# A correction model for the noise emissions of light electric vehicles during acceleration

Sacha Baclet, Julien Cesbron, Pierre Aumond, Arnaud Can, Romain Rumpler

► To cite this version:

Sacha Baclet, Julien Cesbron, Pierre Aumond, Arnaud Can, Romain Rumpler. A correction model for the noise emissions of light electric vehicles during acceleration. Applied Acoustics, 2025, 236, pp.110713. 10.1016/j.apacoust.2025.110713. hal-05023958

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# A correction model for the noise emissions of light electric vehicles during acceleration

Sacha Baclet<sup>a,b, ID*</sup>, Julien Cesbron<sup>c, ID</sup>, Pierre Aumond<sup>c, ID</sup>, Arnaud Can<sup>c, ID</sup>, Romain Rumpler<sup>a,b, ID</sup>

## ARTICLE INFO

**Keywords:**

Electric cars

Electric vehicles

Acceleration

Deceleration

Noise emission model

## ABSTRACT

The transition from light internal combustion engine (ICE) vehicles, such as cars and vans, to light electric vehicles (EVs) presents an opportunity to reduce road traffic noise exposure in urban environments, which still needs to be quantified. Although the noise emissions of light ICE vehicles are generally well understood, including during acceleration and deceleration, the noise emitted by light EVs has so far not been studied as thoroughly, in particular during acceleration.

This study thus proposes a correction model for the noise emissions of light EVs during acceleration, based on pass-by measurements under reference conditions. Data were collected for 6 vehicle models at both steady speed and full acceleration. The difference in noise levels between these two conditions was analysed to develop the correction model.

This correction model accounts for both speed and acceleration at an octave-band level. The resulting model shows that acceleration has no impact on the noise emissions of light EVs in the 63 and 125 Hz octave bands, and that acceleration may increase the overall A-weighted emissions of a light EV by up to 5 dBA, at 20 km/h. Furthermore, the analysis suggests that deceleration does not increase noise emissions for light EVs.

This contribution paves the way for the integration of EV-specific noise emissions into noise exposure assessment frameworks, enabling a more comprehensive understanding of the potential benefits associated with the transition towards EVs.

# 1. Introduction

## 1.1. General introduction

The European Union, through the amended Regulation (EU) 2019/631 [13], has established a target to reduce CO₂ emissions from new passenger cars by 55% by 2030 and achieve a 100% reduction (*climate neutrality*) by 2035, in order to reduce the impacts of transportation on climate. In order to reach these reductions in CO₂ emissions, ICE vehicles are expected to be progressively replaced with electric vehicles, which may, in turn, reduce the exposure to noise pollution from transport. In fact, the European Commission has set a target for the reduction of the number of people chronically disturbed by noise pollution from transport of 30% in 2030 compared to 2017, in the *Zero Pollution Action Plan* [14].

In 2019, at least 20% of the EU population was still exposed to noise levels considered harmful to human health, according to EEA [15]. This burden is mostly due to road traffic noise, with more than 100 million EU citizens affected by high noise levels that exceed the WHO recommendation [44]. According to the European Alternative Fuel Observatory, the electric vehicle (EV) fleet in the European Union (EU) has grown exponentially over the last decade. In the EU, the number of EVs in the light passenger car category, which includes battery and plug-in hybrid EVs, reached 7.8 million in 2023, representing a 22% market share of new registrations, but the impact of this transition on noise pollution exposure remains uncertain.

For ICE vehicles, engine noise is the predominant source of noise emissions at speeds below 50 km/h [17]. In contrast, for EVs, the significant reduction in powertrain noise shifts the primary noise source

<footnote><sup>a</sup> The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), Department of Engineering Mechanics, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden</footnote>

<footnote><sup>b</sup> Digital Futures and The Centre for ECO2 Vehicle Design, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden</footnote>

<footnote><sup>c</sup> Univ Gustave Eiffel, CEREMA, UMRAE, F-44344, Bouguenais, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: baclet@kth.se (S. Baclet).</footnote>
to tyre/road interactions for steady speeds above 20 km/h [18,32]. Al-
though some contributions have attempted to estimate the impact of a
transition to EVs on noise pollution exposure [2,5,8,21,23,41,43], these
studies generally overlook the impact of acceleration on the noise emis-
sions of EVs, due to the lack of suitable data and models to quantify
it.

However, a few articles have measured the emissions of light EVs
during acceleration, and established that the increase of noise emissions
due to acceleration was significant. This can be mainly explained by an
increase in rolling noise caused by tyre torque during acceleration [20].
Indeed, in free rolling conditions, the tyre is mainly excited by radial
block impacts and the road surface texture. However, under torque, the
tread blocks experience the so-called stick-snap and snap-out effects due
to increased shear forces at the tyre/road interface, resulting in addi-
tional tangential excitation of the tyre structure. These phenomena are
well documented in the tyre/road noise literature [38]. Compared to
ICE vehicles, EVs have a higher power-to-mass ratio and a wider engine
speed range at which maximum torque is reachable, starting from very
low speeds [34]. Therefore, in some scenarios such as open-throttle ac-
celeration, the tyre torque effect on noise emission is likely to be more
pronounced for EVs than for ICE vehicles.

In addition to the extra tyre/road interaction noise produced during acceleration, the driveline and electric engines also produce electromagnetic noise and aerodynamic noise from rotating components and cooling systems [37], but the impact of these emissions on overall exterior noise remains uncertain, as these noise sources are difficult to distinguish from rolling noise, due to their proximity with the tyres [34], and are thus often lumped with rolling noise.

In Kaliski et al. [23], the noise emissions of a 2012 Chevrolet Volt were measured at constant speed and during full acceleration. This car model is an early electric vehicle, which is far from representative of today's electric car fleet. However, the results showed an increase in the measured noise levels of approximately 20 dBA during full acceleration compared to constant speed at 8 km/h, 15 dBA at 16 km/h, 10 dBA at 32 km/h, 6 dBA at 48 km/h, 4 dBA at 64 km/h and above.

The FOREVER project [35] explored the noise emissions of a light
EV during full acceleration, the Citroen C-Zero. This car model was
released in 2010 and is now also discontinued. However, this project
demonstrated that the noise emissions of an electric car do not increase
significantly during deceleration compared to constant speed, and that
the noise emissions during full acceleration are linear with $log_{10}(v)$, with
a slope different from that of noise at constant speed.

Although the focus of their research was to compare the noise emis-
sions of ICE and electric vehicles, Schweizer et al. [39] conducted mea-
surements of the noise emissions of multiple types of light EVs at con-
stant speed and during acceleration at 3 microphone positions A, B and
C, respectively associated with a pass-by speed of 20 km/h, 40 km/h
and 60 km/h. The exact value of the acceleration at each of these points
was not specified, although the setup required that it be increasing from
A to B to C. According to the measurements conducted in this research,
the increase in noise emissions due to acceleration for a light EV were,
on average, approximately 5–6 dBA at 20 km/h or 40 km/h, and ap-
proximately 1–2 dBA at 60 km/h.

The LIFE E-VIA European project [28] dealt with the development of low-noise tyres and road surfaces in the context of a growing EV fleet and the need to reduce noise in densely populated urban area. Part of LIFE E-VIA activities dealing with the implementation of a low noise prototype and the assessment of EV tyre/road noise performance were carried out on the reference test track of Université Gustave Eiffel in Nantes (France) [9]. As part of these activities, pass-by noise measurements were performed for several EVs rolling on different kinds of road surfaces at constant speed, in acceleration and in deceleration conditions. From microphone array measurements at 2.7 m from the vehicle rolling on a ISO 10844 road surface, a significant increase in noise radiation from the driven wheel area was observed for all EVs in accelerating

conditions by comparison with cruising at constant speed [33]. The in-
crease of noise in this area generally exceeded 5 dBA around 50 km/h
and reduced progressively at higher speeds with decreasing accelera-
tion rate. Pass-by noise measurements in full acceleration of an EV at 4
m/s², fitted with different kinds of tyres rolling on prototype road sur-
faces with low texture, also showed an increase in noise level relative
to 50 km/h constant speed between 5 dBA and 7.5 dBA, depending on
the testing configuration [20].

Although these contributions have carried out valuable measure-
ments which have allowed to draw some early conclusions about the
acceleration noise of light EVs, very few works have attempted to in-
troduce a general model for the noise emissions of individual light EVs,
such as cars and vans, during acceleration.

Such a study was conducted by Lan et al. [25], proposing a model to estimate the equivalent noise level $L_{Aeq}$ measured near the road for a specific light EV as a function of speed and acceleration. However, in that article, a single car model (BAIC BJEV160), not sold internationally, was tested. Additionally, 3 distinct models linear with the log of the speed were developed for constant speed, acceleration and deceleration, instead of trying to establish a single model in which the value of the acceleration may be set to zero, positive or negative values. The coefficients of determination for the models presented in that article are relatively low compared to those in studies such as Pallas et al. [35]. This suggests that the model chosen in Lan et al. [25], expressed as $L_{Aeq} = c_0 + c_1 \cdot log_{10}(v) + c_2 \cdot a$, where v is the speed, a is the acceleration, and $c_0, c_1$ and $c_2$ are numerical coefficients, may not be well-suited to capture the acceleration noise of electric cars. In particular, a model of this form does not account for the dependency of acceleration noise on speed.

To the authors' knowledge, no correction model has yet been devel-
oped to adapt already existing constant-speed noise emission models to
account for the noise emissions of individual light EVs during acceler-
ation, particularly at the octave-band level. Developing such a model
is important in the context of the growing use of meso- and micro-
scopic road traffic simulations in environmental acoustics. These models
replicate individual vehicle behaviour and interactions within a traffic
system, providing detailed information about the position, speed and
acceleration of individual vehicles over time at short time intervals,
and may be coupled with noise simulations to improve the accuracy
of noise exposure assessment [1,7,10,11,19,26,42,45] and to calculate
advanced noise exposure indicators, such as the number of noise events
experienced by the population [1,3,4,42] or vehicle-specific noise expo-
sure cost (NEC) [29-31]. However, their use requires the existence of
individual noise emission models for each category of vehicles, ideally
taking into account emissions due to acceleration.

Conveniently, some existing data may be used to create such a model. While the aforementioned pass-by noise measurements performed during the LIFE E-VIA project were primarily intended to characterise EV noise sources and focused on tyre/road interaction [9], some of these data may serve as a basis to model the noise emissions of light EVs during acceleration.

Thus, the objective of the present study is to use these data to de-
velop a correction model for the noise emissions of light EVs during
acceleration compared to constant speed, which may be used in com-
bination with existing models for the constant-speed noise emissions of
light EVs.

In Section 1.2, the present contribution explores some existing mod-
els for the noise emissions of individual light EVs.

1.2. Existing models for light EVs

This section presents some key existing models related to the noise
emissions of individual light EVs. In fact, to the knowledge of the au-
thors, very few models exist for the noise emissions of individual light
EVs, with the ones listed below being based on the CNOSSOS-EU framework. Please note that the current contribution does not aim at developing a new emission model for light EVs, but only a correction model for the noise emissions due to acceleration, which may then be applied to any existing emission model at constant speed.

### 1.2.1. The CNOSSOS-EU emission model

CNOSSOS-EU is a common framework for noise assessment in the European Union meant to enable noise pollution comparisons between European cities [24]. This model calculates the source strength of an individual vehicle's rolling noise and propulsion noise separately, as recalled in Eqs. (1) and (2), respectively,

$$L_{WR,i,m} = A_{R,i,m} + B_{R,i,m} \cdot \log_{10}\left(\frac{v}{v_{\text{ref}}}\right) + \Delta L_{WR,i,m}, \quad (1)$$

$$L_{WP,i,m} = A_{P,i,m} + B_{P,i,m} \cdot \left( \frac{v - v_{\text{ref}}}{v_{\text{ref}}} \right) + \Delta L_{WP,i,m}, \quad (2)$$

for a vehicle driving at speed $v$. The total source strength, $L_W$, is subsequently evaluated as the logarithmic sum of the rolling and propulsion noise contributions, such that

$$L_{W,i,m} = 10 \cdot \log_{10} \left( 10^{L_{WR,i,m}/10} + 10^{L_{WP,i,m}/10} \right). \quad (3)$$

In Eqs. (1) and (2), coefficients $A$ and $B$ are dependent on the vehicle category $m$ and frequency band $i$, and are defined for a reference speed of $v_{\text{ref}} = 70$ km/h. The correction term $\Delta L$ incorporates effects of the road surface, road gradients, etc.

The official CNOSSOS-EU model includes emission coefficients for light, medium-heavy, heavy, and two-wheeled vehicles, but all are assumed to be ICE vehicles. A fifth, optional category of vehicle is intended for future vehicle types, such as electric or hybrid vehicles, but no official model has been made available yet for this category. However, some researchers have developed models for the emissions of light EVs from measurements that they carried out.

### 1.2.2. Pallas et al.'s correction model for light EVs

In 2016, Pallas et al. [32] introduced a model for the emissions of electric cars at constant speed, formulated as a correction to the emission model of CNOSSOS-EU category 1 vehicles (light ICE vehicles). The correction coefficients proposed in this work were based on the emission coefficients provided in CNOSSOS-EU 2015; however, the CNOSSOS-EU coefficients were updated in 2020 [12] to correct some data processing mistakes made when the 2015 coefficients were determined, which may imply reconsidering the validity of Pallas et al.'s correction model with these updated CNOSSOS-EU coefficients.

After analysis of the methodology employed by Pallas et al., the authors of the present contribution have determined that this change in the CNOSSOS-EU coefficients does not affect the correction model developed in the 2016 article, meaning that this correction model is still valid with the updated 2020 coefficients. Indeed, the method employed by Pallas et al. only relies on the coefficients $B_p$ from the emission model of category 1 vehicles in CNOSSOS-EU, corresponding to the slope of the affine relationship between the emitted propulsion noise $L_{WP}$ and the normalised speed, which remained unchanged in the 2020 amendment of CNOSSOS-EU.

### 1.2.3. Licitra et al.'s emission model for light EVs

In 2023, Licitra et al. [27] developed a standalone model for the emissions of light EVs at constant speed, based on controlled pass-by (CPB) measurements conducted in the city of Florence, Italy. This model is independent from the existing coefficients in CNOSSOS-EU, and instead proposes coefficients for a new vehicle category of light EVs.

In Sections 2 to 5, the correction model for the acceleration of light EVs is developed, described and discussed.

<caption>**Table 1**</caption>

EV models tested in Cesbron et al. [9] and used in the present study.

<table><caption>**Table 2**</caption><thead><tr><td>Make</td><td>Model</td><td>Year</td></tr></thead><tbody><tr><td>Renault</td><td>Kangoo ZE</td><td>2016</td></tr><tr><td>Renault</td><td>ZOE</td><td>2016</td></tr><tr><td>BMW</td><td>i3s</td><td>2018</td></tr><tr><td>Nissan</td><td>LEAF</td><td>2019</td></tr><tr><td>Tesla</td><td>Model 3</td><td>2019</td></tr><tr><td>Peugeot</td><td>e-208</td><td>2020</td></tr></tbody></table>

Maximum acceleration of the tested EV models, in m/s².

<table><thead><tr><td>model</td><td>a<sub>max, global</sub> (m/s<sup>2</sup>)</td></tr></thead><tbody><tr><td>BMW i3s</td><td>4.6</td></tr><tr><td>Kangoo ZE</td><td>2.6</td></tr><tr><td>Nissan LEAF</td><td>3.8</td></tr><tr><td>Peugeot e-208</td><td>4.4</td></tr><tr><td>Tesla Model 3</td><td>8.3</td></tr><tr><td>Renault ZOE</td><td>3.4</td></tr><tr><td>Average</td><td>4.5</td></tr></tbody></table>

## 2. Measurements and data

The LIFE E-VIA project [9], concluded in 2023, aimed to investigate the interaction between the tyres of light EVs and various road surfaces with respect to noise emissions. In this project, CPB acoustical measurements were conducted on a test track on 6 models of light electric vehicles, following the NF EN ISO 11819-1 (2002) standard for the microphone's position (7.5 m from the centre of the lane, at a height of 1.2 m above the ground). In particular, for the tested vehicles, noise measurements were performed at constant speed, during maximum acceleration, and during a $-2$ m/s² deceleration, for multiple values of the speed. Thus, these measurements make it possible to derive a model for the noise emissions of an electric car during maximum acceleration, compared to constant speed.

The EV models used in the present study are listed in Table 1. Additional information on these vehicles is available in Tables 2.3 and 2.4 in Cesbron et al. [9].

A single pass-by test was conducted for each vehicle and driving condition (chosen speed, and either constant speed, full acceleration, or deceleration). Based on the experience of the LIFE E-VIA testing team, the repeatability of this type of CPB test is within $\pm 1$ dBA. During the tests at steady speed, cruise control was used when available, otherwise, speed was maintained visually using an onboard high-precision GPS receiver. Constant deceleration was regulated using the same GPS receiver. Full acceleration was obtained by fully pressing the accelerator pedal. The speed and acceleration during each pass-by were measured precisely using two infrared cells located 5 m before and after the microphone, with two reflective plates fixed on each vehicle, near the front and the rear of the body. The speeds at which the measurements were performed at constant speed varied between 18 and 112 km/h. Similarly, the speeds during full acceleration varied between 38 and 104 km/h, and the speeds during deceleration varied between 25 and 88 km/h. Data was not collected at low speeds (below 38 km/h) during full acceleration due to technical constraints within the allocated measurement time; the high acceleration capabilities of light EVs result in rapid speed increases over very short distances, making it challenging to obtain reliable measurements in this range. The absolute maximum measured acceleration of each tested vehicle, as well as the average maximum acceleration over all vehicles, is given in Table 2. The measurements performed at constant speed were $L_{A,max}$ (maximum A-weighted sound pressure level recorded during the pass-by test) while the measurements during acceleration and deceleration were $L_{A,F}$ (A-weighted
sound pressure level measured with a Fast time-weighting filter) as the vehicle passed right in front of the microphone, integrated over a constant time of 125 ms. The experimental data indicate that the $L_{A,max}$ measurements, at constant speed, were obtained very close to the axis of the microphone, suggesting that the effect of the discrepancy between the $L_{A,max}$ and $L_{A,F}$ measurements is minimal enough for them to be used jointly to create an emission model during acceleration.

While EV noise has been tested on different kind of road surfaces in Cesbron et al. [9], the present study only considers the data from two impervious road surfaces: a Dense Asphalt Concrete (DAC) 0/10, namely E1, and a Stone Mastic Asphalt (SMA) 0/10, namely E3. Road surfaces E1 and E3 were deemed closest to the virtual reference road surface used in CNOSSOS-EU (average of a DAC 0/11 and an SMA 0/11). Therefore, the measurements performed on these two surfaces were selected for analysis in the next sections.

### 3. Methodology

Multiple approaches were considered to propose a model for the increase in noise emissions due to acceleration for electric cars from the available measurements, including:

1. a correction term in the noise emission model, as a function of the acceleration, but independent of speed, for each octave band, similar to the Harmonoise [22] and IMAGINE [36] models for ICE vehicles;

2. the derivation of a new independent noise source, added to the existing propulsion noise and rolling noise;

3. a correction to the total noise per octave band during maximum acceleration.

To the authors' knowledge, methodologies using approaches 2 and 3 have not yet been published in the literature. Previous studies [23,35] have shown that the increase in noise emissions due to full acceleration compared to constant speed was highly dependent on speed, for light EVs, which excludes option 1. Option 2 was considered, but was found to be overly complex to express concisely, which left option 3 as the chosen option.

The following assumptions have been introduced:

* The reduced set of selected vehicle models is assumed to cover a spectrum of light EVs (small cars, family cars, sports cars, light commercial vehicles). This is further supported by earlier research, which suggests that no clear relationship exists between the segment of a light EV and its noise emissions [8].

* The noise emissions of a light EV at constant speed and during full acceleration may be reasonably approximated as a relationship $c_1 + c_2 \cdot \log_{10}(v)$ where $v$ is the speed, for the range of speeds at which measurements were performed in Cesbron et al. [9]. This is supported by existing noise emission models for light EVs at constant speed [27,32] and by measurements during acceleration in Pallas et al. [35], which were closely approximated by such a model.

The methodology chosen to derive a correction during full acceleration follows five main steps, namely:

1. At constant speed, for each vehicle model $m$ and each octave band $i$, the relationship between the measured noise level $L_{const,m,i}$ and the speed $v$ is determined such that

$$L_{\text{const,m,i}} = A_{\text{const,m,i}} + B_{\text{const,m,i}} \cdot \log_{10}(v) \quad (4)$$

where $A_{\text{const,m,i}}$ and $B_{\text{const,m,i}}$ are numerical coefficients.

2. During full acceleration, for each vehicle model $m$ and each octave band $i$, the relationship between the measured noise level $L_{acc,m,i}$ and the speed $v$ is determined such that

$$L_{\text{acc,m,i}} = A_{\text{acc,m,i}} + B_{\text{acc,m,i}} \cdot \log_{10}(v) \quad (5)$$

where $A_{\text{acc,m,i}}$ and $B_{\text{acc,m,i}}$ are numerical coefficients.

3. A model for the extra noise emissions during maximum acceleration $\Delta L_{m,i,a_{\text{max}}}$ is calculated to be

$$\Delta L_{m,i,a_{\text{max}}} = L_{\text{acc,m,i}} - L_{\text{const,m,i}} \quad (6)$$

which, by linearity, gives

$$\Delta L_{m,i,a_{\text{max}}} = A_{\text{corr,m,i}} + B_{\text{corr,m,i}} \cdot \log_{10}(v) \quad (7)$$

where $A_{\text{corr,m,i}} = A_{\text{acc,m,i}} - A_{\text{const,m,i}}$ and $B_{\text{corr,m,i}} = B_{\text{acc,m,i}} - B_{\text{const,m,i}}$.

4. The coefficients obtained for all vehicle models are averaged as corrective coefficients representative of a light electric vehicle, leading to

$$\Delta L_{i,a_{\text{max}}} = A_{\text{corr,i}} + B_{\text{corr,i}} \cdot \log_{10}(v), \quad (8)$$

where $A_{\text{corr,i}}$ and $B_{\text{corr,i}}$ are the average values of the $A_{\text{corr,m,i}}$ and $B_{\text{corr,m,i}}$ coefficients over all tested vehicle models $m$.

5. As an anticipation that the model will result in negative corrections for high values of $v$, due to the use of a regression model linear with $\log_{10}(v)$, the minimum correction is set to 0, i.e.,

$$\Delta L_{i,a_{\text{max}}} = \max(A_{\text{corr,i}} + B_{\text{corr,i}} \cdot \log_{10}(v), 0). \quad (9)$$

Note that the current methodology calculates the average difference between the noise levels at full acceleration and at constant speed for each vehicle. An alternative approach, in which the emission models of all vehicles were averaged separately at constant speed and full acceleration, and the difference between these averages was then calculated, would have yielded the same results. Moreover, there is no need to estimate sound power levels from the measured sound pressure levels at any point in the methodology, since only the difference between two sets of measurements (full acceleration and constant speed) is used to determine the correction model, which may then be applied to any noise emission model.

The model determined in step 5 of the methodology is valid for light EVs during maximum acceleration. However, in real driving conditions, light EVs are unlikely to use their maximal acceleration constantly. It is thus essential to derive a way to correct the noise emissions of light EVs during an acceleration which is lower than the maximal acceleration. Previous research has established correction models for the noise emissions of ICE-powered light vehicles during acceleration, as documented in Can and Aumond [6]. Most of these existing models only consider the corrective factor of noise emissions during acceleration as a binary value: acceleration is either zero or non-zero. However, the most advanced models, such as the one developed in the Harmonoise project [22], and refined in the IMAGINE project [36], assume proportionality of the correction applied to the emission model of the propulsion noise with respect to the acceleration of light ICE vehicles. For instance, in the IMAGINE acceleration model, the correction $\Delta L_{w,i,prop}$ for octave band $i$ at acceleration $a$, assumed to be comprised between $-1 \text{ m/s}^2$ and $2 \text{ m/s}^2$, is expressed as

$$\Delta L_{w,i,prop} = C_i \cdot a \quad (10)$$

where $C_i$ is a numerical coefficient for octave band $i$ and $a$ is the acceleration in $\text{m/s}^2$.

In order to create an emission model for light EVs during acceleration which may be used in conjunction with existing models for ICE-powered light vehicles, and due to the lack of data necessary to establish a more refined model for the dependency of the noise increase with absolute acceleration, an assumption of proportionality of the acceleration-related
<figure><img src="image_3.png" /><figcaption>Fig. 1. Flowchart of the main methodological steps.</figcaption></figure>

correction is made, in line with e.g. the IMAGINE model. However, the maximum acceleration of a light EV varies greatly with the vehicle model, while the objective of the present contribution is to establish a general correction model for acceleration noise. This makes it impossible to create an emission model dependent on the absolute value of the acceleration.

In order to introduce proportionality to the correction model derived in step 5 above while accounting for the various acceleration characteristics of different vehicle models, a “fractional acceleration” $a_{frac}$ is introduced. It is defined as the ratio of the absolute acceleration $a$ to the maximum acceleration $a_{max}$, such that

$$a_{frac} = \frac{a}{a_{max}}. \qquad (11)$$

6. The increase $\Delta L_i$ in noise levels due to acceleration for a light EV may thus be expressed as

$$\Delta L_i = \Delta L_{i,a_{max}} \cdot a_{frac}, \qquad (12)$$

i.e.

$$\Delta L_i = \max(A_{corr,i} + B_{corr,i} \cdot \log_{10}(v), 0) \cdot a_{frac} \qquad (13)$$

where $v$ is the speed in km/h and $a_{frac}$ is the fractional acceleration of the vehicle model of interest, at the current speed ($a_{frac} = 0$ at constant speed, $a_{frac} = 1$ at full acceleration).

The steps of the methodology are represented as a flowchart in Fig. 1.

# 4. Results

## 4.1. Preliminary analysis

### 4.1.1. About deceleration

Analysis of the experimental data confirms that a deceleration of -2 m/s² does not significantly increase the noise emissions of the tested light EVs, as found in Pallas et al. [35]. An example of the collected measurements for two vehicle models at constant speed and during deceleration is given in Fig. 2. A statistical analysis is detailed in Table A.4, in Appendix A. In this analysis, a regression linear with $log_{10}(v)$ is done on the $L_{A,max}$ at constant speed, and the error of the resulting model is calculated for the measurements conducted at constant speed and during deceleration. The results confirm that the effect of deceleration on global noise levels ($L_{A,max}$) is negligible in the measurements conducted on road surfaces E1 and E3.

### 4.1.2. At lower frequencies

A second finding made during analysis is that no significant effect of the acceleration on noise emissions is observed in the 63 Hz and 125 Hz octave bands, when considering all tested vehicle models. Indeed, no clear trend emerges for the tested vehicles in these octave bands, and the values of the change in measured noise levels during acceleration appear relatively small compared to other octave bands. Detailed data for these octave bands are available in Fig. B.9, in Appendix B. It should also be noted that these octave bands have a low impact on the overall $L_{WA}$ emissions of an electric vehicle due to the A-weighting. These octave bands are thus discarded from the model in the following sections.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Noise levels measured during pass-bys with (a) a Nissan LEAF and (b) a Renault ZOE maintaining constant speed (grey, $L_{A,max}$) or decelerating (green, $L_{AF}$) on road surface E1.</figcaption></figure>

### 4.1.3. About the choice of model

In the methodology (Section 3), the authors justified their choice to fit a model of the form $A + B \cdot \log_{10}(v)$, for the noise levels measured at constant speed and during full acceleration, based on existing literature.

To assess the validity of this model with the current dataset, the authors applied the well-known Least Absolute Shrinkage and Selection Operator (LASSO) regression method [40] to investigate the dependence of noise emissions on multiple functions of speed $v$, in particular a linear combination of $v$, $v^2$, $v^3$, and $\log_{10}(v)$. The LASSO method performs both variable selection and regularization in linear regression by adding an L1 penalty to the least-squares error. This penalty forces some regression coefficients to shrink to exactly zero, effectively selecting the most relevant variables while preventing overfitting. The results of this method and standard linear optimisation showed that the best fit was obtained by using a model of the form $A + B \cdot \log_{10}(v)$.

## 4.2. Determination of models linear with $\log_{10}(v)$ for each vehicle model and octave band (steps 1 to 3)

First, a model is determined for noise emissions per octave band at constant speed and during acceleration. This process is conducted for each vehicle model and each octave band. Two examples of the resulting regressions are shown in Fig. 3. As observed in this figure, two linear models with respect to $\log_{10}(v)$ were determined, as per steps 1 and 2 of the methodology; the model during maximum acceleration has a larger intercept but a lower slope than the model at constant speed, which is true for nearly all vehicles and octave bands tested. The values of the coefficients of determination for each vehicle, octave band, and road surface are given in Table C.5, in Appendix C. Most of these coefficients exceed 0.9, indicating a strong correlation between the measurement and the derived models, in particular for the bands which contribute the most to the A-weighted sound level (1000, 2000, 4000 Hz).

The next step consists in determining the correction model for the increase in noise levels during maximum acceleration. This is done by simply subtracting the model for constant speed from that during maximum acceleration, as per step 3 of the methodology. This process is repeated for each vehicle model and each octave band. An example is given in Fig. 4 for the 1000 Hz octave band on the E1 surface. The average model results in negative values for values of speed above 90 km/h, which is a consequence of the chosen method based on regressions linear with $\log_{10}(v)$. Note, however, that this does not prefigure the behaviour of the model in other octave bands.

The two resulting models for each octave bands, respectively on the E1 and E3 road surfaces, are averaged to obtain the final model, see Section 4.3.

## 4.3. Noise emission model during maximum acceleration (steps 4 and 5)

After averaging the two models obtained respectively for road surfaces E1 and E3, the resulting correction model for acceleration is obtained; its coefficients are presented in Table 3.

As a reminder, coefficients $A_{corr,i}$ and $B_{corr,i}$ provide the increase in noise emissions $\Delta L_i$ in the octave band $i$ at speed $v$, in km/h, during full acceleration, according to Eq. (9).

The resulting correction applied to each octave band is plotted in Fig. 5 for speeds up to 100 km/h.

## 4.4. Correction for fractional acceleration (step 6)

As mentioned in Section 3, the authors of the present contribution have made the decision to create a correction model which is proportional to the fractional acceleration.

The correction model for any fractional acceleration is given in Eq. (13), with the coefficients detailed in 3.

## 4.5. Application of the correction model to existing emission models

To model the noise emissions of light EVs, Pallas et al. [32] proposed a correction to the propulsion noise component of light ICE vehicles in the CNOSSOS-EU noise emission model [24]. Although the CNOSSOS-EU emission model was updated in 2020 [12], the correction model by Pallas et al. is still valid, as mentioned in Section 1.2.2.

The acceleration correction model proposed in the present contribution is therefore applied to the emission model by Pallas et al., and plotted in Fig. 6. Note that while the correction model presented in this contribution was developed from the difference between measurements of sound pressure levels (SPLs) during full acceleration and constant speed, it may be used to correct the sound power levels (SWLs) emitted by EVs directly, given that the measurements were carried out in identical reference conditions, with free-field propagation. When applying the correction for the noise emitted during full acceleration to this noise emission model, the A-weighted sound power level increases by approximately 5 dBA at 20 km/h, compared to the sound power level at constant speeds, and the correction tends to 0 dBA as the speed exceeds 100 km/h. The reader may notice that the curves plotted in Fig. 6 are
<figure><img src="image_5.png" /><figcaption>Fig. 3. Linear regressions with respect to $log_{10}(v)$ of the noise levels measured during pass-bys at constant speed (blue) or during maximum acceleration (red) in (a) the 2000 Hz octave band with a Nissan LEAF, and (b) the 500 Hz octave band with a BMW i3s, on road surface E1.</figcaption></figure>

<caption>Table 3</caption>

Coefficients of the correction model for the increase in noise emissions during maximum acceleration for light EVs.

<table><thead><tr><th>Octave band (Hz)</th><th>63</th><th>125</th><th>250</th><th>500</th><th>1000</th><th>2000</th><th>4000</th><th>8000</th></tr></thead><tbody><tr><th>A<sub>corr,i</sub></th><td>0.0</td><td>0.0</td><td>16.5</td><td>24.5</td><td>8.1</td><td>15.9</td><td>29.1</td><td>27.1</td></tr><tr><th>B<sub>corr,i</sub></th><td>0.0</td><td>0.0</td><td>-9.1</td><td>-12.6</td><td>-4.1</td><td>-7.5</td><td>-13.7</td><td>-12.7</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Correction models for acceleration noise compared to constant speed noise obtained for each vehicle (light colours) and resulting average correction (thick red line) for the 1000 Hz octave band on the E1 road surface.</figcaption></figure>

not linear with $log_{10}(v)$. The reasons for this phenomenon are that (1) the emission model by Pallas et al., to which the correction is added, is not exactly linear with $log_{10}(v)$ due to some engine noise at low speeds, and (2) the correction model is only linear with $log_{10}(v)$ in each octave band, but after applying the correction, adding A-weighting and summing the energy of all octave bands to obtain the overall A-weighted sound power level, the linearity with $log_{10}(v)$ does not hold true for the resulting sound levels.

## 4.6. Acceleration as a function of speed

In order to apply the correction model to a real-case scenario, the value of $a_{frac}$ must be known for a given light EV. However, in order to calculate $a_{frac}$ from an absolute acceleration $a$ in m/s$^2$, as per Eq. (11), the absolute value of $a_{max}$, the maximum reachable acceleration or “full acceleration”, must also be known.

The maximum reachable acceleration or “full acceleration” of a light EV is a function of the vehicle model $m$ and the current speed $v$, and may thus be denoted $a_{max,m}(v)$, generally tending to decrease at higher speeds. From the data collected in the LIFE E-VIA project, the maximum acceleration of each tested vehicle model with respect to its speed may be estimated. The data used in this section is identical to the one used in the previous sections, the only difference being that the measured values of the absolute acceleration (in m/s$^2$) are considered here, while they were hidden behind the notion of “full acceleration” in previous sections.

The global maximum acceleration reachable by a vehicle model $m$ over all speeds is denoted $a_{max,global,m}$, such that

$$a_{max,global,m} = \max_{v} a_{max,m}(v). \qquad (14)$$

The relative maximum acceleration of a vehicle model as a function of speed may thus be expressed as

$$a_{rel,m}(v) = \frac{a_{max,m}(v)}{a_{max,global,m}}. \qquad (15)$$

In Fig. 7, the relative maximum acceleration $a_{rel,m}$ of each of the tested vehicles is plotted as a function of speed, in grey, for surface E3. From this figure, it appears that the tested EVs reach their global maximum acceleration at low speeds, but that the maximum reachable acceleration decreases linearly, as a first approximation, as speeds cross
<figure><img src="image_7.png" /><figcaption>Fig. 5. Correction per octave band for a light electric vehicle during maximum acceleration.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. A-weighted sound power level of a light electric vehicle according to the emission model by Pallas et al. at constant speed (blue), and when applying the maximum acceleration correction model developed in the present contribution (red).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Relative maximum acceleration with respect to speed for the tested models of vehicles (grey) and resulting average model for an electric vehicle (red) on surface E3.</figcaption></figure>

a threshold. An average model for all tested vehicles is derived from these curves, and plotted in red. Although this plot is made with the data collected during the tests on road surface E3, the results are nearly identical with road surface E1. This model may be expressed as

$$a_{\text{rel}} = \begin{cases} 1.0 & \text{if } v \le 45 \text{ km/h,} \\ 1.0 - 0.0123 \cdot (v - 45) & \text{otherwise.} \end{cases} \qquad (16)$$

Knowing, for an average light EV, the value of $a_{rel}$ as a function of speed (Eq. (16)) and the maximum value of the acceleration (Table 2), it is possible to calculate $a_{frac}$ for various acceleration values, and plot the resulting noise emissions; this is done in Fig. 8.

Indeed, when considering an average light EV, whose global maximum acceleration is $a_{max, global} = 4.5 \text{ m/s}^2$, accelerating at $a \text{ m/s}^2$, $a_{frac}$ may be calculated at any speed, from $a_{frac} = a/(a_{rel} \cdot a_{max, global})$. In a scenario where $a = 2.0 \text{ m/s}^2$, at 40 km/h, $a_{rel} = 1$, so $a_{frac} = 2.0/(1 \cdot 4.5) = 0.44$; at 70 km/h, $a_{rel} = 1.0 - 0.0123 \cdot (70 - 45) = 0.69$,

so $a_{frac} = 2.0/(0.69 \cdot 4.5) = 0.64$. Then, the value of $a_{frac}$ along with the speed may be input into Eq. (13) to obtain the associated noise emission correction.

# 5. Discussion and limitations

## 5.1. Comparison with existing measurements

The increase in noise emissions given by the proposed correction model, and plotted in Fig. 6, is consistent with the measurements performed by Schweizer et al. [39] on a vast variety of light EVs. The increase is slightly lower than that found in Pallas et al. [35], and much lower than in Kaliski et al. [23], both of which were carried out on earlier EVs from the early 2010s, which may explain this difference.
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** A-weighted sound power level of an average light EV, with a global maximum acceleration of 4.5 m/s², according to the emission model by Pallas et al. at constant speed (blue) and for various values of the acceleration (shades of grey).</figcaption></figure>

## 5.2. Inter-vehicle variability

Different vehicle models may have different noise emission levels, even at constant speed, despite belonging to the same vehicle category, e.g. light EVs or light ICE vehicles. To take this variability into account when applying noise emissions models to individual vehicles in, e.g., microscopic traffic simulations, the noise emissions of a vehicle within a vehicle type may be modelled following a normal distribution, whose standard deviation must be measured for each vehicle category.

In the case of light ICE vehicles, Gozalo et al. [16] have used measurements from 57 locations to quantify the standard deviation of the distribution of emissions of light ICE vehicles for all speeds, with a 10-km/h step. On average, between 0 and 70 km/h – the speeds most encountered in urban areas –, the standard deviation of the emissions of light ICE vehicles was found to be 2.4 dBA.

From the data collected in the LIFE E-VIA project, the standard deviation of the emissions of light EVs may also be estimated. The standard deviation over all speeds may be estimated directly from Table 2.13 in Cesbron et al. [9], giving approximately 1.2 dBA on road surface E1 and 1.3 dBA on road surface E3, assuming the tested vehicles are representative of the fleet of light EVs and the distributions are normal. These results suggest that the inter-vehicle variability of light EVs is smaller than that of light ICE vehicles, although this variability should still be accounted for in the emissions of individual vehicles.

It should be noted that a similar inter-vehicle variability exists for the correction of the noise emissions due to acceleration, as shown, e.g., in Fig. 4. However, taking into account this variability in each octave band is not a straightforward process, as the implementation of, e.g., a normal law in the correction of each octave band would introduce a bias in the resulting $L_{Aeq}$, due to the logarithmic nature of the decibel scale. The effects of accounting for this variability in a noise emission model should thus be carefully studied before implementation.

## 5.3. Limitations

The developed model presents some limitations, including the following:

1. the model is based on EV models most representative of the European EV fleet in 2019-2020, and may not entirely reflect the current European EV fleet, which includes some newer EV models;

2. the measurements were only carried out on vehicles at full acceleration, while obtaining data for various values of the acceleration at each speed would have been beneficial to refine further the proposed correction model;

3. the assumption of linear relationship between the correction and the value of the acceleration was chosen arbitrarily, as a first approximation based on the current state-of-the art for ICE vehicles, and should be confirmed by further research;

4. the correction model is not based on measurements at lower speeds (< 40 km/h). Pass-by noise emission measurements are difficult at very low speeds, especially for EVs, for which the signal-to-background-noise ratio may be critical, but should nevertheless be investigated further. The noise emissions from acoustic vehicle alerting systems (AVAS) should also be included at low speeds.

While these limitations may appear significant, the lack of a correction model for the acceleration of light EVs at the present time may outweigh them. This contribution represents a significant, necessary advancement in noise emission modelling for EVs and highlights the need for future refinements to further benefit the scientific community.

## Conclusion

The present contribution proposes a correction model per octave band for the noise emissions of light electric vehicles during acceleration, from measurements conducted on 6 vehicle models. The proposed model is a function of both speed and acceleration, and may be used in conjunction with any existing octave-band-based emission model for light EVs.

The main findings of this contribution may be summarised as follows:

1. No extra noise emission is observed during the deceleration of light EVs at $-2 \text{ m/s}^2$ compared to constant speed;

2. A model linear with $log_{10}(v)$, described in Eq. (13), is created for the noise emissions per octave band of a light EV during full acceleration, and its coefficients are listed in Table 3;

3. The contribution proposes an extrapolation of the model for lower values of the acceleration, proportionally to the fractional acceleration of a given vehicle, i.e. the ratio of its acceleration to its maximum acceleration.

The proposed model has some clearly identified limitations, the most notable being its lack of validation for low speeds (below 40 km/h) and the exclusive use of measurements conducted at full acceleration, which limits the validity of the model when extrapolating to lower values of the acceleration. Nevertheless, this remains, to date, the best available model to account for the noise emissions of light EVs during acceleration, and this contribution highlights the need for future refinements to further improve the assessment of noise pollution exposure.

## CRediT authorship contribution statement

**Sacha Baclet:** Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Julien Cesbron:** Writing – review & editing, Resources, Methodology, Investigation, Conceptualization. **Pierre Aumond:** Writing – review & editing, Methodology, Investigation, Conceptualization. **Arnaud Can:** Writing – review & editing, Investigation, Funding acquisition, Conceptualization. **Romain Rumpler:** Writing – review & editing, Supervision, Funding acquisition.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Acknowledgements

The data used in this work were collected during the LIFE18ENV/IT/ 000201 LIFE E-VIA project funded by the European Commission within the LIFE2018 programme. The authors wish to thank Marie-Agnès Pal-

las for her help and discussion in accessing these experimental data. The authors gratefully acknowledge the financial support from Digital Fu- tures (DIRAC and GEOMETRIC projects), Formas (Grant 2021-01532), Stockholm Region (Grant 2021-0317), the Richert Foundation (Grant 2021-00697).

## Appendix A. Effect of deceleration on noise emissions

<caption>Table A.4</caption>

Mean absolute error (MAE) and mean error (ME) of the regression linear with $log_{10}(v)$ on $L_{A,max}$ at constant speed, for the measurements conducted at constant speed and during deceleration, on road surfaces (a) E1 and (b) E3.

<table><thead><tr><th>Vehicle</th><th>MAE Constant</th><th>MAE Deceleration</th><th>ME Deceleration</th></tr></thead><tbody><tr><td>BMWi3</td><td>0.323</td><td>0.635</td><td>0.635</td></tr><tr><td>KANGOOZE</td><td>0.534</td><td>0.397</td><td>0.303</td></tr><tr><td>LEAF</td><td>0.191</td><td>0.233</td><td>0.128</td></tr><tr><td>PEUGEOTe208</td><td>0.786</td><td>0.545</td><td>-0.545</td></tr><tr><td>TESLA</td><td>0.216</td><td>0.385</td><td>0.313</td></tr><tr><td>ZOE</td><td>0.448</td><td>0.237</td><td>-0.201</td></tr></tbody></table>

(a) Road surface E1.

<table><thead><tr><th>Vehicle</th><th>MAE Constant</th><th>MAE Deceleration</th><th>ME Deceleration</th></tr></thead><tbody><tr><td>BMWi3</td><td>0.340</td><td>0.744</td><td>0.744</td></tr><tr><td>KANGOOZE</td><td>0.360</td><td>1.048</td><td>1.048</td></tr><tr><td>LEAF</td><td>0.308</td><td>0.655</td><td>0.346</td></tr><tr><td>PEUGEOTe208</td><td>0.581</td><td>0.556</td><td>-0.556</td></tr><tr><td>TESLA</td><td>0.275</td><td>0.981</td><td>0.847</td></tr><tr><td>ZOE</td><td>0.418</td><td>0.360</td><td>-0.360</td></tr></tbody></table>

(b) Road surface E3.
Appendix B. Acceleration noise in the 63 Hz and 125 Hz octave bands

<figure><img src="image_11.png" /><figcaption>Fig. B.9. Measured increase in noise levels during acceleration compared to constant speed in octave bands (a, c) 63 Hz and (b, d) 125 Hz on road surfaces (a, b) E1 and (c, d) E3 for all tested vehicles.</figcaption></figure>
# Appendix C. Coefficients of determination of the regressions

## Table C.5

Coefficients of determination for the regressions per octave band and per vehicle model done in Section 4.2.

### (a) Coefficients of determination for constant speed on road surface E1.

<table><thead><tr><th>Octave band (Hz)</th><th>BMWi3</th><th>KANGOO</th><th>LEAF</th><th>e208</th><th>TESLA</th><th>ZOE</th></tr></thead><tbody><tr><td>250</td><td>0.925</td><td>0.959</td><td>0.926</td><td>0.908</td><td>0.957</td><td>0.987</td></tr><tr><td>500</td><td>0.982</td><td>0.995</td><td>0.975</td><td>0.982</td><td>0.981</td><td>0.980</td></tr><tr><td>1000</td><td>0.996</td><td>0.988</td><td>0.996</td><td>0.987</td><td>0.998</td><td>0.989</td></tr><tr><td>2000</td><td>0.985</td><td>0.989</td><td>0.992</td><td>0.897</td><td>0.984</td><td>0.998</td></tr><tr><td>4000</td><td>0.958</td><td>0.989</td><td>0.980</td><td>0.941</td><td>0.895</td><td>0.974</td></tr><tr><td>8000</td><td>0.871</td><td>0.946</td><td>0.871</td><td>0.809</td><td>0.827</td><td>0.890</td></tr></tbody></table>

### (b) Coefficients of determination for acceleration on road surface E1.

<table><thead><tr><th>Octave band (Hz)</th><th>BMWi3</th><th>KANGOO</th><th>LEAF</th><th>e208</th><th>TESLA</th><th>ZOE</th></tr></thead><tbody><tr><td>250</td><td>0.574</td><td>0.733</td><td>0.734</td><td>0.918</td><td>0.947</td><td>0.891</td></tr><tr><td>500</td><td>0.909</td><td>0.996</td><td>0.754</td><td>0.948</td><td>0.592</td><td>0.759</td></tr><tr><td>1000</td><td>0.970</td><td>0.951</td><td>0.981</td><td>0.988</td><td>0.990</td><td>0.992</td></tr><tr><td>2000</td><td>0.913</td><td>0.981</td><td>0.945</td><td>0.941</td><td>0.992</td><td>0.981</td></tr><tr><td>4000</td><td>0.939</td><td>0.869</td><td>0.430</td><td>0.779</td><td>0.890</td><td>0.875</td></tr><tr><td>8000</td><td>0.735</td><td>0.670</td><td>0.431</td><td>0.627</td><td>0.533</td><td>0.717</td></tr></tbody></table>

### (c) Coefficients of determination for constant speed on road surface E3.

<table><thead><tr><th>Octave band (Hz)</th><th>BMWi3</th><th>KANGOO</th><th>LEAF</th><th>e208</th><th>TESLA</th><th>ZOE</th></tr></thead><tbody><tr><td>250</td><td>0.916</td><td>0.954</td><td>0.926</td><td>0.923</td><td>0.954</td><td>0.942</td></tr><tr><td>500</td><td>0.983</td><td>0.986</td><td>0.988</td><td>0.984</td><td>0.974</td><td>0.965</td></tr><tr><td>1000</td><td>0.994</td><td>0.994</td><td>0.995</td><td>0.987</td><td>0.996</td><td>0.988</td></tr><tr><td>2000</td><td>0.983</td><td>0.994</td><td>0.995</td><td>0.960</td><td>0.992</td><td>0.997</td></tr><tr><td>4000</td><td>0.934</td><td>0.991</td><td>0.993</td><td>0.960</td><td>0.985</td><td>0.985</td></tr><tr><td>8000</td><td>0.806</td><td>0.960</td><td>0.931</td><td>0.791</td><td>0.869</td><td>0.917</td></tr></tbody></table>

### (d) Coefficients of determination for acceleration on road surface E3.

<table><thead><tr><th>Octave band (Hz)</th><th>BMWi3</th><th>KANGOO</th><th>LEAF</th><th>e208</th><th>TESLA</th><th>ZOE</th></tr></thead><tbody><tr><td>250</td><td>0.291</td><td>0.615</td><td>0.747</td><td>0.882</td><td>0.699</td><td>0.780</td></tr><tr><td>500</td><td>0.863</td><td>0.971</td><td>0.612</td><td>0.887</td><td>0.763</td><td>0.685</td></tr><tr><td>1000</td><td>0.947</td><td>0.992</td><td>0.985</td><td>0.988</td><td>0.987</td><td>0.989</td></tr><tr><td>2000</td><td>0.932</td><td>0.979</td><td>0.963</td><td>0.967</td><td>0.981</td><td>0.997</td></tr><tr><td>4000</td><td>0.932</td><td>0.813</td><td>0.834</td><td>0.932</td><td>0.970</td><td>0.937</td></tr><tr><td>8000</td><td>0.792</td><td>0.702</td><td>0.782</td><td>0.565</td><td>0.932</td><td>0.508</td></tr></tbody></table>

## Data availability

The authors do not have permission to share data.

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