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In this paper, we present a novel interdisciplinary approach to study the relationship between diffusive surface structures and their acoustic performance. Using computational design, surface structures are iteratively generated and 3D printed at 1:10 model scale. They originate from different fabrication typologies and are designed to have acoustic diffusion and absorption effects. An automated robotic process measures the impulse responses of these surfaces by positioning a microphone and a speaker at multiple locations. The collected data serves two purposes: first, as an exploratory catalogue of different spatio-temporal-acoustic scenarios and second, as data set for predicting the acoustic response of digitally designed surface geometries using machine learning. In this paper, we present the automated data acquisition setup, the data processing and the computational generation of diffusive surface structures. We describe first results of comparative studies of measured surface panels and conclude with steps of future research.
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A data acquisition setup for data driven
acoustic design
Building Acoustics
2021, Vol. 28(4):345–360
©The Author(s) 2021
Reprints and permission:
sagepub.com/journals-permissions
DOI: 10.1177/1351010X20986901
journals.sagepub.com/home/bua
SAGE
Romana Rust1, Achilleas Xydis1, Kurt Heutschi3, Nathanael Perraudin2, Gonzalo Casas1,
Chaoyu Du1, J¨urgen Strauss, Kurt Eggenschwiler3, Fernando Perez-Cruz2, Fabio Gramazio1
and Matthias Kohler1
Abstract
In this paper, we present a novel interdisciplinary approach to study the relationship between diffusive surface structures
and their acoustic performance. Using computational design, surface structures are iteratively generated and 3D printed
at 1:10 model scale. They originate from different fabrication typologies and are designed to have acoustic diffusion and
absorption effects. An automated robotic process measures the impulse responses of these surfaces by positioning
a microphone and a speaker at multiple locations. The collected data serves two purposes: first, as an exploratory
catalogue of different spatio-temporal-acoustic scenarios and second, as data set for predicting the acoustic response of
digitally designed surface geometries using machine learning. In this paper, we present the automated data acquisition
setup, the data processing and the computational generation of diffusive surface structures. We describe first results of
comparative studies of measured surface panels and conclude with steps of future research.
Keywords
Architecture, Acoustics, Digital Fabrication, Computational Design, Machine Learning
Introduction
The acoustic quality of a room is an important criterion
for the perception and subsequently the sense of well-being
for its inhabitants1,2. However, today’s architectural acoustic
design is mainly focused on typologies that demand high-
end acoustics, like concert halls or auditoriums. The acoustic
design of the vast majority of the built environment is often
overlooked, leading to reduced comfort, negative health
effects from acoustic pollution, cost for noise abatement
measures and unaesthetic retrofitting of built structures both
indoors and outdoors.
One of the main reasons for this is the lack of
accurate and easy-to-use simulation tools3that can be well
integrated into computational design workflows, enabling
the assessment of acoustic quality without the need for
acoustic specialists. Thus, acoustics is only considered
at a later stage of the architectural planning process
(and often concerns only the installation of standard
absorption panels). Still, computational room acoustics is
a field that has been intensively studied over the past 50
years4. Fundamentally, there are two main approaches for
computationally modelling the acoustics of a room, which
are either based on numerically solving the wave equation,
or on the assumptions of geometrical acoustics (GA). Wave-
based modeling is able to provide the most accurate results,
but is too computationally expensive5,6for an iterative design
and evaluation workflow. GA is faster, but less accurate. Here
sound is assumed to propagate as rays and the wave-nature
of sound is neglected. Thus, all wave-based phenomena,
such as diffraction and interference are missing. Available
room acoustic modelling software such as ODEON7, CATT,
EASE, Ramsete8or RAVEN9are offering hybrid GA
methods, where the image source approach is combined
with ray-tracing that allows to consider diffuse reflections10 .
The scattering properties of a surface are usually described
by a simple one-parameter model that assumes Lambert
reflection directivity. This approach splits up the reflected
power into a specular and a scattering part, whereas the
ratio between the two contributions depends on the frequency
and the structure depth. This coarse reflection model can
not consider specific surface properties that can generate
particular reflection patterns. In order to be able to work in
room acoustic design with surfaces with specially designed
reflective properties, other solutions are necessary.
Another method to validate room acoustics utilize physical
scale models11. Here, sound sources are installed at pre-
defined positions, emitting sound in a scaled frequency
range while the corresponding audio signals are recorded.
The resulting measurements can be used to analyse the
acoustic performance5and improve the design12 . However,
this method is extremely time- and resource-inefficient, as
the number of design iterations are limited to the number of
built models.
1Gramazio Kohler Research, ETH Zurich, Switzerland
2Swiss Data Science Center, Switzerland
3Laboratory for Acoustics / Noise Control, Empa, Switzerland
Corresponding author:
Romana Rust
Chair of Architecture and Digital Fabrication
ETH Zurich, HIB E 43
Stefano-Franscini-Platz 1, 8093 Zurich, Switzerland
Email: rust@arch.ethz.ch
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2Building Acoustics 28(4)
In this paper, we present a novel interdisciplinary
approach to study the mutual relationship between diffusive
surface textures and their acoustic performance through data
science methods. In order to leverage data gathered from
physical scale models, we employ an automated robotic
measurement setup to record the impulse responses in front
of 3D printed acoustically diffusive surfaces at 1:10 scale.
They represent surface structures created through certain
fabrication typologies, such as brick or stone walls, for
which we collect diverse acoustic scenarios. The recorded
data set serves as a foundation to analyse relations between
geometrical and acoustical configurations and to determine
performance clusters. The final goal is to use the created data
set as a basis for a data-driven acoustic simulation that will
allow to predict the acoustic properties of newly created 3D
surfaces, thus omitting the need for a physical scale model.
The main challenge of building this data set arises from
the need to define and collect sufficient, relevant, and reliable
data in a short amount of time. Additionally, the post-
processing of the input data needs to be identified, since both
geometric and acoustic information are high dimensional.
This is necessary for both the data visualisation and the
future ML system. In the following sections, we describe
the data acquisition setup, the parameters of the data set
and the post-processing of the impulse response to extract
meaningful measures, such as the reflected cumulative
energy per frequency band. These evaluated indicators
allow different panels to be compared. We introduce the
computational generation of diffusive surface structures and
conclude with strategies for shaping the data set and future
work.
Acoustic data acquisition setup
The constituent parts of the multi-robotic setup were
developed collaboratively by evaluating architectural and
acoustic requirements, in addition to the requirements from
the perspective of data science and the constraints of a
physical setup. Several tests were performed to guide the
development and to validate the quality of the measured data.
Some of these tests can be found in the project’s open data
repository13.
Figure 1. Acoustic data acquisition setup with two Staubli
TX2-60L robots in an acoustically shielded and absorbent room.
Figure 2. Double-sided 3D printed panel placed in a special
fixture.
The multi-robotic measurement setup consists of two
6-axis Staubli TX2-60L*robotic arms with a reach of
920 mm each (see Fig. 1). They are equipped with two
different end-effectors: one with a speaker and the other
one with a microphone. During the measurement process
they reconfigure from position to position in an irregular
measurement grid above a 3D printed acoustic panel. For
each combination of microphone and speaker position, a
sweep signal in a scaled (1:10) frequency range of 2–40
kHz is emitted, a recording is taken, and the corresponding
impulse response (IR) is calculated. The sweep signal
covers the frequency range that can be reproduced by the
loudspeaker and determines the lower and upper frequency
limit of the data. The time spent on each measurement
combination averages at 12.3 seconds and the measurement
process per acoustic surface takes approximately 10 hours,
during which the data of 2951 measurement combinations
are stored. To avoid acoustic reflections, the robotic arms are
covered with custom 3D knitted sound absorbing cloths. The
robot controllers are installed in the adjacent room to prevent
their operating noise from affecting the measurement. The
whole setup is installed inside a sound insulated room, in
which all surfaces are covered with 50 mm melamine foam.
In the following paragraphs, the core components of the
setup are described.
3D printed acoustic panels
The goal of the research project is to produce a large and rich
data set during the project’s time span. However, the main
constraints are the measurement time, the acoustic panel’s
size and its fabrication time. The print-bed of the in-house
Voxeljet VX1000 3D sand printer and the defined operation
hours, constrain the acoustic panel’s size to a bounding
box measuring 585x585x100 mm (WxLxH), enabling the
production of maximal five panels per week. To increase
the amount of measurable surfaces, we designed the panel
with two sides (see Fig. 2), thus two acoustic surfaces per
These robotic arms are accurate (absolute positioning accuracy 0.2 mm,
repeatability 0.02 mm) and they have the ability to programmatically turn
the joint motors off and on, such that their operating noises do not affect
acoustic measurements.
Basotect®G+ Melamine foam from Vibraplast AG.
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Rust et al. 3
panel. A square panel shape was selected for the possibility
of applying standard data augmentation techniques: based on
the assumption that the measurements are symmetric, the
data can be virtually mirrored and rotated four times (90
degrees each time), resulting in an overall increase of the
collected data by a factor of eight.
A panel produced with a binder-jet 3D printer is porous
and highly absorbing. In order to obtain a surface that
represents rigid non porous materials, the panel is coated.
We evaluated different surface treatments and compared the
respective normal incidence absorption coefficients obtained
by impedance tube measurements. If left untreated, or
baked in an oven, the absorption coefficient is 0.47-0.58
for frequencies between 2–6 kHz. If infiltrated with resin,
or coated with two layers of acrylic paint, the absorption
coefficient is below 0.1. We decided to proceed with the
application of two layers of a plant-based, water-borne
paint using a compressed air spray gun. We compared the
panel’s surface reflectivity after coating by comparing the
measurements from a coated flat 3D printed surface (referred
to as Flat, see Table 1) with a flat MDF panel (referred
to as Wood). Compared to Wood,Flat reflected on average
29.3% less energy. This unavoidable loss in reflected energy
and the variations of the measurements is considered in
the subsequent evaluations by normalisation (see Section
Impulse response and data post-processing), that is to say all
indicators are consequently calculated in relation to Flat.
Measurement grid
The measurement locations are set in an irregular point grid
based on the defined dimensions of the 3D printed panel,
the robots’ working space, and acoustic considerations. The
grid’s dimensions are defined to avoid measurements with
edge diffraction as much as possible. The density of the
measurement grid was calculated based on three criteria:
a) to ensure a uniform surface coverage, b) to maximize
the number of data points per panel, and c) to allow two
acoustic surfaces to be measured within a 24-hour cycle.
To do so, we calculated the first Fresnel zone14 ‡ for each
microphone and speaker combination for both the lowest
and highest used frequencies, assuming a planar surface.
By calculating all possible combinations of speaker and
microphone positions (excluding some immeasurable cases),
the final measurement grid contains 78 measurement points
(see Fig. 3) and a total of 2951 measurement combinations.
The measurement points are placed on four planar layers,
each with a different number of measurement points located
at different offsets from the panel’s surface. The first layer
contains 6x6 measurement points, the second 5x5, and the
third 4x4, with average offsets of 124, 214, and 304 mm
from the surface and respective distances of 75, 93.75 and
125 mm between measurement points. The fourth layer has
only one measurement point with an average offset of 474
mm from the surface. Finally, the Fresnel zones for the
lowest frequency (2 kHz) have a minimum ellipse diameter
of 195 mm and a maximum of 560 mm, and for the highest
frequency (40 kHz) 43 mm and 140 mm respectively.
Figure 3. Left: Measurement grid with 4 layers in relation to
robotic setup and 3D printed panel. Right: Panel topview with
surface coverage in layer 1 at 40’000 Hz (top) and 2’000 Hz
(bottom) calculated by Fresnel zones.
Figure 4. Microphone (left) and speaker end-effector (right).
The microphone is attached to an acoustically transparent steel
mount and the speaker is tilted to optimize directivity and
ensure robot reachability.
Microphone and speaker end-effector
In order to record clean audio responses, shielding and
scattering from the robotic arms is avoided to the greatest
possible extent. The microphone is positioned such that it is
far from the robot’s flange (approx. 0.5 m) and it is fixed
on an acoustically transparent steel mount (see Fig. 4). The
precise tool manufacturing and the accuracy of the robotic
arm allows to achieve a positional accuracy of 0.17 mm
for the microphone. The microphone consists of a G.R.A.S.
40BE capsule attached on a Microtech Gefell MV 220 high-
impedance transducer. The microphone is of free-field type
and has a flat amplitude response up to 40 kHz (-1 dB)
for sound incidence on axis. For 30and 60off-axis, the
sensitivity at 40 kHz drops by 2 and 4 dB respectively.
Fresnel zones on a surface are the intersections of Fresnel spheroids with a
flat surface between a source and the image of the receiver. The foci of the
Fresnel spheroid are the source and the image of the receiver. The resulting
intersections have the form on an ellipse.
After the absolute calibration of the robotic arms we have a mean precision
of 0.17 mm and a max@90% of 0.28 mm.
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4Building Acoustics 28(4)
Label Material Purpose
Wood MDF plate Reference for a surface of high reflection.
Flat 3D printed and coated Reference for the surface of highest reflection possible
with the used 3D printed and coated material. Used to
normalise the measurements.
Foam Acoustically absorbent melamine foam§Reference for a surface of high absorption. Used
for subtracting the direct sound signal from the
measurement.
2D-PRD 3D printed and coated 2D Primitive Root Diffuser. Reference for a surface of
high and uniform diffusion.
0015 0 3D printed and coated Reference for a specific macrostructure with no meso-
and microstructure.
Table 1. Reference panels
On the source side, a Beryllium tweeter was selected as a
loudspeaker that is capable of exiting frequencies between
2 and 40 kHz. As a direct consequence of the 20 mm
membrane diameter, the loudspeaker shows a directivity
pattern with a tendency to focus sound radiation on axis
at high frequencies. Several tests with conical attachments
and scattering objects in front of the membrane showed
an improved (closer to omni-directional) radiation pattern,
however with a degradation of the temporal signature. To
maintain the excellent time response of the tweeter, it was
decided to do without measures to optimize directivity
but carefully orient the speaker in each measurement
configuration. This is the reason for the 45tilt of the steel
mounting (see Fig. 4), ensuring reachability by the robotic
arm.
The microphone and speaker are connected to a Focusrite
Scarlett 2i4 2nd Gen audio interface. We use two of the mono
balanced output channels. One is connected to an amplifier
that drives the Beryllium tweeter and the other is connected
back to one of the audio interface’s inputs and used as a
loopback channel for computing the impulse response (IR)
(See Impulse response and data post-processing).
Automation, control setup and sensors
COMPAS FAB15 and MoveIt16 were used to calculate
collision-free robot trajectories for each of the 2951
measurement configurations of microphone and speaker
along a defined sequence. For the data acquisition phase, a
workstation running Ubuntu 16.04, together with the audio
interface and the two St¨
aubli CS9 robot controllers were
installed in the adjacent control room. ROS Kinetic17 is used
as the base of a distributed system with the following nodes:
main controller service, ambient measurement service, audio
interface service, two VAL3 robot driver instances and
websockets ROS bridge18 . The main controller service
was built using COMPAS FAB15 and it coordinates all
other services. After positioning, the controller powers the
robots off, so that their operating noises do not affect the
measurement. Then it invokes the audio interface to start
playback and recording while the ambient measurement
service collects external sound level, temperature, relative
humidity, and atmospheric pressure using an Arduino board.
The external sound level values are employed to track
exogenous sounds that can influence the quality of our
measurements. After recording, the impulse response is
calculated and validated to ensure that the measurement is
not distorted by unwanted signals, and, repeated if needed.
Metrics of the process are continuously collected in an
InfluxDB time-series database and Grafana is used for
monitoring. Tracked metrics include values from all ambient
measurement sensors, system metrics based on collectd, and
process metrics.
Data set, post-processing and visualisation
The acoustic data acquisition setup collects different
spatio-temporal-acoustic scenarios, which are stored in a
multivariable data set. One data point in the data set
consists of the computationally generated geometry of the
measured diffusive surface, plus 2951 impulse responses,
supplemented by measured environmental data (temperature,
humidity, atmospheric pressure). The geometric information
of the data set includes input parameters of the geometry
generation algorithm (see Diffusive surface structures),
together with the algorithm itself, and the representation
of the surface as a polygon mesh. The mesh data is
directly used for the panel fabrication with the binder-jet 3D
printer. Additionally, each 3D panel is labeled with a unique
identifier and suffixed with 0 or 1 indicating the panel side
(e.g. 0015 0). This identifier is used to determine the 3D
printed physical object with the data set entry.
Reference panels
Some datapoints in the data set are baseline measurements
obtained from special reference panels with the same
dimensions as our 3D printed acoustic surfaces. These serve
to put the measurements of the 3D printed acoustic panels in
relation to other materials or panels with a different surface
geometry. Table 1lists the baseline measurements with their
respective label, material and purpose. Two of these baseline
panels (Flat and Foam) are also used in the post-processing
of the data, which is part of both the ML processing pipeline
and the data visualisation.
Impulse response and data post-processing
The primary measurement result for a specific surface and
speaker/microphone combination is the impulse response
(IR). The IR is the richest representation possible as it
contains all of the acoustic information linking the source
and the receiver. Furthermore, one advantage of the IR is
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(a) Filter bands (b) Cumulative energy of Flat (c) Cumulative energy of panel 0072 0
Figure 5. (5a) Constructed filters to separate the content of the IR in frequency. Stacked cumulative energy curves of panel Flat
(5b) and panel 0072 0 (5c) . The colours relate to the filter band colours of Fig. 5a.
the fact that different contributions appear lined up on the
time axis. As a result, the 2951 IRs offer a very precise and
relatively complete representation of the acoustic response
of a panel surface. Nevertheless, the IRs present some
challenges as well. First, IRs are not easily interpretable
with respect to perceptional aspects, especially because the
phase information is very complex. Second, for human
data analysis it is necessary to compress the information
contained in the 2951 IRs such that it can be comprehensibly
visualised per acoustic surface. Third, for the future ML
system the direct modelling of the IRs might be challenging
or even impossible given the low amount of available
samples at the end of the research project. In consequence,
we identified other indicators that represent the desired
acoustic information of a surface from an acoustic design
perspective.
Information extraction. First, to obtain the IR, we play a
linear frequency sweep ranging from 2 to 40 kHz and record
the microphone signal as raw data. The IR is then computed
by deconvolution and temperature compensation is applied.
Afterwards, we crop the IR after 4 ms and suppress the direct
sound. Due to small path length differences between direct
and reflected sound in some geometries, a time-windowing
based separation is not applicable. For that reason, the direct
sound time signal obtained from an IR measurement with
an absorbing panel (referred to as Foam) is subtracted.
Third, the IR is band-pass filtered with the help of the
filter bank described below (see Fig. 5a). This allows the
derivation of frequency dependent reflection properties of the
surface. Details about these first three steps are available in
Appendix Impulse response post-processing details. Fourth,
the filtered IRs are converted to cumulative energy curves
(see Fig. 5b) that display, on one hand, total reflected energy
and its distribution among the different filter bands, and,
on the other hand, the temporal pattern of energy arrival.
The cumulative energy curves are then put in relation to the
measurements obtained from a reference flat panel (referred
to as Flat) by normalisation. For simplification, we refer to
the resulting curves as NCE curves and the resulting total
value as TNCE in the following. The TNCE measure allows
comparing different panels with each other. For example,
if we contrast the stacked cumulative energy plots of Fig.
5b and Fig. 5c and refer to Table 2for the TNCE values,
the following information can be extracted: First, we see
that panel 0072 0reflects 14.1% less energy than the Flat
panel. Second, the energy distribution among the different
frequency bands changes. The 2.5 kHz and 5 kHz bands are
exhibiting an energy increase, 10 kHz band has almost no
difference (<0.2%), and the two higher bands a significant
decrease. Additionally, the slope of the NCE curve relates to
the degree of diffusiveness where a steep gradient indicates
a rather specular reflection and a slow increase represents a
diffuse reflection. In this case, panel 0072 0 has a slightly
less steep slope.
Panel ID 2.5 kHz 5 kHz 10 kHz 20 kHz 40 kHz Total
Flat 0.092 0.216 0.169 0.309 0.213 1.000
0072 0 0.136 0.291 0.169 0.157 0.106 0.859
energy 47.4% 34.5% 0.18% -49.2% -50.3% -14.1%
difference
Table 2. TNCE values for Flat and panel 0072 0. The values
relate to Fig. 5b and Fig. 5c
Filterbank design. The signal is separated into different fre-
quency bands using an ”itersine” wavelet construction. For-
mally, we use the mother function c(ω) = sinπ
2cos(πω)
and scale, warp and translate it as in19. Selecting the right
parameters, we construct the set of five filters shown in (see
Fig. 5a). The filters are centered at 5, 10, 20 kHz and are
logarithmically stretched (warped). The blue and green filters
correspond to the the remaining low and high frequency
bands. Note that, because everything is 1:10 scaled, the three
bandpass filters correspond to 0.5, 1 and 2 kHz bands. Note
that this set of filters form a unitary tight frame, meaning
that the total energy of the signal is conserved after the
application of the filters. The proposed construction does
not satisfy a particular norm for octave based filter bank
such as IEC 61260.1:201920. However, it is tailored to our
application because it conserves the energy and has good
localization properties both in the time and the frequency
domain.
Data visualisation
For 150 measured surfaces, the TNCE values range between
0.02 and 24.32, however the value of the 95th percentile is
1.67. To represent those values in a compact way and to
not clip high numbers, we map them on a logarithmic dB
scale by applying the function f(x) = 10 log10 (x). Figure
6shows all data that relate to a given microphone index
at the corresponding location in the measurement grid for
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6Building Acoustics 28(4)
three of the reference panels. The TNCE values are first
mapped on the logarithmic dB scale, then converted to
a color, and finally grouped based on measurement grid
layers (horizontally) and filter bands (vertically). The data
is always read relative to the Flat panel: white indicates
less cumulative energy (minimum -20dB) and black an equal
amount (0 dB). Situations, where an amplification due to
focusing occurs, are represented with red (maximum +6 dB).
In this way, the high dimensional information of the panel
measurements can be visually compared and evaluated (see
Section Comparative experiments).
(a) Flat
(b) Wood
(c) 2D-PRD
Figure 6. Layered grid plot of band-separated TNCE. Layer 0 is
the closest to the surface and layer 2 the furthest away. ”M”
indicates the microphone’s position.
Diffusive surface structures
Surface articulations play a significant role in the resulting
acoustic response. When a sound wave is incident on a
surface, the shape and size of these articulations define which
frequencies will be specularly reflected and which will be
scattered21. Diffusion is an important acoustic phenomenon
that can promote spaciousness, prevent flutter echoes, and
improve speech intelligibility. Although a reasonably big
library of absorption coefficients for different materials is
available, the same is not true for scattering coefficients5.
With the goal to investigate diffuse surface properties, we
generate geometric typologies stemming from architectural
fabrication techniques, ensuring compatibility with past and
current building systems (rubble stone walls, river rock
walls, slated stone walls, brick walls). These are chosen
based on their ability to diffuse sound within a broadband
or a selective frequency range. The typologies vary with the
motivation to a) uncover new possibilities within the domain
of acoustics, possibly integrating diffusion and absorption
within one surface, and b) to diversify the acquired data-
set. To ensure the latter, data acquisition and the generation
of new surface geometries are performed in parallel. In this
way, results from a measured panel can be used to inform the
generation of new ones.
Computational generation of diffusive surface
structures
For each fabrication typology, the essential geometric
characteristics were extracted and implemented in a
geometry generation algorithm that controls the surface
geometry, represented by a polygon mesh, with a set
of functions. These functions generate macro-, meso-,
and microstructures based on specific criteria by applying
operations such as mesh subdivision and mesh face
translation. The macrostructures are targeting the low-
frequencies, the mesostructures the mid frequencies, and
the microstructures the high frequencies. For example, for
a stone wall (see Fig. 7), its general shape (depth, straight
or wavy) is controlled by the macrostructure, the overall
size and placement of stones by the meso-structure, and
finally, the surface roughness of each stone, and the shape
of the joint between them, by the microstructure. Through
this modular surface generation process, panels of the same
macro structure, but different micro structure, or similar
combinations can be compared and analysed.
Due to the limited time span of this research project,
there is a limited amount of surface variations per
typology that can be explored. At the beginning of each
typology exploration, value ranges of all surface articulation
parameters are defined. Then, random step sizes to sample
these value ranges are chosen, and a first group with a certain
number of panels is generated and produced. After this group
has been measured, the acoustic data are compared against
each other, and the step sizes for the next group of panels are
adjusted. If the compared data are very similar, the step sizes
need to be increased. If the data are significantly different,
the step sizes need to be decreased. This allows for diversity
in the data set while avoiding unexplored areas.
Comparative experiments
Comparative studies are used to investigate the relationship
between geometry and resulting acoustical properties. These
studies serve two main purposes: first, they help to verify
certain acoustic assumptions, and thus validate the data
set; and second, they serve to develop quantitative design
guidelines for acoustic planners and architects, which can
be used in their design workflow. For each typology,
experiments are designed to test how the size, rotation,
spacing, protrusion and roughness of the base element
(e.g brick, stone) influence the acoustic response. This
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Figure 7. Geometry generation steps for a Flemish bond brick wall. From left to right: initial single-faced flat mesh, flat mesh
subdivided according to typology, thickened mesh with macrostructure deformation, final mesh with microstructure deformation.
section describes three of these studies, comparing the
captured acoustic data of several panels to determine how
a chosen geometrical characteristic influences the acoustic
performance.
Brick wall joints. This experiment investigates brick walls
and the acoustic effect of different mortar joint heights and
depths. Considering building parameters for brick walls, an
average joint height ranges between 5 to 10 mm (0.5 mm to
1.0 mm in 1:10 scale). The mortar can be either flush with the
surface of the bricks, or recessed by a few millimeters. Given
the small size of the joint in relation to the overall surface,
we only expect an influence on the high frequencies. To
test this assumption, we compare three panels with the same
macrostructure: two of them feature a Flemish-bond brick
wall typology, with a raked joint type and an average height
of 0.6 mm (0012 1), and 1.2 mm (0011 1) respectively; both
with a joint depth of 1 mm. The third panel features only
the macrostructure (0015 1), representing a brick wall with
a joint height of 0.6 mm and a joint depth of 0 mm. Table 3
shows the mean TNCE of the 90th percentile for each filter
band. As expected, the joint height does not affect the first
three filter bands (2.5, 5, 10 kHz). For the two higher ones,
panel 0012 1 shows 1.04 and 1.84 dB less energy compared
to the reference panel 0015 1, and panel 0011 1 2.6 and
3.01 dB respectively. Therefore, a small, but noticeable,
reduction in the high frequencies energy can be achieved just
by recessing the mortar joint and by increasing the mortar
height. It is important to note that if we look at the mean
TNCE for the full spectrum, the difference is very small.
Both panel 0011 1 and panel 0012 1 have very similar values
and are only 0.68 and 0.46 dB respectively less than the one
from panel 0015 1.
Macrostructure. In this experiment we compare panels Flat,
0015 0, and 0031 0 and focus solely on the effect of the
macrostructure. Each panel has a different macrostructure,
but no microstructure. Compared to Flat (see Fig. 6a),
an apparent disruption on the homogeneity of the energy
distribution is visible (see Fig. 8). Microphone-speaker
combinations where their Fresnel zone falls in a convex
shape exhibit less energy. Contrary, combinations in which
their Fresnel zone falls in a concave part of the surface
Panel Mortar 2.5 kHz 5 kHz 10 kHz 20 kHz 40 kHz Total
ID height 90% 90% 90% 90% 90% 90%
0015 1 0 -7.66 -3.66 -9.18 -7.02 -5.54 -0.4
0012 1 0.6mm -7.8 -4.14 -9.58 -8.06 -7.38 -1.02
0011 1 1.2mm -7.86 -3.89 -9.19 -9.62 -8.55 -0.86
Table 3. Mortar on brick walls experiment. Mean TNCE values
of the 90th percentile per filter band. Mortar height in mm (1:10)
and energy values in dB. For every frequency band, red
indicates the value with the smallest difference to the reference
Flat and green the one with the highest.
exhibit increased energy due to the focusing effect (see red
squares in Fig. 8b). When comparing two panels that share
the same macrostructure but have different microstructures
(see Fig. 10), the cumulative energy plots show that the
macrostructure influences all frequency bands and the
microstructures start having an influence only after 10 kHz.
Stone vs. brick walls. This experiment aims to determine
whether stone walls or brick walls are better in diffusing
sound. We generated and measured 46 stone and 92 brick
walls. Our analysis shows that brick walls diffuse sound
more consistently. Polygonal rubble stone walls generally
diffuse less energy in the lower frequencies, but the results
were inconclusive for the mid and high frequencies. To
illustrate the findings we present two extreme cases (see Fig.
9).
Panel 0005 1 is from the polygonal rubble stone wall
typology. It features, on average, nine stones per square
meter, a joint width between 20-30 mm, a joint depth
between 50-80 mm, and a stone surface roughness of ±30
mm (numbers in 1:1). Panel 0013 1 is from the brick
typology and resembles a standard stretcher-bond brick wall.
It features standard bricks measuring 215x65x102.5 mm
(WxHxD) and a raked joint around 15 mm wide ( ±1 mm)
and 10 mm deep ( ±1 mm) (numbers in 1:1). Both panels
0005 1 and 0013 1 share the same macrostructure with panel
0015 1. Compared to panel 0015 1 (Fig. 10a), panel 0005 1
(Fig. 10b) exhibits higher TNCE values across all filter bands
(see Table 4), with the exception of 40 kHz, but only by
0.4 dB. On the contrary, panel 0013 1 (Fig. 10c) exhibits
less cumulative energy across all filter bands. The difference
is smaller in the two lower filter bands (-0.49, -1.6 dB), in
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8Building Acoustics 28(4)
(a) Panel 0015 0
(b) Panel 0031 0
Figure 8. TNCE values for macrostructure comparative
experiment with varying macrostructures. ”M” indicates the
microphone’s position and ”+” a point with no data.
Figure 9. 3D printed and coated panels. Left: Surface 0013 1
from the brick typology. Right: Surface 0005 1 from the
polygonal rubble stone wall typology.
which the effect of the macrostructure is more dominant, but
more present in the upper three bands (-3.6, -4.03, -5.03 dB).
In comparison to panel 0015 1, the TNCE of panel 0005 1 is
higher by 2.03 dB, and of panel 0013 1 lower by -1.88 dB.
Panel 2.5 kHz 5 kHz 10 kHz 20 kHz 40 kHz Total
ID 90% 90% 90% 90% 90% 90%
0015 1 -7.66 -3.66 -9.18 -7.02 -5.54 -0.4
0005 1 -7.44 -3.09 -6.96 -5.96 -5.94 1.63
0013 1 -8.15 -5.26 -12.78 -11.05 -10.57 -2.28
Table 4. Stone vs. brick walls. Mean TNCE of the 90th
percentile per filter band. All values are relative to the reference
Flat.
(a) Panel 0015 1
(b) Panel 0005 1
(c) Panel 0013 1
Figure 10. TNCE values for stone vs brick walls - experiment.
(10a) Panel with only the macrostructure, (10b) Stone wall
typology panel with the same macrostructure as panel 0015 1,
(10c) Brick wall typology panel with the same macrostructure as
panel 0015 1
Conclusions and future work
In this paper, we presented a novel approach to study the
mutual relationship between diffusive surface structures and
their acoustic performance through data science methods.
We described the post-processing of the measured data, the
evaluated indicators and showed that they can be used for the
quantitative assessment of different surface structures; thus
providing a valid evaluation system.
By the end of this research project we target to measure
350 acoustic surfaces; this amounts to approximately 1
million impulse responses in total. To create high diversity,
the data set is continuously shaped through analysis and
subsequent surface generation. This approach should enable
the future ML model to generalize as well as possible.
Analytical tools, for example PCA22 and PCC23 , will
be evaluated to identify the most important geometrical
characteristics that influence certain acoustic responses. Self-
organising maps (SOM)24 are also tested to cluster the
surfaces based on geometrical (fabrication typology) and
acoustical characteristics (i.e. absorption, scattering). This
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Rust et al. 9
will help to identify unexplored areas in the design and data
space and test new hypotheses that emerge during analysis.
Currently, we can only speculate on the output and
accuracy of the ML system. However it is foreseeable that
the limited number of data set samples will be critical. This
limitation can be mitigated by leveraging the large number
of impulse responses present in each sample and by the data
augmentation naturally emerging from the setup symmetries.
From our preliminary testing on 100 acoustic surfaces, we
believe that an exact prediction of the impulse response
is likely impossible. Hence, we will focus our efforts on
predicting the compressed information obtained from the
post-processing step presented in this paper. Our preliminary
ML architecture is able to predict the energy reflected
(more precisely the TNCE) in every measured position for
geometries that present similarities with the training set.
Our future ML model shall be used as a fast acoustic
evaluation tool for diffusive surfaces, which facilitates
acoustic driven form-finding in early design phases. Together
with the developed design guidelines for certain fabrication
typologies, this will enable more acoustic aware designs,
thus bringing acoustics closer to the architectural practice.
Copyright
Copyright © 2021 SAGE Publications Ltd, 1 Oliver’s Yard,
55 City Road, London, EC1Y 1SP, UK. All rights reserved.
Acknowledgements
This research is jointly supported by the Swiss Data Science Center
and the Chair of Architecture and Digital Fabrication, ETH Zurich.
The authors would like to thank Michael Lyrenmann and Philippe
Fleischmann from the NCCR Digital Fabrication, ETH Zurich, for
their help with building the multi-robotic measurement setup, Dr.
Mariana A. Popescu for her assistance producing the 3D knitted
sleeves for the robots, and Anton Johansson for his help in the
measurement process. Furthermore, Dr. Mathias Bernhard, Patrick
Bedarf, and Pietro Odaglia from the Chair of Digital Building
Technologies, ETH Zurich for their support with the in-house 3D
printer and Alessandro Tellini from Raplab, ETH Zurich for his
help and support using the digital workshop, and finally, a sincere
thank you to Dr. Lauren Vasey for her diligent proofreading of this
manuscript.
APPENDIX
Impulse response post-processing details
The post-processing of the impulse response consists of the
following 3 steps which are illustrated in Figure 11:
1. Deconvolution. The deconvolution operation is carried
out using a simple division in the Fourier domain. Given
ˆx=Fxthe Fourier transform of xand x=F1ˆxits inverse
operation, the deconvolution of the signal xwith the sweep
sis given by
xd=F1(Fx/Fs),
where sis the sweep and the division is performed
elementwise. Note that Fsis never close to 0 because the
sweep contains all frequencies.
2. Temperature correction. To adjust for the room
temperature change, we estimate the speed of sound at
temperature T(in °C)
c=c0p1+(T/273.15),
where c0is the temperature at 0°C25. The impulse response
is then resampled at the frequency c/cref fs, where cref
is the speed of sound at 20°Cand fs= 96kHz the
sampling frequency. We use the polyphase filtering method
(“resample poly“) from the SciPy python package).
3. Removal of direct sound. The direct sound removal
is performed by subtracting the impulse response of the
absence of a wall (an absorbent foam inserted instead of the
panel, see Table 1,Foam).
Figure 11. Impulse response post-processing. Top:
measurements. Middle: after deconvolution, temperature
correction is applied. We used 30°Cand 15°Cto emphasize
the effect of resampling. Bottom: eventually direct sound is
removed.
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10 Building Acoustics 28(4)
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