered[0].wavelengths_m[0])
# B 16.0 0.5   20 m less 2 m at either end, and the longest band whose filter settles
print(round(filtered[0].level_at(0.0315), 1), round(spectra[0].level_at(0.0315), 1))
# -2.5 -2.6   dB re 1 um in the 3,15 cm band, Method B and Method A

On a stationary record the two methods agree to the precision their estimates allow. A tone read by Method A exactly reads within the class 0 limits of the filter’s relative attenuation by Method B, and a record spread evenly across a band reads within the 0,15 dB of its integrated response; on these rails the two spectra differ by a few tenths of a decibel, the scatter of averaging a few metres of random roughness. check_reference_track holds each line analysed by Method B to its 15 m: the two rails above, at 16 m each, meet it.

One record, two analyses: Method B reaches the 0,5 m band from 16 m of record, Method A stops at a quarter of its 1 m segments, and where both report they agree to the scatter of the estimate.

The track decay rate is the attenuation of the vibration along the rail, in decibels per metre, one value per one-third octave band (EN 15461, 3.6). An accelerometer sits on the rail at the middle of a sleeper bay and a hammer strikes the rail at the positions of Figure 2, every quarter bay out to two and a half, then more sparsely, to 66 bays (6.7, track_decay_excitation_positions). From the band magnitudes $|A(x_n)|$ of the responses, the direct one $A(x_0)$ first, Formula 1 estimates the rate from the integral of the squared response rather than from a fitted slope,

where $\Delta x_n$ is the length of rail each position stands for (Annex A). A grid that stops at $x_{\max }$ cannot measure a rate below ${\mathrm{DR}}_{\min }=4,343/x_{\max }$ (Formula 2), and a band whose rate is not at least twice that is unsuitable; the farthest response also has to be 10 dB below the direct one (6.7).

bands = [100.0, 125.0, 160.0, 200.0, 250.0, 315.0, 400.0, 500.0, 630.0,
         800.0, 1000.0, 1250.0, 1600.0, 2000.0, 2500.0, 3150.0, 4000.0, 5000.0]
# The rates a ballasted track with concrete sleepers might have, dB/m.
vertical = [9.0, 8.0, 6.0, 4.0, 3.0, 3.5, 7.0, 8.0, 7.0, 3.0, 1.2, 0.9, 0.9, 1.0, 1.1, 1.3, 1.5, 1.8]
lateral = [6.0, 5.0, 4.0, 3.0, 3.0, 2.2, 1.2, 0.9, 0.7, 0.6, 0.5, 0.5, 0.6, 0.8, 0.9, 1.0, 1.2, 1.4]
x_hammer = environment.track_decay_excitation_positions(sleeper_spacing_m=0.6)

def responses(rates_db_per_m):
    """Exponentially decaying band magnitudes on the hammer grid, one row per position."""
    beta = np.asarray(rates_db_per_m) / (20.0 * np.log10(np.e))
    return np.exp(-np.outer(x_hammer, beta))

decay = [
    environment.track_decay_rate(responses(vertical), frequencies_hz=bands, direction="vertical"),
    environment.track_decay_rate(responses(lateral), frequencies_hz=bands, direction="lateral"),
]
print(x_hammer[-1], round(decay[0].minimum_measurable_db_per_m, 3), decay[1].far_field_sufficient)
# 39.6 0.11 True
print(round(decay[0].rate_at(1000.0), 2), round(decay[1].rate_at(1000.0), 2))
# 1.19 0.5

Formula 1 returns 1,19 dB/m for a response that decays at exactly 1,2 dB/m: on the grid of Figure 2 the sum stands in for the integral, and it reads an exponential about 1 % low. The limits are ISO 3095’s Figure 3, which prints them in a table beside its curves, fourteen bands from 250 Hz to 5 kHz for each direction (REFERENCE_TRACK_DECAY_LIMITS_DB_PER_M); below 250 Hz it sets none.

Both decay rates above the lower limits of Figure 3, the vertical one only just in the 1,25 kHz and 1,6 kHz bands.

check_reference_track brings the two halves together with the geometry of 6.2.2 and returns one verdict, whose passes is the answer and whose conditions are every requirement it judged, each with the clause it comes from and the numbers it was judged on. When the decay rates come with their grid, the floor of Formula 2 and the 10 dB drop of EN 15461 are judged too. The verdict has no truth value of its own, so it cannot be tested with if by mistake; the answer is .passes.

check = environment.check_reference_track(
    spectra, decay, speed_kmh=160.0, curve_radius_m=6000.0, track_gradient_ratio=0.002
)
print(check.passes)
# False
for condition in check.failed:
    print(condition.clause, "|", condition.requirement, "|", condition.detail)
# 6.2.5 | roughness at or below the limit of Figure 2 | exceeds by 2.4 dB at 0.0315 m

EN 15610 clause 8 allows no band above the limit, and neither does 6.2.5 on its own. It adds one way out.

Annex C accepts a track whose roughness exceeds the limit when the exceedance changes the pass-by level by no more than 1 dB, judged at each speed on a measured pass-by spectrum. The rails are averaged on their mean squares; the just-compliant spectrum is the measured one held down to the limit (Formula C.1); both are carried from wavelength to frequency at the train speed, $f=v/\lambda$, and their band energies redistributed over the normalised one-third octave bands, the synthesis of EN 15610 Annex C adapted to bands of unequal width; their difference is the correction $\Delta L_{r,\mathrm{rail}}(f)$ (Formula C.2). The measured noise spectrum less that correction is the revised spectrum (Formula C.3), the least that could have been measured on a compliant track, and the effect is the energy sum of the measured spectrum less that of the revised one (Formula C.4):

noise = [68.0, 69.5, 71.0, 72.5, 74.0, 76.0, 78.0, 80.5, 83.0,
         85.5, 87.0, 87.5, 86.5, 84.5, 82.0, 79.0, 75.5, 72.0]   # L_pAeq,Tp(f) at 160 km/h, dB
average = environment.average_roughness_spectra(spectra)
small = environment.check_small_roughness_deviations(
    average, noise, frequencies_hz=bands, speed_kmh=160.0
)
print(round(small.impact_db, 2), small.passes)
# 0.57 True
check = environment.check_reference_track(
    spectra, decay, speed_kmh=160.0, curve_radius_m=6000.0,
    track_gradient_ratio=0.002, small_deviations=small,
)
print(check.passes)
# True

At 160 km/h the 5 cm to 2,5 cm bands land between 890 Hz and 1,8 kHz, which is where this pass-by spectrum peaks, so the correction is 0,7 dB to 1,6 dB in the three bands from 1 kHz to 1,6 kHz and the effect on the level is 0,57 dB: the track is accepted for this vehicle at this speed. The same exceedance at another speed falls on other frequencies and has to be judged again, and check_reference_track refuses an Annex C verdict computed at another speed, on anything but the quadratic average of the rails it judges (C.2.1), or against any limit but the one it judges them against (Formula C.1).

What the roughness above the limit could have added, band by band, and in total less than the 1 dB Annex C allows.

import matplotlib.pyplot as plt

passby.plot()                     # the level history and the interval T_p
check.plot(panel="roughness")     # the rails against Figure 2
check.plot(panel="decay")         # the decay rates against Figure 3
small.plot()                      # the Annex C spectra
plt.show()

Annex E answers a neighbouring question, whether two test sites are comparable in roughness: roughness_comparability forms the minimum and maximum envelopes of their two roughness spectra (Formula E.1), carries each through the Annex C chain against each site’s noise spectrum and bounds the difference roughness alone could make in the pass-by level (Formulae E.4 and E.5).

Annex G treats the result as the reading plus uncorrelated corrections, so every sensitivity coefficient is 1 (Formulae G.1 and G.4); an input known only by its limits $\pm a$ has $u=a/\sqrt{3}$ (Formula G.2), the combined standard uncertainty is the root sum of squares (Formula G.5) and the expanded uncertainty is twice that (Formula G.6). Table G.2 works the budget of a standstill measurement through, and it is the numeric oracle of the module:

from phonometry import metrology

rows = [  # Table G.2: input, mean value correction and standard uncertainty, dB
    ("cal, reference", 0.0, 0.14), ("cal, long term", 0.0, 0.04),
    ("cal, supply voltage", 0.0, 0.06), ("cal, distortion factor", 0.105, 0.06),
    ("slm, direction", 0.0, 0.25), ("slm, frequency", 0.0, 0.25),
    ("slm, level linearity", 0.0, 0.46), ("calibrator, meteorological", 0.0, 0.14),
    ("slm, wind screen", 0.06, 0.03), ("tripod", 0.0, 0.35),
    ("distance", 0.0, 0.06), ("ground level", 0.515, 0.30), ("rounding", 0.0, 0.29),
]
budget = environment.pass_by_uncertainty(
    55.0, [metrology.Quantity(v, u, name=n) for n, v, u in rows]
)
print(round(budget.level_db, 2), round(budget.combined_uncertainty_db, 2),
      round(budget.expanded_uncertainty_db, 2))
# 55.68 0.83 1.66   Table G.2 prints 55,68, 0,83 and 1,66
print(round(metrology.rectangular(0.0, 0.8).uncertainty, 2))
# 0.46   the level linearity row of Table G.1, +/-0,8 dB over the square root of 3

Figure G.1 draws each input’s share of the variance, largest first, and the result draws the same bars in the same order; the conformance suite checks the order against the figure’s labels.

The budget of Table G.2 as Figure G.1 draws it: the linearity of the meter, the tripod and the ground carry three fifths of the variance.

budget.plot()
plt.show()

Three smaller pieces complete the tests. Annex A characterises impulsive noise by the steepest rise of $L_{p\mathrm{AF}}(t)$ over the stretches that climb without a break by at least 10 dB (Formula A.1). 6.3.4 accepts a vehicle coupled to the unit under test when it adds no more than 2,0 dB to the pass-by level, both levels rounded to one decimal. Annex D corrects a level for a steady background it stands more than 3 dB above (Formula D.1).

times = np.arange(0.0, 3.0, 0.01)              # an L_pAF history every 10 ms
levels = np.full(times.size, 70.0)
levels[100:121] = 70.0 + 0.6 * np.arange(21)   # 12 dB in 0.2 s, from 1 s
levels[121:] = 82.0
print(round(environment.impulsiveness_rise_speed(times, levels).rise_speed_db_per_s, 1))
# 60.0   dB/s
neutral = environment.check_adjacent_vehicle_neutrality(83.04, 81.06)
print(neutral.difference_db, neutral.passes)
# 1.9 True
print(round(environment.background_level_increase(78.0, 72.0), 2))
# 1.26   dB the background adds to the 78 dB measured

The oracle rows of Table G.1 and Table G.2 do not all agree, and the errata registry has the arithmetic of each: the standard uncertainty of the 25 m microphone distance is printed as 0,004 dB where its interval gives 0,04 dB; the ground level at 7,5 m is 0,55 dB in Table G.1 and 0,30 dB in Table G.2, which Formula G.2 gives; and the interval of the wind screen is printed with its bounds out of order. None of them changes a number the library computes: the conformance rows read Table G.2 as printed and hold the Table G.1 rows that Formula G.2 reproduces. In EN 15610, the spike-removal loop of the Annex B listing repeats while any second derivative is below the threshold, without the change of sign that clause 7.2 c) also asks of a spike, so it never ends on a sharp bend of the rail that is no spike at all. Neither it nor the clause’s “until no further spike is detected”, read literally, ends on a peak that is detected and then kept by the height test; the library ends the sweep when a pass removes nothing, which is how it reads the clause. The same listing does Method B with third-order Butterworth filters run forward and back (filtfilt), which squares their response: 6,02 dB down just inside the band edges, where Table 1 of EN 61260:1995 allows at most 5,5 dB for class 2, and a filter integrated response of $-0,58$ dB to $-0,59$ dB, where 4.5.3 allows $\pm 0,5$ dB. Clause 7.4.3 asks for filters that comply with EN 61260; the listing’s do not, in any band or class, and read a band whose spectrum is flat about 0,6 dB low. The library’s bank is class 0 on both.

• Covered

  The computations of ISO 3095:2013 from measured records and levels: pass_by_measurement (the equivalent level over any interval, the maximum with time weighting F, the record margins of 6.6.3 and the transit exposure level of ISO 3095:2005 or Formula B.1), transit_exposure_level, pass_by_time, stationary_unit_level and stationary_test (Formulae 1 to 3 and 5.8.1), rolling_stock_test for the constant-speed, starting and braking tests with the spread of 9.3, type_test_speeds, minimum_curve_radius, acceleration_test_positions, impulsiveness_rise_speed (Annex A), check_adjacent_vehicle_neutrality (6.3.4), background_level_increase (Annex D), check_small_roughness_deviations (Annex C), roughness_comparability (Annex E), check_reference_track (6.2) and pass_by_uncertainty (Annex G). From EN 15610:2009, the spike removal, the curvature processing, Method A with the band synthesis of Annex C, Method B with its filter bank graded against EN 61260:1995 (filtered_roughness_spectrum, roughness_filter_bank) and the 15 m it asks of each line, the average of 7.6 and the lines of 6.4.3; from EN 15461:2008+A1:2010, the decay rate of Formula 1 on the grid of Figure 2 with the floor of Formula 2 and the 10 dB drop. The limits of Figures 2 and 3 are read-only tables, and every result draws itself with .plot().

• Not covered

  The measurement itself: laying out the stationary mesh, finding $T_1$ and $T_2$ inside a train, the site and weather checks, which are the tester’s, and the special cases of Annex B beyond Formula B.1. The speed normalisation 6.7.1 mentions, for which the standard gives no formula; the tonal difference, which 6.7.2 hands to ISO 1996-2 or DIN 45681; the platform, stopping-point and bridge measurements of Annex F. In EN 15610, the editing out of joints, welds and defects (Annex A shows what they look like; the operator does it), and the joining of records of 7.5. A record yields wavelengths up to a quarter of its length, which the library applies; to assess longer ones, 7.5 has the measured records concatenated by overlapping them, rules that “the overlap shall not be used for spectral components of 0,1 m or less” and asks for the concatenation method to be described in the report. It sets no length of overlap, no way to line two records up or to match their heights, no rule for how the samples they share are combined and no test that a join is valid (its NOTE only asks for attention to that), so the standard leaves the joining method to the tester, who must describe it in the report. In EN 15461, the measurement of the frequency response functions: the rates are computed from their band magnitudes. The roughness of the wheels, which the rail standards do not cover.