Sound insulation of lightweight wooden floor structures: ANN model and sensitivity analysis

Mohamad Bader Eddin 1 , Sylvain M´ e nard 2

Department of Applied Sciences, University of Quebec at Chicoutimi 555 Bd de lÚniversité, Chicoutimi, QC G7H 2B1, Canada

Delphine Bard 3

Engineering Acoustics, Lund University John Ericssons v¨ a g 1, 223 63 Lund, Sweden

Jean-Luc Kouyoumji 4

Technological Institute FCBA All. de Boutaut, 33000 Bordeaux, France

Nikolaos-Georgios Vardaxis 5

Engineering Acoustics, Lund University John Ericssons v¨ a g 1, 223 63 Lund, Sweden

ABSTRACT The study aims to develop an artificial neural networks (ANN) model to estimate the acoustic performance for airborne and impact sound insulation curves of di ff erent lightweight wooden floors. The prediction model is developed using 252 standardized laboratory measurement curves in one-third octave bands ( 50 − 5000 Hz). Each floor structure has been divided into three parts in the database: upper, main and ceiling parts. Physical and geometric characteristics (materials, thickness, density, dimensions, mass, and more) are used as network parameters. The results demonstrated that the predictive ability of the model is satisfactory. The forecast of the weighted airborne sound reduction index R w was calculated with a maximum error of 2 dB. However, it is increased up to 5 dB in the worst case prediction of the weighted normalized impact sound pressure level L n , w . A sensitivity analysis explored the essential parameters on sound insulation estimation. The thickness and the density of upper and main parts of the floors seem to a ff ect estimations the most in all frequencies. In addition, no remarkable attribution has been found for the thickness and density of the ceiling part of the structures. Keywords: sound insulation, prediction model, artificial neural networks, sensitivity analysis

1 Mohamad.Bader-Eddin1@uqac.ca

2 Sylvain_Menard@uqac.ca

3 Delphine.Bard@construction.lth.se

4 Jean-Luc.Kouyoumji@fcba.fr

5 Nikolaos.Vardaxis@construction.lth.se

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

1. INTRODUCTION

Timber has been used widely in construction engineering because of its availability in nature and ease of handle [1]. In addition, it has a significantly low carbon footprint (in comparison with concrete) and provides good thermal performance [2,3]. In North America, wood-frame structure systems have been the most common in housing in the 20 th century because its advantages [4]. While those types of structures did minimize construction cost and time, they o ff er lower subjective sound insulation quality than that of heavy structures with the same sound insulation data [5,6]. Controlling the acoustic environment of building residents is an essential issue of new and old renovated buildings [7]. The characterization of sound insulation for certain structural elements is usually obtained from standardized measurements, such as ISO and ASTM [8–14]. However, those measurements are time and cost demanding [5]. In addition, the obtained sound insulation data concern certain elements and cannot be generalized and adapted for all kind of structures. The simplest approach to predict the sound insulation of a certain element is based on mass, sti ff ness, and losses [14]. This might be e ff ortless for a single leaf element, but it is not the situation for multi-layered and lightweight constructions. An accurate estimation of sound insulation for double structures has been and remains a challenge [14]. Some construction details, such as mechanical connections between di ff erent materials, can hardly be considered especially in the analytical approaches [15]. Furthermore, the standardized method that is indicated in ISO 12354 Part 1 and 2 [16, 17], are presently not appropriate for multi-layered complex and lightweight structures [18]. The standardized methods are widely used and were developed based on data from heavy monolithic constructions [18]. Lately, Machine Learning and its applications have been used widely for solving complex and di ff erent problems in di ff erent fields, such as image classification, speech recognition and building acoustic applications [19–22]. A strength of many machine learning techniques, and artificial neural networks (ANN) in particular, is that the analytic and predictive power are improved significantly when huge data sets are provided. In building acoustics, ANN models were used to predict the weighted sound reduction index R w and sound transmission class STC values of sandwich partition panels [23]. The results were acceptable with errors of ± 3 dB in estimation of R w and S TC . Similar research was done on wooden windows to estimate the weighted sound reduction index R w based on di ff erent technical parameters [24]. However, the two previous studies were limited to the prediction of single number quantities (SNQs) and without considering the complete sound insulation spectrum in di ff erent frequency bands. Another use of ANN was performed to predict airborne sound insulation curves of masonry walls [22]. Thirty-four laboratory measurements of simple monolithic brick walls were collected considering geometric and physical parameters. Then, a sensitivity analysis determined the most statistically significant parameters for the estimation of airborne sound insulation [22]. Although the predicted values showed an agreement with the measured ones, the study was limited to a specific kind of construction. In a previous study by the authors [25] ANN was utilized to predict the whole acoustic spectrum of di ff erent lightweight wooden floors. The study was limited to 67 measurements and used the thickness and the installation order of the materials as the only parameters in the model. However, the model showed better accuracy in low frequencies than high ones, providing indications that confident estimations could be achieved with more parameters and measurement data. The scope of this study is to develop a prediction tool based on artificial neural networks for airborne and impact sound insulation estimation of floors. The data used consists of collected standardized laboratory measurements performed on various lightweight wooden floor configurations. Finally, a feature attribution analysis is carried out to explore the e ff ects of parameters on the predictions.

2. METHODS

2.1. Artificial neural networks The idea of artificial neural networks was motivated by the structure of a real human brain [26]. It uses very simple computational operations (additions, multiplication and fundamental logic elements) to solve complex and ill-defined problems [27,28]. The architecture of ANN consists of layers, and each layer contains computation units that are referred to as neurons [29]. Those units are connected to one another through weights, which take the same role as the strength connections in biological organisms. Weights are used to scale each input to a neuron. The training data contains examples of input-output pairs of the function to be learned. It provides feedback to the weight values depending on the accuracy of the network in prediction the output values. The features of an ANN (weights and bias) are evaluated and adjusted during the learning phase. Neural networks are generally organized in layers, each layer is an array of processing neurons. Each neuron can be defined as a mathematical function that takes one or more input values. The neuron is identified as follows,

y = f ( X ( w i x i + b )) , (1)

where y , w i , x i , and b represent output, weight value, input and bias of a specific neuron, respectively. The output values of neurons are known as activation values and used as an input to the activation function.

2.2. Sensitivity analysis Neural networks models are usually considered as black box tools because explaining their mechanism is cumbersome [31]. To find out which parameters the prediction model relies on, a problem of attributing the prediction power to input parameters must be identified. A challenge with attribution techniques is that they are di ffi cult to evaluate empirically. In addition, it is di ffi cult to set apart between errors which are made by misbehaviour of the attribution method or by misbehaviour of the model. This gap can be addressed by taking an axiomatic approach, called integrated gradients (IG) [35]. The latter is indicated as IG i ( x ) and uses a function F : R n → [0 , 1] that presents an ANN model and an input x = ( x 1 , ..., x n ) ∈ R n . An attribution of the prediction at the input x relative to a baseline input z ∈ R n is a vector A F ( x , z ) = ( a 1 , ..., a n ) ∈ R n , where a i is the attribution of x i of the prediction function F ( x ). The integrated gradients can be interpreted as the integral of the gradients along the straight path from the baseline input z to the input x . The integrated gradient for the i th dimension between a baseline and an input is explained by [35],

IG i ( x ) = ( x i − z i ) ∗ Z 1

∂ F ( z + α × ( x − z ))

∂ x i d α. (2)

α = 0

3. STUDY DESIGN

3.1. Structure samples In this study, 252 standardized laboratory measurements are used to develop the database. The measurements are received from Lund University in Sweden, FCBA in France, FPinnovations and CNRC [37] in Canada. The measurements consist of airborne and impact sound insulation tests performed on 142 di ff erent floors in the frequency range of 50 Hz to 5 kHz . The airborne sound reduction index measurements were carried out according to ISO 140-3 (1995) [38] or the latest ISO 10140-2 (2010) [8] and ASTM E90-09 (2016) [12]. The impact sound pressure level data were

measured following ISO 140-6 (1998) [39] or the latest ISO 10140-3 (2010) [10] and ASTM E492-09 (2016) [13]. Sound insulation curves based on ASTM standards were converted to comply with ISO standards descriptors, the weighted airborne sound R w and the weighted normalized impact sound pressure level l n , w . The latter are reported in ISO 717-1 (2013) [40] and ISO 717-2 (2013) [41] respectively. This conversion is done in order to have a total agreement with the acoustic descriptors. Figures 1 and 2 and shows the mean and standard deviation values of the airborne and impact sound insulation curves in the frequency bands (50 − 5000 Hz ). For each floor structure, there are the technical and materials parameters, the airborne sound reduction index data and / or the normalized impact sound pressure levels data. There are 107 structures that have both airborne and impact sound insulation data, 26 that have only airborne sound data and 12 that have only impact sound curves (Table 1).

Mean and standard deviation values for all airborne sound insulation curves 100 80 60 40 20 Airborne sound reduction index R (dB) Frequency (Hz)

Figure 2: Mean and standard variation of the standardized laboratory measurements.

Figure 1: Standardized measurements for airborne sound reduction index.

Table 1: Description of the database number and their divided sets in ANN model

Database ANN model

Measurements No. 252 252

airborne impact training set validation set testing set

133 119 204 24 24

24 di ff erent floor structures were used to validate the features of the model and another 24 to test its accuracy. Figure A1 in the Appendix illustrates the testing data cases of floor configurations, which were randomly selected from the total observations. In the database, each floor is split into three: upper, main, and ceiling parts, following the order of material layers. The main part presents the dominant material that is used in a floor construction among all floor components. The upper and ceiling parts represent materials which are clustered

Impact sound pressure level Ln (dB) 100 80 60 40 20 Mean and standard deviation values for all impact sound insulation curves SEES PIESHPPESESEYS Frequency (Hz)

and located above and below the main part of each structure, respectively (Figure 3). Another classification is applied to study the influence of dry and wet floor solution systems on the predictions. Wet floor systems refer to floors with a concrete layer on top as a floating panel, while dry systems are defined as floors without any concrete layer on top.

Figure 3: An example of a description schematic showing the database organization for floor components.

Table 2: List of structural parameters used as inputs to train the ANN model. Parameters used in the prediction model Units Classes

− Material types – i.e., concrete layer, CLT panel, insulation materials, etc.

− Material installation order – first / second / ...

− Material thickness mm –

− Group thickness mm upper, main and ceiling parts

− Total thickness of the floor mm –

− Material density kg / m 3 –

− Group density kg / m 3 upper, main and ceiling parts

− Total density of the floor kg / m 3 –

− Area of the floor structure S m 2 –

− Volume of the receiving room V m 3 –

− Ratio S / V – –

− Joist depth mm –

− Spacing between joists mm –

− Resilient channels depth mm –

− Spacing between resilient channels mm –

− Curve slope – low (50 − 200 Hz ), middle (250 − 1000 Hz )

and high frequencies (1250 − 5000 Hz )

The database is organized using MySQL software [42]. The parameters are arranged with respect to: material type, material layers order, thickness, density, joists depth and spacing between them, area of the floor ( S ), volume of the receiving room ( V ), the ratio ( S / V ), total density of the structure, depth of the resilient channels and spacing between them, slope of curves in three di ff erent frequency ranges (low: 50 − 200 Hz , middle: 250 − 1000 Hz and high: 1250 − 5000 Hz ), and the spectrum of airborne and impact sound insulation in dB in one-third octave bands (50 − 5000 Hz ). The structural parameters are presented in Table 2. All those parameters are used as inputs to train the ANN model, while the model’s output values are sound insulation curves in dB in one-third octave bands.

EEE | °st000 Uover SE — insviation mat sin { etre cone {TT — cancn pert

3.2. Prediction model configuration The ANN model is based on a multilayer perceptron algorithm which consists of two hidden layers of 40 and 30 neurons in each layer respectively. The LeakyReLU (Leaky Rectified Linear Unit) function [43] was used as an activation function for both layers. Adam optimizer [44] was utilized in training phase. All the measurements in the database is split into three subsets: training, validation and test set. The training set is used to initiate the ANN features such as weights, bias. The validation set is employed for optimizing the architecture of the model in order to find a suitable one, while the test set is used for estimating the predictive capabilities of the chosen model. The cost function is used to evaluate the performance of the ANN. Since the prediction deals with continuous values (as the target is to predict the full spectrum), the root-mean-squared error (RMSE) can be used as a cost function,

v t

n X

1 n

RMS E =

i = 1 (ˆ y i − y i ) 2 , (3)

where n is the total number of measurements used as a training set, ˆ y i and y i are predicted and measured values, respectively.

4. RESULTS AND DISCUSSION

4.1. Prediction of airborne sound insulation The ANN model was trained and validated with 202 and 24 standardized laboratory measurements, respectively. Another set of 24 sound insulation curves are chosen randomly to test the accuracy of the model (12 for airborne sound reduction index and 12 for impact sound pressure levels). The acoustic spectrum (in dB) in one-third octave bands (50 Hz − 5 kHz ) is a dependent set of variables to be predicated by the model. Figure 4 illustrates a comparison between measured and predicted curves of di ff erent floor configurations for airborne sound insulation. It is found that the predicted curves are close to the measured ones, especially at low frequencies, while the deviations tend to increase in certain cases in the high frequency bands. The smallest deviation is noticeable in floor #1 with a RMSE value of 1 . 65 dB , while the largest one is in floor #9 with 7 . 63 dB . Sometimes, the most significant variations are noticed at high frequencies (1 . 25 − 3 kHz ), where the critical frequency of lightweight structures is usually located. This is the frequency at and above which the sound radiates easily and e ffi ciently due to resonance [45]. This phenomenon is observed a lot in building acoustic insulation measurements and every individual layer corresponds better to a plate-type component in theory [14]. Occasionally, similar variations can be observed at low frequencies, below 150 Hz, where the fundamental resonances (first eigenfrequencies) occur [14], e.g., floors #4 and #9. These resonance frequencies a ff ect the airborne sound estimations more than the model can predict. Table 3 reveals the total root-mean-square di ff erences between measured and predicted airborne sound insulation curves for each test floor configuration in one-third octave bands. It also shows the measured and predicted single-number quantities (SNQs), R w and R wPredicted respectively, for each test structure. The variations between the weighted indices vary from zero deviation (floors #3, #5, and #7) to a maximum deviation of 2 dB (floors #2, #4, #8, and #11) as seen in Table 3. The calculated and predicted correction terms C 100 − 3150 and C 50 − 5000 , also presented in Table 3, reveal similar di ff erences that do not exceed the deviations in the weighted reduction index comparison.

Figure 4: Comparison between measured and predicted curves of airborne sound reduction index.

Table 3: Comparison between measured and predicted sound reduction indices for airborne sound insulation.

Floor No. RMSE ( dB ) R w ( dB ) C 100 − 3150 C 50 − 5000 R wPred ( dB ) C Pred 100 − 3150 C Pred 50 − 5000

1 1.65 38 0 1 39 -1 0

2 3.59 61 -2 -4 59 -2 -2 3 2.07 54 -2 -1 54 -2 -1

4 5.18 35 0 0 37 -1 0

5 2.33 49 -4 -5 49 -4 -5

6 1.9 48 -3 -3 50 -4 -5

7 5.84 54 -2 -2 54 -1 0

8 3.31 43 0 0 41 -1 0

9 7.63 57 -1 -3 56 -2 -1

10 2.21 50 -3 -5 51 -4 -5

11 1.75 44 -2 -2 46 -4 -4

12 2.68 55 -3 -4 54 -4 -5

Airborne sound reduction index R (dB) Measured and predicted airborne sound insulation curves for test floor structures —~ Measured cave Frequency (Hz)

4.2. Prediction of impact sound insulation The same 12 test floor structures were utilized to evaluate the ANN model in estimating the normalized impact sound pressure level curves in the frequency range of 50 Hz to 5 kHz (Figure 5).

Figure 5: Comparison between measured and predicted curves of impact sound pressure level.

Table 4: Comparison between measured and the predicted weighted normalized impact sound pressure levels for impact sound insulation.

Floor No. RMSE ( dB ) L n , w ( dB ) C I , 100 − 2500 C I , 50 − 5000 L n , wPred ( dB ) C Pred I , 100 − 2500 C Pred I , 50 − 5000

1 1.93 64 1 1 64 0 0

2 3.96 48 2 6 53 4 6

3 2.68 53 3 4 48 2 4

4 3.54 88 -4 -4 85 -4 -4

5 3.07 68 0 3 67 1 4

6 3.16 66 1 4 68 2 4

7 7.07 64 -2 -1 66 -5 -2

8 4.7 64 -1 0 66 1 1

9 6.74 64 -2 1 60 0 1

10 4.46 63 1 5 60 1 5

11 1.76 60 1 6 60 0 5

12 2.28 68 0 2 70 0 3

Impact sound pressure level Ln (dB) Measured and predicted impact sound insulation curves for test floor structures“ esswei cine Frequency (Hz)

In most cases, the model depicts a good agreement between the measured and predicted curves, especially at low and middle frequencies. The lowest variation is 2 . 28 dB (RMSE) in the floor configuration #12, while it is 7 . 07 dB in floor #7. At frequencies around 1 . 25 kHz , there are often gaps between measured and predicted curves and again probably due to the critical frequency e ff ect, as seen in floors #3, #4, and #10. Likewise, similar deviations occur at fundamental resonances (first eigenfrequencies) below 200 Hz , e.g., for floors #2, #3, #4, #7, and #9 (Figure 5). This is significant because low frequencies are usually vital in building acoustics [46–48], where higher measurement uncertainties exist [49]. Regarding single-number quantities, the weighted normalized impact sound pressure level index ( L n , w ) and the predicted one ( L n , wPredicted ) are calculated and presented in Table 4. The maximum deviation is up to 5 dB (RMSE) in the worst cases of floors #2 and #3, while the estimated weighted index is equal to the measured one in floors #1 and #11. The calculated and predicted correction terms, C I , 100 − 2500 and C I , 50 − 5000 , in table 4, also show errors between 0 − 3 dB , without any extreme values and within the deviation range for the weighted indices ( L n , w and L n , wPred ).

4.3. Sensitivity analysis A feature attribution technique is performed to explore the relationships among parameters and how they a ff ect the sound insulation estimations. It also can provide an overview of their influences in every frequency band. The sensitivity analysis is a useful tool to highlight the essential parameters on the prediction of sound insulation. In those kinds of graphs, a reader can evaluate the results as follows: the y − axis presents the e ff ect size that determines the attribution of each parameter to the predictions. If y values are greater than zero, this suggests a direct relationship between parameters and output values, whereas an amount close to zero, indicates a weaker relationship. The integrated gradient analysis usually produces signed values, which are considered ambiguous to be understood in specific applications [31]. The decision of taking the absolute values or not, firmly depends on the characteristics of the data. In this study, the objective being to concentrate on the most significant parameters, the use of the absolute values of the gradient could lead to a better understanding of the results.

4.3.1 Feature attributions for airborne sound insulation

Figure 6 reveals the role of the density and the thickness of upper, main, and ceiling parts of dry and wet floor solution systems in estimation of airborne sound insulation. Unexpectedly, the e ff ect of the ceiling part appears to be minimal in all floor systems. In dry floor systems, the thickness of the upper part shows a noticeable attribution to the prediction at low and very high frequencies. At middle and high frequencies, the e ff ect size of the density and the thickness of the main part are evident. In wet floor systems, the thickness and the density of the upper part (a concrete layer is included) a ff ects airborne sound estimations across all frequencies. In addition, and in the main part, they seem to have an influence on the predictions, particularly at middle and high frequencies.

4.3.2 Feature attributions for impact sound insulation

The results in Figure 7 depict the contributions of the thickness and the density of the upper, main, and ceiling parts in dry and wet floor systems for impact sound estimations. In dry floor systems, the thickness of the upper part has the highest e ff ect on the impact sound prediction at all frequencies, especially at low and middle frequencies. Thickness and density of the main part seems to a ff ect the estimations in the middle and high frequencies. A small attribution is noticed for the thickness and the density of the ceiling part at high frequencies. In wet floor systems, almost the same trends appear for the main part, but in a lower degree in terms of the size e ff ect. However, the thickness of the upper part (in wet solutions) seems to a ff ect the estimation higher than the density in low frequencies.

Figure 6: Feature attributions of upper, main and ceiling parts of dry and wet floor solutions for airborne sound prediction.

For wet and dry systems: feature attributions for airborne sound insulation =~ (rap oosm as _—_UPREF part Dry solution Main part ry slution Cling pre-e sottion 2 => a _ zo 4g __Uoner pat wat seuton Main ar - Wet solution Ceting pare Wet soution 8 Frequency (Hz)

Figure 7: Feature attributions of upper, main and ceiling parts of dry and wet floor solutions for impact sound prediction.

Sensitivity For wet and dry systems: feature attributions for impact sound insulation Upper part Dry solution ain part - Ory solution Celing part- Dry solution ———— ain par Wet solution Ceting par - Wet station a Frequency (Hz)

Thickness and density of the ceiling part have negligible e ff ects for both dry and wet floors solutions except at high frequencies. The data in Figure 7 agrees with the classic mass-spring-damping system approach [14]. In low frequencies or sti ff ness-controlled region (below the first eigenfrequency), the thickness is the dominant parameter in the impact sound insulation prediction, where the system’s properties are mainly governed by the sti ff ness. At middle and high frequencies, where the mass- controlled and coincidence-controlled regions are located (separated by the critical frequency), the results reveal a significant increase of the attributions of density and thickness. This conclusion was also assumed in previous studies [50].

4.4. Common observations for airborne and impact sound prediction The biggest deviations in the results can be found in the simplest floor configurations, such as floor #4 in Figure 4 and floor #9 in Figure 5. This can be explained due to the lack of measurements performed on simple structures in the database, which may have an influence on the accuracy. The results also point out that the main estimation di ffi culties can be found at high frequencies. One reason is probably due to the presence of the critical frequency of the test floors. Similar problem appears at fundamental frequencies in the low frequency range. Table 5 illustrates a comparison between the measured and the predicted airborne and impact sound insulation curves divided into three di ff erent ranges: low (50 − 200 Hz ), middle (250 − 1000 Hz ) and high frequencies (1250 − 5000 Hz ). Again, the error variations are calculated by the root-mean- square error ( RMS E ) function. At low frequencies, the RMS E values for airborne and impact sound estimations are very close. However, better predictive ability is shown for airborne sound estimations at middle frequencies. At high frequencies, the accuracy decreases for both kinds of estimations (airborne and impact sound). That is probably due to the presence of critical frequency. Overall, Table 5 summarizes that the airborne sound estimations are better than impact ones, especially at middle frequencies. The sensitivity analysis showed that the thickness of the upper part (in both dry and wet solutions) a ff ects the estimations, especially at low frequencies. Similar trend is applicable for the density of upper and main parts. However, no remarkable importance was noticed for density and thickness of the ceiling part in wet and dry systems.

Table 5: Comparison between measured and predicted airborne sound reduction index R and normalized impact sound pressure levels L n clustered in low, middle, and high frequencies by using the RMSE function for test floor structures.

root-mean-square errors in dB

Frequency range Low Middle High

50 − 200 Hz 250 − 1000 Hz 1250 − 5000 Hz

R (airborne sound) 3.76 2.55 4.79

L n (impact sound) 3.79 3.48 4.97

5. CONCLUSIONS

The present publication demonstrates a potential of artificial neural networks model in prediction of airborne sound reduction index R and normalized impact sound pressure levels L n using 252 standardized laboratory measurements of lightweight wooden floors. The developed model shows an acceptable accuracy with root-mean-square error ( RMS E ) values within 1 . 67 − 7 . 63 dB for estimating of insulation curves (airborne and impact) in the frequency bands 50 − 5000 Hz . The accuracy is

improved when considering only the single-number quantities: the weighted airborne sound reduction index R w (within 0 − 2 dB ) and the weighted normalized impact sound pressure level L n , w (within 0 − 5 dB ). Overall, the presented ANN model demonstrates a better accuracy for airborne sound than impact sound prediction, especially at middle frequencies (250 − 1000 Hz ). However, the predictions around the fundamental frequencies and the critical frequency, in many cases, showed deviations, focusing on the importance of the resonance e ff ects and the occasional prediction ine ffi ciency near that areas. A sensitivity analysis employed to explore the e ff ects of the parameters on the prediction of sound insulation. Thickness and the density of upper and main parts in the floor components are important parameters across all frequencies. Further research would be on developing an ANN model to predict the airborne sound insulation curves of lightweight wooden façades. A sensitivity analysis may be applied to reveal the most important parameters on the estimations.

ACKNOWLEDGMENTS

The authors are grateful to Natural Sciences and Engineering Research Council (NSERC) of Canada for the financial support through its IRC and CRD programs (IRCPJ 461745-18 and RDCPJ 524504- 18), the Region Nouvelle-Aquitaine for the financial support (ref. 2017-1R10223), and the industrial partners of the NSERC industrial chair on eco-responsible wood construction (CIRCERB). Special thanks to Lund university, FCBA, FPInnovations and CNRC for providing sound insulation data.

A. APPENDIX

Figure A1: Test floor configurations used to evaluate the predictive accuracy of airborne and impact sound insulation curves.

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