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Modeling of interior sound field in railway vehiclesSpecial focus on sound transmission between vestibules and saloons
Masters Thesis in the Masters programme in Sound and VibrationATA CAN CORAKCI
STEFAN TOBER
Department of Civil and Environmental Engineering
Division of Applied Acoustics
Vibroacoustics Group
CHALMERS UNIVERSITY OF TECHNOLOGY
Gteborg, Sweden 2009Masters Thesis 2009:11
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Department of Civil and Environmental Engineering
Division of Applied Acoustics
Vibroacoustics Group
CHALMERS UNIVERSITY OF TECHNOLOGY
Gteborg, Sweden 2009
Modeling of interior sound field in
railway vehicles
Special focus on sound transmission between vestibules and saloons
ATA CAN CORAKCI
STEFAN TOBER
MASTER'S THESIS 2009:11
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Cover:
Photography of scale model built for sound field measurements.
Master's Thesis 2009:11
Department of Civil and Environmental Engineering
Division of Applied Acoustics
Vibroacoustics Group
Chalmers University of TechnologySE-41296 Gteborg
Sweden
Tel. +46-(0)31 772 1000
Modeling of interior sound field in railway vehicles
Special focus on sound transmission between vestibules and saloons
Ata Can Corakci, Stefan Tober, 2009
Reproservice / Department of Civil and Environmental Engineering
Gteborg, Sweden 2009
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Acknowledgements
I would like to thank my colleague Stefan Tober for his great friendship and to
express my grateful to our supervisor Wolfgang Kropp, the head of the Department
of Applied Acoustics at Chalmers University, for his great help during our master
thesis work. Thanks to all staff and all my friends in the department for their interest
on our nice train model, and would like to thank everyone who helps us to assembly
the model.
And also want to thank everyone who has great help on our work during the time in
Bombardier Transportation in Vsters.
Can
I would first and foremost like to thank my colleague Can Corakci and our
supervisor Wolfgang Kropp for the fun we had while working on this project.
Wolfgang was a great help for this work in so many ways. He was always willing to
sacrifice some of his valuable time, not only during the day, but also at night and on
weekends. The many Skype-discussions we had, significantly contributed to this
work. Many thanks also to Brje Wijk for his endless help in technical belongings
and for letting me use his workshop. Thanks to all students and staff at applied
acoustics who contributed their part to the great atmosphere at the department.
I am also grateful for the help from the team at Bombardier Transportation, namely
Karl-Richard Fehse, Ulf Orrenius, Anders Frid and Thorsten Kohrs. I appreciated
their valuable inputs during our conference calls. Furthermore, I would like to thank
the rest of the Specialist Engineering team in Vsters for the nice time there. Last but
not least, I would like to express my gratitude to Bombardier Transportation for
giving me the opportunity to work on this project and especially for paying for my
new bike
Stefan
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Contents1. Introduction ...................................................................................... 92. Background ..................................................................................... 10
2.1. Sound distribution in closed rooms ..................................................... 102.2. Sound distribution in long, corridor shaped rooms .......................... 122.3. Brains Bombardier Railway Noise Software .................................... 12
3. Scale model ...................................................................................... 143.1. Scaled sound source ................................................................................ 163.2. Microphones ............................................................................................ 193.3. Microphone rack 1 .................................................................................. 223.4. Microphone rack 2 .................................................................................. 233.5. Measurement setup ................................................................................ 253.6. Data post processing ............................................................................... 26
4. Reverberation time measurements .............................................. 284.1. Motivation ................................................................................................ 284.2. Setup ......................................................................................................... 284.3. Reverberation time measurement using MATLAB ........................... 294.4. Results ....................................................................................................... 30
5. Sound field measurements ........................................................... 335.1. Influence of absorption on sound decay .............................................. 37
5.1.1 Measurement in empty scale model...................................................385.1.2 Measurement with absorption on ceiling ..........................................395.1.3 Measurement with absorption on seats and ceiling (as in Regina)405.1.4 Measurement with absorption on seats and ceiling and two toilet
rooms ......................................................................................................415.1.5 Summary influence of absorption on sound decay ......................42
5.2.
Influence of screen opening area on sound decay ............................. 43
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5.2.1 Measurement with small screen opening ..........................................445.2.2 Measurement with standard screen opening ....................................455.2.3 Measurement with large screen opening ..........................................465.2.4
Summary influence of screen opening area on sound decay ......47
6. Ray tracing method ........................................................................ 48
6.1. Theory ....................................................................................................... 486.2. Odeon ........................................................................................................ 486.3. Simulation ................................................................................................ 506.4. Influence of absorption on sound decay .............................................. 50
6.4.1 Simulation of empty model .................................................................516.4.2 Simulation with absorption on ceiling ...............................................526.4.3 Simulation with absorption on seats and ceiling as in Regina ....546.4.4 Simulation with absorption on seats and ceiling and two toilet
rooms ......................................................................................................556.4.5 Summary influence of absorption on sound decay ......................57
6.5. Influence of screen opening area on sound decay ............................. 586.5.1 Simulation with small screen opening ...............................................586.5.2 Simulation with standard screen opening .........................................596.5.3 Simulation with large screen opening ...............................................616.5.4 Summary influence of screen opening area on sound decay ......63
7. Statistical Energy Analysis (SEA) ................................................ 647.1. Theory ....................................................................................................... 647.2. Implementation Setup of SEA model for Regina ............................ 657.3. Influence of absorption on sound decay .............................................. 69
7.3.1 Simulation of empty scale model........................................................707.3.2 Simulation with absorption on ceiling ...............................................717.3.3 Simulation with absorption on seats and ceiling (as in Regina) ....727.3.4 Summary influence of absorption on sound decay ......................73
7.4. Influence of screen opening area on sound decay ............................. 747.4.1 Simulation with small screen opening ...............................................747.4.2 Simulation with standard screen opening .........................................757.4.3 Simulation with large screen opening ...............................................767.4.4 Summary influence of screen opening area on sound decay ......77
8. Comparison ..................................................................................... 78
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8.1. Influence of the absorption .................................................................... 788.2. Influence of the Screen opening ............................................................ 808.3. The Regina case ....................................................................................... 82
9. Conclusions: Possible implementation for sound fieldprediction in trains ......................................................................... 869.1. Estimation of sound decay from SEA results ..................................... 869.2. Introducing sound decay by an increased number of subsystems .. 93
Appendix A .......................................................................................... 95Detailed comparison ........................................................................................ 95
Empty .................................................................................................................95Absorption on ceiling ........................................................................................96Small opening .....................................................................................................97Standard opening ...............................................................................................98Large opening .....................................................................................................99Regina ...............................................................................................................100Regina two toilet rooms ...............................................................................101
Appendix B ......................................................................................... 103
Odeon Results ................................................................................................. 103Appendix C ........................................................................................ 109
MATLAB Code SEA model: ......................................................................... 109Appendix D ........................................................................................ 128
Reverberation time measurements using paper-level-recorder .............. 128Appendix E ......................................................................................... 129
Scale model photos ........................................................................................ 129Scale model drawings .................................................................................... 130
Sign convention ................................................................................. 134Bibliography ....................................................................................... 135
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1.Introduction
The sound field in vehicles, in trains as well as passenger cars has become an
important part of the design process over the past years. Knowledge about the sound
perceived by the passenger is not only interesting in terms of avoiding annoyance
from high noise levels; it also helps to build a quality image of a vehicle. In the same
way as an appealing sound in a car can give the passenger a feeling of quality and
maybe even an indication of the purchase price of the car, this can be applied to
trains. Therefore it is desirable for train designers to predict the interior sound field
of their train to be built as early in the design phase as possible. In an early state
sound design measures can be relatively simple and cheap to do where on the otherhand changes to an already built train are mostly very hard to implement and can be
very cost-intensive.
The purpose of this work is to analyze the physics behind the sound distribution in
train interiors to provide a solid base for the implementation of the acquired
knowledge in future prediction tools. This is not particularly easy as the well known
simple theories for sound distribution in regularly shaped rooms can only be used if
a diffuse and evenly distributed sound field can be assumed. For the special case of
rail vehicle interiors, the problem is more complex due to the corridor like shape of
the room. This leads to an uneven distribution of energy and sound decay along thelength of the corridor. For train interiors the sometimes present screens separating
the entrance vestibules from the seating area can have an important effect on the
sound field as well. To describe this in a proper way, a special theory is required to
predict sound distribution inside railway vehicles.
In order to understand the distribution of sound in trains better, a number of
different approaches were used. A scale model of a complete car of Regina, a
regional train built by Bombardier Transportation, has been built for the purpose of
extensive sound decay measurements (360 microphone positions in the train car).Additionally numerical simulation methods, particularly a ray tracing method, and
an analytical method, statistical energy analysis (SEA) have been used to describe the
sound field in the train.
Combining the results of all these different approaches gave a good understanding of
how sound distributes in railway vehicles and led to a suggestion of a simple model
based on statistical energy analysis for future implementation in sophisticated
prediction tools for the sound field in railway vehicles.
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2.Background2.1. Sound distribution in closed rooms
In a regularly shaped room with big enough dimensions to have a sufficiently high
modal density in the frequency range of interest; it is common to describe the sound
field in the room by a statistical model. This model is known as the diffuse field
model. A diffuse sound field is one in which there is an equal energy density at all
points in the room with an equal probability that sound will arrive from any
direction [11].
As the number of modes plays a key role in this definition, it has been calculated for
the saloons of Bombardiers Regina train.
For a room the modal density can be calculated to [10]
3
2
2
4
28 c
Vf
Vfc
Sf
c
Ln i
i
iii
+
+
=
. ( 2.1)
With Libeing the total edge length, Sithe surface area and Vithe volume of the room.
As ni represents number of modes per Hz, this quantity can be multiplied by the 1/3
octave band width to get the number of modes per 1/3 octave band.
Figure 2.1: Number of modes per 1/3 octave band 3 different saloons in Bombardiers Regina
(Saloon 1 and 3 have same size and therefore same modal density)
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As seen in figure 2.1 there is a high number of modes present in the saloons of
Bombardiers Regina train. The number of modes per 1/3rd octave band exceeds 30 for
frequencies greater than 200 Hz.
The eigenfrequencies of a rectangular room can be calculated to2/1
222
2
+
+
=
z
z
y
y
x
xqxqyqz
l
q
l
q
l
qcf . ( 2.2)
0 100 200 300 400 500 600 700 800 900 1000
nx 0 0
0 ny 0
0 0 nz
nx ny 0
nx 0 nz
0 nx ny
nx ny nz
Figure 2.2: Eigenfrequencies 1st class saloon Bombardier Regina
Figure 2.2 shows the eigenfrequencies calculated for the first saloon of Bombardiers
Regina.
Eigenfrequencies denoted nx, ny and nz refer to modes in lateral direction,
longitudinal direction and vertical direction respectively.
The Schrder frequency defined as,
V
Tfs
602000 ( 2.3)
is commonly used to estimate above which frequency the diffuse field model can be
considered valid. It calculates to =sf 180 Hz for the first saloon of Regina as an
example. (T60 = 0.3 s, V = 37m, see section 4)
This and the high number of modes would lead to the conclusion that the diffuse
field model can be considered valid above about 180 Hz for a saloon of Regina, and
that energy should be distributed evenly above this frequency.
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2.2. Sound distribution in long, corridor shaped rooms
Everything said above is only valid for regularly shaped rooms with evendistribution of absorption. When one room dimension is significantly different from
the others, as it usually is the case for trains, the diffuse field model and the
assumption of an even distribution of energy is not valid any more. In such cases
energy decay along the length of the room (the one dimension that is much greater
than the others) can be observed. To describe the sound field in such rooms,
alternative models are required that are able to include the uneven distribution of
energy. Such models have been developed by several authors. Hodgson [20] has
published a review of several of these models. He concluded that some models,
namely Kuttruffs [10] and his own model were predicting the sound field accurately,
whereas others were inaccurate. Redmore [14] published an experimental model
describing the sound decay in corridors already in 1982 and Franzoni [18] presented
an experimental and an analytical model in 1999.
Unfortunately, none of these models considers large internal barriers or
constructions can be found in train interiors. In the case of Bombardiers Regina train,
there are screens separating the entry area from the seating area. These screens cover
the whole cross section of the train except for a 0.75 m wide door opening. It is
believed, that these screens will have a strong influence on the sound field in the
interior of the train. This might be the reason why sound decay models usually used
for empty corridors, like the one from Redmore, are not able to represent the
sound field in train interiors properly.
Therefore a new model describing the sound field in the special case of trains would
be required. This work should help to develop such a model for the use in future
tools for prediction of the sound field in train interiors.
2.3. Brains Bombardier Railway Noise Software
Bombardier Transportation has developed their own in house prediction tool to
describe the sound field in train interiors. This software is an SEA compatible
framework to facilitate an efficient handling of energy input to different cavities
along the corridor based on Redmores corridor model [15]. In the present state of
Brains, the model treats the train interior as a corridor with no internal barriers. It
includes the effect of vestibule screens in a simplified manner in that the coupling
between cavities is reduced in proportional to the reduced open cross section. This is
believed to be the reason why the model does not give satisfying results for trains as
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Bombardiers Regina series, which have screens separating the entry area from the
seating area [1].
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3.Scale modelFor a detailed analysis of the sound field and the spatial sound decay in train
interiors and the evaluation of BRAINS as a prediction tool for spatial sound decay,
extensive measurements were necessary. These measurements should ideally be
performed in a number of different trains with different interior configurations to get
an idea of the influence of variations in geometry and absorption. To achieve this, we
would need access to a number of train cars for a significant amount of time. It
would also be nice to be able to change the interior of a given train (e.g. seating,
screens) or to evaluate the effect of absorption (e.g. the foam layer on the seats) or
screens on the spatial sound decay. All this is not really an option in a real train.
Train down time is usually very expensive and it is obviously not possible to alter
the interior of a train in normal revenue service just for the purpose of sound
measurements.
Therefore we decided to build a scale model of a train car for our measurements. The
model could be placed in the laboratory of Applied Acoustics, so it would be easily
accessible at any time and the interior could be designed flexibly to allow changes
with reasonable effort.
The first thing that needed to be decided was the scaling factor of the model. For the
measurement of air borne sound only, as in our case, a scaling of the geometry by a
certain factor requires a scaling of the wave length by the same factor. If wave
lengths are scaled down, frequencies will be scaled up. So the scaling factor is mainly
determined by the desired frequency range for the measurements. It has been agreed
with Bombardier that 125 Hz to 4000 Hz for full scale measurements would need to
be replicated in the scale model measurements. In order to perform measurements
efficiently, a multi channel measurement system would be desirable. The Hewlett
Packard VXI stations available at Applied Acoustics have a frequency range of 20
kHz, which gives the upper frequency limit for the scale model measurements. This
results in a maximal scaling factor of SF = 20 kHz/ 4 kHz = 5. The lower frequency
limit is determined by the ability of the used noise source. For a scaling factor of 5 the
source needs to produce sufficient power from 5 * 125 Hz = 625 Hz and above.
The model has been built as a 1:5 scale model of a Bombardier Regina, commonly
used in Sweden. With this scaling factor the desired frequency range was achievable
and the model had a length of 4.6m, which is quite long, but still manageable in the
laboratory.
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Figure 3.1: Bombardier Regina
All dimensions for the scale model have been taken from the drawing shown in
Figure 3.1. The paper drawing has been scaled to 1:50 with the help of a photo copier
and all dimensions have been measured from there. (probably not the most accurate
method, but the only one available) With these dimensions a simplified full scale
CAD model has been drawn. The CAD model was then scaled to 1:5 and all wall
thicknesses where adapted to commercially available material dimensions. The
model was built from medium dense fiber board (MDF) and Plexiglas. (Makrolon)
Figure 3.2: Scale model drawing
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Figure 3.3: Photo of scale model (more photos in appendix)
Figure 3.4: Notation for different sections of Regina interior
All sections in the train are referred to as indicated in Figure 3.4 throughout this
report.
3.1. Scaled sound source
It would have been desirable for our measurements to have a noise source with
monopole characteristics. A breathing sphere would have such a radiation
characteristic. One way to approximate this for a certain frequency range is the use of
a so called dodecahedron source. It consists of 12 loudspeaker cones mounted on the
surface of a dodecahedron. This approximates a breathing sphere for frequencies
where the individual loudspeakers radiate with low directivity. Commercially
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available dodecahedron sources intended for room acoustic measurements usually
have a diameter of about half a meter. For our scale model, we would obviously need
something much smaller. As the market did not fulfill our need, we had to build a
source ourselves. With the above mentioned dodecahedron source in mind we triedto utilize the same principle but shrink it as much as possible. This led to a cubical
source of 55mm edge length with 6 pieces 20mm dome tweeters mounted on the
surface.
Figure 3.5: B&K source Type 4292 and homemade Regina source Type 0001
The perfect noise source for our scale model measurements would have no
directivity and a flat power spectrum for frequencies from 630 Hz to 20 kHz. Toevaluate the performance of our real source, we measured its sound pressure at
different angles from 0 to 180 with increments of 15 at a distance of 200mm. The
source was placed on a rotating pole in a semi absorbent environment. For
comparison, also a single tweeter was measured under the same conditions. All
measurements on the source were done with ARTA (commercial software for
acoustical measurements) and a Creative E-MU sound card on a standard laptop
computer. The measurements are not calibrated but the same setup has been used for
all measurements. So they are comparable to each other. The desired frequency
response is indicated in the graphs below (dashed line). A perfect source wouldshow this frequency response for all angles.
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103
104
-70
-65
-60
-55
-50
-45
-40Directivity of the Tweeter
Magnitude[dB]
Frequency
Figure 3.6: Single tweeter SPL at different angles
Figure 3.6 above shows the results for the single tweeter. The frequency responsemeasured for different angles shows strong deviations (~4dB@5kHz and 30) and the
radiated sound power is low for frequencies below 2 kHz. This would not be a
desired characteristic for our measurements.
103
104
-65
-60
-55
-50
-45
-40
-35Directivity of Regina Source
Magnitude[dB]
Frequency
Figure 3.7: Regina source SPL at different angles
The measured response of the Regina source shown in Figure 3.7 is much more
similar to the desired response. It shows negligible directivity up to approximately 12
kHz. This proves that the cubical source is much closer to the ideal breathing sphere
as the single dome tweeter. The power output for low frequencies is much higher as
for only one tweeter. (~20dB at 2 kHz) This is due to the improved radiation
impedance when using more tweeters and a passive network that boosts the
electrical input power at about 600 Hz. The electrical network is a 12dB high pass
consisting of 82F and 1mH that has been developed using BOXSIM [19]. The thick
red line in Figure 3.7 shows the average sound pressure over all directions.
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Figure 3.8 shows the input voltage in dBV at the Regina source due to the electrical
network, relative to a case without any electrical network (0dBV).
Figure 3.8: Regina source amplification characteristics of the electrical network
3.2. Microphones
The microphones for our measurements should be scaled down in the same way as
the source. We used very small commercially available electret condensermicrophones from Panasonic. (Type WM60) The microphones have an outer
diameter of 6mm which corresponds to 30mm in full scale and is therefore slightly
bigger than a common 1 microphone. They should be sufficiently small for our
purpose. (d=30mm => k*a=1 at 3600 Hz)
Figure 3.9: Panasonic ECM Type WM60
All microphones have been individually calibrated in an anechoic environment using
the Regina source and a high quality reference microphone (Larson&Davis). Each
microphone was powered by its individual power supply and amplified by the
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matching channel of the later used microphone pre-amplifier (MIC AMP 8.0).
Therefore possible deviations in these components have been calibrated as well. The
microphone in test has been put as close as possible on the reference microphone and
sound from the Regina source has been recorded by an Agilent VXI station. Distancefrom source to both microphones was 250mm. The power spectrum of each test
microphone has been calculated relative to the reference microphone and saved as a
correction vector for individual calibration. This calibration vector, individual for
each microphone, has then been used to correct all scale model measurements.
Figure 3.10 shows the sound pressure level (1/3 octave band) of the Regina sound
source measured with calibrated microphones in an anechoic environment. As seen
in the graph, the microphones measure virtually the same power spectrum for
frequencies up to 10 kHz but show little deviation in the 12.5 and 16 kHz band. This
has later been identified as caused by placing the different microphones not exactly
in the same position while measuring in the anechoic room.
103
104
-10
-5
0
5
10
15
20Comparison of Calibrated Microphones
1/3-Octave Band Center Frequency [Hz]
RefMic
Mic1
Mic2
Mic3
Mic4
Mic5
Mic6
Mic7
Figure 3.10: Comparison of calibrated microphones (anechoic)
To evaluate this closer, all microphones have been measured at the exact same
position in the scale model. Figure 3.11 below shows the result of that measurement.
It shows the sound pressure level measured with different microphones at exactly
the same position and the average of all these measurements. The high frequency
deviation is present in the scale model as well.
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103
104
-20
-15
-10
-5Different microphones in identical position relative to RefMic
1/3-Octave Band Center Frequency [Hz]
SoundPressure
Level
Mic7
Mic6
Mic5
Mic4
Mic3
Mic2
Mic1
AVG
Figure 3.11: Different microphones in identical position in scale model
103
104
-5
-4
-3
-2
-1
0
1
2
3
4
5Correction to average
1/3-Octave Band Center Frequency [Hz]
S
oundPressureLevel
Mic7
Mic6
Mic5
Mic4
Mic3
Mic2
Mic1
Figure 3.12: individual microphone correction
103
104
-25
-20
-15
-10
-5Different microphones in identical position relative to RefMic - average corrected
1/3-Octave Band Center Frequency [Hz]
SoundPressureLevel
Mic7
Mic6
Mic5
Mic4Mic3
Mic2
Mic1
Figure 3.13: Corrected microphones show identical SPL reading
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To correct this deviation, the average of all measurements has been calculated. Then
the difference from each microphone (figure 3.12) to this average has been subtracted
from each microphone. After this procedure every microphone gives exactly thesame result for the measured position. (Figure 3.13) Of course the calibrated relation
from the real value of sound pressure to the one measured by the corrected
microphones is not valid any more after this procedure. But the differences between
the individual microphones have vanished. For our measurements, the differences
between microphones are much more important than the absolute value so we
decided to focus on getting the difference as accurate as possible.
3.3. Microphone rack 1
For measuring the spatial sound decay with all seats in the model a set of six
microphones, hanging from the ceiling, needed to be moved through the train model.
The individual microphones have been mounted to a rack made of 2 mm steel wire.
The rack was hung from a string tied to both end walls of the model. In this way the
rack of microphones could be moved through the train model on a straight line and
with constant distance between the microphones. The microphones hung 1.2m above
ground and had a constant distance of 1m to each other. (Full scale dimensions)
Figure 3.14: Sketch of microphone rack 1 in scale model
(longitudinal section view, scaled dimensions in mm)
Figure 3.15: Sketch of microphone rack 1 in scale model
(cross section view, scaled dimensions in mm)
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Figure 3.16: Microphones on rack 1 in scale model (view through ceiling)
3.4. Microphone rack 2
For measuring the spatial sound decay of the empty scale model (without seats and
toilet room) another microphone rack has been built. With this rack, the microphones
were spread in a 4x3 matrix in the cross section of the train. As we could only use
seven microphones at a time, the train has been measured in two passes. Six
microphones recorded one half of the 4x3 matrix and one was used for comparison
on a mirrored position. For the second pass, the rack was flipped and now measuredthe other six matrix positions plus the one for comparison. Figure 3.17 shows the
microphone rack 2 for both passes. The microphones were placed at 0.5m, 1.0m and
1.5m above ground with a distance of 0.75m to each other. The rack has been used at
30 longitudinal positions with 0.5m and 1.0m between them. (Full scale dimensions)
Figure 3.17: Sketch of microphone rack 2 in scale model
(cross section view, scaled dimensions in mm)
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Figure 3.18: Microphone rack 2 in scale model (position for pass 2)
As the measurements were done in two passes, it might be worth while looking at
the difference between each pass. For that purpose seven and not only 12/2 = 6
microphones have been recorded in each position.
Figure 3.19 shows the difference between the two passes for a number of measured
positions. It has been calculated as the difference of two microphones that end up in
the same position when the rack is flipped. Microphone 7 pass 1 has been subtracted
from microphone 6 pass 2 and microphone 6 pass 1 from microphone 7 pass 2
respectively. The difference is lower than 1 dB and takes into account the
repeatability in positioning of the rack and any change that might be caused by
opening and closing the model to turn the rack around. The differences are
reasonably small, so the method seems to be appropriate.
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103
104
-3
-2
-1
0
1
2
3i i i
1/3-Octave Band Center Frequency [Hz]
Powerspectrum
Figure 3.19: Difference between the two passes
3.5. Measurement setup
Figure 3.20: Block diagram of measurement setup
Figure 3.20 shows a block diagram of the scale model measurement setup. The
signal of seven microphones on a moveable rack and the signal of a static reference
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microphone was amplified by 6dB and then fed to an Agilent VXI station. (VXI
E8408A Mainframe) There the time signal of 9 channels was recorded and handed
over to MATLAB for real time processing. The MATLAB code Trigger Happy Real
Time Version 4.0 written by Patrik Andersson from Applied Acoustics was used tocalculate and plot auto spectra, cross spectra and coherence for each channel. The
excitation signal was random noise produced by the VXI station, amplified by a
NAD 310 series and radiated by the Regina Source Type 0001 described earlier. The
output noise was looped back to input CH1 as a reference.
3.6. Data post processing
103
104
-90
-80
-70
-60
-50
-40
-30
-20
-10
0Raw data
Frequency [Hz]
Voltage(dB)
Mic1
Mic2Mic3
Mic4
Mic5
Mic6
Mic7
Mic8
Figure 3.21: Raw data- transfer functions from Trigger Happy
Figure 3.21 shows the raw data as it was saved by Trigger Happy. It shows the
transfer functions from the electrical output signal (CH1 in Figure 3.20 ) to the input
signal from each microphone. (CH2 to CH9 in Figure 3.20 ) These transfer functions
have been filtered to 1/3 octave bands in the frequency domain. For each of these 1/3
octave bands the power spectrum has been calculated to
xx
f
f
xy SHH *~
22
1
= ( 3.1)
With Hxy being the H1 estimate of the frequency response function and Sxx and Sxy the
averaged auto and cross spectra, respectively.
xx
xy
xyS
SH = ( 3.2)
Then the individual calibration correction was applied to the resulting power
spectrum of each microphone and the data was presented relative to a reference
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microphone located in a corner of vestibule 1. This procedure results in a frequency
response for each microphone as seen in Figure 3.22.
103
104
-30
-25
-20
-15
-10
-5
0Calibrated Microphones rel. to RefMic
1/3-Octave Band Center Frequency [Hz]
Powerspectrum
Mic1
Mic2
Mic3
Mic4
Mic5
Mic6
Mic7
Figure 3.22: 1/3 octave power spectrum of each microphone relative to a static
reference microphone
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4.Reverberation time measurements4.1. Motivation
In order to make scale model and full scale Regina comparable, not only the
dimensions must be scaled properly, also the absorption respectively, the
reverberation time has to be adjusted in a proper way. This means that absorption
has to be introduced to the scale model in a way, which is similar to the spatial
distribution of absorption in full scale Regina. Of course the absorption should also
have similar frequency characteristics. In order to achieve this, different materials
have to be tested in a scale model reverberation chamber.
To measure the absorption coefficients of materials with Kundts tube was not
realistic due to the frequency limit depending on the tube diameter. The desired
frequency range (up to 20 kHz) was not suitable for the Kundts tube that was
available at the department of applied acoustics.
Therefore the scale model reverberant chamber was considered as best choice.
However, it required to divide the saloon 1 with an MDF board from the rest of the
train. With this separation of saloon 1 from the first vestibule we obtained a room
with dimensions of (5.8 x 2.9 x 2.1m, full scale). The room was much smaller than itshould be according to ISO 354 [6], but the room shape and reverberation time of the
empty room are according to the standard
4.2. Setup
After the scale model reverberation room was built, microphones and the
loudspeaker were placed according to ISO standard (ISO 354-1985) [6]. A 3D plot of
the interior setup can be seen in figure 4.1. Eventual leaks were covered with tape
and the room was rearranged with the absorption material under test for each case.
We used the same microphone rack during all the measurements.
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Figure 4.1: Setup of reverberation time measurementsred - first microphone positions, blue - second microphone positions
yellow - first source position, green - second source position
No commercial product was found to do the measurements up to our desired
frequency range, which was 20 kHz. So the same VXI station which was used for all
other scale model measurements in this work was used for the reverberation time
measurements as well. Based on measured frequency response functions, impulse
response functions were calculated and the Schroeder backwards integration [10]
was used to calculate the energy decay. The raw data was processed with the help of
MATLAB.
4.3. Reverberation time measurement using MATLAB
Before we started to do our measurements, we wanted to be sure that the signal to
noise ratio was good to do our measurements properly. This ratio can be seen in the
following figure. The achieved signal to noise ratio of more than 50dB is sufficient for
the measurements.
102
103
-10
0
10
20
30
40
50
60
70
80Signal to noise ratio - RT measurements
1/3-Octave Band Center Frequency [Hz]
Powerspectrum
Source on
Source off
SNR
Figure 4.2: Signal to noise ratio for reverberation time measurements
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For each interior configuration, time signals were recorded with the VXI station from
five microphones mounted on microphone rack 1. Impulse responses were calculated
from the recorded time signal for each microphone position. The energy decay was
obtained from calculated impulse responses by Schroeder backwards integrationmethod. 45 different combinations of source and microphone positions were
measured and averaged to give one reverberation time curve. To get the
reverberation time, the -10dB drop in energy decay was found and extrapolated to
get RT60 for the scale model.
The disadvantage of this method is the limited signal to noise ratio which only
allowed for evaluating the 10 dB drop time. This certainly brings up the question of
how accurate the extrapolated results are. Therefore we have used an old Brel &
Kjaer paper-level-recorder to verify the reverberation time measurements done with
the VXI station and Schroeder backwards integration. The paper-level-recorder
basically plots the sound decay inside the room over time after a source is switched
off. The following table shows a comparison of both methods. The differences are
reasonably small to consider the measurements as correct. Paper plots can be found
in appendix D.
f Paper-level-recorder VXI+MATLAB
125 Hz 1,8 1,8
160 Hz 4,5 4,9
200 Hz 4,0 [4,5-5,5]
Because we wanted to compare this reverberation time with the full scale model, the
time axis needed to be scaled to get RT60 for full size Regina. A reverberation time,
measured in the scale model, of 1 second results to 5 seconds after scaling it back to
full scale. (Scale model 1:5)
4.4. Results
A wide range of materials were measured but the following plots are only showing
those configurations/materials, which at the end were selected to adjust thereverberation time to the one in the Regina train. The following figure shows the
reverberation time of saloon 1 scaled to full scale. The red, dash-dot curve shows the
reverberation time as function of frequency in the Regina train for saloon 1, as it has
been measured by Bombardier [5]. The blue curve called mineral wool 114x39 15mm
seats is the final reverberation time for our scale model (transferred to full scale).
This was the best fit to the reverberation time measured in full scale Regina, which
we could achieve with reasonable effort. 114x39x2cm mineral wool on the ceiling
(570x195x10cm full scale) and 1.5cm thick foam on all seats (7.5cm full scale) was
used to achieve this result.
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It turned out that the absorbing mineral wool on the ceiling was essential to gain
sufficient low frequency absorption but it added too much additional absorption at
higher frequencies. Therefore the mineral wool has been covered with a thin foil to
reduce its absorption for high frequencies. The foil is effective above approximately 1kHz.
102
103
0
1
2
3
4
5
6Reverberation Time
1/3-Octave Band Center Frequency [Hz]
RT10[sec
]
Mineral wool 114x39cm
Mineral wool 114x39cm 15mm seats
Empty Train
Bombardier Regina Measurement
Figure 4.3: Results of scale model reverberation time measurements and reverberation time
measured in full scale Regina
Figure 4.4: Absorber setup in scale model 1.5cm foam and 2cm mineral wool covered with foil
Figure 4.4 shows the absorber setup in our scale model.
The reverberation time curves were used to calculate the absorption coefficients
using Sabines formula. These values were mainly used in our ray tracing model,
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described in section 6, to assign the materials to correspondent surfaces. The
absorption coefficients can be seen in figure 4.5.
102
103
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
absorption coefficient - full scale
1/3-Octave Band Center Frequency [Hz]
absorptioncoefficient
empty
15mm 10seats
mineral 114x39
Figure 4.5: Absorption coefficient of different materials used in ray tracing simulation
black solid MDF walls, blue dash - seat foam, red dash dot mineral wool
Figure 4.6 shows the mean absorption in saloon 1 for different cases. The mean
absorption was used in a statistical energy analysis in section 7 and is also used in
BRAINS.(Mean absorption is the absorption coefficient which the total boundary surface of
the room would need to have to replicate the measured reverberation time)
102
103
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Average Absorption - full scale
1/3-Octave Band Center Frequency [Hz]
averag
eabsorption
Scale model - full abs
Scale model - ceiling abs
Scale model - empty
full scale Regina
Figure 4.6: Average absorption in saloon 1 for different absorber setups
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5.Sound field measurementsDetailed scale model measurements have been performed to investigate parameters
affecting the sound field in train interiors. The sound absorption in the highly
damped saloons and the sound insulation due to vestibule screens is believed to
have a major effect on the sound field. Therefore these parameters have been studied
by measurements. The purpose of the measurements was not only to understand the
sound field in trains better but also to give a solid baseline for judging the quality of
computer models which will be designed and studied in the following sections of
this work.
Before starting with the scale model measurements it was important to know if the
model represents reality appropriately. For this we compared the sound decay
measured in full scale Regina [5] with the decay measured in our scale model of
Regina. The two measurements were unfortunately not directly comparable as the
setup was a bit different. In full scale Regina, the source was placed in Vestibule 2
and in our measurements it was placed in Vestibule 1. As the interior layout is
almost symmetrical this should not result in big deviations. For comparison, the full
scale data is presented similar to our scale model measurements, so the source was
assumed to be in Vestibule 1 for this comparison. The dashed lines in figure 5.1 show
the decay for full scale Regina and the solid lines represent the decay in our scale
model (configuration of the scale model can be seen in section 4.4). The decay rates
are similar. Even though the two measurements are not directly comparable, this
indicates that the scale model represents full scale Regina appropriately and can be
used for further investigations.
0 5 10 15 20-35
-30
-25
-20
-15
-10
-5
0
5Decy comparison - full scale vs. scale model 1:5
length
SPL1/3oct.
scale 250Hz
scale 500Hz
scale 1000Hz
scale 2000Hz
scale 4000Hzscreen
full 250Hz
full 500Hz
full 1000Hz
full 2000Hz
full 4000Hz
Figure 5.1: Comparison sound decay full scale Regina vs. scale model Regina
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For all measurements in the scale model with seats removed, it was possible to use a
floor standing microphone rack as described in section 3.4. With this rack we
measured 12 microphone positions in the cross section at 30 longitudinal positions.
This gives the sound pressure level for a total of 360 different positions in the train asa result. (Figure 5.2a, one layer visible)
For the case with seats in the model the floor standing microphone rack could not be
used. In all these cases, a hanging microphone rack as described in section 3.3 has
been used. With this rack, only positions in one longitudinal line have been
measured as the vestibule screens and the seats interfere with the rack or the
supporting string in other positions. (See figure 3.15 and 5.2b)
a)
b)
Figure 5.2: Microphone positions for different interior setup
a) cases with no seats b) cases with seats
All frequencies shown in the following plots are transformed to full scale. So 1 kHz
in the plots equals 1 kHz in reality. As all measurements have been done in the scale
model, the measured frequencies were actually five times higher than this.The results from all microphones in one horizontal layer (120 of 360 positions) are
shown in figures 5.3 to 5.6. The figures show the sound pressure level in each
microphone position relative to a static reference microphone in Vestibule 1.
(Absorption on ceiling only) The positions of the vestibule screens are indicated by 4
walls in the plots.
Table 1: Microphone positions (full scale) rack 2 no seats
Saloon 1 Vestibule 1 Saloon 2 Vestibule 2 Saloon 3
micPos.(m) mic
Pos.(m) mic
Pos.(m) mic
Pos.(m) mic
Pos.(m)
1 0,28 7 6,44 9 7,79 23 15,75 25 17,24
2 1,20 8 6,68 10 8,25 24 16,25 26 18,22
3 2,20 11 8,74 27 19,23
4 3,21 12 9,24 28 20,23
5 4,20 13 9,74 29 21,23
6 5,20 14 10,25 30 22,23
15 10,75
16 11,24
17 11,75
18 12,25
19 12,75
20 13,25
21 13,7422 14,25
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Table 1 shows the longitudinal positions for all microphones when rack 2 was used.
In cases with seats in the model, where microphone rack 1 had to be used, the first
microphone was placed at 0.5m and all others were spread with a distance of 1.0m
between them. (Full scale dimensions)
05
1 01 5
2 0
0
0 .5
1
1 . 5
2
2 .5
3
-3 0
-2 5
-2 0
-1 5
-1 0
-5
w i d t h
l e n g t h
l o w l a y e r 1 2 5 H z
SPL
1/3oct.
Figure 5.3: Measured SPL for 120 microphone positions 125 Hz 1/3 octave band
(relative to reference microphone)
0 5 10 15 20
0
0.5
1
1.5
2
2.5
3
-30
-25
-20
-15
-10
-5
wi
length
low layer 250Hz
SPL1/3oct.
Figure 5.4: Measured SPL for 120 microphone positions 250 Hz 1/3 octave band
(relative to reference microphone)
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0 510 15 20
0
0. 5
1
1. 5
2
2. 5
3
-30
-25
-20
-15
-10
-5
widt
length
low layer 500Hz
SPL1/3oct.
Figure 5.5: Measured SPL for 120 microphone positions 500 Hz 1/3 octave band
(relative to reference microphone)
0 5 10 15 20
0
0.5
1
1.5
2
2.5
-30
-25
-20
-15
-10
-5
length
low layer 1000Hz
SPL1/3oct.
Figure 5.6: Measured SPL for 120 microphone positions 1000 Hz 1/3 octave band
(relative to reference microphone)
The figures above give a fairly good impression of the sound field in the train
interior, but are somewhat hard to compare for the different cases we measured.
Therefore it has been decided to present the data in 2D plots instead.
We calculated the average sound pressure level for each cross section as the mean
value of the 12 microphones in this cross section. This results in 30 data points along
the longitudinal axis for every 1/3 octave band between 125 Hz and 4000 Hz. For
frequencies as low as 125 Hz where single modes can dominate the sound field in
lateral and vertical direction, this averaging can result in inconsistent values. Figure
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5.3 gives an indication of the lateral sound distribution. This problem can be seen in
some of the following plots. Therefore any conclusions drawn from the plots for
frequencies below about 200 Hz should be treated with care.
The location of the vestibule screens is indicated by vertical lines in each plot. Allshown curves in the plots are shifted in a way to have their maximum values in
vestibule 1, where the sound source was placed. This way, the attenuation along the
longitudinal axes can be easily compared.
5.1. Influence of absorption on sound decay
The spatial decay in a corridor shaped room is mainly caused by absorption of
acoustical energy at its boundaries. In order to investigate the influence of absorption
on the spatial sound decay, different cases have been measured in the scale model ofBombardiers Regina. The first case measured was the almost empty scale model. All
seats and the toilet room have been removed so that only the vestibule screens and
the luggage shelves remained. For the second case, absorption was added to the
ceiling only. Mineral wool was used as an absorber. The mineral wool was 2cm thick
and 39cm (10cm x 195cm in full scale) wide and covered the entire length of each
saloon. (See section 4 for more details) It was covered with plastic foil to reduce the
else present increase of absorption for high frequencies (effective from about 1 kHz).
Having the absorption evenly spread along the longitudinal direction and on the
ceiling only, should not introduce any unwanted effects as diffraction or shielding.This could happen when absorption is introduced by seats with absorbing foam on
them. This is why we have included the seats not until case three where we tried to
replicate the absorption as it is in full scale Regina as close as possible.
No additional absorption material has been added to the vestibules.
Figure 5.7 shows the reverberation time for the different cases as it was measured in
Saloon 1. (See section 4)
102
103
0
1
2
3
4
5
6Reverberation Time - full scale
1/3-Octave Band Center Frequency [Hz]
RT10-fullscale
empty
full abs ceiling+seats
mineral wool ceiling
Figure 5.7: Measured reverberation time with different amounts of absorption (same as Figure
4.3)
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5.1.1 Measurement in empty scale model
0 5 10 15 20-35
-30
-25
-20
-15
-10
-5
0
5Energy in Cross Section - empty (rel to ref mic)
length
averageS
PL1/3oct.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.8: Measured result for empty scale model
The measurement in the empty scale model shows strong influence of the vestibule
screens. For low frequencies, there is no sound decay visible in the saloons and for
high frequencies a slight decay can be seen in the second saloon. This can be
explained by the strong variation in absorption which can be seen in the
reverberation time shown in figure 5.7 as well.
The sound decay from vestibule 1 to saloon 3 is measured to about 13dB at 1 kHz.
Please keep in mind that the plot shows the average SPL in the cross section
calculated from 12 microphone positions. For the 125 Hz 1/3 octave band, this
average might not be a good representation due to the possibility of dominant single
modes which were only picked up by some of the 12 microphones in the cross
section. See also figure 5.3 for an impression of the sound field at low frequencies.
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5.1.2 Measurement with absorption on ceiling
0 5 10 15 20-35
-30
-25
-20
-15
-10
-5
0
5Energy in Cross Sect ion - with Absorption (rel to ref mic)
length
averageSPL1/3oct.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.9: Measured result for scale model with absorption on ceiling
In this case, only the mineral wool absorber described earlier in this chapter has been
used. The resulting reverberation time in saloon 1 is shown in figure 5.7 mineral
wool ceiling. ( sec7.060 T )
When absorption is introduced to the saloons, a slight sound decay can be observed
in the measurements. Nevertheless, the influence of the screens is still dominant over
the decay due to absorption.
With increased absorption the sound decay from vestibule 1 to saloon 3 increases to
about 19dB at 1 kHz.
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5.1.3 Measurement with absorption on seats and ceiling (as in Regina)
0 5 10 15 20-35
-30
-25
-20
-15
-10
-5
0
5SPL along longitudinal line - Regina (rel to ref mic)
length
SPL1/3oct.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.10: Measured result for scale model with absorption as in Regina
When more absorption is added by adding foam covered seats, the sound decay in
the saloon increases significantly. The reverberation time with added seats is roughly
half of the one with mineral wool on the ceiling only. (See figure 5.7, sec3.060 T )
The screens still seem to have a strong effect but it is harder to distinguish between
sound insulation due to screens and the sound decay due to absorption.
With absorption increased further to a level as in real Regina, the sound decay from
vestibule 1 to saloon 3 increases dramatically to about 31dB at 1 kHz.
Please keep in mind that microphone rack 1 was used in this case. Only a single
position has been measured in each cross-section. For low frequencies, single modes
can dominate the sound field and therefore the measured sound pressure can vary
strongly for different positions. The microphone could measure a modal peak in one
position and a dip in another. This might be the reason why the curves for 125 Hz
and 250 Hz are not as smooth as the ones for higher frequencies.
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5.1.4 Measurement with absorption on seats and ceiling and two toilet
rooms
0 5 10 15 20-35
-30
-25
-20
-15
-10
-5
0
5SPL along longitudinal line - Regina - 2 toilets (rel to ref mic)
length
SPL1/3oct.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.11: Measured result for scale model with absorption as in Regina
and a second toilet room (as in Regina variant)
This case was measured as a replica of a Regina variant where there will be two toilet
rooms opposite to each other. The measurement has been performed to investigate if
there is any influence from the resulting narrow corridor.
The results are very similar to the above case with only one toilet room. So the
influence of this configuration on the sound decay can be neglected.
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5.1.5 Summary influence of absorption on sound decay
0 5 10 15 20
-30
-20
-10
0
Measurements - 125 Hz
length
averageSPL1/3oct.
0 5 10 15 20
-30
-20
-10
0
Measurements - 250 Hz
length
averageSPL1/3oct.
0 5 10 15 20
-30
-20
-10
0
Measurements - 500 Hz
length
averageSPL1/3oct.
0 5 10 15 20
-30
-20
-10
0
Measurements - 1000 Hz
length
averageSPL1/3oct.
0 5 10 15 20
-30
-20
-10
0
Measurements - 2000 Hz
length
averageSPL
1/3oct.
0 5 10 15 20
-30
-20
-10
0
Measurements - 4000 Hz
length
averageSPL
1/3oct.
Figure 5.12: Comparison influence of absorption
red solid - empty, blue dashed abs on ceiling, green dash dot abs as Regina
Figure 5.12 shows a comparison for different absorption in the scale model. Theinfluence of absorption on the sound decay can be clearly seen. It can also be noticed,
that the difference in decay between the empty case and the case with absorption on
the ceiling is decreasing with frequency. This can be explained by looking at the
reverberation time measurements for these two cases in figure 5.7. For high
frequencies the reverberation times are similar (diff. ~ 0.5 sec), whereas for low
frequencies the difference is fairly big (diff. ~ 4 sec). Therefore also the decay rate is
similar for high frequencies. The sound insulating effect of the vestibule screens can
be clearly seen as well. This effect will be studied further in the following section.
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5.2. Influence of screen opening area on sound decay
The influence of the screen opening area has been measured in three differentconditions:
1. with wider screens leaving only a gap of 0.31m (full scale),
2. with the Plexi glass screens removed leaving a 1.8m wide gap formed by the
remaining MDF boards and
3. with the standard opening of 0.75m for comparison.
The three conditions are indicated in figure 5.13. Only the screen between Vestibule 1
and Saloon 2 has been changed. All other screens have been left untouched.
Therefore measurements were only done in Vestibule 1 and Saloon 2 as the sound
pressure in other cavities should hardly be affected by these changes. Hence, the
length coordinate in the plots is shown only from 5m to 15m.
The sound pressure level is again shifted to have its maximum value in Vestibule 1 to
ensure ease of comparison. For all the following measurements the scale model was
empty, except for the screens and luggage shelves.
Figure 5.13: Screen opening for three different cases (only right screen has been changed)
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5.2.1 Measurement with small screen opening
5 6 7 8 9 10 11 12 13 14 15-20
-15
-10
-5
0
5Energy in Cross Section - small opening (rel to ref mic)
length
average
SPL
1/3oc
t.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.14: Measured result for empty model with small opening
Figure 5.14 shows the sound pressure measured with small screen opening. The
sound insulation from the screens is with about 10dB at 1 kHz significantly greater
than in the standard case. As the saloons are empty, there is hardly any sound decay
visible.
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5.2.2 Measurement with standard screen opening
5 6 7 8 9 10 11 12 13 14 15-20
-15
-10
-5
0
5Energy in Cross Section - s tandard opening (rel to ref mic)
length
average
SPL1
/3oc
t.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.15: Measured result for empty model with standard opening
The measurement with the standard opening is shown for comparison. The sound
insulation is about 7dB at 1 kHz for this case and therefore less then with the small
opening.
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5.2.3 Measurement with large screen opening
5 6 7 8 9 10 11 12 13 14 15-20
-15
-10
-5
0
5Energy in Cross Section - large opening (rel to ref mic)
length
average
SPL1
/3oc
t.
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 5.16: Measured result for empty model with large opening
With the large screen opening the achieved sound insulation is down to almost 4dB
at 1 kHz.
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5.2.4 Summary influence of screen opening area on sound decay
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct.
Measurements - 125 Hz
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct.
Measurements - 250 Hz
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct.
Measurements - 500 Hz
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct.
Measurements - 1000 Hz
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct
.
Measurements - 2000 Hz
5 10 15-20
-15
-10
-5
0
5
length
averageSPL1/3oct
.
Measurements - 4000 Hz
Figure 5.17: Comparison influence of screen opening
red solid small, blue dashed standard, green dash dot large opening
Figure 5.17 shows a summary of the influence of screen opening area on the sound
field. The results for all cases are quite consistent. There seems to be a strong
dependence of the sound insulation on the screen opening area. The insulation even
for the standard case of a 0.75m wide opening is significant. So the screens should
not be neglected in any model used for predicting the sound field in train interiors
with screens.
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6.Ray tracing method6.1. Theory
In physics, ray tracing is a method for calculating the path of waves or particles
through a system with regions of varying properties of the medium and the
boundaries i.e. absorption, surface impedance. Under these circumstances, wave rays
may bend, change direction or reflect from the surface they hit while propagating.
This aspect is used to understand the sound propagation in space with different
medium characteristics.
It can be explained in the following way; a sound source in space emits sound rays in
all directions. The strength variation of the source gives the directivity pattern of the
source itself. All sound rays travel in a straight line, and when they hit an obstacle,
the rays are reflected, diffracted or scattered according to the geometry of the
obstacle.
When a ray hits an object some of the energy is absorbed by the object in proportion
to the absorption coefficient of the object surface. The energy absorbed is usually
calculated in a way where the incoming energy can be reduced by a factor of 1-,
where is the absorption coefficient of the object.The path of the ray is followed until the total energy of this ray is lower than a
certain level. Each time only one ray can be calculated. When the ray reaches one of
the receivers a result can be calculated with the energy it has at that time at that point
[13].
6.2. Odeon
During our thesis work ODEON was used for the ray tracing method. Before we
started to use the software, 3-D drawings of each model were created with
commercial 3-D software. Then these models were imported to ODEON. Full scale
of the models was investigated with different interior configurations. The interior
details were adjusted for each case to get the same geometry effect as in the scale
model for sound field measurements.
Six different models were simulated and presented in the report for different
frequencies.
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1. Empty train
2. Empty train with absorption on the ceiling
3. Regina train
4.
Regina train with two toilet rooms5. Empty train with small screen opening
6. Empty train with large screen opening
A point source was defined and placed exactly at the same position where the real
source was placed during the measurements.
The overall gain of the point source was set to 90 dB; this gain gave 99dB total power.
Then the materials were assigned to the surfaces and the absorption coefficient and
the scattering coefficient of each material was entered as an input to the software.
The absorption coefficients of the materials were calculated from the scale model
measurements. More details can be found in reverberation time section (section 4).
After the materials were selected and placed to their place, with the help of the
software the estimated reverberation time can be seen, the longest reverberation time
of the room has to be noted and 2/3 of the time should be used as an impulse
response length to simulate it correctly. This is an important parameter, if it is shorter
than 60% of the reverberation time in the room, the T60 cannot be calculated because
the dynamic range of the decay curve is less than 35dB. 33204 rays were used for
each model to have even distribution in the saloons.
Before running the program, the receiver grid has to be defined if a grid response is
wanted. In our work; a pre-defined grid was used which can be created by the
software by just entering the step size and the height of the grid, and a manually
entered 120 receiver positions (multi receiver point) were created to replicate one
layer of the microphone positions used during the measurements (120 of 360
positions). Both responses can be seen in the following part. The positions of the
multi receiver points, grid and the source can be seen on the following figure.
Figure 6.1: Position of the receiver points (blue dots), source (red dot). Height is 1.2m for all
receivers. Distance between the receivers in the first saloon is 1.0 m, 0.5m in the
second saloon and again 1m in the third saloon.
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Figure 6.2: View of the grid which is defined by the software.
Area of each square is 0.5m and at 1,2m height
6.3. Simulation
In the following part the results from the 6 cases are presented in two different plots.
The energy in the cross section for each case with a view of the correspondent train
model can be seen in the first figures. These curves were calculated from the
response of the manually defined receiver points (Figure 6.1). The average soundpressure level was calculated as the mean value of 4 microphones for each
longitudinal position. All curves have been shifted to have their maximum level in
vestibule 1 to allow an easy comparison of the sound decay curves.
The second plot is the response in all grid positions of the whole train. The resolution
of the grid is (0.25m*0.25m) and the height is 1.2m from the floor (Figure 6.2). More
detailed plots of the grid response of the whole train can be seen in Appendix B.
6.4. Influence of absorption on sound decayFirst of all, the influence of the absorption material was investigated. For that reason
the empty train model has been simulated to see the energy decay in the cross
section. In the second case the same size of mineral wool with the same absorption
coefficient as in the measurements was used in the ray tracing model. Lastly we
simulated the Regina train itself with the same interior configuration as in the real
train, and with an extra toilet room.
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6.4.1 Simulation of empty model
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0
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length
averageSPL1/3oct.
Odeon - Energy in Cross Section empty train (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.3: Odeon result - Energy in Cross Section Empty (without any absorption material, seefigure 4.3)
Figure 6.3 shows the average sound pressure over the length axis of the train. All SPL
curves are normalized to the SPL in the vestibule where the source is situated for
ease of comparison. The vertical lines in the plot show the positions of the vestibule
screens in each figure.
The sound reduction for the empty train is mainly due to the screens. For low
frequencies, there is no visible sound decay in the saloons and for high frequencies a
slight decay can be seen in the second saloon. This can be explained by the strong
variation in absorption. The sound decay from vestibule to the third saloon is about16dB for 1 kHz. Figure 6.4 shows the response in all grid positions of the whole train
for 1 kHz. The difference in grey scale represents the sound decay in the train. It gets
lighter when we go further from the first vestibule where the source is situated.
Screens ScreensPoint source Shelf
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Figure 6.4: Odeon result - Grid response SPL of the empty train at 1000Hz (Not normalized to
the SPL in the vestibule)
6.4.2 Simulation with absorption on ceiling
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0
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length
averageSPL1/3oct.
Odeon - Energy in Cross Secti on with Absorption (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.5: Odeon result - Energy in Cross Section with Absorption on the ceiling
Absorption material on the ceiling
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Figure 6.5 shows the case with the absorption material on the ceiling. The calculated
absorption coefficients of the mineral wool from the scale model measurements are
used. As more energy is dissipated in the saloons, less energy reaches to the second
vestibule. The sound decay from vestibule 1 to saloon 3 is about 21dB at 1 kHz whichis bigger than in the empty case. The effect of the absorption material on the ceiling
can be seen in figure 6.6 as well. Presence of the mineral wool on ceiling absorbs
more energy in comparison to the empty case. This can be seen by observing the
difference between the second saloon and the third saloon.
Figure 6.6: Odeon result - Grid response SPL of the train with absorber on the ceiling at 1000Hz
(Not normalized to the SPL in the vestibule)
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6.4.3 Simulation with absorption on seats and ceiling as in Regina
0 5 10 15 20-40
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0
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length
averageSPL1/3oct.
Odeon - Energy in Cross Section with Absorption on seats and ceiling (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.7: Odeon result - Energy in Cross Section with Absorption on the seats and ceiling
(Regina Case)
When more absorption is added to the saloons in form of seats with absorption
material, the sound decay increases further in comparison to the first two cases. The
interior of the train is close to be as similar as possible to Regina train. The measured
absorption coefficient of the 15 mm open cell foam is used for the seats and the same
coefficient for the mineral wool which has been already used in the previous case.
With this setup the reverberation time represents the conditions in full scale Regina
(see section 4.4). The sound decay from vestibule 1 to the end saloon 3 is about 33dB.
Again the figure 6.6 shows the grid response of the whole train. The big difference
can be seen clearly from the vestibule to the end of the train.
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Figure 6.8: Odeon result - Grid response SPL of Regina train with absorber on the seats and the
ceiling at 1000Hz (Not normalized to the SPL in the vestibule)
6.4.4 Simulation with absorption on seats and ceiling and two toilet
rooms
In this case an extra toilet room is placed in the Regina train, the rest stays the same.
The two toilet rooms form a narrow corridor right after the vestibule screens as seen
in figure 6.10. From figure 6.9, an increase in the sound decay can be observed when
it is compared to the case where there is only one toilet room. But then there is a
sudden drop after the toilet rooms (more than the previous case with one toilet
room). This sudden drop has an effect on the sound decay at the end of the train. The
sound decay from vestibule 1 to saloon 3 is 30 dB at 1 kHz for this time. The corridor
effect of adding an extra toilet room can be also seen in figure 6.10.
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0 5 10 15 20-40
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0
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length
averageSPL1/3oct.
Odeon - Energy in Cross Section with Absorption on seats and ceiling and 2 t oilets (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.9: Odeon result - Energy in Cross Section with Absorption on seats and ceiling
and two toilet rooms
Figure 6.10: Odeon result - Grid response SPL of empty train with absorber on the seat and the
ceiling (2 toilet rooms) at 1000Hz (Not normalized to the SPL in the vestibule)
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6.4.5 Summary influence of absorption on sound decay
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0
length
averageSPLoct.
ODEON - 125 Hz
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length
averageSPLoct.
ODEON - 250 Hz
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length
averageSPLoct.
ODEON - 500 Hz
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length
averageSPLoct.
ODEON - 1000 Hz
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length
averageSPLoct.
ODEON - 2000 Hz
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length
averageSPLoct.
ODEON - 4000 Hz
Figure 6.11: Comparison influence of absorption
red solid empty, blue dashed abs on ceiling, green dash dot abs as Regina
Figure 6.11 shows a comparison of different absorption in the scale model. The
influence of absorption on the sound decay can be clearly seen. The differences on
the sound decay can be explained due to the different reverberation times for each
case. Also the decay due to the screens can be seen from the above plots. This effect is
going to be studied further in the following section.
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6.5. Influence of screen opening area on sound decay
As shown in section 6.4 even though the sound decay in the saloons is due to the
absorption in the train, the screens also have a strong effect on the sound field. Tounderstand the effects of the screens different sizes of the opening between vestibule
1 and saloon 2 have been investigated. All other openings have not been changed.
The width was chosen to be 0.31m for the small opening, 0.75m for the standard
opening as it is found in Regina, and lastly 1.8 m for the large opening. All
simulations have been done using an empty train model as it is in section 6.4.1.
6.5.1 Simulation with small screen opening
0 5 10 15 20-35
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0
5
length
averageSPL1/3oc
t.
Odeon - Energy in Cross Section empty with s mall opening (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.12: Odeon result - Energy in Cross Section empty with small opening
As we are expecting, the screens have substantial sound insulation depending on the
width of the opening. The reduction is almost 10dB from the first vestibule to the
second saloon when we have a small opening. As the saloons are empty, there is no
clear sound decay due to absorption. The sound insulation due to the vestibule
screen between the saloon 1 and saloon 2 can be clearly seen in Figure 6.13.
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Figure 6.13: Odeon result-Grid response SPL of the empty train with small opening at 1000Hz
(Not normalized to the SPL in the vestibule)
6.5.2 Simulation with standard screen opening
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0
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length
averageSPL
1/3oct.
Odeon - Energy in Cross Sect ion empty with s tandard opening (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.14: Odeon result - Energy in Cross Section empty with standard opening
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In this section standard Regina opening has been investigated. The SPLs in saloon 1
and saloon 2 are almost equal as the same opening area is used on both sides of the
vestibule resulting in similar energy flow from vestibule 1 to both saloons. There is
almost 5 dB drop in SPL from the vestibule to the following saloons. These equal
energy flows can be seen in the figure 6.15. The energy on the saloon 1 and saloon 2
is almost at the same level.
Figure 6.15: Odeon result - Grid response SPL of the empty train with standard opening at
1000Hz (Not normalized to the SPL in the vestibule)
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6.5.3 Simulation with large screen opening
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length
averageSPL1/3oct.
Odeon - Energy in Cross S ection empty with large opening (rel to ref mic)
125Hz
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Figure 6.16: Odeon result - Energy in Cross Section empty with large opening
In this section a large opening at the vestibule has been investigated. The energy flowto saloon 2 is higher than to saloon 1. This result agrees with the previous variations
of screen opening size. There is 3dB sound reduction from vestibule 1 to saloon 2,
whereas we have 6dB to saloon 1.The results seem to be consistent. A decrease in
opening area by a factor of 2.4 results in an increase in sound decay by 3dB. From the
following figure the effect of the screens can be clearly seen for 1 kHz.
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Figure 6.17: Odeon result - Grid response SPL of the empty train with large opening at 1000 Hz
(Not normalized to the SPL in the vestibule)
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6.5.4 Summary influence of screen opening area on sound decay
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length
average
SPLoc
t.
ODEON - 125 Hz
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length
average
SPLoc
t.
ODEON - 250 Hz
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length
average
SPLoc
t.
ODEON - 500 Hz
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average
SPLoc
t.
ODEON - 1000 Hz
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length
average
SP
Loc
t.
ODEON - 2000 Hz
0 5 10 15 20
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length
average
SP
Loc
t.
ODEON - 4000 Hz
Figure 6.18: Comparison influence of screen opening
red solid small, blue dashed standard, green dash dot large opening
Figure 6.18 shows a summary of the influence of screen opening area on the sound
field. It seems that the screens have strong effect on the sound decay and due to that
they cant be neglected. The sound decay difference is proportional to the screen
opening area.
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7.Statistical Energy Analysis (SEA)
7.1. Theory
In this section a very brief introduction to SEA will be given. Thus mathematical
developments were left out for the benefit of a quick overview. Readers interested in
a deeper insight into SEA are referred to Statistical energy analysis, an overview [7].
The main idea in statistical energy analysis is dividing the structure under study intosubsystems and analyzing their stored and exchanged energies. Let us consider first
a system consisting of only one subsystem. Any excitation of this subsystem can be
described by its p