Estimating Fluctuation Strength for exhaust sound of motorbikes with 1st, 2nd and 3rd fluctuations
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Estimating Fluctuation Strength for exhaust sound of motorbikes
with 1st, 2nd and 3rd fluctuations
Nozomiko YASUI1, and Masanobu MIURA2
1
Graduate School of Science and Technology, Ryukoku University,
1-5, Yokotani, Oe-cho, Seta, Otsu 520-2194, JAPAN
2
Faculty of Science and Technology, Ryukoku University.
ABSTRACT
Our previous study described a procedure for estimating Fluctuation Strength (FS) observing both constant
(called "1st fluctuation") and deviation ("2nd fluctuation") for time and amplitude that were approximately
estimated from only tremolo played on the mandolin. Here, we present a novel procedure for estimating FS
from the exhaust sound of various motorbikes by using new indexes. FS from the exhaust sound is
subjectively compared under two conditions (i) various 2nd fluctuations for a motorbike, and (ii) various
motorbikes for a specified 2nd fluctuation. For (i), we found that our procedure correctly estimated FS, which
was consistent with the study for the mandolin tremolo. For (ii), because the shape of the amplitude envelope
on explosive sounds differs among motorbikes and may affect FS, we need to take this into consideration in
order to correctly estimate FS. Therefore, we added the characteristics for the shape of the amplitude
envelope to the procedure for estimating FS. Specifically, multiple regression analysis was conducted to
estimate FS using subjective evaluation results and indexes, where the indexes for the 1st and 2nd
fluctuations were calculated from the procedure in our previous studies and the indexes for the shape such as
acoustic power, normalized acoustic power, fluctuation depth for rising and falling, slope for rising and
falling, duration for rising and falling and spectral centroid, named as "3rd fluctuation", were newly
calculated. The results showed that the FS for exhaust sounds with various shapes of amplitude envelope was
correctly estimated by considering the 3rd fluctuation.
Keywords: Fluctuation strength, Exhaust sound of motorbikes, 1st fluctuation, 2nd fluctuation, 3rd
fluctuation
1. INTRODUCTION
In our previous study, we developed a procedure for estimating Fluctuation Strength (FS) of a
tremolo produced by irregular plucking of a mandolin [1]. Specifically, the constant fluctuation of a
tremolo elicited with only the average plucking rate was called the “1st fluctuation”, and that elicited
with deviation for time and amplitude was called the “2nd fluctuation”. In the procedure, FS was
estimated using the extracted indexes for the 1st and 2nd fluctuations. However, the study used only
the tremolo, actual noise given by constructions and/or traffics have not yet been employed.
Therefore, we present a novel procedure for estimating FS from the exhaust sound of various
motorbikes by using new indexes.
2. BACKGROUND AND AIM OF THIS STUDY
2.1 Fluctuation Strength
Modulated sounds elicit the sensation of hearing fluctuation. Previous studies represented the
sensation of hearing fluctuation as FS by conducting psychoacoustical experiments [2,3]. FS is elicited
for modulated sounds with a modulation frequency of up to around 20 Hz. The findings were that the
1
n-y@mail.ryukoku.ac.jp
2
miura@rins.ryukoku.ac.jp
1FS from an Amplitude-Modulated broadband noise (AM BBN) with a modulation frequency within
4-8 Hz is larger than that outside this range [2, 3].
Another study computed FS from physical parameters of fluctuating sounds [3-8]. The FS
estimated by extracting characteristics of the fluctuation from acoustic signals was confirmed to
correspond approximately to the sensation of hearing fluctuation. The FS estimated using that
procedure and commercial software for evaluating sound quality were found to represent the
sensation of hearing fluctuation from an AM BBN [4, 8]. However, fluctuating sounds produced at
constructions and/or traffics have not yet been investigated.
2.2 Our Previous Study
In our previous study, we focused on the tremolo as fluctuating sounds produced with musical
instruments and developed a procedure for estimating FS of a tremolo produced by irregular plucking
of a mandolin [1]. The tremolo was characterized by the average plucking rate, as well as the onset and
amplitude deviations. We defined an “ideal performance” as a completely constant performance in
terms of time and amplitude. The onset deviation means deviation from the ideal onset time, defined as
a completely constant inter-onset interval, i.e., the average plucking rate. The amplitude deviation
means deviation from the ideal amplitude defined as completely constant amplitude at the onset time,
where the completely constant amplitude is defined as the maximum level of amplitude.
We investigated a procedure for estimating FS of tremolo with the 1st and 2nd fluctuations by
using the extracted indexes for these fluctuations. The investigations were conducted using
synthesized sounds instead of tremolos from actual performances because the 2nd fluctuations of an
actual performance of professional musicians cannot be completely controlled; therefore, actual
performances were not appropriate for use in this study. Instead, we synthesized tremolos with
various 2nd fluctuations by maintaining the progression tendency in time of the 2nd fluctuations of
sounds performed by musicians. These tremolos are desired to be perceived the sensation of only
hearing fluctuation without timbre being perceived proficiency in producing a tremolo. So, we used
pseudo down-stroke and pseudo up-stroke sounds, not the actual down-stroke sounds, in the
synthesis. We called a synthesized tremolo “imitated tremolo”.
It was confirmed that our procedure using the indexes for the 1st and 2nd fluctuations on the
imitated tremolo approximately represents the sensation of hearing fluctuation (adjusted R2 = 0.77),
which is better than the representation when using only the index for the 1st fluctuation (R2 = 0.58).
However, the study used only the tremolo, actual noise given by constructions and/or traffics have
not yet been employed.
2.3 Aim of This Study
We present a novel procedure for estimating FS from the exhaust sound of various motorbikes by
using new indexes. The exhaust sound consists of various explosive sounds. As well as tremolo used
in our previous study [1], exhaust sounds of motorbikes has not only a constant fluctuation (1st
fluctuation) but also both onset and amplitude deviations (2nd fluctuation). Unlike the tremolo, the
shape of amplitude envelope on an explosive sound is different among motorbikes. So, procedure for
estimating FS from the exhaust sound was investigated under two conditions (i) various 2nd
fluctuations for a motorbike, and (ii) various motorbikes for a specified 2nd fluctuation. In the
procedure for estimating FS, for (i), the indexes for the 1st and 2nd fluctuations were calculated
using the proposed procedure [1]. For (ii), because the shape of the amplitude envelope on explosive
sounds differs among motorbikes and may affect FS, we need to take this into consideration in order
to correctly estimate FS. Therefore, we propose the characteristics for the shape of the amplitude
envelope. So, the indexes for the fluctuation of shape such as acoustic power, normalized acoustic
power, fluctuation depth for rising and falling, slope for rising and falling, duration for rising and
falling and spectral centroid, named as "3rd fluctuation", were newly calculated for (ii). In addition,
subjective scores for fluctuation are estimated using parameters obtained by decreasing dimensions
based on the principal component analysis. Specifically, as well as tremolo used in our previous study
[1], multiple regression analysis was conducted to estimate FS using subjective evaluation results
and indexes for the 1st, 2nd and 3rd fluctuations.
3. SYNTHESIS OF EXHAUST SOUND
To present a novel procedure for estimating FS from the exhaust sound of various motorbikes,
exhaust sounds with various 2nd fluctuations were needed here to appropriately realize various type of
2the sensation of hearing fluctuation because recording the exhaust sounds could not generate various
2nd fluctuation. So, exhaust sounds with various 2nd fluctuation were synthesized by giving
explosive sound exaggerated or suppressed deviations with keeping the trend of deviation in the
actual exhaust sound, as well as the procedure proposed in our previous study [1]. In addition,
because exhaust sound synthesized using actual explosive sound is possible to perceive not only the
sensation of hearing fluctuation but also other features, exhaust sounds with various 2nd and 3rd
fluctuation were synthesized using pseudo explosive sounds, where these pseudo sounds were
synthesized by interpolating a pink noise with envelopes extracted from actual explosive sound. Here,
synthesized exhaust sound used actual explosive sound is called “simulated exhaust sound”, while
the sound used pseudo explosive sound is called “imitated exhaust sound”. To synthesize imitated
exhaust sounds with also various 3rd fluctuations, various pseudo explosive sounds with envelope of
actual explosive sounds produced by different motorbikes were used.
Specifically, onset and amplitude deviations were extracted from an acoustic signal recorded, the
onset deviation named as "ODk" (k = 1 ~ N) and the amplitude deviation named as "ADk", where k
represents the ID of the onset time and N represents the total number of explosive sounds. Then,
these deviations were suppressed or exaggerated using the feature exaggeration method [9]. Next,
these suppressed or exaggerated deviations were set into pseudo explosive sounds, which were
alternately conjoined. Then, because it sometimes happened that duration on pseudo explosive
sounds set exaggerated deviations is shorter than Inter-Onset Interval (IOI) on imitated exhaust
sound, the forward-linear-prediction was conducted for explosive sounds, where optimum order of
Linear Prediction Coefficient (LPC) were decided based on Akaike Information Criterion (AIC). A
procedure for synthesizing imitated exhaust sound is shown in Fig. 1.
Recorded exhaust sound
Extracting onset and amplitude deviations
Extracting five explosive sounds
ODk and ADk
Moving average
Forward-linear-prediction
^ and AD
OD ^
k k
Extracting amplitude envelope by full-wave rectification
Exaggerating onset and amplitude deviation
based on Morita’s method [9]
Interpolating pink noise to amplitude envelope OD'k and AD'k
Selecting pseudo explosive sound at random Imitated exhaust sound
Conjoining imitated explosive sounds
Figure 1 – Procedure for synthesizing imitated exhaust sound
4. INVESTIGATION UNDER CONDITION (i)
4.1 Experiment Using Magnitude Estimation Method
To obtain the subjective scores for sensation of hearing fluctuation from simulated exhaust sounds
with various 2nd fluctuations for a motorbike, we conducted magnitude estimation experiment with
five listeners in a soundproof room.
Stimuli were a total of 32 simulated exhaust sounds with onset and amplitude deviations on each
explosive sound (4 deviation patterns for the onset deviation × 4 deviation patterns for the amplitude
deviation × 2 types of motorbikes). Used motorbikes were GrassTracker (SUZUKI MOTOR
CORPORATION) and SR400 (Yamaha Motor Co., Ltd.). For each motorbike, these sounds were
synthesized based on the method described in chapter 3. Pairs of stimuli were presented to the listeners
on each motorbike. A number (e.g. 100) representing the magnitude of fluctuation was assigned to the
first pair. The listeners were asked to rate the fluctuation of the second stimulus within each pair and
compare it to this assigned number. For example, for a decrease in fluctuation by a factor of two, the
3listeners had to write the number 50 on an answer sheet. A stimulus with no deviation was chosen as
the first stimulus of each pair. The stimuli were presented to the listeners through a pair of earspeakers.
Electrostatic earspeakers (SR-303, STAX Ltd.) and an amplifier (SRM-313, STAX Ltd.) were used for
the evaluation. Before the experiment, each listener was allowed to adjust the acoustic sound level to
one that best enabled him or her to listen to the amplitude-modulated sounds. The average level was
about LA = 53.0 dB.
4.2 Analysis for Simulated Exhaust Sound
To investigate whether or not the proposed procedure [1] can apply to not only tremolo but also
exhaust sound, as well as our previous study [1], multiple regression analysis was conducted to
estimate FS using subjective evaluation results and indexes for the 1st and 2nd fluctuations.
4.2.1 Extracting the Index for the 1st Fluctuation
To obtain the characteristics of the 1st fluctuation, we extracted a fluctuation component. The
levels of acoustic power of imitated exhaust sounds were equalized. We performed a Fast Fourier
Transform (FFT) for the acoustic signal converted to absolute values. A weighted Band Pass Filter
(BPF) between 1-20 Hz was used to omit signals of other regions of the converted signal in which the
weighted BPF was obtained from the experimental results of Fastl's study [2, 3], which refers to the
sensation of hearing fluctuation for AM SIN and are the same as another study on the calculating
fluctuation quantity [4]. We performed an Inverse Fast Fourier Transform (IFFT) on these results by
omitting the signals, and the Root Mean Square (RMS) of the obtained waveforms was calculated.
4.2.2 Extracting the Indexes for the 2nd Fluctuation
As well as our previous study [1], we calculated the indexes for the 2nd fluctuation based on a
previous method [10]. First, the moving average for onset and amplitude deviations on imitated
exhaust sounds and the deviation trend curves were calculated. Next, the characteristics of the 2nd
fluctuation p2ndi,j (i = 1-2, j = 0-4) were obtained using previous method [10]. The suffix i in p2nd i,j
distinguishes OD (i = 1) or AD (i = 2), and the suffix j in p 2nd i,j distinguishes the represents the ID of
feature parameters of the onset and amplitude deviations.
4.2.3 Multiple Regression Analysis for Simulated Sounds
Multiple regression analysis was conducted to estimate the sensation of hearing fluctuation, in
which the results of magnitude estimation reported in Section 4.1 was used as an objective variable
and parameters obtained by decreasing dimensions based on principal component analysis for the
indexes for the 1st and 2nd fluctuations were used as explanatory variables. As a result, the adjusted
R2 between the evaluation results and scores obtained by using all principal components for indexes
for the 1st and 2nd fluctuation (adjusted R2 = 0.61 for GrassTracker, adjusted R2 = 0.72 for SR400)
are higher than the R2 between the evaluation results and scores obtained by using only the index for
the 1st fluctuation (R2 = 0.34 for GrassTracker, R2 = 0.48 for SR400). So, we found that our
procedure [1] correctly estimated FS, which was consistent with the study for the mandolin tremolo.
5. INVESTIGATION UNDER CONDITION (ii)
5.1 Experiment Using Method of Scheffe's Paired Comparison
To obtain the subjective scores for sensation of hearing fluctuation from imitated exhaust sounds
with various motorbikes for a specified 2nd fluctuation, we conducted subjective evaluation
experiment with five listeners in a soundproof room.
Stimuli were a total of 54 imitated exhaust sounds with onset and amplitude deviations on each
explosive sound (3 deviation patterns for the onset deviation × 3 deviation patterns for the amplitude
deviation × 6 types of motorbikes). Used motorbikes were not only GrassTracker and SR400 but also
CB400ss, FTR (Honda Motor Co., Ltd.), SEROW250 and WR250X (Yamaha Motor Co., Ltd.). For
each specified 2nd fluctuation, these sounds were synthesized based on the method described in
chapter 3. The levels of acoustic power of the stimuli were equalized. The stimuli were presented to the
listeners through a pair of earspeakers same as the experiment described in Section 4.1. Before the
experiment, each listener was allowed to adjust the acoustic sound level to one that best enabled him
or her to listen to the amplitude-modulated sounds. The average level was about LA = 52.1 dB.
The experiment was carried out using the method of Scheffe's paired comparison. For each
specified 2nd fluctuation, pairs of stimuli were presented to the listeners. The two stimuli were
presented one immediately after the other, and listeners were asked to subjectively rate roughness on
4a seven point scale.
5.2 Analysis for Imitated Exhaust Sound
To investigate validity of the novel procedure for estimating FS from the exhaust sound of various
motorbikes by using new indexes, multiple regression analysis was conducted to estimate FS using
subjective evaluation results and indexes for the 1st and 3rd fluctuations.
5.2.1 Extracting the Index for the 3rd Fluctuation
The features of the 3rd fluctuation were extracted. First, the time when the minimum envelope
around every period was estimated from imitated exhaust sounds as the offset time. Then, 9 features,
such as acoustic power, normalized acoustic power, fluctuation depth for rising and falling, slope for
rising and falling, duration for rising and falling and spectral centroid were extracted on each
waveform among offset times. Next, 4 statistical amounts, such as average (AVE) and standard
deviation (SD) and the range (DL) of those features, sum (SUM) of absolute amounts of change on
those feature were calculated. So, 36 indexes for the 3rd fluctuation p3rd l,m(l = 1~9, m = 1~4) were
obtained (9 extracted features 4 kinds of amount of statistics). The p 3rd l,m are listed in Table 1. An
outline of 6 features for form of envelope, such as the fluctuation depth for rising and falling, the
slope for rising and falling, the duration for rising and falling is shown in Fig. 2.
Table 1 – List of p3rd l,m
AVE DL SD SUM
acoustic power p3rd 1, 1 p3rd 1, 2 p3rd 1, 3 p3rd 1, 4
normalized acoustic power p3rd 2, 1 p3rd 2, 2 p3rd 2, 3 p3rd 2, 4
fluctuation depth for rising p3rd 3, 1 p3rd 3, 2 p3rd 3, 3 p3rd 3, 4
fluctuation depth for falling p3rd 4, 1 p3rd 4, 2 p3rd 4, 3 p3rd 4, 4
slope for rising p3rd 5, 1 p3rd 5, 2 p3rd 5, 3 p3rd 5, 4
slope for falling p3rd 6, 1 p3rd 6, 2 p3rd 6, 3 p3rd 6, 4
duration for rising p3rd 7, 1 p3rd 7, 2 p3rd 7, 3 p3rd 7, 4
duration for falling p3rd 8, 1 p3rd 8, 2 p3rd 8, 3 p3rd 8, 4
spectral centroid p3rd 9, 1 p3rd 9, 2 p3rd 9, 3 p3rd 9, 4
Slope for rising Slope for falling
Fluctuation depth for rising Fluctuation depth for falling
Time [s] Time [s]
Duration for rising Duration for falling
:Onset time :Offset time
Figure 2 – An outline of 6 features for form of envelope
5.2.2 Multiple Regression Analysis for Imitated Sounds
Multiple regression analysis was conducted to estimate the sensation of hearing fluctuation, in
which the results of magnitude estimation reported in Section 5.1 was used as an objective variable
and parameters obtained by decreasing dimensions based on the principal component analysis for the
indexes for the 3rd fluctuations were used as explanatory variables. FS from the exhaust sound is
estimated under 4 conditions, Conventional Method (CM), Specified Features (SF), Specified
Statistics (SS) and All Parameters (AP). For condition CM, the index for the 1st fluctuations was
used as an explanatory variable. For condition SF, parameters obtained using the indexes for the 3rd
fluctuations on one of features, for example p3rd 1, m (m = 1~4), were used as explanatory variables.
For condition SS, parameters obtained using those on one of statistics, for example p3rd l, 1 (l = 1~9),
were used as explanatory variables. For condition AP, parameters obtained using all those were used
as explanatory variables.
The R2 and adjusted R2 calculated for each condition are shown in Fig. 3, where the adjusted R2
for condition SF and AP are higher than the R2 for condition CM.
51.0
1 .0 1.0
1 .0
:Condition CM : Condition PM
:Condition CM :Condition SF :Condition SS :Condition AP
R2 or Adjusted R2
0.8
0 .8 0.8
0 .8
R2 or Adjusted R2
0.6
0 .6 0.6
0 .6
0.4
0 .4 0.4
0 .4
0.2
0 .2 0.2
0 .2
00 .0 00 .0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
OD [%] 0 150 300 0 150 300 0 150 300 OD [%] 0 150 300 0 150 300 0 150 300
AD [%] 0 0 0 150 150 150 300 300 300 AD [%] 0 0 0 150 150 150 300 300 300
Figure 3 – Calculated R2 and adjusted R2 Figure 4 – Calculated R2 and adjusted R2 for CM and PM
6. DISCUSSION
The procedure for condition SF and AP, as shown in Fig. 8, correctly estimates FS, which is
greater than the estimation when using the procedure for condition CM. Although the validity of
using the indexes for the 3rd fluctuation is confirmed, the validity of using each feature for form of
envelope on explosive sound is not confirmed. Therefore, we compared the adjusted R2 obtained
using each indexes for the 3rd fluctuation among each of features. As a result, the adjusted R2
obtained using those on normalized acoustic power, fluctuation depth for rising or falling, slope for
rising, or duration for rising were larger than 0.6 on all patterns of 2nd fluctuation. So, multiple
regression analysis was conducted to estimate FS using indexes for the 3rd fluctuation on those
features, using those indexes named as condition Proposed Method (PM). The R2 for condition CM
and adjusted R2 for condition PM are shown in Fig. 4, where the adjusted R2 for condition PM are
higher than the R2 for condition CM. Therefore, we successfully presented a novel procedure for
estimating FS from the exhaust sound of various motorbikes by using new indexes
7. CONCLUSION
We presented a novel procedure for estimating FS from the exhaust sound of various motorbikes by
using new indexes. Our results show that the procedure using specified features for shapes of
amplitude envelope on explosive sound correctly estimates FS. In future work, we plan to estimate
FS based on other 1st fluctuation.
ACKNOWLEDGEMENTS
This study is partly supported by the Grants-in-Aid for Scientific Research from Japan Society for
Promotion of Science (22700112).
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