# Perceived unpleasantness of aircraft flyover noise: Influence of temporal parameters

Arthur Pathé, Catherine Lavandier, Antoine Minard, Ingrid Legriffon

► To cite this version:

Arthur Pathé, Catherine Lavandier, Antoine Minard, Ingrid Legriffon. Perceived unpleasantness of aircraft flyover noise: Influence of temporal parameters. Acta Acustica united with Acustica, 2017, 103 (1), pp.34-47. 10.3813/AAA.919031. hal-01461591

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# Perceived Unpleasantness of Aircraft Flyover Noise: Influence of Temporal Parameters

Arthur Paté<fnref n="1" />), Catherine Lavandier<fnref n="1" />), Antoine Minard<fnref n="2" />), Ingrid Le Griffon<fnref n="3" />)

The perceived unpleasantness due to aircraft flyover noise is mostly explained by a) non-acoustical factors, and b) the noise level, on which future progress will be prospectively hard and expensive to obtain. However, the literature suggests that sound-quality approaches may provide new solutions for reducing the perceived unpleasantness. The study reported here investigates the effects of the temporal parameters of single aircraft flyover sound signatures on the unpleasantness experienced by people outside the aircraft. Two listening tests (semantic differential, synthesised stimuli) were conducted. In the first test the stimuli were equalised according to the EPNL in order to concentrate on the slope, duration and amount of fluctuation of the sound signatures. In the second test the influences of the temporal aspects and of the noise level were compared. Statistical analyses were performed. Although slope and duration were made independent, their perceptions remain correlated. Descriptors are proposed for assessing the duration and the amount of fluctuation. For both configurations (stimuli equalised or not), a model is proposed, in which the unpleasantness is explained by the duration, the amount of fluctuation and the noise level. Unsurprisingly the noise level is the most influential factor for the unpleasantness, but the temporal factors are also important. The amount of fluctuation strongly correlates with the unpleasantness. The duration has a two-sided effect: short flyover noises exhibit higher peak levels and so increase the unpleasantness; long flyover noises maximise the length of sound exposure and also increase the unpleasantness.

## 1. Introduction

The noise annoyance experienced by humans is among the most important environmental issues that have to be addressed. In urban or semi-urban areas, one of the major sources of noise is the air traffic, causing various reactions from annoyance to stress-induced health problems. Public policies and public or private initiatives have therefore participated in reducing the noise due to aircraft for at least 60 years [1]. The problem of noise annoyance due to aircraft or transportation (also train or road traffic) noise is in itself transdisciplinary. As a matter of fact, a big portion of the variance observed in noise annoyance judgements is explained by non-acoustical factors [2], such as personal [3, 4] or socio-economic factors [5, 6, 7, 8].

Despite the strong influence of non-acoustical factors, it is commonly accepted that the variance in the exposure to noise (measured with the noise level) is responsible for about a third of the variance in the annoyance [5, 9], and even more in certain conditions (e.g. extreme noise ex-

posure [10]). There is still room for acoustical improvements leading to a decrease in noise annoyance. Examples of contributions to changing the annoyance due to noise exposure are the reduction of the number of aircraft [11], or the design of alternative take-off and landing trajectories [12].

Considering a single aircraft flyover, there is no doubt that the noise level is the most influential acoustical parameter on the perceived unpleasantness [13, 14, 15]. The noise level has been reduced so much in the past decades [16, 17, 18] that future progress will be very hard and expensive to obtain [19, 20], needing radical new redesigns of aircraft and stringent trade-offs with other issues like e.g. gas emission [21]. On the other hand, sound quality improvements are a promising way to reduce the annoyance experienced by the inhabitants of airport neighbourhoods [22, 23, 24]. The context of this study will be limited to acoustical parameters and sound quality assessment, so the effects of noise will be measured in terms of unpleasantness, and not of annoyance (a broader concept also including e.g. people's activities and emotions) [25, 26]. In line with the sound quality-based approach, many studies have focused on the spectral aspects of the aircraft flyover noise [15, 27, 28, 29, 30], mostly on the

<footnote n="1">1) Université de Cergy-Pontoise, laboratoire MRTE, 5 mail Gay-Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise Cedex, France. pate.arthur.lam@gmail.com</footnote>

<footnote n="2">2) Genesis, Domaine du petit Arbois, BP69, 13545 Aix-en-Provence Cedex 4, France</footnote>

<footnote n="3">3) ONERA, 29 avenue de la Division Leclerc, 92320 Châtillon, France</footnote>
hissing noise (“blade passing frequency”) or on the hum-
ming noise (“buzz-saw noise”). Studies about temporal as-
pects of noise can be found in the transportation acous-
tics literature. The following temporal aspects of aircraft
or transportation noise are regularly reported to be percep-
tually relevant:

* The slope, or “rise time”, or “rate of noise level growth”, or “onset rate”, describing the “suddenness” of traffic [31], train [32, 33] or aircraft noise [24, 34];

* The duration, or “exposure time”, characterising “short/long” signals [24, 32, 35];

* The turbulence (time variations of temperature, wind velocity, pressure and density of the atmosphere [36]) effects, resulting in non-periodic amplitude modulations perceptually described as “staccato-like”, “fluctuating” or “unsteady” [24, 32, 37];

* The speed, characterising “fast/slow” signals: It is sometimes shown to be correlated with the slope [24], and it sometimes includes duration and slope aspects [37]. The sensation of speed may also be related to spectral aspects (Doppler-effect in the blade-passing frequency tones).

Very few studies however have investigated the temporal aspects of aircraft flyover noises in particular. The stimuli in [34] were generated with a synthesis method presumably too rough to produce realistic noises (filtered white noises with sine tones). Furthermore, the temporal characteristics were those of military aircraft, to which only a few people are exposed. Barbot et al. [24] used recordings and carried out a scoping study about both spectral and temporal parameters. In [24] relevant temporal characteristics and associated verbal descriptions were identified and shown to make sense for the listeners: they have thus been used in the present study. However, these studies do not clearly establish a link between the temporal aspects and the unpleasantness, which is in the end one of the meaningful figures for assessing the well-being of people. Clarifying this link, particularly for aircraft noise, is the main objective of the present study. Furthermore, for the particular case of aircraft noise, slope and duration of usual (i.e. recorded or synthesised with realistic parameters) noises are correlated [32]: a fast flyover necessarily results in a noise with a steep slope and a short duration. The present study introduces the idea of decorrelating the temporal aspects from one another, in order to disentangle the effects, as opposed to [34] where slope and duration are correlated. The flyover speed is used as a varying parameter allowing us to decorrelate slope and duration. The present paper investigates the effects of the temporal aspects (decorrelated from one another) of single civil aircraft flyover sound signatures on the unpleasantness, as experienced by people outside the aircraft.

Two tests have been conducted. The first test (T1) inves-
tigated the effects of the previously defined, decorrelated
temporal parameters on the perceived unpleasantness<fnref n="1" />. T1

<figure><img src="image_2.png" /><figcaption>Figure 1. PNL of an example flyover signal. The level PNL<sub>max</sub> is reached at t<sub>0</sub>. t<sub>1</sub> and t<sub>2</sub> are the times at which the level PNL<sub>max</sub> – 10 PNdB is reached.</figcaption></figure>

used EPNL-equalised stimuli, in order to prevent global
noise level changes from masking temporal effects. The
second test (T2) re-introduced global noise level changes
in order to compare the influence of temporal effects re-
tained from T1 with that of global noise level changes.

## 2. Temporal aspects of aircraft noises

In this study, the temporal aspects refer to the noise level evolution over time. According to the usual practice in aircraft noise studies, the perceived noise level (or PNL [39], unit: PNdB, computation step: 0.5 s [40]) was used to describe the noise level evolution over time. The PNL is computed, and not the PNLT (i.e. without tone correction factor), because the present study focuses only on the temporal aspects and not on the spectral aspects. Furthermore, preliminary informal tests on the stimuli of the present study showed that loudness-equalisation (for discarding the loudness effects) was better attained with the effective perceived noise level (EPNL) without tone correction, than either with the equivalent sound pressure level (unweighted L<sub>eq</sub>(SPL) or A-weighted L<sub>eq</sub>(A)) or with the loudness models (Zwicker's or Moore's). Figure 1 presents the PNL of an example aircraft flyover.

The present study focuses on 3 temporal aspects, derived from the PNL as follows:

**The slope:** The times at which the PNL reaches its maximal value PNL<sub>max</sub> (t<sub>0</sub> in Figure 1), and at which it first reaches the value PNL<sub>max</sub> – 10 PNdB (t<sub>1</sub>) are detected. The slope is then derived from a linear regression of the PNL-curve between t<sub>0</sub> and t<sub>1</sub>.

**The duration:** (referred to as “DUR” when used as a descriptor) This is the time difference between the 2 instants at which the level PNL<sub>max</sub> – 10 PNdB is reached (t<sub>1</sub> and t<sub>2</sub> in Figure 1). Note that the present definition of the duration differs from the “duration time” defined in [34] as the time during which the signal remains at its peak level. As this plateau effect has not been observed on actual flyover recordings, it was not investigated here. Our definition of the duration is closer to what is called the “exposure duration time” in [34], and which is strongly correlated with the “onset rate” (or slope) in their corpus.

**The amount of fluctuation:** It is defined here as the maximum modulation depth of the amplitude of the signal (more details in Section 3.1.1).

<footnote n="1">¹ Part of this work (T1 and its principal component analysis) was pre-
sented at Internoise 2015 [38].</footnote>
# 3. Experimental procedure

The experimental apparatus (Section 3.2) and protocol (Section 3.3) are common to T1 and T2. The stimuli (take-off noises) were generated with the method described in Section 3.1.

## 3.1. Stimuli

The experimental designs should include stimuli whose amount of fluctuation, slope and duration a) have a wide but realistic range of variations, and b) are uncorrelated. With the current standardised take-off procedures as well as the time limitations of a measurement campaign, such signals can not be obtained with only actual recordings of take-offs. A synthesis method presents the advantage of controlling the characteristics of the stimuli.

### 3.1.1. Generation of the noises

The detailed description of the synthesis method is beyond the scope of this article, further details are available in [41, 42]. The synthesis is based on audio recordings of actual take-offs of typical civil aircraft measured at 3 km from a runway. From a total of 12 aircraft, two standard medium-haul aircraft, called “A” and “B” in the following, were chosen because they sounded perceptually similar: neither aggressive tonality nor aggressive buzz-saw. Two-sample t-test shows that aircraft A and B get similar unpleasantness ratings during T1 (16 stimuli from aircraft of type A, 12 from aircraft of type B, t(26) = 1.75, p = 0.09) and T2 (21 stimuli from aircraft of type A, 15 from aircraft of type B, t(34) = 0.96, p = 0.34). Therefore in the following the aircraft is not considered as a factor.

The recordings were analysed (time-frequency decomposition) and re-synthesized, using a simplified propagation model between the current aircraft positions and the recording point. Figure 2 shows a) a recording and b) the corresponding synthesis: Informal listening by the authors and the partners of the project confirmed the original and synthesised signals to be very similar, and no participant noticed that the stimuli were not “actual” aircraft noises.

The description of the signal into time-frequency frames and the knowledge of the aircraft positions allow us to control the amount of fluctuation, the speed and the altitude of the flyover. The amount of fluctuation was controlled by an empirical model based on the generation of pseudo-random amplitude modulations. For each synthesis the modulation frequency is limited to 2 Hz and a maximum modulation depth is set<fnref n="2" />. Three levels of maximum modulation depth were chosen during preliminary listening tests, leading to the 3 levels of fluctuation F1, F2 and F3 shown in Figure 3. F2-level corresponds to the recordings made with clear and calm weather: this is the baseline fluctuation level. F1 corresponds to a maximal amplitude modulation depth approximately twice as small and

<figure><img src="image_3.png" /><figcaption>Figure 2. Spectrograms of a) an example flyover noise recording and b) the corresponding synthesis.</figcaption></figure>

F3 approximately twice as high. Different speeds and altitudes are obtained by multiplying their nominal value (270 km/h and 579 m for aircraft A, 270 km/h and 391 m for aircraft B) by physically plausible factors (0.63, 0.8, 1.26 and 1.6) and defining accordingly new trajectories as inputs of the synthesis model. The speed and the altitude of a flyover have an influence on the slope and duration of the corresponding noise: High-speed and low-altitude flyovers produce sharp-slope and short-duration signals; low-speed and high-altitude flyovers produce flatslope and long-duration signals.

One hundred fifty aircraft flyover noises (2 aircraft, 5 factors for altitude and speed, 3 fluctuation levels) were initially generated, in order to identify the variation range for the slope and duration. Slopes ranged approximately from 0.5 to 2.7 PNdB/s and durations ranged approximately from 8 to 52 s, which is typical of actual recordings of aircraft flyovers at various altitudes and speeds. This set of initial noises additionally confirmed the high correlation<fnref n="3" /> between slope and duration: r = -0.81**.

### 3.1.2. Modification of the noises

By construction, the amount of fluctuation is uncorrelated from the slope and duration. The method for decorrelating

<footnote n="2">² The actual modulation depth is further weighted depending on frequency and aircraft/listener distance.</footnote>

<footnote n="3">³ In this article, Pearson product-moment correlation coefficients are denoted “r” and followed by ** (resp. *) if they are statistically significant at the level α = 0.01 (resp. α = 0.05).</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 3. (Colour online) PNL of an example flyover noise, computed with 3 amounts of fluctuation: low (F1, green, thin), moderate (F2, black, intermediate), high (F3, pink, thick).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4. (Colour online) Example of noise modification. PNL of an original flyover noise signal (black) and of its modification (red, or gray in the printed version). Dashed lines and arrows indicate the duration and slope. The horizontal dashed line at the bottom indicates the background noise level.</figcaption></figure>

slope and duration was based on envelope modification. Applying different (positive or negative) gains on different parts of a signal alters its envelope and thus its slope and duration. Figure 4 shows in black the PNL of an original signal, as output by the synthesis algorithm. The modified PNL is in red colour: its slope has been increased (values at the beginning of the signal lowered) and its duration has been kept constant (values at the end slightly raised). The sound files had a length of 58 s. Exponential fade-in (starting from amplitude 0) and fade-out (finishing at amplitude 0) were applied onto respectively the first 2 seconds and the last 2 seconds of each signal, so that the aircraft noises would be perceived as progressively emerging from the background noise.

## 3.2. Apparatus

The listening tests took place in a semi-anechoic room fitted with artificial grass, green plants and wooden fence near the front wall. Figure 5 presents a drawing of the experimental setup. The subjects used the *Matlab* test interface on a laptop, in order to control the playback of the stimuli (soundcard *RME Fireface UC*) and to give the ratings on the semantic scales. The subjects wore *Sennheiser HD 650* open headphones. A *Polhemus Patriot*

<figure><img src="image_6.png" /><figcaption>Figure 5. Drawing of the experimental setup.</figcaption></figure>

3D-headtracker mounted on the headphones was used in conjunction with a 3D-spatialisation program by *Genesis*: the monophonic synthesised signals were made binaural by applying HRTF filters adapted in real-time according to the headtracker data. Hence the aircraft flyovers kept their front-to-rear target trajectory, independently of the subject's head motion. In addition, a background noise was rendered by two *Genelec 1031A* loudspeakers. The background noise was a recording of a semi-urban noise activity, a continuous traffic flow without identified events. Its equivalent noise level $L_{eq}(A)$ was set to 49 dB(A) — equivalent to approximately 60 EPNdB.

## 3.3. Protocol

Prior to the test, the subjects were given the instruction to imagine themselves relaxing in a private garden located in a semi-urban neighbourhood.

The semantic differential method was chosen for the 2 tests. The subjects were asked to judge each noise on several continuous scales. For each scale, a slider was to be moved between 2 opposed adjectives. The slider positions were converted into a continuous “score” ranging from -10 (leftmost position) to 10 (rightmost position). T1 proposed 5 semantic scales (Section 4.1.1) and T2 proposed 4 semantic scales (Section 5.1.1).

The evaluation phase was preceded by a training phase, in which 3 stimuli were presented. These 3 stimuli were selected because they featured the most extreme characteristics of the experimental design.

During the experiment, the subjects were allowed to listen to the current stimulus as many times as wanted. Each stimulus had to be played at least once, and the stimulus playback could not be interrupted. The order of presentation of the stimuli was randomised.

## 3.4. Statistical requirements

The hypotheses of normality (Jarque-Bera test) and of homogeneity of variance (Levene test) always failed to be rejected with the output data (each subject giving a rating on each scale for each stimulus) of both tests. In order to control the violations of sphericity, the Greenhouse-Geisser correction was used for the p-values of the ANOVA. It was
<table><caption>Table I. T1: Characteristics of the 28 stimuli. The unpleasantness ratings are given in terms of mean and standard deviation (34 subjects).</caption><thead><tr><th></th><th>Plane</th><th>Speed</th><th>Altitude</th><th>Slope<br>PNdB/s</th><th>Duration<br>cat.</th><th>Fluct.<br>cat.</th><th>PNL<sub>max</sub></th><th>L<sub>eq</sub> (A)<br>(PNdB)</th><th></th><th></th></tr></thead><tbody><tr><td>1</td><td>A</td><td>×1.26</td><td>×0.63</td><td>1.62</td><td>S2</td><td>11.0</td><td>D1</td><td>87.9</td><td>65.0</td><td>f</td><td>1.63 ± 4.91</td></tr><tr><td>2</td><td>A</td><td>×1.26</td><td>×0.63</td><td>1.64</td><td>S2</td><td>11.0</td><td>D1</td><td>87.9</td><td>65.1</td><td>f</td><td>4.46 ± 4.14</td></tr><tr><td>3</td><td>A</td><td>×1.26</td><td>×0.63</td><td>0.75</td><td>S1</td><td>12.5</td><td>D1</td><td>88.9</td><td>65.2</td><td>m</td><td>2.37 ± 4.31</td></tr><tr><td>4</td><td>A</td><td>×1.26</td><td>×0.63</td><td>1.62</td><td>S2</td><td>11.0</td><td>D1</td><td>89.3</td><td>65.3</td><td>o</td><td>2.12 ± 4.32</td></tr><tr><td>5</td><td>A</td><td>×1.6</td><td>×0.63</td><td>2.30</td><td>S3</td><td>11.0</td><td>D1</td><td>88.1</td><td>65.1</td><td>f</td><td>0.10 ± 5.28</td></tr><tr><td>6</td><td>A</td><td>×1.6</td><td>×0.63</td><td>2.30</td><td>S3</td><td>11.0</td><td>D1</td><td>88.2</td><td>65.0</td><td>f</td><td>4.13 ± 4.19</td></tr><tr><td>7</td><td>A</td><td>×1.6</td><td>×0.63</td><td>2.30</td><td>S3</td><td>11.0</td><td>D1</td><td>88.4</td><td>65.1</td><td>o</td><td>2.20 ± 4.75</td></tr><tr><td>8</td><td>A</td><td>×1</td><td>×0.8</td><td>1.58</td><td>S2</td><td>21.0</td><td>D2</td><td>86.1</td><td>65.1</td><td>o</td><td>0.95 ± 4.69</td></tr><tr><td>9</td><td>A</td><td>×0.8</td><td>×1.26</td><td>0.86</td><td>S1</td><td>40.0</td><td>D4</td><td>84.0</td><td>64.9</td><td>f</td><td>1.31 ± 4.03</td></tr><tr><td>10</td><td>A</td><td>×0.8</td><td>×1.26</td><td>0.89</td><td>S1</td><td>43.0</td><td>D4</td><td>83.0</td><td>65.0</td><td>f</td><td>3.07 ± 3.85</td></tr><tr><td>11</td><td>A</td><td>×0.8</td><td>×1.26</td><td>1.51</td><td>S2</td><td>40.0</td><td>D4</td><td>83.2</td><td>65.1</td><td>m</td><td>0.04 ± 4.47</td></tr><tr><td>12</td><td>A</td><td>×0.8</td><td>×1.26</td><td>2.29</td><td>S3</td><td>40.0</td><td>D4</td><td>83.3</td><td>64.9</td><td>m</td><td>1.10 ± 4.30</td></tr><tr><td>13</td><td>A</td><td>×0.8</td><td>×1.26</td><td>0.88</td><td>S1</td><td>44.5</td><td>D4</td><td>83.3</td><td>65.1</td><td>o</td><td>0.31 ± 5.03</td></tr><tr><td>14</td><td>A</td><td>×1</td><td>×1.26</td><td>0.80</td><td>S1</td><td>28.5</td><td>D3</td><td>85.2</td><td>65.4</td><td>o</td><td>1.60 ± 4.19</td></tr><tr><td>15</td><td>A</td><td>×1</td><td>×1</td><td>0.75</td><td>S1</td><td>20.0</td><td>D2</td><td>86.3</td><td>65.1</td><td>m</td><td>2.36 ± 3.95</td></tr><tr><td>16</td><td>A</td><td>×1</td><td>×1</td><td>1.10</td><td>S1</td><td>23.5</td><td>D2</td><td>86.7</td><td>65.1</td><td>o</td><td>1.63 ± 3.64</td></tr><tr><td>17</td><td>B</td><td>×0.63</td><td>×0.63</td><td>0.74</td><td>S1</td><td>35.0</td><td>D4</td><td>83.0</td><td>66.0</td><td>f</td><td>-0.14 ± 4.54</td></tr><tr><td>18</td><td>B</td><td>×0.63</td><td>×0.63</td><td>0.73</td><td>S1</td><td>35.0</td><td>D4</td><td>83.9</td><td>66.1</td><td>f</td><td>3.05 ± 4.60</td></tr><tr><td>19</td><td>B</td><td>×0.63</td><td>×0.63</td><td>0.73</td><td>S1</td><td>35.0</td><td>D4</td><td>83.3</td><td>66.0</td><td>o</td><td>0.99 ± 4.64</td></tr><tr><td>20</td><td>B</td><td>×0.8</td><td>×0.63</td><td>1.35</td><td>S2</td><td>28.5</td><td>D3</td><td>84.1</td><td>66.0</td><td>f</td><td>0.34 ± 4.41</td></tr><tr><td>21</td><td>B</td><td>×0.8</td><td>×0.63</td><td>1.37</td><td>S2</td><td>28.5</td><td>D3</td><td>85.4</td><td>66.0</td><td>f</td><td>2.60 ± 5.23</td></tr><tr><td>22</td><td>B</td><td>×0.8</td><td>×0.63</td><td>2.25</td><td>S3</td><td>30.0</td><td>D3</td><td>83.3</td><td>66.0</td><td>m</td><td>-0.83 ± 4.60</td></tr><tr><td>23</td><td>B</td><td>×0.8</td><td>×0.63</td><td>1.36</td><td>S2</td><td>28.5</td><td>D3</td><td>84.1</td><td>66.0</td><td>o</td><td>0.28 ± 4.42</td></tr><tr><td>24</td><td>B</td><td>×1</td><td>×0.63</td><td>1.48</td><td>S2</td><td>20.0</td><td>D2</td><td>85.4</td><td>66.1</td><td>f</td><td>0.31 ± 4.68</td></tr><tr><td>25</td><td>B</td><td>×1</td><td>×0.63</td><td>1.43</td><td>S2</td><td>19.0</td><td>D2</td><td>85.4</td><td>66.3</td><td>f</td><td>1.88 ± 4.59</td></tr><tr><td>26</td><td>B</td><td>×1</td><td>×0.63</td><td>2.30</td><td>S3</td><td>20.0</td><td>D2</td><td>85.6</td><td>66.2</td><td>m</td><td>0.47 ± 4.03</td></tr><tr><td>27</td><td>B</td><td>×1</td><td>×0.63</td><td>1.48</td><td>S2</td><td>20.0</td><td>D2</td><td>85.7</td><td>66.3</td><td>o</td><td>0.25 ± 5.03</td></tr><tr><td>28</td><td>B</td><td>×1</td><td>×1</td><td>0.75</td><td>S1</td><td>33.5</td><td>D3</td><td>83.5</td><td>66.3</td><td>o</td><td>3.28 ± 3.28</td></tr></tbody></table>

also checked that a Ward's clustering of the subjects' ratings did not show any particular grouping of the subjects: no subject was rejected.

## 4. Test 1

T1 focused on the temporal aspects of the flyover noises, and their effect on the perceived unpleasantness.

### 4.1. Method

#### 4.1.1. Stimuli and semantic scales

From an initial set of 150 synthesised noises (Section 3.1.1), 10 noises were selected (called “original” or “o”) for their typical values of duration and slope<fnref n="4" />. Eighteen further signals were generated, either changing the amount of fluctuation (“f”) or the slope and duration (“modified” or “m”). Twenty-eight stimuli were eventually used in T1. Figure 6 shows the experimental design of T1: “o” signals are represented with boxed numbers, “f” signals with underlined numbers, and arrows connect “m” signals to their “o” version. According to the distribution of the stimuli on the duration/slope plane, we define the categories of

<caption>Figure 6. (Colour online) Experimental design for T1. Stimuli are represented in the duration/slope plane. Green circles are used for F1-stimuli, black crosses for F2-stimuli, purple upward-triangles for F3-stimuli. The dashed arrows link original stimuli (boxed numbers) to the corresponding modified stimuli (other numbers). The signals modified in amount of fluctuation are underlined.</caption>

duration D1 (duration $D < 16$ s), D2 ($16s < D \le 25$ s), D3 ($25s < D \le 34$ s), D4 ($D > 34$ s), and the categories of slope S1 (slope $S < 1.2$ PNdB/s), S2 (1.2 PNdB/s < $S \le 1.8$ PNdB/s), S3 (1.8 PNdB/s < $S$). Table I summarises the characteristics of the stimuli of T1.

In order to discard the effects of global noise level on the unpleasantness and to concentrate on the temporal aspects

<figure><img src="image_7.png" /></figure>

<footnote n="4">⁴ Note that the signals named “o” in this paper are re-synthesised sounds of original recordings.</footnote>
only, the stimuli were equalised to a level of 85 EPNdB (without tone correction), which is typical of the noise level measured for a take-off at approximatively 3 km from a runway, corresponding to the distance where the recordings were made and to the approximate distance of the closest inhabited airport neighbourhoods.

In addition to the 3 temporal factors investigated here (slope, duration, amount of fluctuation), the perceived fly-over speed was assessed. This parameter has indeed been shown to be perceptually relevant [24], even if speed and duration are correlated here. According to a previous study about verbal descriptors of aircraft noise [24], the 5 scales of the semantic differential were labelled as follows:

* "Steady" vs. "Fluctuating" (original French "Régulier" vs. "Saccadé");

* "Slow" vs. "Fast" (original French "Lent" vs. "Rapide");

* "Sudden" vs. "Gradual" (original French "Soudain" vs. "Progressif");

* "Long" vs. "Short" (original French "Long" vs. "Court");

* "Not unpleasant at all" vs. "Extremely unpleasant" (original French "Pas du tout désagréable" vs. "Extrêmement désagréable").

In the following, the second label (italicised) will be used to refer to each semantic scale, e.g. the scale *steady* vs. *fluctuating* will be referred to as *fluctuating*. *Unpleasant* will be used instead of *extremely unpleasant*. The words "scale" or "adjective" will be used interchangeably.

### 4.1.2. Subjects

Thirty-four subjects (18 female, 16 male, mean age 28.5, standard deviation 12.2) took part in the experiment (mean duration 51 min.). Each participation was financially rewarded. All subjects had a normal hearing (thresholds below 20 dB H.L. between 125 and 8000 Hz).

## 4.2. Analysis

### 4.2.1. Principal component analysis

For each of the 28 stimuli, the ratings on the 5 scales were averaged over the 34 subjects. A principal component analysis (PCA) was carried out from this average rating of each stimulus on each of the 5 scales. The first 2 components explain 87.5% of the variance. They were rotated with the VARIMAX method [43]. Figure 7 shows the projection of the 5 adjectives (black lines) and 28 stimuli (pink triangles for F1, black crosses for F2, green circles for F3) on the component 1/component 2 plane. There seems to be no difference between original and modified (slope and duration) noises since original and modified noises are quite close in the perceptive space (at the level F2, black crosses).

*Observations on the projection of the stimuli on the axes of the PCA* First, the categories of duration and the ratings on the scale *short* are consistent: D1 (resp. D4) stimuli tend to be rated as “short” (resp. “long”). Listing the pairs of stimuli within which the duration increases while the

<figure><img src="image_8.png" /><figcaption>Figure 7. T1, PCA: Projection of the stimuli, adjectives and physical descriptors on the component 1/component 2 plane. The stimuli selected for T2 are overlined. Original (i.e. without modification of slope, duration or amount of fluctuations) are boxed. Stimuli with modified amount of fluctuations (levels F1 and F3) are underlined.</figcaption></figure>

slope and amount of fluctuation are constant shows that in 29 cases out of 38 (76%), an increase in duration provokes an increase in the mean judgement of *short* (mean “perceived duration”).

Second, the categories of slope are not particularly consistent with the axis *gradual*. Listing all pairs of stimuli with increasing slope and constant duration and amount of fluctuation, one observes that in only 5 cases out of 22 (23%), an increase in slope provokes an increase in the mean judgement of *sudden*. In 6 (27%) other cases there is no change in the judgement of *sudden*. In the 11 (50%) remaining cases, a slope increase results in a decrease in the judgement of *sudden*. A slope increase is not clearly perceived as an increase of “suddenness”.

Third, there is a good agreement between the categories of amount of fluctuation and their perception. With only a few exceptions, stimuli at levels F1, F2 and F3 are well sorted along the *fluctuating* axis. Furthermore, F3-stimuli are well separated from F1- and F2-stimuli.

*Adjectives and acoustic characteristics* The axes *short*, *fast* and *gradual* are very well correlated with one another, and with component 1. This suggests that those 3 aspects describe similar sensations. The high correlation between *fast* and *short* (*r* = 0.82**) is not surprising: A fast flyover naturally produces a short noise. Both the natural experience of the listeners and the way of creating the stimuli explain it. In the following we will thus discard the flyover speed and investigate the duration instead. The descriptor that maximises the correlation with the mean rating on the scale *short* is the duration DUR (as defined in Section 2): *r* = -0.75**.
At first sight, the correlation between short and gradual (r = -0.58**) and between fast and gradual (r = -0.68**) is surprising, because in this study slope and duration were made independent. This independence does not correspond to the common sensory experience of listeners for aircraft flyover noises, hence noises with the most unnatural modifications (e.g. with a long duration and a steep slope) may have challenged the way the subjects evaluate the duration and the slope. People know ("real-life" experience), consciously or unconsciously, that fast passing-by airplanes have very steep level variation (i.e. are sudden): the subjects have produced a judgement of sudden which is correlated with the judgement of duration (again r = -0.58** between short and gradual, and r = 0.44** between gradual and the duration). As a consequence, it can be stated that although the slope and duration of the stimuli have been decorrelated on a physical basis, they are still perceptually correlated. The evaluation on the scale gradual can be considered as a judgement of duration, and not as a judgement of slope. The correlation between gradual and the slope (r = -0.06, not significant) confirms it. The "declining slope" (linear regression on the PNL computed between the times t₀ and t₂ of Figure 1) better correlates with gradual (r = 0.65**): The higher the declining slope (note that a high declining slope is negative and close to 0), the longer the aircraft receding phase and the more gradual the perception. This is in line with the previous interpretation assimilating the evaluation of slope to an evaluation of duration.

Very close to component 2, fluctuating can be considered as independent of short, fast and gradual. The fluctuation strength [44] is conventionally used as a descriptor of periodic amplitude modulation. Sontacchi's implementation [45] accounts for non-periodic amplitude modulation and has been used in this study<fnref n="5" />: The fluctuation strength is quite well correlated with fluctuating (r = 0.66**), as shown in Figure 7. We introduce a new descriptor, in order to better correlate with the perceived amount of fluctuation. In this study the modulation depth is the parameter controlling the amount of fluctuation. It is thus quite natural to describe the fluctuations as oscillations around a "smoothed" (i.e. without non-periodic amplitude modulation) PNL curve. The proposed computation method for a new descriptor called "FLUC" (illustrated in Figure 8) is:

1. Compute the PNL of an aircraft noise (written y, digitised signal with N samples);

2. Compute the "smoothed" PNL $\bar{y}$ by application of a 3-point average filter: $\bar{y}_n = \frac{y_{n-1} + y_{n} + y_{n+1}}{3}$ where n is the current sample;

3. Define FLUC as the root mean square error (RMSE) between y and $\bar{y}$:

$$FLUC = \sqrt{\frac{\sum_{i=1}^{N} (y_i - \bar{y}_i)^2}{N}} \quad (1)$$

<figure><img src="image_9.png" /><figcaption>Figure 8. (Colour online) PNL of the stimulus (red solid line) and corresponding "smoothed" PNL (black dotted line) of an aircraft noise. The filtering method uses 3-point average.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 9. (Colour online) T1: Descriptor FLUC (big markers and font size) and fluctuation strength (small markers and font size) as a function of the rating of fluctuating (r = 0.87**, and r = 0.66** respectively). The solid lines are the linear regression (thick line, R² = 0.75 for FLUC; thin line, R² = 0.42 for the fluctuation strength). A colour-code is used for the different amounts of fluctuation. The numbers correspond to the stimuli numbers.</figcaption></figure>

As Figure 7 shows, the descriptor FLUC is very well correlated<fnref n="6" /> with fluctuating (r = 0.87**). Note that the definition of the levels F1, F2 and F3 made the perception of the amount of fluctuation categorical, as well as the FLUC values: F1- (0.09<FLUC<0.19), F2- (0.16<FLUC<0.24) and F3- (0.26<FLUC<0.35) stimuli are clearly separated in Figures 7 and 9. Even if FLUC is well-adapted for the stimuli of the present study, it is impossible to conclude about the quality of this descriptor for continuous variations of fluctuation. Further tests should consider amounts of fluctuation varying continuously in order to conclude about the relevance of FLUC. Furthermore, in this study the fluctuations are generated by changing only the depth of non-periodic amplitude modulations. Other effects of the turbulence, such as its temporal evolution or the frequency of modulation have not been studied here: future definitions of FLUC should be enhanced accordingly. Fig-

<footnote n="5">⁵ Note that other indicators of non-periodic amplitude modulation have not been tested in this study.</footnote>

<footnote n="6">⁶ Note that also 5- and 7-point average filters were computed, as well as 3-, 5- and 7-point median filters. As an alternative to the computation of the RMSE, the count of the crossings between y and $\bar{y}$ was computed. None of these solutions gets better correlation with fluctuating.</footnote>
ure 9 also presents a comparison between FLUC and the fluctuation strength: the trends are similar, but linear regression calculation confirms that FLUC is better adapted than the fluctuation strength to account for the judgement of fluctuating.

*Fluctuating* and *unpleasant* are well correlated (r = 0.74**): the unpleasantness can be expected to be partly explained by the judgement of fluctuations. *Gradual* and *unpleasant* are less correlated (r = -0.54**); *short* and *unpleasant* are not correlated (r = 0.11): It seems that the relationship between the duration (or suddenness) and the unpleasantness is not as simple as the relationship between the fluctuations and the unpleasantness.

### 4.2.2. ANOVA

An analysis of variance (ANOVA) allows us to investigate the relationship between the unpleasantness and the temporal aspects in more details. Section 4.2.1 showed that the amount of fluctuation is clearly correlated with the unpleasantness, but the experimental design is incomplete and does not allow us to carry out an ANOVA with this factor. The ANOVA considered the remaining effects only: slope and duration.

A 3 (slopes S1, S2 and S3) × 4 (durations D1, D2, D3 and D4) repeated-measures ANOVA was run with the individual unpleasantness ratings of all F2-stimuli (in black in Figure 6). In order to run the ANOVA, only one value has to be kept for each combination of factors (each cell in Figure 6). Paired t-tests showed no significant difference in the unpleasantness ratings of 2 stimuli in the same cell, so the mean unpleasantness rating of stimuli 15 and 16 (respectively 27 and 8, 14 and 28, 19 and 13) was used for the combinations of factors S1D2 (respectively S2D2, S1D3 and S1D4).

According to the ANOVA, neither the slope (F(2,66) = 2.55, p = 0.09) nor the interaction slope × duration (F(6,198) = 1.23, p = 0.30) has a significant<fnref n="7" /> effect on the unpleasantness. Only the duration has a significant influence (F(3,99) = 6.49, p<0.001) on the unpleasantness. HSD post-hoc tests show that D1-stimuli (mean unpleasantness rating 2.23) are significantly more unpleasant than D3 (0.10) and D4 (0.60).

### 4.2.3. Regression

Previous sections showed that the amount of fluctuation and the duration have a significant influence on the unpleasantness. FLUC and DUR are the best indicators for these factors, and are not correlated with one another (r = -0.01). A linear regression on the unpleasantness (averaged across subjects) was thus computed with FLUC and DUR as the explanation variables. The regression model (adjusted R² = 0.72, F(2,25) = 35.47, p<0.001) shows that the amount of fluctuation (coefficient = 15.86, standardised coefficient = 0.79, t(25) = 7.74, p<0.001) contributes to the unpleasantness 2.4 times more than the duration (coefficient = -0.04, standardised coefficient = -0.33, t(25) =

<figure><img src="image_11.png" /><figcaption>Figure 10. (Colour online) T1: Mean value (crosses) ± 1 standard deviation (circles) of PNL<sub>max</sub> (blue, solid) and unpleasantness ratings (brown, dashed), arranged by category of duration (D1 to D4).</figcaption></figure>

-3.22, p<0.001). Negative coefficients for DUR indicate that the shorter the noise, the more unpleasant the rating.

### 4.2.4. Interpretation

Shorter aircraft noises were perceived as more unpleasant. This apparently contradicts the intuitive interpretation, stating that a shorter noise would be less unpleasant than a longer one. There is no doubt that the subjects were able to evaluate the duration: a) no subject reported having experienced issues when evaluating the duration, and b) the judgement of *short* corresponds to the duration. The PCA shows that DUR and *unpleasant* are not correlated, suggesting that the duration as an ‘exposure time” does not contribute to the unpleasantness. Yet because of the EPNL equalisation of the stimuli, the duration and the peak level (PNL<sub>max</sub>) are correlated: Shorter signals have higher peak levels than longer signals. This is confirmed by a) an ANOVA on the PNL<sub>max</sub> with the category of duration as a factor (F = 121.7, p<0.001) showing that the mean PNL<sub>max</sub> values for each category of duration significantly differ (blue lines in Figure 10), and b) the good correlation between the PNL<sub>max</sub> and the *short* ratings (r = 0.70**), as Figure 7 shows. This effect is taken into account by the descriptor DUR in the ANOVA and in the regression: Increasing the duration of stimuli equalised according to the overall level decreases the peak level and consequently decreases the unpleasantness rating. This may explain why D1-stimuli are significantly more unpleasant than D3- and D4 stimuli (brown lines in Figure 10). For longer signals (D2 to D4), the effect of the peak level has been presumably compensated by the natural effect of a long exposure to noise, increasing the unpleasantness: In Figure 10, the brown line (mean unpleasantness rating) stops following the blue line (PNL<sub>max</sub>) between D3- and D4-stimuli.

## 5. Test 2

Among the three proposed temporal aspects, it was shown in T1 that only the duration and the amount of fluctuation have an influence on the unpleasantness. T2 re-introduced

<footnote n="7">⁷ In this article, the level for significance is set to α = 0.05</footnote>
the global noise level as a factor, in order to compare its influence on the unpleasantness to those of the duration and of the amount of fluctuation. T2 was a semantic differential test with stimuli from or based on the stimuli of T1.

## 5.1. Method

### 5.1.1. Stimuli

Some stimuli from the experimental design of T1 were selected according to the results of Section 4.2. In Figures 7 and 9, F3 and F2 stimuli were perceived as clearly different, but this was not so clear for F2 and F1 stimuli. Furthermore, for T2 there was the need to handle a reasonable number of stimuli, and to keep the baseline fluctuation level F2. Hence only the fluctuation levels F2 and F3 were kept for T2. For each fluctuation level, stimuli covering the whole variation range of perceived duration (judgment on the scale *short*) were selected. Selected stimuli are overlined on Figure 7. At fluctuation level F2, stimuli 7 and 19 were selected because they have respectively the smallest and highest value for perceived duration. In between those extreme perceived durations, 3 pairs of stimuli were selected: stimuli 3 and 4, 15 and 16, 23 and 22. These pairs of stimuli (see Table I) have the same computed duration (DUR), but different perceived durations. At the fluctuation level F3, stimuli 6, 2, 18 and 21 were chosen because they have the same computed duration as stimuli 7, 4, 19, and 22 respectively. Furthermore, these stimuli are uniformly spread over the axis of perceived duration (*short*).

Informal listening by the authors suggested that differences of 2 and 3 EPNdB were quite easily discriminated. Furthermore, [30] showed that a difference of 3 EPNdB (sometimes 1.5 EPNdB) has a significant influence on the unpleasantness. Although this remains to be tested in further studies, the just noticeable difference in noise level of a whole aircraft flyover noise appears to lie between 1.5 and 3 EPNdB. In order to compare the effect of the noise level with the effect of the temporal aspects, each of the 12 selected stimuli, previously equalised at 85 EPNdB, was presented at 3 different global noise levels:

* L1, the original level reduced by 1.5 EPNdB,

* L2, the original level at 85 EPNdB,

* L3, the original level raised by 1.5 EPNdB.

Thirty-six stimuli were eventually used in T2. The characteristics of the stimuli for T2 are presented in Table II.

The resulting experimental design is presented in Figure 11. Amount of fluctuation, global noise level and duration were the 3 factors of this experimental design, with the unpleasantness as the dependent variable. Therefore the semantic scales for T2 were:

* "Steady" vs. "Fluctuating";

* "Soft" vs. "Loud" (original French "Faible" vs. "Fort");

* "Long" vs. "Short";

* "Not unpleasant at all" vs. "Extremely unpleasant".

<figure><img src="image_12.png" /><figcaption>Figure 11. (Colour online) Experimental design for T2. Stimuli are represented in the duration/amount of fluctuations plane. Blue squares are used for L1-stimuli (global noise level), black crosses for L2-stimuli, red triangles for L3-stimuli.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12. (Colour online) T2, PCA: Projection of the stimuli, adjectives and physical descriptors on the component 1/component 2 plane.</figcaption></figure>

### 5.1.2. Subjects

A new set of 37 participants (19 female, 18 male, mean age 24.5, standard deviation 7.3) with normal hearing took part in T2 (mean duration 59 min.). Each participation was financially rewarded.

## 5.2. Analysis

### 5.2.1. Principal component analysis

A PCA was carried out from the ratings on the 4 scales (averaged over the 37 subjects for each of the 36 stimuli). The first 3 components explain 98.2% of the variance. They were rotated with the VARIMAX method. Figures 12 and 13 show the projection of the 4 adjectives and 36 stimuli on the perceptual planes.

Observations on the projection of the stimuli on the axes of the PCA It is clear from Figures 12 and 13 that L3-stimuli are all on the right side of the axis *loud*, and all
<table><caption>Table II. T2: Characteristics of the 36 stimuli. The unpleasantness ratings are given in terms of mean and standard deviation (37 subjects).</caption><thead><tr><th>Number</th><th>Aircraft</th><th>Duration (s / cat.)</th><th>Fluctuation</th><th>Global noise</th><th>PNL<sub>max</sub> (PNdB)</th><th>L<sub>eq</sub> (A)</th><th>Unpleas. rating</th></tr></thead><tbody><tr><td>2</td><td>A</td><td>11</td><td>D1</td><td>F3</td><td>87.9</td><td>65.1</td><td>3.42 ± 3.71</td></tr><tr><td>2-</td><td>A</td><td>11</td><td>D1</td><td>F3</td><td>86.4</td><td>63.6</td><td>1.86 ± 3.54</td></tr><tr><td>2+</td><td>A</td><td>13.5</td><td>D1</td><td>F3</td><td>89.5</td><td>66.6</td><td>3.73 ± 3.80</td></tr><tr><td>3</td><td>A</td><td>12.5</td><td>D1</td><td>F2</td><td>88.9</td><td>65.2</td><td>1.26 ± 4.09</td></tr><tr><td>3-</td><td>A</td><td>12.5</td><td>D1</td><td>F2</td><td>87.3</td><td>63.7</td><td>0.30 ± 4.19</td></tr><tr><td>3+</td><td>A</td><td>12.5</td><td>D1</td><td>F2</td><td>90.4</td><td>66.7</td><td>2.85 ± 4.14</td></tr><tr><td>4</td><td>A</td><td>11</td><td>D1</td><td>F2</td><td>89.3</td><td>65.3</td><td>0.97 ± 4.43</td></tr><tr><td>4-</td><td>A</td><td>11</td><td>D1</td><td>F2</td><td>87.7</td><td>63.8</td><td>-0.81 ± 4.69</td></tr><tr><td>4+</td><td>A</td><td>11.5</td><td>D1</td><td>F2</td><td>90.8</td><td>66.8</td><td>2.70 ± 3.62</td></tr><tr><td>6</td><td>A</td><td>11</td><td>D1</td><td>F3</td><td>88.2</td><td>65.0</td><td>2.59 ± 3.98</td></tr><tr><td>6-</td><td>A</td><td>10.5</td><td>D1</td><td>F3</td><td>86.6</td><td>63.5</td><td>0.66 ± 4.31</td></tr><tr><td>6+</td><td>A</td><td>11</td><td>D1</td><td>F3</td><td>89.7</td><td>66.5</td><td>4.35 ± 3.35</td></tr><tr><td>7</td><td>A</td><td>11</td><td>D1</td><td>F2</td><td>88.4</td><td>65.1</td><td>2.72 ± 4.15</td></tr><tr><td>7-</td><td>A</td><td>11</td><td>D1</td><td>F2</td><td>86.9</td><td>63.6</td><td>-0.34 ± 4.44</td></tr><tr><td>7+</td><td>A</td><td>11</td><td>D1</td><td>F2</td><td>90.0</td><td>66.6</td><td>2.13 ± 5.29</td></tr><tr><td>15</td><td>A</td><td>20</td><td>D2</td><td>F2</td><td>86.3</td><td>65.1</td><td>0.14 ± 3.99</td></tr><tr><td>15-</td><td>A</td><td>19</td><td>D2</td><td>F2</td><td>84.7</td><td>63.6</td><td>-1.25 ± 4.36</td></tr><tr><td>15+</td><td>A</td><td>20</td><td>D2</td><td>F2</td><td>87.8</td><td>66.6</td><td>2.47 ± 3.81</td></tr><tr><td>16</td><td>A</td><td>23.5</td><td>D2</td><td>F2</td><td>86.7</td><td>65.1</td><td>1.15 ± 4.52</td></tr><tr><td>16-</td><td>A</td><td>23.5</td><td>D2</td><td>F2</td><td>85.1</td><td>63.6</td><td>-0.20 ± 3.79</td></tr><tr><td>16+</td><td>A</td><td>24</td><td>D2</td><td>F2</td><td>88.2</td><td>66.6</td><td>1.15 ± 4.03</td></tr><tr><td>18</td><td>B</td><td>35</td><td>D4</td><td>F3</td><td>83.9</td><td>66.1</td><td>1.37 ± 4.16</td></tr><tr><td>18-</td><td>B</td><td>35</td><td>D4</td><td>F3</td><td>82.3</td><td>64.6</td><td>1.95 ± 3.16</td></tr><tr><td>18+</td><td>B</td><td>35</td><td>D4</td><td>F3</td><td>85.4</td><td>67.6</td><td>3.42 ± 4.17</td></tr><tr><td>19</td><td>B</td><td>35</td><td>D4</td><td>F2</td><td>83.3</td><td>66.0</td><td>-0.04 ± 3.94</td></tr><tr><td>19-</td><td>B</td><td>35</td><td>D4</td><td>F2</td><td>81.8</td><td>64.5</td><td>-0.86 ± 3.29</td></tr><tr><td>19+</td><td>B</td><td>35</td><td>D4</td><td>F2</td><td>84.9</td><td>67.5</td><td>1.53 ± 4.06</td></tr><tr><td>21</td><td>B</td><td>28.5</td><td>D3</td><td>F3</td><td>85.4</td><td>66.0</td><td>1.36 ± 4.71</td></tr><tr><td>21-</td><td>B</td><td>28.5</td><td>D3</td><td>F3</td><td>83.8</td><td>64.5</td><td>1.34 ± 4.52</td></tr><tr><td>21+</td><td>B</td><td>28.5</td><td>D3</td><td>F3</td><td>87.0</td><td>67.5</td><td>1.79 ± 5.30</td></tr><tr><td>22</td><td>B</td><td>30</td><td>D3</td><td>F2</td><td>83.8</td><td>66.0</td><td>0.83 ± 3.33</td></tr><tr><td>22-</td><td>B</td><td>30</td><td>D3</td><td>F2</td><td>82.3</td><td>64.5</td><td>0.13 ± 4.03</td></tr><tr><td>22+</td><td>B</td><td>30</td><td>D3</td><td>F2</td><td>85.4</td><td>67.5</td><td>2.39 ± 3.38</td></tr><tr><td>23</td><td>B</td><td>28.5</td><td>D3</td><td>F2</td><td>84.1</td><td>66.1</td><td>-0.09 ± 4.37</td></tr><tr><td>23-</td><td>B</td><td>28.5</td><td>D3</td><td>F2</td><td>82.6</td><td>64.6</td><td>-1.55 ± 4.45</td></tr><tr><td>23+</td><td>B</td><td>28.5</td><td>D3</td><td>F2</td><td>85.7</td><td>67.6</td><td>2.26 ± 3.60</td></tr></tbody></table>

L1-stimuli are on the left side. The L2-stimuli lie globally in between, with a few stimuli perceived as louder (resp. softer) than some L3 (resp. L1) stimuli.

The judgements on the scale fluctuating (Figure 13) are consistent with the amounts of fluctuation: F2- and F3-stimuli are well separated on this axis.

Similarly, the judgements on the scale short (Figure 12) are quite consistent with the durations: D1-stimuli tend to be on the “short side” of the axis, D4-stimuli on the “long side”, whereas D2- and D3-stimuli tend to be in between.

### Adjectives and acoustic characteristics
The projection of the adjectives clearly shows that components 1, 2 and 3 are related to the *loud*, *short* and *fluctuating* aspects, respectively. The correlation coefficients between adjectives are: r = 0.15 (not significant) between fluctuating and loud, r = -0.29 (not significant) between fluctuating and short, r = -0.02 (not significant) between loud and short. That is to say, the *loud*, *short* and *fluctuating* aspects of the stimuli are perceived as independent of one another.

As in T1, the best descriptor of short is DUR (r = -0.77**). As in T1, the correlation between the fluctuation strength and fluctuating (r = 0.59**), although significant, could be improved. FLUC, introduced in Eq. 1, shows a much better correlation with fluctuating (r = 0.79**). However, this good correlation is to be qualified because the values of FLUC as well as the judgements of fluctuating remain categorical in T2, as Figure 14 shows: again, further tests should consider amounts of fluctuation varying continuously in order to conclude about the relevance of FLUC. Figure 14 also presents a comparison between FLUC and the fluctuation strength: again linear regression calculation confirms that FLUC is better adapted than the fluctuation strength to account for the judgement of fluctuating.

Loud correlates well with the PNL<sub>max</sub> (r = 0.68**) and with the maximum A-weighted sound pressure level L<sub>A,max</sub> (r = 0.89**). However, the descriptor that best correlates with loud is the N5 (r = 0.93**), defined as the
<figure><img src="image_14.png" /><figcaption>Figure 13. (Colour online) T2, PCA: Projection of the stimuli, adjectives and physical descriptors on the component 1/component 3 plane.</figcaption></figure>

loudness exceeded 5% of the time [44]. Inspired by the N5, other descriptors have been tested: The PNL₁₀ (PNL exceeded 10% of the time) and the PNL₅ (PNL exceeded 5% of the time) are also well correlated with *loud* (r = 0.83** and r = 0.80** respectively).

*Unpleasant* is very well correlated (r = 0.86**) with *loud*. The expected prominency of the overall noise level is here confirmed. The correlations between *fluctuating* and *unpleasant* (r = 0.47**), and *short* and *unpleasant* (r = -0.18, not significant) would indicate that the *fluctuating* aspect has a lesser influence on the unpleasantness, and that the *short* aspect has no influence. In the PCA and correlation analysis, the individual evaluations of each subject for a given stimulus on a given semantic scale are not directly taken into account but averaged. This could contribute to minimise the contribution of *short* and *fluctuating* to the unpleasantness. This is addressed in the next section.

### 5.2.2. ANOVA

Since the experimental design is not fully-balanced, an ANOVA was possible on sub-planes only. In order to include as many stimuli as possible, the ANOVA was carried out on the stimuli from cells D1F2, D1F3, D3F2, D3F3, D4F2 and D4F3 of Figure 11. As a consequence, the level D2 was not part of the analysis. Like in T1, some cells (D1F2, D1F3, D3F2) contain several stimuli. According to the results of paired t-tests showing that the unpleasantness ratings of the stimuli in the same cell do not differ significantly, the value given as input to the ANOVA was the mean unpleasantness rating of the stimuli in the same cell.

In the end, a 3 (global noise levels L1, L2 and L3) × 2 (amounts of fluctuation F2 and F3) × 3 (durations D1, D3

<figure><img src="image_15.png" /><figcaption>Figure 14. (Colour online) T2: Descriptor FLUC (big markers and font size) and fluctuation strength (small markers and font size) as a function of the rating of *fluctuating* (r = 0.79** and r = 0.59**, respectively). The solid lines are the linear regression (thick line, R² = 0.63 for FLUC; thin line, R² = 0.35 for the fluctuation strength). A colour-code is used for the different amounts of fluctuation. The numbers correspond to the stimuli numbers.</figcaption></figure>

and D4) repeated-measures ANOVA on the unpleasantness ratings was done. The amount of fluctuation (F(1,36) = 13.03, p<0.001) and global noise level (F(2,72) = 33.28, p<0.001) have a significant influence on the unpleasantness. There is no significant interaction. HSD post-hoc tests show that F3-stimuli (mean unpleasantness rating 2.17) are significantly more unpleasant than F2-stimuli (0.73), and that the levels L1 (0.45), L2 (1.29) and L3 (2.61) are significantly different, higher levels being significantly more unpleasant than smaller levels. The duration (F(2,72) = 3.28, p = 0.045) is hardly significant and HSD tests showed no difference between the categories of duration. The effect of the duration on the unpleasantness has presumably been reduced by the introduction of global noise level differences.

### 5.2.3. Regression

Section 5.2.2 showed that the duration, amount of fluctuation and global noise level have a significant influence on the unpleasantness. Descriptors of these 3 factors (best correlates, respectively DUR, FLUC, N5) were used in a regression model of the unpleasantness (averaged across subjects). These descriptors are not correlated with one another: r = -0.38 for FLUC and DUR, r = -0.33 for N5 and DUR, r = 0.07 for N5 and FLUC. D2-stimuli were not considered here<fnref n="8" />, in order to be consistent with the ANOVA.

The regression model (adjusted R² = 0.80, F(3,32) = 42.46, p<0.001) shows that the N5 (coef. = 0.75, standardised coef. = 0.79, t(32) = 9.37, p<0.001) contributes 3 times as much as DUR (coef. = 0.03, standardised coef. = 0.23, t(32) = 2.52, p = 0.02) to the unpleasantness, and FLUC (coef. = 13.36, standardised coef. = 0.53, t(32) = 6.14, p<0.001) twice as much as DUR. The more fluctuating and/or the louder the noise, the more unpleasant the

<footnote n="8">⁸ The results are the same when including D2-stimuli: the regression model (adjusted R² = 0.80, F(3,32) = 34.06, p<0.001) gives the coefficients 0.78, 0.04 and 13.46 for N5, duration and FLUC respectively.</footnote>
<figure><img src="image_16.png" /><figcaption>Figure 15. (Colour online) T2: Mean value (crosses) ± 1 standard deviation (circles) of PNL<sub>max</sub> (blue, solid) and unpleasantness ratings (brown, dashed), arranged by category of duration (D1, D3 and D4).</figcaption></figure>

rating, which is in line with the results of the previous sections. Yet it also shows that the shorter the noise, the less unpleasant the noise, which is apparently in contradiction with the regression of T1 (Section 4.2.3). An interpretation is given in Section 5.2.4.

### 5.2.4. Interpretation

This section provides an explanation for the apparently contradictory results of the regression models of Sections 4.2.3 (shorter noises are more unpleasant) and 5.2.3 (longer noises are more unpleasant).

As expected, the unpleasantness is mostly explained by the noise level, which we can split into two components: the overall level (described and controlled by the EPNL) and the peak level (described by the PNL<sub>max</sub>, see Figure 15). People's judgement of unpleasantness seems to focus mainly on the overall level: Higher-EPNL noises are clearly more unpleasant (T2). Yet when the overall level is constant (T1), the perception of the peak level seems to contribute to the unpleasantness: With its “negative” contribution to the unpleasantness in the regression, the duration DUR (correlated with the peak level because of the equalisation of the stimuli) allows us to take this effect into account. In the regression model on the unpleasantness for non-constant overall noise level (T2), both overall and peak level effects are taken into account by N5 the descriptor of overall level (r = 0.70** between the N5 and the PNL<sub>max</sub>). The descriptor DUR (no longer correlated with the N5 or PNL<sub>max</sub>) now contributes “positively” to the unpleasantness: It seems to describe an “exposure time” effect, counterbalancing the effect of the noise level.

## 6. Conclusion

The noise level is known to be the acoustical factor having the greatest influence on the unpleasantness of aircraft noise. The other acoustical factors having a known or potential influence on the unpleasantness, can be split into two groups: the temporal aspects and the spectral aspects. This paper reported two perceptual tests aimed at assessing

the influence of the temporal aspects. The first test (T1) focused on temporal aspects only (duration, slope and fluctuations), and the second test (T2) added the global noise level to the investigated factors.

When only temporal parameters are varying (T1), the amount of fluctuation and the duration are well identified by the subjects and are shown to have a significant influence on the unpleasantness. The slope is not perceptually recognised as a slope or a rising time. In our experiment, physically uncorrelated slope and duration are not perceived independently: The evaluation of the slope (scale “Sudden” vs. “Gradual”) is actually an evaluation of duration. Note that other experimental methods and designs (e.g. [34] studying aircraft-like signals with characteristics of military aircraft) can show that much higher slopes have an influence on the unpleasantness. However, in [34] the “onset rate” (corresponding to the “slope” in this article) and the “exposure duration time” (the “duration” in this article) were correlated by construction.

When global noise level variations are added to temporal variations (T2), the amount of fluctuation and the global noise level are found to have a significant influence on the unpleasantness. This is in line with the results of the literature: see e.g. [24, 32] for the fluctuations, and [28, 27] for the noise level.

Regression models for the prediction of the unpleasantness have been derived for each test. Adequate indicators of global noise level, amount of fluctuation and duration have been found and the respective influence of each parameter on the unpleasantness has been assessed. In terms of unpleasantness “sources”, the global noise level is unsurprisingly the most important. The contribution of the fluctuations is important too. The contribution of the duration on the unpleasantness has two complementary aspects:

* The higher peak levels of shorter signals<fnref n="9" /> increase the perceived unpleasantness. The relationship between peak level and duration is due to the equalisation of the stimuli, as discussed by [32];

* Longer noises increase the perceived unpleasantness (this result is in line with those of [34], where low “onset rates” increase the “exposure duration time” and thus the annoyance).

Further tests need to be done, in particular in order to identify significance thresholds (minimal differences in duration producing significant differences in perceived unpleasantness), and to study the possibility of an optimal (presumably intermediate) duration minimising the unpleasantness. For those further studies, both shorter (<10s) and longer (>45s) durations for a single flyover should be investigated (if physically relevant), making e.g. the listener/aircraft distance vary over a larger range. Furthermore, we focused here on single flyovers, whereas the inhabitants of airport neighbourhoods are rather exposed

<footnote n="9">⁹ Emphasised by the equalisation according to the EPNL, this effect also holds for natural non-equalised stimuli because shorter noises are produced by nearer aircraft, necessarily resulting in louder noises.</footnote>
to many flyovers leading to an intermittent but long-term noise exposure. The concept of “duration” may be extended to such long-term noise exposure. Other slope values may also be investigated, in order to generalise our findings. The descriptor FLUC, as defined in this article, has proven relevant for explaining the evaluation of fluctuating. However, the amount of fluctuations as well as the values of FLUC were discontinuous in this study: amounts of fluctuation varying continuously should be investigated in further studies in order to conclude about the relevance of FLUC.

It has been shown that the equalisation of the stimuli leads to introducing a correlation between the peak level and the duration: Further studies should investigate the effect of the duration on the unpleasantness independently of the noise level.

This study focused on take-off procedures with straight, constant-speed trajectories. Further studies should investigate landing procedures, where the jet thrust is likely to be varying, or both take-off and landing procedures with more complex (e.g. non-rectilinear) trajectories.

Parallel studies have been led in order to investigate the influence of spectral parameters [30]. Further work should concentrate on bringing together temporal and spectral aspects as well as global noise level into a unique test, in order to disentangle, compare and rank the respective influences of each factor on the unpleasantness. Interactions between temporal (exposure time, fluctuations) and spectral (buzz-saw noise, tonality) aspects are expected, e.g. hissing components (such as blade passing frequency tones) can be either highlighted in long noises (increased exposure duration) or hidden by fluctuation effects. The identification of parameters other than noise level which contribute to the unpleasantness should eventually lead to new noise abatement strategies, which are easier to implement than pure noise level reduction.

## Acknowledgements

This study was funded by the FRAE (Fondation de recherche pour l'aéronautique et l'espace / Research foundation for aeronautics and space) through the project PARA-SOFT (PsychoAcoustics Research aiming at Assessing SOnic unpleasantness of aircraFT flyovers). The authors warmly thank all the subjects and beta-testers of the tests. Special thanks to Timothy Wofford for his careful proofreading of the manuscript.

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