Determination of the sound absorption coefficient of ETFE cushions in-situ using the genetic material optimizer in Odeon ®

Abstract

ETFE cushions are used as cladding in predominantly mid to large size architectural projects. Smaller cushions are about 10 m² in size and the biggest single cushions can be several hundreds of square metres large. They are composed of ETFE membranes a few hundred of micrometres thick. From a point of view of room acoustics, their acoustic transparency, which increases with decreasing frequency, makes them to effectively act like sound absorbers. Their voluminous nature and transparency make it challenging to measure the sound absorption coefficient of ETFE cushions in a laboratory. Using the genetic material optimizer of Odeon^® software, the effective sound absorption coefficient of ETFE cushions in four rooms was extracted from room acoustic parameters, which were in turn derived from measured room impulse response data. The results were compared and interpreted by the help of theoretical modelling and measurements on small cushions in a reverberant room. There is a relatively good agreement between the three types of results, possible causes for the differences are explained in the paper.

Introduction

ETFE cushions are used as cladding material, separating the inside and outside environments of buildings. They consist of multiple thin Ethylene tetrafluoroethylene (ETFE) membranes that are clamped together in a metal frame. The cushions are kept under pressure by an air handling unit. The excess air pressure inside the cushions is typically around 250 Pa (0.00025 bar). Depending on the project, the sizes of the membranes vary considerably, both in thickness and surface area.

In general, ETFE is used in projects where the designer wants to create the feeling for the user that he/she is outside while still being protected from the rain, wind and snow. These membranes are translucent, making them an alternative design choice to glass panes in some situations. ETFE claddings are almost always used in combination with more traditional types of roofing to house other functions such as offices, shops, living units, hotel rooms.

ETFE-cladding projects have been built until now and the systems are claimed to be more durable than glass pane claddings. No comprehensive overview of the building stock exists, Vector Foiltec GMBH, the company that supported this research through samples and access to buildings, has advertised to have installed a dozen of projects with ETFE cushion surfaces upwards of 20,000 m² and more smaller projects. ¹ Other manufacturers and installers are active on the market.

From a room acoustic point of view, the partial transparency of ETFE cushions for acoustic waves, mainly towards low frequencies, makes them to effectively act as sound absorbers. This has been previously described (specifically for ETFE cushions) in literature by Chiu et al. ² Rain noise is reported to be a problem in some situations, the tensioned membranes are easily excited by rain droplet impacts. Mitigation for that is possible.

More detailed knowledge of their effective sound absorption coefficient would be useful for assessing the acoustic comfort in those spaces by calculating room acoustic parameters that relate to speech intelligibility or the Sound Pressure Level (L_p). Despite the prevalence of these cushion systems in the building stock, to the best of our knowledge, the effective sound absorption coefficient of these cushion systems has not been reported in literature.

In the following chapters, we first describe the basic physics involved in the effect of the presence of ETFE cushion systems on the acoustics of a space. Next, a description is given on performed in-situ room impulse measurements on different loudspeaker and microphone locations. Measurements have been performed in four halls (large rooms) with ETFE constructions, in Liège (Belgium), Berlin (Germany), London (United Kingdom) and Rotterdam (the Netherlands). We then describe how the genetic optimizer of Odeon^® has been utilized to extract the acoustic absorption spectrum from room acoustic parameters that were in turn extracted from room impulse response measurements. The results are compared, and an interpretation is given concerning the similarities and differences observed. In the next chapter we describe our method for extracting an absorption coefficient in a building acoustics laboratory. Following that, we present some numerical simulation results. Finally, we compare all absorption coefficients obtained with the three methods and discuss the possible causes for differences.

Acoustic absorption mechanism of ETFE cushions

In a building containing a relatively large amount of ETFE cushion surfaces, the absorption spectrum of those cushions has a significant influence on the colouration of the sound. This indicates the need for an adequate determination of the sound absorption spectrum of ETFE cushions.

As already mentioned, energy that is not reflected by an ETFE cushion is not converted to heat but simply assumed to be transmitted to the outdoor environment. In other words, from the perspective of room acoustics, any sound that is transmitted through the cushions can be considered as absorbed (unless a reflective surface is present behind the membranes, which seems to be rarely the case in practice). Due to the small thickness of the ETFE membranes, their acoustic transparency and thus effective acoustic absorption is significant in mid frequency range, and very large towards low frequencies. This is contrary to much thicker and solid glass claddings, which are highly reflective and thus poorly absorbing throughout most of the audible spectrum.^3,4 Please find a schematic cross-section of an ETFE cushion system in Figure 1.

Figure 1.

Schematic cross-section of a typical four-layer ETFE cushion. The supporting structure varies according to the specific structural needs of the building. The clamping profiles make sure that the membranes are clamped together. This ensures air tightness (for inflation of the cushions) and water tightness (rain).

The acoustics of membranes has been explored in literature. According to multiple authors, the tension in membranes has a negligible influence. The flow resistivity of the membranes and the surface mass are mentioned as being the most important factors.^5–9 Since the membranes are designed to hold air their flow resistivity can be assumed to be infinite. The typical surface mass of ETFE membranes applied as ETFE cushions is between 175 and 450 g/m².

In-situ measurements

We deliberately selected four rooms covered in various (absolute and relative) amounts of m² of ETFE cushions and total room volume. The Médiacité in Liège, the MOA Mercure Hotel Lobby in Berlin, the Drijvend Paviljoen in Rotterdam and Devonshire Square atrium in London. The set is somewhat representative of the typical ETFE covered rooms in terms of shape, volume, and relative surface area of ETFE (vs the surface areas of other materials). The Rotterdam room is more of an exception in terms of shape, but its high relative ETFE surface area gave us an opportunity to lower the uncertainty on our measurement. All rooms were covered by ETFE cushions manufactured and installed by Vector Foiltec GMBH. We have no reason to believe that the latter has any considerable impact on the results.

Measurement procedure

The impulse response of four rooms was measured using a slightly modified ISO3382-1 measuring approach. From the impulse response, the reverberation times T₂₀ and the Clarity C₈₀ were determined for different loudspeaker and microphone locations. Table 1 shows that in the four evaluated locations, the total surface of ETFE cushions represented a substantial fraction of the total of all surfaces. This insured that the absorption of the ETFE cushions had a substantial influence on the room acoustic parameters, which is a necessary condition for the ETFE properties to be extracted from the measured values of those parameters.

Table 1.

Basic features of the measured rooms and their ETFE cushion coverage.

Name	Location	Tot. ETFE area (m²)	%ETFE area relative. to total	Room volume (m³)	Reverberation radius average (estimated) (m)	Avg cush. size (m²)	Std. dev. cush. size (m2)	# layers	Thickness (µm)
Mediacité	Liège, BE	13,136	19.5	26,177	5.19	46	55	4	150 - 100 - 100 - 200
Devonshire square	London, UK	9800	13	31,042	4.76	56	0	2	150 - 200
MOA Mercure Hotel	Berlin, DE	6376	20.5	17,288	3.15	18	7	3	150 - 150 - 200
Drijvend Paviljoen	Rotterdam, NL	1847	46	3981	5.63	13	2	2	150/200 -200/250

These data were obtained from a 3D model that was reconstructed based on information obtained from Vector Foiltec GMBH and manual and scan measurements on site.

In the Berlin, Rotterdam and London measurement locations, a Bruel & Kjaer type 4295 omnidirectional source was used. The Acoustics Engineering type Zircon loudspeaker used in Liège is more powerful but not omnidirectional. A dBX-RTA-M microphone and a 12-channel Roland^® soundcard were used to measure impulse responses using REW software.

In Table 2, an overview of the measurement conditions is given.

Table 2.

Fact sheet of the measured rooms.

Location	Volume (m³)	Number of measurement combinations	Temp. (°C)/rel. air humidity (%)	Number of people in room
Mediacité, Liège	26,177	24	30.0/38	3
MOA Mercure Hotel, Berlin	17,288	12	24.3/60	4
Drijvend Paviljoen, Rotterdam	3981	22	12.6/60	2
Devonshire square, London	31,042	10	9.3/65	5

Mediacité, Liège, Belgium

Mediacité in Liège (Figures 2 and 3) is a shopping centre of which the main hall is covered by a steel canopy with ETFE cushions clamped in metal frames. The main hall is long and organically shaped. The roof is double curved. The cushions consist of three or four layers. The distribution of the two is unknown; near the measurement area some three-layer cushions have been observed. To simplify the modelling and simulation, only the part of the 400 -m-long hall that was roughly within 10 m from the microphone and loudspeaker locations was modelled in detail. In Figure 3, the bottom image shows the plan view of the truncated model. The far ends of the model were assumed to be 100% absorbing, corresponding with the assumption of a situation without or with only far away back-reflecting objects. The measurements in Liège deviated somewhat from the ISO3382-1 standard because of the not omnidirectional character of the loudspeaker. This directionality was inserted later into the source characteristics of the Odeon model so that it could be considered for the optimization.

Figure 2.

Picture of the inside of the Mediacité in Liège, Belgium, at the location where the room was measured. Note: this picture was taken during a different time and in different conditions (with people present) than during the measurement.

Figure 3.

Ground plan of the of the Mediacité in Liège, Belgium, including the source positions (‘S#’), the measurement positions are indicated by the small circles, for the sake of clarity these positions were not labelled. The top image is a zoomed-in version of the bottom image. The bottom image shows the entirety of the simulated model with its boundaries.

MOA Mercure Hotel Lobby, Berlin, Germany

The hotel lobby of the MOA Mercure Hotel in Berlin (Figures 4 and 5) is covered by ETFE cushions. This space has a more conventional shape than the one in Liège, it has straight walls and a slightly arching roof consisting of ETFE cushions. The hall is used as a lobby and sometimes as a professional event room.

Figure 4.

Picture of the inside of the MOA Mercure Hotel lobby.

Figure 5.

Ground plan of the of the MOA Mercure Hotel lobby, including the source positions (‘S#’), the measurement positions are indicated by the small circles, for the sake of clarity these positions were not labelled. The bottom image is a plan view of the model that was used for the optimization. The bottom image shows the entirety of the simulated space. The top image is a zoomed-in version to clearly specify the source and receiver locations.

Drijvend Paviljoen, Rotterdam

The floating pavillion in Rotterdam (Figures 6 and 7) is a small conference/reception centre that is built on a floating pontoon. The structure consists of the base pontoon with three coupled geodesic domes constructed out of 20 cm steel hollow tube sections. The cells of the geodesic domes are hexagonal, combined with a few pentagons to fill the gaps (chamfered dodecahedron). The ETFE cushions are enclosed in the cells. The background noise in Rotterdam was too high to get a reliable reading in the 63 Hz octave band. This band was therefore omitted from further analysis.

Figure 6.

Ground plan of the of the Drijvend Paviljoen in Rotterdam, including the source positions (‘S#’), the measurement positions are indicated by the small circles, for the sake of clarity these positions were not labelled. The dotted line circle to the left of the measured volume shows a part of the building that is not part of the measured volume as listed in Table 1. It is a closed-off auditorium that was also fully sealed during the measurements.

Figure 7.

Picture of the inside of the Drijvend Paviljoen, Rotterdam. Note that several cushions in the picture have a higher opacity. This is a sign that the active solar control system was activated. More information and a discussion of the possible implications for the study are given in section 6.2.

Devonshire square, London

The Devonshire square building (Figures 8 and 9) has a main atrium that is covered by ETFE cushions. It resembles the Berlin room in the sense that the cushions span from one short side to the other, except that the cushions are wider and slightly longer. The atrium is also approx. 2.5 times higher than the Berlin room. The cushions consist of two layers only.

Figure 8.

Ground plan of the of the Devonshire Square Building courtyard in London, including the source positions (‘S#’), the measurement positions are indicated by the small circles, for the sake of clarity these positions were not labelled. The bottom image shows the entirety of the simulated space. The top image is a zoomed-in version of the bottom image with indication of source and receiver positions.

Figure 9.

Picture of the inside of the Devonshire square building atrium. The cushions cover the atrium along the entire length (78 m).

Measurement results

Figures 10 and 11 show that the spectra of the reverberation time (T₂₀) and Clarity (C₈₀) are quite different between the four investigated locations. This is due to differences in volume, interior elements and fraction of ETFE coverage. Differences in Clarity can also be due to differences in the used microphone-loudspeaker distances or the relative difference between microphone-loudspeaker distances and the dimensions of the room. When the size of a room increases but the source-receiver distance stays the same, the Clarity can increase. The latter is most likely the reason why the Clarity is higher for Liège and London, the two biggest rooms in the set. Only the reverberation time above 4 kHz is similar between all rooms, due to the substantial volume of all spaces, and the dominance of air absorption over surface absorption on the reverberant sound field in that case. The London room has the highest reverberation time in the low to mid frequency range, most likely because the ETFE surface is relatively small and far away. The walls of the atrium, consisting of brick and glazed surfaces, are dominating the sound field. In the other rooms, the ETFE surfaces are closer to the receiver (and typical user or visitor locations), their relative surface area is also higher. Both geometrical properties lower the reverberation time in the low to mid frequency range.

Figure 10.

Average values of measured reverberation times (T₂₀) in the four rooms with indication of standard deviation as error bars.

Figure 11.

Average measured Clarity (C₈₀) in dB in the four rooms with indication of standard deviation as error bars.

While the absolute values of both the reverberation time (T₂₀) and Clarity (C₈₀) were not predictable, the differences between them for various rooms is in line with expectations with knowledge of room acoustic theory.

Genetic algorithm (GA) optimization

To extract the absorption spectrum of ETFE surfaces (A_ETFE), the equivalent absorbing surface spectrum can be obtained from the measured reverberation time spectrum (T₂₀) using Sabine’s formula, or from the Clarity spectrum (C₈₀) using a diffuse field model. If the total ETFE surface (S_ETFE) is known, the absorption spectrum of ETFE cushions (α_ETFE) can be determined as A_ETFE/S_ETFE. However, the extraction of A_ETFE from T₂₀ or C₈₀ depends on certain conditions. The ETFE surface should cover a significant fraction of the total surface area, and its value should be larger than the uncertainties in other absorption spectra (α_j). Uncertainties in absorption values and the attenuation of sound in the air can affect the accuracy of the extracted A_ETFE.

The Odeon^® genetic optimizer is a software module that optimizes the absorption properties of surfaces, specifically ETFE cushion surfaces, by fitting experimentally obtained room acoustic quantities from room impulse responses. ¹⁰ The optimization minimizes the squared differences between measured and calculated room acoustic quantities by searching for optimum values of the acoustic absorption of surfaces in a predefined geometrical model. It starts from user-guessed values and iteratively adjusts them based on fitness criteria that reflect the correspondence between the combined differences between, on one hand, the room acoustic parameters (for each octave band: the values of C₈₀ and T₂₀) that are calculated by assuming the guessed values in the model calculation, and, on the other hand, the measured room acoustic parameters. Random mutations are applied to explore a wider parameter space and avoid local minima. Multiple measurement scenarios are considered to enhance the robustness of the optimization.

The influence of different surfaces on the impulse response varies with the time after the excitation of the impulse. Surfaces near the loudspeaker and microphone dominate the early response, while echoes from multiple surfaces contribute to the later response. Multiple impulse responses obtained from different loudspeaker and microphone locations can provide a balanced view of surface influences and improve the extraction of A_ETFE.

When calibrating a virtual 3D model for ray-based simulation, absorption coefficients of interior surfaces are estimated based on material databases. For existing buildings, the above-described fitting procedure can be used. It involves fine-tuning the absorption and scattering values of surfaces with unknown properties based on the measured room acoustic parameters. This calibration process can be laborious, prone to biases and challenging to optimize with multiple measurement positions.

In this optimization, the effective absorption spectrum (α_ETFE and others) is varied to match the simulated and measured octave band spectra of T₂₀ and C₈₀. The optimization uses a single cost function defined as the sum of squared differences normalized by the just noticeable difference. It aims to find model parameters that best match the measurements in terms of human perception.

Before each optimization, tentative initial values for absorption characteristics are assigned based on literature or transfer matrix calculations. These values are left free within a realistic search range during the optimization. The search range for ETFE surfaces is unrestricted, while other materials have restricted search ranges. Optimizations are performed with different starting values and larger search ranges to test robustness.

The obtained absorption spectra of ETFE claddings in the measurement sites are comparable and consistent, providing confidence in the derived ETFE absorption. However, there is variability in the low-frequency range due to standing wave modes in the rooms, and the absorption values for the Rotterdam site differ from the other sites above 630 Hz.

Note that the complexity of the fit impeded a robust determination of variance and covariance-based error bars on the absorption values. See section 4.1 for a discussion of different causes of uncertainty on the measured room acoustic parameters and the extracted absorption values. The result suggests that the difference between the Rotterdam result and the others is statistically significant.

One measurement related difference between the Rotterdam site and the others is that the Rotterdam model was simpler in terms of number of materials. Only six different types of materials had to be modelled (see Appendix A). Other than the absorption values of the ETFE cushions, most of the surface area of the materials’ characteristics are thought to be quite well known (hard and smooth floor, glass windows, aluminium profiles). The ETFE cushions represented 46% of the total surface area in the room and thus had a significant influence on the room acoustic parameters. We thus expect this optimization problem to be the least prone to error and the most accurate.

The obtained absorption coefficient from the Rotterdam model, which is thought to be the most accurate, has been applied to the ETFE surfaces in the other models (Berlin, London, Liège) and simulated again in Odeon. The resulting T₂₀ and C₈₀ errors in JND are shown in Appendix B (B5–B7). The obtained JND errors are higher than the ones observed from the first optimizations. A difference/delta graph is given in Appendix B8. Interestingly, the difference in errors is significantly higher for the Berlin model than for the Liège model. These two models have a similar amount of relative ETFE surface area (relative to the total surface area (see Table 1). The difference is the largest for the 1 kHz octave band, this is because the difference between the different absorption coefficients (of Rotterdam and Berlin/London/Liège) is the highest in that band.

Sources of uncertainty

As mentioned above, the reliability of the fitted ETFE absorption values depends on the sensitivity of the considered room acoustic parameters, C₈₀ and T₂₀, to α_ETFE, and on the accuracy of the those parameters, which in turn depends on the accuracy of the impulse response.

• The directivity of the source used in the Liège measurement (Zircon) was imported into Odeon (Odeon source properties). The Common Loudspeaker Format (CLF) profile of the used speaker was not available, but a polar plot of each octave band was obtained from the manufacturer. A comparable source directivity profile (based visual comparison) was chosen from the presets in Odeon. For the Bruel & Kjaer Omnisource, omnidirectionality was assumed. In reality, deviations can be expected for high frequencies.

• Odeon makes use of ray tracing, the image source method, and effective scattering coefficients, implying that it does not meticulously model diffraction, scattering, interference etc. In the performed simulations, curved cushions were simplified as flat surfaces in the 3D models and given a scattering coefficient of 0.3.

• The genetic optimization algorithm not only searches for the best fitting ETFE absorption, but it also searches, albeit within limited ranges, the best fitting absorption of the other materials. This extension of the dimensionality of the search space results in additional uncertainty due to fitting covariance between the many fitting parameters: some influences of ETFE properties on the room acoustic parameters can be compensated or masked by influences of properties of other surfaces. The severeness of this effect scales with the contribution of the respective surfaces to the total effective absorption A. In the studied cases, fortunately, the contribution to A of surfaces other than ETFE was small.

• The search ranges chosen for the different materials in the different rooms could in principle be too small so that an optimum situated outside of it might not have been found. The Figures in Appendix A show that the search ranges were large enough. In order to further look into this, some optimizations with even larger search ranges were executed for the Berlin model. Despite the larger search ranges, no difference was found in terms of the outcome for α_ETFE(f) (see Figure 13 for the comparison).

• The starting value of the absorption coefficients of each material could in principle have an influence on the final optimized result. Therefore, in the case of the Berlin model, an additional optimization was done in which random starting values (within the original search range space) were chosen. It turned out that despite the random starting values, the optimum was not significantly different from the original optimization, except for higher frequencies (See Figure 12 for a comparison).

• Figure 14 shows, for a scenario as in Liège, the uncertainty on the acoustic absorption that is induced by a realistic amount of 10% uncertainty on the humidity.^11,12 Due to the high influence of air attenuation towards high acoustic frequencies, the effect of humidity variations becomes significant above 5 kHz (3 –4 JNDs). Below 5 kHz, the effect is too small to be relevant for the observed differences between Rotterdam and the other sites.

Figure 12.

Absorption coefficients of ETFE cushions obtained using the genetic material optimizer module in Odeon. Results obtained in the 63 Hz band are reliable since the input data for all measurements in this band has been copied from the 125 Hz octave band (due to measurement errors).

Figure 13.

Obtained absorption coefficients resulting from alternative optimization strategies for the Berlin model. In blue: increasing the search ranges of the materials that are not ETFE (from an average of 10%–20% to 50%), in grey: using the original starting value and randomizing it within the bounds of the original search ranges.

Figure 14.

Absorption coefficient of ETFE cushions as extracted from impulse response measurements in Médiacité in Liège using Sabine’s formula, assuming a humidity of 40%. The error bars indicate the effect, via the m-term, of adding and subtracting 10% humidity on the extracted absorption values. m was calculated using the ISO 9613 standard for a temperature of 30°C was used.

Laboratory measurements

Method

A sample of a cushion was obtained from a manufacturer. The square cushion was stretched inside an aluminium frame and is approximately 135 × 153 cm large. The cushion consisted of three 250 µm thick layers. The total depth of the cushion was about 20 cm in the middle. This is not typical of cushions applied in real buildings where a 150-100-200 µm type configuration is more common. In other words, the total surface mass of the sample was higher than what can typically be found in practice (this information is available to us via Vector Foiltec GMBH).

The cushion was measured according to ISO 354 in the reverberant chamber of the Laboratory of Acoustics of KU Leuven. ¹³

Since we were trying to characterize the material as placed in between the inside and the outside of a building (with no obstructions behind the membranes from the point of view of the room), an ISO 354 type E mounting was opted for. A box with a depth of 610 mm was constructed out of 18 mm thick medium-density fibre board (MDF) wood panels. The inside was filled with glass wool, as shown in Figure 15. The thick glass wool layer was meant to act as the absorber, commonly represented by the open air in real world situations.

Figure 15.

Basic experimental setup in a reverberation chamber: a 61 cm high MDF box filled with 60 cm of mineral wool was used to absorb the acoustic energy that was transmitted through the membrane, so that the inside of the box mimicked an outdoor environment. The wooden box was made such that the frame fitted flush on the box. Cross section components: Compacted foam mats, Aluminium frame with ETFE cushion 3 × 250 µm thick with approximately maximum air pocket depth 100 mm, and approx. 250 Pa delta with the surrounding air, MDF panels 18 mm thick, rolled up foam mats, glass wool panels 100 mm thick and laboratory floor (concrete). Only one box is shown here , two identical boxes were put against each other.

ISO 354 dictates that the minimum size of a sample shall be 10 m². Unfortunately, we were only able to place two of such boxes in the room due to the limited availability of the material. A maximum of 4.16 m² of ETFE cushions was available to us (projected surface area).

Measurements were performed with two boxes with each one cushion on them (4.16 m² ETFE). As is custom, the humidity and temperature were carefully monitored. Long exponential sine sweeps were used to obtain the reverberation times using the integrated impulse response method (capture software: REW). The cushion(s) were inflated to a typical operating pressure of 250 Pa (measured with manometer with ±3 Pa accuracy).

In an ISO 354 measurement, the reverberation room should be measured without any sample to obtain a reference reverberation time. This reverberation time can be used to check the contribution of the sample to the absorption in the room, thus correcting for the (low) absorption of the room boundaries. Since in this measurement the wooden box would also contribute to the absorption in the room (while it is not part of a ‘normal’ ETFE cushion setup), we decided to include the box without any absorptive material in the reference to be able exclude it from the result. In other words, we measured the reverberation time in the reverberant room with the empty wooden boxes present to capture their contribution as well. The boxes were closed off at the top. Thick 22 mm panels were used, and the box walls were flat, impermeable, and stiff and there were no visible gaps in the box construction. This was done to minimize panel absorption to a maximum extent and was verified by first considering the boxes as samples and determining their absorption, using the completely empty room as a reference. Figure 16 shows that the absorption is effectively small across the whole audible spectrum.

Figure 16.

Absorption spectrum of two empty closed boxes measured using ISO 354 in the reverberant room. The reverberant room has a volume of 197 m³.

For measuring the absorption of the ETFE cushion sample in conditions equivalent to a cushion in the cladding of a building, the assumption was that the thick absorptive layers below the ETFE cushions absorb virtually all sound, as if the inside of the box would be an open outdoor environment. To check this assumption, a measurement of the box without ETFE was performed but with absorptive material in the box (filled to the brim as in Figure 15). The result is shown in Figure 17. For frequencies above 250 Hz, as expected, the resulting absorption coefficient is hovering around 1 within the uncertainty of the measurement. Towards low frequencies, the absorption coefficient drops off, most likely because of the small size of the sample relative to the respective wavelengths.

Figure 17.

Absorption spectrum obtained with ISO354 of two box constructions as depicted in Figure 15 but without ETFE membranes above the 61 cm absorptive layer. Some results are unphysical (above 1), this area is coloured in red on the figure.

Finally, the reverberation time in the reverberant room was measured with the complete setup present (boxes + absorption + cushions). The resulting effective absorption spectrum of the cushion sample, which was obtained by considering the room with closed boxes as reference, is shown in Figure 18, together with the absorption coefficients obtained from genetic algorithm results. Above 125 Hz, there is reasonably good agreement with the genetic algorithm absorption coefficient obtained from the Rotterdam model.

Figure 18.

Effective absorption spectrum of ETFE cushion as measured using ISO 354 with the closed box reverberation times (that were the basis for Figure 16) as a reference. The absorption coefficients obtained through the genetic algorithm approach are added for comparison’s sake.

Discussion and comparison

Layer model comparison

The differences between one hand the Rotterdam results and the laboratory results, and, on the other hand, the genetic algorithm results for the three other locations, raises the question to what extent differences in size, air pressure, multilayer structure, shape and clamping conditions of ETFE cushions can lead to differences in effective acoustic absorption (or, equivalently, acoustic transparency). Due to their complex 3D shape, simulating the absorption of cushions is challenging. Some impression on the influence of the ETFE construction parameters on the acoustic absorption is given by the absorption spectra in Figure 19a and b, which were calculated for the following scenarios, using the Odeon material calculator, a layer model that is integrated in the software. This layer model uses the transfer matrix model to calculate the absorption coefficients of different types of configurations.

Figure 19.

(a) Sound absorption coefficients obtained with the layer model module integrated in Odeon® software in scenarios (A and D). (b) Sound absorption coefficients obtained with the layer model module integrated in Odeon® software in scenarios (E and I). A. Single infinite ETFE membrane of 0.1 mm thickness, B. Single infinite ETFE membrane of 0.15 mm thickness, C. Single infinite ETFE membrane of 0.25 mm thickness, D. Single finite size (1.53 × 1.35 m) clamped ETFE membrane of 0.25 mm thickness, E. Double ETFE membrane (0.15 + 0.25 mm) with an air cavity of 100 mm thick. F. Double ETFE membrane (0.15 + 0.25 mm) with an air cavity of 200 mm thick. G. Triple ETFE membrane (0.1 + 0.15 + 0.25 mm) with two air cavities of 100 mm thick. H. Triple ETFE membrane (0.1 + 0.15 + 0.25 mm) with two air cavities of 200 mm thick. I. Finite (1.53 × 1.35 m) Triple ETFE membrane (0.25 + 0.25 + 0.25 mm) with two air cavities of 100 mm thick.

Varying the shape and pressure inside the cushions was not possible using this model simply because the layer model considers parallel layers. Another important note is that when finite dimensions were added to the layers, it modelled the surface as a finite and virtually surrounded by 100% reflective material (infinite). This is significantly different from an ETFE surface in practice, where a cushion might have finite dimensions, but is surrounded by other cushions.

The following observations can be made:

• At low frequencies, the membranes are almost 100% transparent, a phenomenon that is also evidenced from the optimizations (despite the unreliability of the data in the lowest octave band).

• For typical ETFE thickness values, the effective absorption coefficient can change significantly.

• Multi-layer compositions can result in a higher effective absorption coefficient than a single thick (0.25 mm) layer of ETFE for mid to low frequencies.

• Multi-layer compositions of the layer model (best compared to cushions) have an effective absorption coefficient that is comparable to the genetic optimization resulting absorption coefficient for the Rotterdam model. The absorption coefficients obtained from optimizations of the three other models exhibit a relatively high absorption coefficient at high frequencies, this does not correspond with the multi-layer model simulation results.

• Clamping an ETFE membrane leads to a drastic reduction of absorption at very low frequencies. The smaller the membrane, the larger is the reduction mainly at low frequencies. This is mainly a consequence of diffraction: the smaller the membrane with respect to the acoustic wavelength, the less the membrane is transmitting and thus the smaller is the effective acoustic absorption. This is in line with the ISO 354 measurements in the previous section. This size effect can partially be extrapolated to a mesh of ‘softly clamped’ membranes connected to each other in an ETFE cladding in a building, where the stiff connection grid acts as a rather hard reflector.

Different conditions in Rotterdam

With respect to the difference between the measurement results in Rotterdam and the others, it is worth to mention that in the Rotterdam building, 41% of the surface area of the ETFE cushions had an increased opacity. This is most probably due to a solar control system that is implemented. By using a pressurization system, the opacity of the cushions can be tuned by pushing the middle layer against the outer layer. Both the middle layer and outer layer are printed with patterns (consisting of silver pigments). The patterns are complementary to each other, meaning that bringing them close to each other results in an increased opacity and thus blocking of sunlight. This state, which is visualized in Figure 20, effectively forms a two-layer cushion, with one side featuring a double membrane structure. Figure 21 depicts the impact on the absorption when the position of an intermediate membrane is varied, dividing the cushion volume into two sub-cavities. The effect of this division on absorption was simulated using Odeon software. The effect is a lower absorption coefficient for mid frequencies and a smaller effect at 2000 Hz and beyond.

Figure 20.

Solar control principle illustrated in a diagram. By pushing the middle layer of the cushion against the outer layer, two overlapping printed patterns make the entire surface of the cushion opaquer.

Figure 21.

Spectra of absorption coefficients of two configurations, obtained by the Odeon^® material calculator. Orange: three-layer configuration (layers parallel) spaced apart 100 mm (two air layers). This configuration is best compared with the drawing at the top of Figure 20. Membrane thicknesses are indicated in the legend. Yellow: two-layer configuration (layers parallel), mimicking the effect of pushing the middle layer of the orange configuration against the outer layer, membranes still 100 mm apart. This configuration resembles the bottom drawing of Figure 20 the best.

Conclusions

The genetic algorithm implemented in the geometrical acoustics Odeon software has been used to determine the spectrum of the acoustic absorption coefficient of large ETFE cushions of four large rooms in Berlin, Liège, London, and Rotterdam. The fitting procedure involved using the JND error of T₂₀ and C₈₀ extracted from the impulse responses of the measurements to compare them to the simulated values of T₂₀ and C_80.

The resulting acoustic absorption spectra of the ETFE cushions in the four investigated sites show the expected decreasing trend with increasing frequency, but there is a noticeable difference between the result in the half dome in Rotterdam on one hand and the three other locations on the other hand, the latter absorption spectrum giving lower values at high frequencies and matching relatively well the (adapted) ISO 354 measurement that were performed on a sample in the reverberant room. The uncertainty of the genetic algorithm results is thought to be relatively high (at least as high as the uncertainty on the ISO 354 measurement) but the precise estimation of these values could not be made.

The sample measured in the lab was 3–10 times smaller in terms of area than a single cushion in the locations observed for this study and even smaller if the entire ETFE cushion surface is considered. This, together with the limiting frequency of the reverberant room, limited the validity of the measurement to the frequencies above 125 Hz. The in-situ measurements are also less reliable for low frequencies due to limitations of the measurement setup. Despite these uncertainties, numerical simulations, and analytical theory^{3 –7} suggest that at low frequencies these ETFE cushions are quasi acoustically transparent.

The 3D cushions and the way they are suspended are quite diverse and complex, making the interpretation of similarities and differences between different sites not straightforward. However, simulations of a set of simple composite membrane structures show some interesting connections between material and geometrical parameters on one hand and absorption spectra on the other hand.

Overall, the good correspondence between the Rotterdam results and measurement and theory, together with the higher robustness of the in-situ measurement-based results in Rotterdam (higher equivalent absorbing area of ETFE cushions) in Rotterdam, suggest that those results are most suitable to be used for future simulations, with expected uncertainty on the obtained reverberation time and Clarity values of the order of 1–3 JNDs.