- Email: [email protected]
Wooden windows: Sound insulation evaluation by means of artificial neural networks
Applied Acoustics 74 (2013) 740–745
Contents lists available at SciVerse ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Wooden windows: Sound insulation evaluation by means of artificial neural networks Cinzia Buratti ⇑, Linda Barelli, Elisa Moretti Department of Industrial Engineering, University of Perugia, Via G. Duranti 1/A4, 06125 Perugia, Italy
a r t i c l e
i n f o
Article history: Received 5 November 2012 Received in revised form 30 November 2012 Accepted 3 December 2012 Available online 4 January 2013 Keywords: Wooden windows Sound insulation prediction Artificial neural network Experimental data
a b s t r a c t Windows are the weakest part of a façade in terms of acoustic performance: the weighted sound insulation index (Rw), measured according to ISO 140-3, is the fundamental parameter to evaluate the façade acoustic insulation. The paper aims at developing an artificial neural network (ANN) model to estimate the Rw value of wooden windows based on a limited number of windows parameters; this is a new approach because acoustic phenomena are non-linear and affected by a plurality of factors and, therefore, usually investigated through experimentation. Data set is taken from experimental campaigns carried out at the Laboratory of Acoustics, University of Perugia. A multilayer feed-forward approach was chosen and the model was implemented in MATLAB. On the basis of the results obtained by means of a preliminary training and test campaign of several ANN architectures, five main parameters were selected as network inputs: window typology, frame and shutters thickness, number of gaskets, Rw of glazing; Rw value of the window is the network output. Different ANN configurations were trained and a root mean-square error less than 3% was obtained, comparable to measurement uncertainty. This approach allows to develop a model which, with input parameters varying within appropriate ranges, can easily estimate the acoustic performance of wooden windows without experimental campaign on prototypes, saving both money and time. If the training data set is large enough, the presented approach could be very useful for design and optimization of acoustic performance of new products. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Acoustic conditions within a building contribute to the global wellbeing of the occupants together with thermal and visual comfort. Noise gets into a building via many different paths and from various noise sources: external, such as road traffic, railways, aircraft, and industry, or internal, such as building mechanical services or human activities [1,2]. The façade airborne sound insulation is crucial in protecting a building against external noise and in assuring indoor acoustic comfort conditions [3]. It depends on the sound insulation index (R) and on the surface area of the different components of the façade, as walls, windows, and doors. In modern buildings, lightweight structures with large windows are often used and they represent the weakest part of the façade in terms of acoustic performance. Therefore, acoustic performance of windows should be carefully investigated, in order to assure an adequate sound insulation of the envelope. In this context, the weighted sound insulation ⇑ Corresponding author. Tel.: +39 075 5853993; fax: +39 075 5853916. E-mail address: [email protected] (C. Buratti). 0003-682X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2012.12.001
index (Rw) is the fundamental parameter to characterize the acoustic performance of windows and it should be known also in order to accomplish the statutory requirements in terms of façade acoustic insulation. Rw is usually measured for each window typology in laboratory, according to ISO 10140-2 procedure [4], spending long time and lot of money. The present study is focused on an artificial neural network (ANN) model to estimate the Rw value of wooden windows, without experimental campaigns on window samples. The difficulties due to the phenomenon complexity, non-linearity and also to the uncertainty affecting sound insulation index measurements are significant if a deterministic approach is tried. Therefore, the artificial neural networks (ANN) technique was chosen; it is a very powerful tool for the study of non-linear systems with available data affected by uncertainty and noise. When a large set of experimental data are in fact available for the ANN set-up, this technique can overcome the limitations of conventional approaches, which require a complex analytical method or several experimental tests. Moreover, ANN methods are able to carry out real time calculations. The ANN model was based on a limited number of windows parameters and it was set up using a data set from the experimental
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campaigns carried out at the Laboratory of Acoustics of the University of Perugia. 2. Background 2.1. Sound insulation of windows Many factors contribute to the sound insulation of a window: type (thickness, cavity width and infill gas) and dimensions of glazing system, type of joinery, joints and seals in the window-opening (system, presence of shutters, and type of the shutter boxes). Nevertheless, the airborne sound insulation mainly depends on the frame and on the acoustic performance of glazing [5]. Sound insulation properties of glazing can be improved by using thick glass panes or expanding the gas space, but laminated glasses or special gases in the interspace have to be installed in order to reach higher Rw values (>35 dB). In the most common cases, as long as Rw of the glazing is under 35 dB and the frame area is less than of 30% of the window area, the influence of the frame on the total acoustic performance can be neglected and it could improve the sound insulation. Nevertheless, when Rw of the glazing varies between 35 and 40 dB, the frame and its air tightness clearly affects the global performance. Finally, windows with a global value of Rw higher than 40 dB require reinforced frames with appropriate gaskets and a very careful installation [6]. Because of the variability of the overall acoustic performance due to numerous parameters which define the window configuration, a simple tool to predict the acoustic performance of a window could be very useful in order to design the building envelope, without laboratory measurements for each configuration. 2.2. Artificial neural networks: basics and acoustic applications Artificial Neural Network (ANN) is a mathematical model able to simulate the biological neural network behavior, like as human brain. ANN simulates a black box model which can learn the relationship between input and output during the learning phase, without detailed information about the investigated system. ANN is constituted by a large number of interconnected artificial neurons [7]. The Multi-Layer Feed Forward Neural Network (MLFFN) is the most commonly used network architecture, where at least three or more layers are present: an input layer, an output layer and a number of hidden layers that allow the network to learn linear and non-linear relationships between input and output vectors. The number of neurons in the input layer is equal to the number of parameters that affect the result, while the number of neurons in the output layer corresponds to the number of parameters to be estimated. The MLFFN model processing consists of two different stages: (1) Training/learning stage, where the network is trained with a data set to predict an output based on input data. (2) Testing/validation stage, where the network is tested to stop or continue the training stage until the calculated error is within the tolerance limits. In the first stage, Back error propagation learning algorithms are widely used, because of their speed. More details about ANN models are reported in the Literature [7]; the equations are described in a previous work [8]. During last years, ANNs have been gradually used as an alternative to conventional methods, in order to solve complex problems and to study non-linear systems in various areas, such
Fig. 1. View of two wooden windows (window and French window) during the experimental campaign: (a) emitting room side and (b) receiving room side.
as engineering, medicine, mathematics, economics, meteorology and many others. Some recent applications are related to thermal engineering and energy systems in buildings [9]. ANN models are applied also in acoustics [10–18]. Literature studies showed that they could predict the distribution of sound
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in rooms [10–14]: the estimated sound pressure levels were in good agreement with experimental data as the values obtained with analytic methods [10]. Neural networks are also powerful alternative methods to predicted reverberation time in rooms [13] and the results agreed with values calculated using Sabine’s and Eyring’s classical equations or ray tracing models; moreover, the results showed that neural network analysis could identify the variables which have the greatest effect on the output [14]. Artificial Neural Network algorithms were also employed to estimate the sound absorption coefficients of different perforated wooden panels with various setting combinations [15] or to evaluate acoustic impedance of walls [16]. Finally, an ANN model was developed in order to predict sound transmission loss during propagation outdoors, with a good accuracy [17].
a single number quantity, the weighted sound insulation index Rw, according to EN ISO 717-1 [22]. 55 different wood samples (two shutters windows (1.23 1.48 m) and two shutters French windows) were investigated in the period between 2009 and 2011. Rw values measured for the samples are reported in Fig. 2 vs. one of the most significant parameters, Rw of the glazing. Results showed that the global performance of a window varies in a wide range (33–44 dB). If Rw of glazing is lower than 37–38 dB, Rw of the window can be higher than the one of the glazing, due to the positive effect of frame. On the contrary, when the acoustic performance of the glazing increases, the frame has a negative effect on the overall Rw value, which is in general lower than the one of the glazing.
3. Materials and methods
3.2. ANN modeling
3.1. Laboratory measurements methodology according to ISO 10140-2 [4]
The aim of the ANN model was to predict weighted sound insulation index of wooden windows, based on a limited number of parameters. A multi-layer feed forward neural network with two hidden layers was chosen and a Back Propagation learning algorithm with binary sigmoid transfer function was considered. The model was implemented in MATLAB, considering a variable learning rate and a random initial distribution of weights. The number of neurons in the input layer was equal to the number of input parameters, whereas only one neuron, corresponding to the Rw value of the window, was in the output layer. The previously described experimental database was divided into two sets: training and testing. The ANN model was trained using 48 randomly selected data, while the remaining data were used for the network validating. The optimal neurons number in the two hidden layers was determined during the training stage.
The experimental campaign was carried out at the Laboratory of Acoustics of the University of Perugia, into two coupled reverberating rooms in compliance with EN ISO 140-1 [19,20]. The volume of the emitting room is 53.36 m3, the one of the receiving room 62.79 m3. The tested windows were installed on a well-insulated brick wall, between emitting and receiving room. The windows were placed on a frame, in the same way as the situ [21]. The joints of the frame were sealed with an elastic sealant on both sides. Fig. 1 shows a view of two samples placed in the test wall. Sound insulation index R vs. frequency was measured in 1/3 octave bands between 100 and 5000 Hz, according to ISO 10140-2 procedure. The frequency dependent values were converted into
Fig. 2. Rw values of the investigated windows and French windows vs. the Rw of the glazing.
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C. Buratti et al. / Applied Acoustics 74 (2013) 740–745 Table 1 Extract from the database. Window typology
Frame thickness (mm)
Shutters thickness (mm)
Rw of glazing (dB)
Number of gaskets
Rw of window (dB, measured data)
Window Window Window Window Window French window French window French window French window French window French window Window French window French window French window French window French window French window French window Window Window French window French window French window Window Window French window French window French window
58 68 69 69 57 68 57 69.3 69.3 69 69 57 57 68 56 70 59 68 68 68 62 68 68 57 69 69 58 68 68
58 68 69 69 68 68 68 69.3 69.3 69 69 67 68 68 62 70 59 68 68 68 62 68 68 57 69 69 58 68 68
44 38 39 29 38 38 38 31 33 41 35 44 40 42 42 44 42 39 40 43 49 41 45 44 46 38 43 41 33
2 2 3 2 1 2 2 2 2 3 2 3 3 3 2 3 2 2 2 3 2 2 2 3 2 2 2 2 2
39 36 39 33 36 39 35 39 39 40 37 41 38 37 37 38 38 38 38 39 38 39 40 39 42 39 36 38 35
The choice of input parameters is an important task in ANN modeling; in the weighted sound reduction index of windows Rw, the following parameters (frame and glazing) should be taken into consideration: – – – – – – – – – –
Table 2 ANN training.
Window typology (window or French window). Frame material (only wooden windows in the present case). Window area. Frame thickness. Shutters thickness. Height of frame connections. Number and kind of gaskets. Glazing typology (single, double or triple glazing). Glazing gas space (gas and thickness). Acoustic performance of glazing (Rw value).
So the starting database was built considering all the possible significant microscopic and macroscopic variables which can affect Rw of the window. A preliminary analysis was carried out to identify the optimal set of input parameters: on the one hand the input set should be sufficiently large to achieve a satisfactory accuracy in the output prediction; on the other hand the inputs should be reduced as much as possible in order to have a practical and userfriendly model. In a preliminary training and test campaign, different ANN architectures were investigated and the Root–Mean– Square (RMS) error made in the test phase was evaluated [8]. On the basis of the obtained results (not shown in details for the sake of brevity), in terms of such a parameter, it was possible to determine the optimal inputs, because in general the best input–output correlation corresponds to the ANN architecture with the lowest RMS error. Finally only five parameters were selected as network inputs: – Window typology (windows and French windows). – Frame thickness (mm). – Shutters thickness (mm).
– Number of gaskets (-). – Rw of glazing (dB). An extract from the wooden windows database is shown in Table 1. 4. Results and discussion On the basis of the preliminary results, a training-test campaign was carried out to optimize the performance of the ANN model by varying the neurons number in the hidden layers. In particular, the number of neurons for each hidden layer was increased from 8 to 30. Table 2 shows the ANN configurations investigated and the corresponding values of the RMS error related to the test phase. The best performance of the ANN model, in terms of RMS error value, was obtained for the configuration characterized by 10–10 neurons in the hidden layers, according to the scheme of Fig. 3.
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Fig. 3. Structure of the developed ANN and limit values of the input parameters.
Fig. 4. Rw predicted data obtained from the ANN model vs. Rw measured data.
Where the input parameters are in the ranges reported in Fig. 3, the ANN model could predict the Rw value of the wooden window within ±3% error. Considering a typical value of Rw, equal to 38 dB for a wooden window, the error corresponds to a very low deviation, equal to about 1.2 dB, and it is comparable with the measurement uncertainty. Preliminary results of this original approach are interesting and encouraging, although the experimental data set is limited. When a larger data set is available, the model could be improved and a better accuracy could be achieved. In fact, when the training data set is large enough, the ANN method could be a useful tool and its accuracy could be compared with complex numerical analysis methods, which are very time-consuming. Moreover, the effect of each model input on the output can be investigated via the ANN model and a complete sensitivity analysis could be carried out if it was developed with a large set of training data.
The ANN model was applied to all the samples of the data set. The data were compared to the experimental ones, as shown in Fig. 4. Results show a good agreement both for windows and French windows, especially in the central range of Rw values. A more significant different is found at the bounds of the range, where less data are available. 5. Conclusion Acoustic performance of windows is necessary when the façade noise insulation has to be calculated. The weighted sound insulation index Rw could be measured in laboratory tests, but it is very time and money demanding. A tool allowing to predict Rw when knowing windows characteristics could be very useful. The present paper aims to show an original application of the artificial neural networks technique, in order to predict the
C. Buratti et al. / Applied Acoustics 74 (2013) 740–745
acoustic performance of wooden windows, and in particular the weighted sound insulation index (Rw). By means of a preliminary ANNs training-test campaign, only five parameters were selected as network inputs: window typology (windows and French windows), frame and shutters thickness, number of gaskets, Rw of glazing. An ANN model with Rw value of window as output was developed by applying Back Propagation algorithm and considering two hidden layers configurations. The ANNs were trained and tested on the basis of an experimental database consisting of 55 wooden windows (tested at the Laboratory of Acoustics of the University of Perugia). The target was a RMS error referred to the test lower than 3% (<1.5 dB considering a typical wooden window). Such values could be considered reliable; in fact they are comparable to measurement uncertainty. In particular the 5–10–10–1 neurons configuration was determined as the optimal one with a test RMS error of 2.37%. Conclusions derived from the study mainly dealt with methodology. Preliminary results showed that the ANN models could represent non-linear systems also with a limited number of parameters. When the input parameters vary within an appropriate range (depending on the data set used for the network training), the ANN model allows to easily estimate the acoustic performance of wooden windows, without experimental campaign on prototypes, allowing to save both money and time. Finally, if the training data set is large enough and it is quite extensive to satisfy the wide variety of manufactured wooden windows, the presented approach could be applied in order to design and to optimize acoustic performance of new products, by selecting the adequate thickness of frames and shutters or gaskets number. References [1] Muneer T, Abodahab N, Weir G, Kubie J. Windows in buildings: thermal, acoustic, visual and solar performance. Oxford: Architectural Press; 2000, ISBN 0 7506 4209 2. [2] Buratti C, Moretti E, Belloni E, Cotana F. Unsteady simulation of energy performance and thermal comfort in non-residential buildings. Build Environ 2013;59:482–91.
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[3] Oral GK, Yener AK, Bayazit NT. Building envelope design with the objective to ensure thermal, visual and acoustic comfort conditions. Build Environ 2004;39(3):281–7. [4] EN ISO 10140-2. Acoustics – Laboratory measurement of sound insulation of building elements – Part 2: Measurement of airborne sound insulation; 2010. [5] Tadeu AJB, Mateus DMR. Sound transmission through single, double and triple glazing. Exp Eval Appl Acoust 2001;62:307–25. [6] Blasco M, Belis J, De Bleecker H. Acoustic failure analysis of windows in buildings. Eng Fail Anal 2011;18:1761–74. [7] Lin CT, Lee GCS. Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems. Prentice Hall; 1996. [8] Buratti C, Barelli L, Moretti E. Application of artificial neural network to predict thermal transmittance of wooden windows. Appl Energ 2012;98:425–32. [9] Kalogirou SA. Artificial neural networks in renewable energy systems applications: a review. Renew Sust Energ Rev 2001;5:373–401. [10] Nannariello J, Hodgson M, Fricke FR. Neural network predictions of speech levels in university classrooms. Appl Acoust 2001;62(7):749–67. [11] Nannariello J, Fricke FR. The use of neural network analysis to predict the acoustic performance of large rooms: Part I: predictions of the parameter G utilizing numerical simulations. Appl Acoust 2001;62(8):917–50. [12] Nannariello J, Fricke FR. The use of neural network analysis to predict the acoustic performance of large rooms: Part II. predictions of the acoustical attributes of concert halls utilizing measured data. Appl Acoust 2001;62(8):951–77. [13] Nannariello J, Fricke FR. The prediction of reverberation time using neural network analysis. Appl Acoust 1999;58:305–25. [14] Nannariello J, Fricke FR. A neural network analysis of the effect of geometric variables on concert hall G values. Appl Acoust 2001;62:1397–410. [15] Lin M, Tsai K, Su B. Estimating the sound absorption coefficients of perforated wooden panels by using artificial neural networks. Appl Acoust 2009;70:31–40. [16] Too G-PJ, Chen SR, Hwang S. Inversion for acoustic impedance of a wall by using artificial neural network. Appl Acoust 2007;68:377–89. [17] Mungiole M, Keith Wilson D. Prediction of outdoor sound transmission loss with an artificial neural network. Appl Acoust 2006;67:324–45. [18] Wilkinson P, Reuben RL, Jones JDC, Barton JS, Hand DP, Carolan TA, et al. Tool wear prediction from acoustic emission and surface characteristics via an artificial neural network. Mech Syst Signal Process 1999;13(6):955–66. [19] EN ISO 140-1. Measurement of sound insulation in buildings and of building elements – requirements for laboratory test facilities with suppressed flanking transmission; 1999. [20] Buratti C, Moretti E. Impact noise reduction: Laboratory and field measurements of different materials performances. 6th European conference on noise control: Advanced solutions for noise control. EURONOISE 2006. Tampere (Finland); 2006. [21] Buratti C, Moretti E. Experimental performance evaluation of aerogel glazing systems. Appl Energ 2012;97:430–7. [22] EN ISO 717-1. Rating of sound insulation in buildings and of buildings elements – Airborne sound insulation; 1996.
Contents lists available at SciVerse ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Wooden windows: Sound insulation evaluation by means of artificial neural networks Cinzia Buratti ⇑, Linda Barelli, Elisa Moretti Department of Industrial Engineering, University of Perugia, Via G. Duranti 1/A4, 06125 Perugia, Italy
a r t i c l e
i n f o
Article history: Received 5 November 2012 Received in revised form 30 November 2012 Accepted 3 December 2012 Available online 4 January 2013 Keywords: Wooden windows Sound insulation prediction Artificial neural network Experimental data
a b s t r a c t Windows are the weakest part of a façade in terms of acoustic performance: the weighted sound insulation index (Rw), measured according to ISO 140-3, is the fundamental parameter to evaluate the façade acoustic insulation. The paper aims at developing an artificial neural network (ANN) model to estimate the Rw value of wooden windows based on a limited number of windows parameters; this is a new approach because acoustic phenomena are non-linear and affected by a plurality of factors and, therefore, usually investigated through experimentation. Data set is taken from experimental campaigns carried out at the Laboratory of Acoustics, University of Perugia. A multilayer feed-forward approach was chosen and the model was implemented in MATLAB. On the basis of the results obtained by means of a preliminary training and test campaign of several ANN architectures, five main parameters were selected as network inputs: window typology, frame and shutters thickness, number of gaskets, Rw of glazing; Rw value of the window is the network output. Different ANN configurations were trained and a root mean-square error less than 3% was obtained, comparable to measurement uncertainty. This approach allows to develop a model which, with input parameters varying within appropriate ranges, can easily estimate the acoustic performance of wooden windows without experimental campaign on prototypes, saving both money and time. If the training data set is large enough, the presented approach could be very useful for design and optimization of acoustic performance of new products. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Acoustic conditions within a building contribute to the global wellbeing of the occupants together with thermal and visual comfort. Noise gets into a building via many different paths and from various noise sources: external, such as road traffic, railways, aircraft, and industry, or internal, such as building mechanical services or human activities [1,2]. The façade airborne sound insulation is crucial in protecting a building against external noise and in assuring indoor acoustic comfort conditions [3]. It depends on the sound insulation index (R) and on the surface area of the different components of the façade, as walls, windows, and doors. In modern buildings, lightweight structures with large windows are often used and they represent the weakest part of the façade in terms of acoustic performance. Therefore, acoustic performance of windows should be carefully investigated, in order to assure an adequate sound insulation of the envelope. In this context, the weighted sound insulation ⇑ Corresponding author. Tel.: +39 075 5853993; fax: +39 075 5853916. E-mail address: [email protected] (C. Buratti). 0003-682X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2012.12.001
index (Rw) is the fundamental parameter to characterize the acoustic performance of windows and it should be known also in order to accomplish the statutory requirements in terms of façade acoustic insulation. Rw is usually measured for each window typology in laboratory, according to ISO 10140-2 procedure [4], spending long time and lot of money. The present study is focused on an artificial neural network (ANN) model to estimate the Rw value of wooden windows, without experimental campaigns on window samples. The difficulties due to the phenomenon complexity, non-linearity and also to the uncertainty affecting sound insulation index measurements are significant if a deterministic approach is tried. Therefore, the artificial neural networks (ANN) technique was chosen; it is a very powerful tool for the study of non-linear systems with available data affected by uncertainty and noise. When a large set of experimental data are in fact available for the ANN set-up, this technique can overcome the limitations of conventional approaches, which require a complex analytical method or several experimental tests. Moreover, ANN methods are able to carry out real time calculations. The ANN model was based on a limited number of windows parameters and it was set up using a data set from the experimental
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campaigns carried out at the Laboratory of Acoustics of the University of Perugia. 2. Background 2.1. Sound insulation of windows Many factors contribute to the sound insulation of a window: type (thickness, cavity width and infill gas) and dimensions of glazing system, type of joinery, joints and seals in the window-opening (system, presence of shutters, and type of the shutter boxes). Nevertheless, the airborne sound insulation mainly depends on the frame and on the acoustic performance of glazing [5]. Sound insulation properties of glazing can be improved by using thick glass panes or expanding the gas space, but laminated glasses or special gases in the interspace have to be installed in order to reach higher Rw values (>35 dB). In the most common cases, as long as Rw of the glazing is under 35 dB and the frame area is less than of 30% of the window area, the influence of the frame on the total acoustic performance can be neglected and it could improve the sound insulation. Nevertheless, when Rw of the glazing varies between 35 and 40 dB, the frame and its air tightness clearly affects the global performance. Finally, windows with a global value of Rw higher than 40 dB require reinforced frames with appropriate gaskets and a very careful installation [6]. Because of the variability of the overall acoustic performance due to numerous parameters which define the window configuration, a simple tool to predict the acoustic performance of a window could be very useful in order to design the building envelope, without laboratory measurements for each configuration. 2.2. Artificial neural networks: basics and acoustic applications Artificial Neural Network (ANN) is a mathematical model able to simulate the biological neural network behavior, like as human brain. ANN simulates a black box model which can learn the relationship between input and output during the learning phase, without detailed information about the investigated system. ANN is constituted by a large number of interconnected artificial neurons [7]. The Multi-Layer Feed Forward Neural Network (MLFFN) is the most commonly used network architecture, where at least three or more layers are present: an input layer, an output layer and a number of hidden layers that allow the network to learn linear and non-linear relationships between input and output vectors. The number of neurons in the input layer is equal to the number of parameters that affect the result, while the number of neurons in the output layer corresponds to the number of parameters to be estimated. The MLFFN model processing consists of two different stages: (1) Training/learning stage, where the network is trained with a data set to predict an output based on input data. (2) Testing/validation stage, where the network is tested to stop or continue the training stage until the calculated error is within the tolerance limits. In the first stage, Back error propagation learning algorithms are widely used, because of their speed. More details about ANN models are reported in the Literature [7]; the equations are described in a previous work [8]. During last years, ANNs have been gradually used as an alternative to conventional methods, in order to solve complex problems and to study non-linear systems in various areas, such
Fig. 1. View of two wooden windows (window and French window) during the experimental campaign: (a) emitting room side and (b) receiving room side.
as engineering, medicine, mathematics, economics, meteorology and many others. Some recent applications are related to thermal engineering and energy systems in buildings [9]. ANN models are applied also in acoustics [10–18]. Literature studies showed that they could predict the distribution of sound
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in rooms [10–14]: the estimated sound pressure levels were in good agreement with experimental data as the values obtained with analytic methods [10]. Neural networks are also powerful alternative methods to predicted reverberation time in rooms [13] and the results agreed with values calculated using Sabine’s and Eyring’s classical equations or ray tracing models; moreover, the results showed that neural network analysis could identify the variables which have the greatest effect on the output [14]. Artificial Neural Network algorithms were also employed to estimate the sound absorption coefficients of different perforated wooden panels with various setting combinations [15] or to evaluate acoustic impedance of walls [16]. Finally, an ANN model was developed in order to predict sound transmission loss during propagation outdoors, with a good accuracy [17].
a single number quantity, the weighted sound insulation index Rw, according to EN ISO 717-1 [22]. 55 different wood samples (two shutters windows (1.23 1.48 m) and two shutters French windows) were investigated in the period between 2009 and 2011. Rw values measured for the samples are reported in Fig. 2 vs. one of the most significant parameters, Rw of the glazing. Results showed that the global performance of a window varies in a wide range (33–44 dB). If Rw of glazing is lower than 37–38 dB, Rw of the window can be higher than the one of the glazing, due to the positive effect of frame. On the contrary, when the acoustic performance of the glazing increases, the frame has a negative effect on the overall Rw value, which is in general lower than the one of the glazing.
3. Materials and methods
3.2. ANN modeling
3.1. Laboratory measurements methodology according to ISO 10140-2 [4]
The aim of the ANN model was to predict weighted sound insulation index of wooden windows, based on a limited number of parameters. A multi-layer feed forward neural network with two hidden layers was chosen and a Back Propagation learning algorithm with binary sigmoid transfer function was considered. The model was implemented in MATLAB, considering a variable learning rate and a random initial distribution of weights. The number of neurons in the input layer was equal to the number of input parameters, whereas only one neuron, corresponding to the Rw value of the window, was in the output layer. The previously described experimental database was divided into two sets: training and testing. The ANN model was trained using 48 randomly selected data, while the remaining data were used for the network validating. The optimal neurons number in the two hidden layers was determined during the training stage.
The experimental campaign was carried out at the Laboratory of Acoustics of the University of Perugia, into two coupled reverberating rooms in compliance with EN ISO 140-1 [19,20]. The volume of the emitting room is 53.36 m3, the one of the receiving room 62.79 m3. The tested windows were installed on a well-insulated brick wall, between emitting and receiving room. The windows were placed on a frame, in the same way as the situ [21]. The joints of the frame were sealed with an elastic sealant on both sides. Fig. 1 shows a view of two samples placed in the test wall. Sound insulation index R vs. frequency was measured in 1/3 octave bands between 100 and 5000 Hz, according to ISO 10140-2 procedure. The frequency dependent values were converted into
Fig. 2. Rw values of the investigated windows and French windows vs. the Rw of the glazing.
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C. Buratti et al. / Applied Acoustics 74 (2013) 740–745 Table 1 Extract from the database. Window typology
Frame thickness (mm)
Shutters thickness (mm)
Rw of glazing (dB)
Number of gaskets
Rw of window (dB, measured data)
Window Window Window Window Window French window French window French window French window French window French window Window French window French window French window French window French window French window French window Window Window French window French window French window Window Window French window French window French window
58 68 69 69 57 68 57 69.3 69.3 69 69 57 57 68 56 70 59 68 68 68 62 68 68 57 69 69 58 68 68
58 68 69 69 68 68 68 69.3 69.3 69 69 67 68 68 62 70 59 68 68 68 62 68 68 57 69 69 58 68 68
44 38 39 29 38 38 38 31 33 41 35 44 40 42 42 44 42 39 40 43 49 41 45 44 46 38 43 41 33
2 2 3 2 1 2 2 2 2 3 2 3 3 3 2 3 2 2 2 3 2 2 2 3 2 2 2 2 2
39 36 39 33 36 39 35 39 39 40 37 41 38 37 37 38 38 38 38 39 38 39 40 39 42 39 36 38 35
The choice of input parameters is an important task in ANN modeling; in the weighted sound reduction index of windows Rw, the following parameters (frame and glazing) should be taken into consideration: – – – – – – – – – –
Table 2 ANN training.
Window typology (window or French window). Frame material (only wooden windows in the present case). Window area. Frame thickness. Shutters thickness. Height of frame connections. Number and kind of gaskets. Glazing typology (single, double or triple glazing). Glazing gas space (gas and thickness). Acoustic performance of glazing (Rw value).
So the starting database was built considering all the possible significant microscopic and macroscopic variables which can affect Rw of the window. A preliminary analysis was carried out to identify the optimal set of input parameters: on the one hand the input set should be sufficiently large to achieve a satisfactory accuracy in the output prediction; on the other hand the inputs should be reduced as much as possible in order to have a practical and userfriendly model. In a preliminary training and test campaign, different ANN architectures were investigated and the Root–Mean– Square (RMS) error made in the test phase was evaluated [8]. On the basis of the obtained results (not shown in details for the sake of brevity), in terms of such a parameter, it was possible to determine the optimal inputs, because in general the best input–output correlation corresponds to the ANN architecture with the lowest RMS error. Finally only five parameters were selected as network inputs: – Window typology (windows and French windows). – Frame thickness (mm). – Shutters thickness (mm).
– Number of gaskets (-). – Rw of glazing (dB). An extract from the wooden windows database is shown in Table 1. 4. Results and discussion On the basis of the preliminary results, a training-test campaign was carried out to optimize the performance of the ANN model by varying the neurons number in the hidden layers. In particular, the number of neurons for each hidden layer was increased from 8 to 30. Table 2 shows the ANN configurations investigated and the corresponding values of the RMS error related to the test phase. The best performance of the ANN model, in terms of RMS error value, was obtained for the configuration characterized by 10–10 neurons in the hidden layers, according to the scheme of Fig. 3.
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Fig. 3. Structure of the developed ANN and limit values of the input parameters.
Fig. 4. Rw predicted data obtained from the ANN model vs. Rw measured data.
Where the input parameters are in the ranges reported in Fig. 3, the ANN model could predict the Rw value of the wooden window within ±3% error. Considering a typical value of Rw, equal to 38 dB for a wooden window, the error corresponds to a very low deviation, equal to about 1.2 dB, and it is comparable with the measurement uncertainty. Preliminary results of this original approach are interesting and encouraging, although the experimental data set is limited. When a larger data set is available, the model could be improved and a better accuracy could be achieved. In fact, when the training data set is large enough, the ANN method could be a useful tool and its accuracy could be compared with complex numerical analysis methods, which are very time-consuming. Moreover, the effect of each model input on the output can be investigated via the ANN model and a complete sensitivity analysis could be carried out if it was developed with a large set of training data.
The ANN model was applied to all the samples of the data set. The data were compared to the experimental ones, as shown in Fig. 4. Results show a good agreement both for windows and French windows, especially in the central range of Rw values. A more significant different is found at the bounds of the range, where less data are available. 5. Conclusion Acoustic performance of windows is necessary when the façade noise insulation has to be calculated. The weighted sound insulation index Rw could be measured in laboratory tests, but it is very time and money demanding. A tool allowing to predict Rw when knowing windows characteristics could be very useful. The present paper aims to show an original application of the artificial neural networks technique, in order to predict the
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acoustic performance of wooden windows, and in particular the weighted sound insulation index (Rw). By means of a preliminary ANNs training-test campaign, only five parameters were selected as network inputs: window typology (windows and French windows), frame and shutters thickness, number of gaskets, Rw of glazing. An ANN model with Rw value of window as output was developed by applying Back Propagation algorithm and considering two hidden layers configurations. The ANNs were trained and tested on the basis of an experimental database consisting of 55 wooden windows (tested at the Laboratory of Acoustics of the University of Perugia). The target was a RMS error referred to the test lower than 3% (<1.5 dB considering a typical wooden window). Such values could be considered reliable; in fact they are comparable to measurement uncertainty. In particular the 5–10–10–1 neurons configuration was determined as the optimal one with a test RMS error of 2.37%. Conclusions derived from the study mainly dealt with methodology. Preliminary results showed that the ANN models could represent non-linear systems also with a limited number of parameters. When the input parameters vary within an appropriate range (depending on the data set used for the network training), the ANN model allows to easily estimate the acoustic performance of wooden windows, without experimental campaign on prototypes, allowing to save both money and time. Finally, if the training data set is large enough and it is quite extensive to satisfy the wide variety of manufactured wooden windows, the presented approach could be applied in order to design and to optimize acoustic performance of new products, by selecting the adequate thickness of frames and shutters or gaskets number. References [1] Muneer T, Abodahab N, Weir G, Kubie J. Windows in buildings: thermal, acoustic, visual and solar performance. Oxford: Architectural Press; 2000, ISBN 0 7506 4209 2. [2] Buratti C, Moretti E, Belloni E, Cotana F. Unsteady simulation of energy performance and thermal comfort in non-residential buildings. Build Environ 2013;59:482–91.
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