Physically-based auralization of railway rolling noise
Julien MAILLARD(1) , Abbes KACEM(1) , Nadine MARTIN(2) , Baldrik FAURE(3)(1) Centre Scientiﬁque et Technique du Bâtiment, Paris-Est University, 24 rue Joseph Fourier, 38400 Saint Martin d’Hères, France,

julien.maillard@cstb.fr(2) Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, 38000 Grenoble, France(3) Société Nationale des Chemins de Fer Français, 1/3 Avenue François Mitterrand, 93210 Saint-Denis, France

Abstract
Railway noise contributes signiﬁcantly to noise pollution both outside and within cities. In recent years, prediction models have been developed to study exposure levels and evaluate abatement solutions. Going one stepfurther, auralization may provide an effective mean for evaluating perceptually the impact of railway noise on
the soundscape near existing or future infrastructures. This paper extends railway noise emission models topropose an auralization approach based on physical parameters. As a ﬁrst step, the approach focuses on rollingnoise radiated by the track and wheels, which represents the main noise source over a wide range of speed. The
excitation of the wheel/rail system by surface roughness is modeled in the time domain based on the system
mobilities. Next, rail emission is modeled as a set of discrete coherent monopoles, while the wheel contribution uses resonant ﬁlters based on its structural response. Finally, the contribution of track sleepers is included
following the standard TWINS model. Validations of the approach compare auralized pass-by levels with measured data. Preliminary results from listening tests evaluating the realism of auralized pass-by noise samples arealso presented.
Keywords: Auralization, Railway noise

1

INTRODUCTION

Railway infrastructures in urban areas represent a good solution to reduce the environmental impact of transportation. With comparatively low CO2 emissions, railway transportation represents however an important sourceof noise pollution. In this context, prediction tools are needed not only to evaluate and mitigate railway noise
but also to inform and communicate with populations. Existing tools, such as the ACOUTRAIN software, manage to predict rolling stock emission levels based on experimental source characterization for the equipments
and the TWINS model for rolling noise emission [1]. However, these models are limited to averaged levels per
frequency bands. Consequently, they are not suited for realistic audio rendering and thus, perceptual evaluation.
Also, these models in the frequency domain do not take into account impulsive sources such as the numerous
rail joints present in urban railway networks, even though they contribute signiﬁcantly to the perceived noise.
Auralization [2] overcomes these limitations by synthesizing the time domain sound pressure signal perceived
by a virtual listener in a simulated environment.
In this paper, we introduce a new approach for the auralization of rolling noise as a ﬁrst step towards theauralization of railway noise as a whole. Previous studies have shown that rolling noise represents the main
railway noise source at speed between 50 and 300 km/h [3]. The approach is based on an existing modelfor the simulation of rolling noise emission levels. This model, from which TWINS is also derived, has beenshown to give reliable predictions [4] and is widely used in the community. It takes as inputs the spectrumof the combined roughness of the rolling surface of the wheels and rails, the track physical parameters andthe train speed. It then calculates the interaction force between the rail and wheel [1]. The radiated soundlevels are then predicted using a model of the vibro-acoustic response of the wheel, rail and sleeper structures.
The auralization model in the present paper follows a similar approach, applied in the time domain, to propose
appropriate audio signal processing for each one of the three rolling noise components.

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Previous work on railway noise auralization started in 2005 within the SILENCE project which lead to the
VAMPPASS software tool for the sound synthesis of a train pass-by [5]. In VAMPPASS, rolling noise issynthesized as a broad band signal shaped according to third octave spectra obtained from measurements orfrom the TWINS model. More recently, a time domain synthesis model was developed for rolling and impact
railway noise [6]. The basis of the proposed model is the generation of the rail and wheel roughness as a broadband signal shaped according to the roughness spectrum. The resulting time signal is then fed to two ﬁltersmodeling the vibro-acoustic behavior of the wheel and track with transfer functions based on the third octave
band spectra of the CNOSSOS-EU railway noise emission model [7]. The modal behavior of the wheel/railsystem is also included in order to improve the realism of the synthesis. Even though it has not been formallyevaluated, the realism of this method appears superior compared to previous work.
The approach presented below introduces an improved auralization model to obtain realistic sound renderingof rolling noise for any wheel/rail system, based on its physical parameters. Unlike previous work, the rail
contribution is modeled as an extended multi-source distribution in order to preserve the rail radiation characteristics. In Section 2, the model is described starting with the rail and wheel response, the wheel/rail excitation
force and signal processing of the auralization system. In Section 3, measured and auralized pass-by signals arecompared in terms of sound pressure levels and perceived realism.

2

APPROACH

Railway rolling noise results from rail, wheels and sleepers vibrations [1]. The analysis of each component
shows that their acoustic contribution dominates the overall response in distinct frequency regions. Therefore, allthree sources must be accounted for in the proposed auralization model. Figure 1 shows the overall schematic of
this model for one wheel/rail contact. In this ﬁgure, the blue-colored blocks represent signal processing modules.
Mechanical parameters

Roughness model

Train speed

Wheel vibro-acoustic
response

TWINS
model

Wheel/rail roughness

Wheel/rail interaction modelf(t)Rail vibro-acoustic
response
Rail synthesis
snrail(t)Wheel synthesis

Sleeper synthesis

swheel(t)ssleeper(t)Receiver position

Wheel directivity

Sleeper directivity

source positions

Sound propagation
srolling(t)Figure 1. Schematic of the auralization model for one wheel/rail contact.
Signal paths in the time domain are represented as thick line arrows. The grey-colored blocks correspond tomodels in the frequency domain. The model inputs consist of the mechanical parameters of the wheel/railsystem, the combined roughness of the wheel and rail contact surfaces and the train speed. Note that train

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speed may vary in time. First, the roughness input spectrum is converted to a frequency spectrum based on
train speed. The wheel/rail interaction model then constructs the time domain signal of the vertical interaction
force, f (t), between the rail and wheel. Next, this signal is fed to two ﬁlter modules representing the acoustic
response, to a unit excitation force, of the rail and wheel structure, respectively. The rail synthesis module
generates N acoustic emission signals, snrail (t), n = 1, . . . , N, associated with the N monopole sources of the rail
radiation model. The wheel synthesis module generates a single emission signal, swheel (t). The third synthesis
module generates the contribution of the track sleeper, ssleeper (t). This contribution is obtained from the TWINS
model using the wheel/rail combined roughness as input. Finally, the sound propagation module applies source
to receiver propagation effects to each emission signals, including the frequency dependent directivity of thewheel and sleeper emission models. The overall radiated sound pressure signal, srolling (t), is obtained as thesum of all contributions. In the following sections, we further discuss each step of the auralization process.
2.1 Vibro-acoustics response of the rail
The rail roughness excitation is mainly in the vertical direction. It produces vertical ﬂexural waves propagatingon each side of the wheel/rail contact point. These waves are the main source of rail noise. Following previous
work [1, 8], the vertical rail response is modeled as an inﬁnite beam continuously supported by a mass between
two spring-damper layers, representing the rail pads, sleepers, and ballast. Assuming a eiωt time dependencewith t, the time and ω, the angular frequency, the rail vertical mobility is expressed as(1)
Yr (x, ω) = iω Ac (ω)e−γc (ω)|x−xe | + i A p (ω)e−γ p (ω)|x−xe | .
where x is the horizontal axis along the rail rolling surface, xe , the position of the excitation, Ac (ω), γc (ω),
and A p (ω), γ p (ω), the amplitude and propagation constant of the near-ﬁeld and propagating waves, respectively.
The propagating structural wave speed is as crail (ω) = ω/λrail (ω) with λrail (ω) = ℑ [γ p (ω)], the wave-number
and ℑ [.], the imaginary part operator. The structural decay rate of the rail vertical ﬂexural wave in [dB/m]is deﬁned as Δs (ω) = 20 ℜ [γ p (ω)] log10 (e) where ℜ [.] is the real part operator. As an example, the decayrate is plotted versus frequency in Figure 2 for two sets of track parameters listed in Table 1 corresponding
to a concrete sleeper track with low and medium stiffness supports, respectively. Parameters derived from themeasured decay rate on the track used for the pass-by recordings is also included. This third track (last columnof Table 1) has wood sleepers with stiff supports.
As seen in Figure 2, the decay rate is small (about

Track decay rate [dB/m]

102
Medium support stiffness
Low support stiffness
101

10

0

10-1

102

103

Frequency [Hz]Figure 2. Rail vertical ﬂexural wave decay rate calculated for the track parameters of Table 1 (concrete sleepers
with “medium” and “low” stiffness supports).
1 dB/m) at high frequencies: vibrations propagate far away from the excitation point and a spatially extended

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Table 1. Rail and track properties used in the simulations.
Rail
Bending stiffness [MN m2 ]Rail loss factor
Shear coefﬁcient
Density [kg/m3 ]Mass per length [kg/m]
Poisson’s ratio

6.42
0.02
0.4
8000
60
0.3

Track
Pad stiffness [MN/m]
Pad loss factor
Sleeper mass [kg]Sleeper spacing [m]Ballast stiffness [MN/m]
Ballast loss factor

medium
300
0.2
240
0.6
100
0.5

low
100
0.2
240
0.6
25
0.5

high
210
1.35
72.8
0.6
25
2

source model is required to represent the rail acoustic emission. As previously proposed, the model uses aline of coherent monopoles [1] equally spaced along the rail longitudinal axis. The spacing between monopoles
is frequency dependent and chosen as a fraction, e.g., 1/5, of the smallest value between the acoustic andstructural wavelengths. The number of monopoles is chosen such that the structural response is attenuated by agiven factor, e.g., 60 dB, past the distribution end points. The complex volume velocity amplitude of monopolen, Q(xn , ω) is proportional to the rail mobility Yr (xn , ω) at xn ,Q(xn , ω) = Q0 (ω)Yr (xn , ω),(2)where the constant Q0 (ω) can be derived analytically [1].
2.2 Vibro-acoustics response of the wheel
Due to its ﬁnite geometry and material properties, the wheel response can be expressed using modal superposition. The vertical and axial wheel mobility at location s on the web surface, Yw (s, ω), due to a verticalexcitation is approximated as the sum of the response of the ﬁrst N modes,
An (s),
2 − ω 2 + 2iζ ωω
ω
n
n
n=1 n
N

Yw (s, ω) = ∑(3)

where the modal parameters An , ωn and ζn are the amplitude, resonant frequency and damping factor, respectively, of mode n. In this work, the above parameters were characterized during previous experimental
measurements on a ﬁxed monobloc wheel [9]. They could also be estimated from the ﬁnite element method.
The wheel radiated pressure can then be evaluated in the far ﬁeld using the Rayleigh approximation applied tothe axial velocity distribution given by Eq. (3). Integrating the far-ﬁeld pressure over a hemisphere enclosing
the wheel and using the orthogonality property of the structural modes, the wheel emitted sound power is thenwritten as
 2
An 
ρ ω2 NW (ω) =
(4) .
∑4πc n=1 ω 2 − ω 2 + 2iζn ωωn 2nwhere ρ is the air density and c, the sound speed. The wheel is now replaced by an equivalent point-sourcewith sound power, W (ω), and directivity function, D(θ , φ , ω), where θ and φ are the azimuth and elevation
angles, respectively.
2.3 Wheel/rail interaction force signal
The structural and acoustic response of the wheel/rail system for a vertical unit excitation being established, thissection now presents the time model of the interaction force. It is based on the vertical wheel/rail interaction
model introduced by Thompson [1]. The force amplitude in the vertical direction is expressed as F(ω) =R(ω)F unit (ω) with R(ω), the combined roughness amplitude, and F unit (ω), a unit roughness point force,
F unit (ω) =

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iω
,
Yr (xe , ω) +Yw (xe , ω) +Yc (ω)(5)

where Yr (xe , ω), Yw (xe , ω) and Yc (ω) are the vertical mobilities, at the point of contact, of the rail, the wheel
and the contact spring, respectively. The contact spring is used to model the wheel/rail connection. Its mobility
is deﬁned as Yc (ω) = iω/KH where KH is the linearized contact stiffness, with a standard value of 950 MN/m.
Note that the contact force spectrum, F unit (ω) exhibits peaks due to the wheel mobility resonance frequencies.
The excitation model of Eq. (5) is now converted in the time domain to construct the wheel/rail contact force
signal f (t), as the convolution of a continuous roughness signal r(t) with the impulse response of the unit
roughness contact force f unit (t),(6)
f (t) = r(t) ∗ f unit (t),where ∗ denotes the convolution product. The unit roughness contact force f unit (t) is obtained as the inverse
Fourier transform of F unit (ω). Similar to the approach proposed by Pieren [6], the roughness signal r(t) is
generated as a ﬁltered white noise with third octave band spectral shaping:Ur(t) = ∑ R(ωu ) . ξu (t),

(7)

u=1

where ξu (t) denotes the normalized signal in band u and U is the number of frequency bands. The combinedroughness RMS amplitude spectrum, R(ωu ), is obtained as the sum of the wheel and rail roughness expressed
as a function of wavelength. A contact ﬁlter is then applied to model the effect of the extended contact area
between the wheel and rail [10]. Finally, the roughness is expressed as a function of frequency ωu using therelation ωu = 2πV /λu where V is the wheel speed in m/s and λu is the roughness wavelength in m.
2.4 Auralization
Recalling Figure 1, the auralization process begins by generating the contact force signal, f (t), as described in
Section 2.3 above. For each frequency band u, the rail equivalent monopole sources are distributed on eachside of the contact point. The number Nωu and locations of the discrete equivalent sources, xn , n = 1 .. Nωu , aredeﬁned such as to satisfy the constraints of source separation and spatial extent at ωu , outlined in Section 2.1.
The rail nth monopole source signal in frequency band u is obtained assn,u (t) = αn,u (t) fu (t − τn,u (t))(8)

where the force signal component in frequency band u, fu (t), is obtained as fu (t) = ru (t) ∗ f unit (t) with ru (t) =R(ωu ) . ξu (t), the roughness signal in band u and f unit (t), the excitation force per unit roughness. The amplitude αn,u (t) represents the sound pressure amplitude radiated by monopole n at frequency ωu for a unit force
excitation at the receiver position. It is function of the monopole volume velocity amplitude given in Eq. 2 andthe source to receiver geometrical spreading factor and possibly additional propagation effects. The propagation
delay, τn,u , for the same source is calculated asτn,u (t) =rn (t) |xn − xe |+,ccrail (ωu )(9)where rn (t) is the source-receiver distance and crail , the frequency dependent speed of the ﬂexural waves in therail. The above delay includes both sound propagation in air and the phase offset between monopoles inducedby the ﬁnite structural wave speed. Note that αn,u (t) and τn,u (t) are time dependent due to wheel motion. The
rail total sound pressure signal is then obtained by summing signals sn,u (t) over all bands and monopoles.
To retain the modal behavior of the railway wheel in the emission synthesis, the wheel source signal generation
uses a series of damped harmonic resonators with resonant frequency, damping factor and amplitude derived
from the radiated pressure at distance 1 m from the wheel equivalent source, with power given by Eq. (4). The
sound pressure source signal emitted by the wheel at 1 m is then obtained asNswheel,1m (t) = ∑ f (t) ∗ hn (t),

(10)

n=1

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with N, the number of resonance modes and hn (t), the impulse response of resonator n.
The sleeper contribution is modeled as a single point source, located at the wheel/rail contact point. The
equivalent source levels are based on the TWINS model which calculates sleeper emission levels in third octave
bands as a function of roughness amplitudes [1]. The sleeper signal is constructed using a band ﬁltered white
noise as for the excitation force signal.
The wheel and sleeper equivalent source pressure signals at 1 m are then propagated to the receiver position
including directivity, propagation delay and attenuation effects.

3

RESULTS

The proposed approach is now applied to construct pass-by sound samples and compare them to recorded
signals of a real train pass-by. Measurements of a Bombardier AGC passenger train composed of 4 wagons
and 5 bogies, with 2 wheels per bogie, were carried out on a dedicated track. Train speed is set to 80 km/h
for which pass-by noise is dominated by the rolling noise contribution. Measurements include two distancesfrom the track, 7.5 m and 25 m. The track decay rate and surface roughness were both measured. Wheelroughness was assumed to be close to previously measured data on a similar wheel. It should be pointed outthat measured decay rate exhibits unusually high values above 2000 Hz. The track parameters derived fromthis measured decay rate, referred to as “high” in Table 1, result in strong ﬂuctuations of each wheel passby levels, the rail behaving as a localized point source above 2000 Hz. However, the same level ﬂuctuations
are not present on the recorded pass-by samples. It was thus decided to test another set of track parameters,
referred to as “low” in Table 1, with values matching standard decay rate measurements found in the literature.
All simulated pass-by samples use U = 22 third octave bands between 50 and 6300 Hz, thus covering the90

LAFeq [dB(A)]80

70
Measurement
High stifness
Low stifness

60

50

1

2

3

4

5

6

7

8

9

Temps [s]Figure 3. A-weighted pass-by sound pressure level at 80 km/h: measured (red solid line), LAeq = 80.4 dB(A);auralized, high stiffness (purple dashed line), LAeq = 77.9 dB(A); auralized, low stiffness (dashed-dotted blueline), LAeq = 82.7 dB(A).
main frequency content of rolling noise. The wheel directivity follows the CNOSSOS-EU simpliﬁed emission

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model [7], and the sleeper contribution is assumed omni-directional [1]. The test samples are generated forseveral model conﬁgurations. Wheel damping is known to increase under rolling conditions compared to values
measured on ﬁxed wheels. Simulated samples thus include a 10 time and a 20 time damping factor. Threerail equivalent source distributions are also included: a single-source conﬁguration with the CNOSSOS-EU rail
directivity, and two multi-source conﬁgurations with 5 and 2 monopoles per wavelength and distribution lengths
associated with a 60 dB and a 5 dB attenuation, respectively.
Figure 3 compares the A-weighted sound pressure level, LAFeq , using a 125 ms (fast) averaging window, of thesimulated and measured sound samples during the train pass-by at 7.5 m. The simulated samples both use arail source distribution with 5 monopole per wavelength and a 60 dB attenuation length and a 20 time damping
factor. The inﬂuence of rail support stiffness on the radiated sound ﬁeld can be clearly seen on the curves.
As explained above, the high support stiffness generates strong level ﬂuctuations which are not present on themeasured levels. The low support stiffness better match the measured levels. Further improvements could beachieved with better track parameter identiﬁcation.
Next, listening tests were carried out to assess the perceived realism of the auralized pass-by noise. Twenty
participants (17 male, 3 female), aged from 21 to 53 years old are asked to judge the realism of a set ofsimulated samples in comparison with the recorded pass-by sample used as the reference. The perceived realism
obtained for the ﬁrst 7.5 m distance is presented in Figure 4. Results show that the single-source rail emission

Figure 4. Listening test ratings of realism. Ratings ranged from 0 (very poor realism) to 100 (very highrealism). Results are averaged across participants and repetitions. Vertical bars represent the 95% conﬁdence
interval of the mean value.
model is better perceived than the multi-source version based on the same track parameters. This is explainedby the strong level ﬂuctuations resulting from the high support stiffness which do not occur on the measured
sample. The single source model does not contain these ﬂuctuations and therefore sounds closer to the measuredcase. Using the low stiffness track parameters yields improved simulated samples in terms of perceived realism.
In this case, realism is similar to the single-source distribution. Results also show that higher wheel damping
improve realism compared to damping values measured on a ﬁxed wheel which is consistent with previous
results showing damping increases under rolling conditions.

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4

CONCLUSIONSThis paper introduces a new auralization model for railway rolling noise based on the physical parameters of
the wheel and track. The approach models the excitation of the wheel/rail system induced by surface roughness
in the time domain, based on the rail and wheel mobility functions. Rail and wheel noise is then obtained byﬁltering the excitation signal through the modeled vibro-acoustic response of each structure. The rail emission
uses a line of coherent monopoles to preserve the spatial characteristics of the radiated sound ﬁeld. The wheel
response which is dominated by its structural modes is modeled as a set of resonant ﬁlters. Finally, track sleeper
noise is included in the synthesis following the TWINS model.
The proposed model is evaluated quantitatively and perceptually by comparing auralized pass-by noise with areal train pass-by recording at 7.5 m from the track. Results show that A-weighted short-time averaged soundpressure levels are predicted within 2 dB, provided the track parameters are well estimated. Preliminary analysisof the listening tests show that the model conﬁguration such as support stiffness, rail structural damping andmulti-source distribution, has an inﬂuence of the perceived realism. Overall, when properly conﬁgured, theproposed technique yields very realistic sounds with perceived realism between 6.5 and 7 on a 0 to 10 scale.

ACKNOWLEDGEMENTS
Authors would like to thank Guillaume Lemaitre, SNCF, for his help in setting up and carrying out the listening
tests.

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