Integrating parametric design and machine learning for room acoustics prediction in the early design stage of concert halls

Abstract

The room acoustics design of concert halls plays an important role in sound quality, and machine learning has been proposed as an advanced approach for predicting room acoustics. However, previous studies often use geometric (such as length, width, and height) and material parameters as features, resulting in high accuracy but limited generality when applied to different room types. Hence, this study proposed a machine learning based parametric design framework on the Rhino-Grasshopper platform. The approach used distributed equivalent absorption areas as features by considering the importance of the first reflection in concert halls, thus improving generality in the early design stage. Trained on a dataset combining two different types of concert halls, the fivefold cross-validation results demonstrated that the Mean Absolute Percentage Error (MAPE) for Reverberation time (T₃₀) and the Root Mean Square Error (RMSE) for both Clarity 80 (C₈₀) and Sound strength (G) remained within 1 Just Noticeable Difference (1 JND). The high accuracy highlights the advantages of this framework in comparing different types of concert halls and broadens the capability of architects to optimize design proposals in the early design stage.

Keywords

room acoustics pachyderm machine learning ANNs model

Introduction

Music, space, and region were inseparable before contemporary room acoustic science was established. In the Middle Ages, music often featured slow, sustained tones, influenced by the spacious volumes of heavy stone-built churches,¹ which contributed to high reverberation times. After the Renaissance, the richly decorated churches, with their shorter reverberation times, fostered the expressive and exquisite forms of baroque music.² Since reverberation time was defined,³ room acoustics have become designable.

Nowadays, acoustic simulation tools enable the prediction and evaluation of room acoustic quality before construction.^4,5 Moreover, acoustic performance-based design has been applied in the design of acoustical buildings to balance different architectural requirements, including esthetics, cultural, and acoustic performance.^6,7 In addition, design methods that shape spaces according to defined acoustic qualities have also been developed.⁸ In the early design stage, combining parametric design allows architects to explore more possibilities for design proposals.⁹ As a tool to support such exploration, Pachyderm¹⁰ is an acoustic simulation plug-in for Rhino Grasshopper, a widely used parametric design modeling tool in architecture. It has been validated through comparisons with measurements and other simulation tools,^11
–13 and has been used to study concert hall optimization,¹⁴ evaluate the performance of narrow street façades,¹⁵ and generate data for machine learning in the design of educational buildings.¹⁶

Though acoustic simulation is widely used, it takes a lot of time to evaluate design proposals.^17,18 To accelerate the process, recent studies have explored the potential of using machine learning as a substitute for simulations.¹⁹ Nannariello and Fricke²⁰ collected datasets of 71 reverberation times from references, using maximum length, width, height, and absorption coefficient as eigenvalues for machine learning, and the prediction shows an error of 2%–38%. Broyles and Rusk²¹ collected reverberation time data from 50 concert halls of different types, applying Random Forest. The MAPE of the prediction is noticeably lower than that of Sabine and Eyring equations. Yeh and Tsay²² used a measurement-calibrated classroom model to generate datasets of 800 simulations by applying different shapes and absorption coefficients. The RMSE and MAPE of each acoustic index prediction through the GBDT model are all under 2 JND. Falcon Perez²³ proposed a machine learning framework using panoramic photo pixels multiplied by the absorption coefficient as eigenvalues to improve the limitations of the Sabine’s equation. The accuracy of the prediction is twice that of the Sabine’s equation. Manesh et al.¹⁶ generated simulation datasets using Pachyderm in Rhino Grasshopper and employed CatBoost and Generative Adversarial Networks (GANs) models to predict acoustic indices such as T₃₀, EDT, C₈₀, D₅₀, and STI, including heatmaps. Borrel-Jensen et al.²⁴ used transfer learning to predict sound propagation in different 3D scenes.

Although predictions of room acoustic quality have significantly diversified, architects still tend to rely on Sabine’s equation or simple acoustic simulations during the early design stages. This may be due to the fact that most of the aforementioned studies are based on constant environments, such as fixed source positions.²⁵ Moreover, room acoustic simulations are often employed to ensure acoustic quality after the design has been finalized. The process of translating models and exchanging information between architects and acoustic engineers,²⁶ even in cases of good collaboration, can be time-consuming.

For concert hall design in the early design stage, estimating room acoustic quality is essential to support architects’ free-spirited design ideas. The aim of this study is to propose a machine learning framework that streamlines the process between architects and acousticians, allowing architects to explore more possibilities in concert hall design. With the advancement of acoustic simulation and machine learning technologies, the concert hall design can become more unrestricted, allowing architects to break from traditional typologies and explore spatial forms and esthetics. By moving beyond the constraints of typological rules, concert hall design can transcend limitations and inspire new realms of creativity.

Method

The workflow of this study is shown in Figure 1. The following steps were all conducted on Rhino-Grasshopper platform to integrate with parametric design for architectural applications. First, two parametric models, representing shoebox and surround-type concert halls, were developed and used to perform acoustic simulations. The resulting acoustic indices, combined with normalized geometric features obtained by splitting the parametric models, were prepared as datasets, intermixed and shuffled to ensure diversity and minimize potential biases. Following fivefold cross-validation, the datasets were split into 80% for training and 20% for validation. Finally, the prediction accuracy, assessed through Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE), was compared with Sabine’s equation, and evaluated using the Just Noticeable Difference (JND).

Figure 1.

Workflow: model construction, acoustic simulation, and ANN prediction.

Indices for room acoustics evaluation

In the early design stage of concert halls, the room acoustic quality assessment of the entire space is the main concern for architects when adjusting design proposals. Hence, not all acoustic indices are equally suitable, it is necessary to select those that provide critical information relevant to the study’s purpose.²⁷ Reverberation Time (RT)³ plays a significant role in room acoustic quality and is also known as the “mother” of room acoustic indices.²⁸ However, reverberation time cannot fully represent the auditory experience.²⁹ It describes the dissipation of sound energy within a space but lacks information about sound energy direction and distribution. To analyze energy distribution over time, Clarity³⁰ is an appropriate acoustic index that describes the ratio of early to late energy. Specifically, Clarity 80 (C₈₀), which considers 80 ms as the boundary between early and late reflections, is often used to study the music clarity of concert halls.³¹

In concert hall design, geometry is an important factor that affects early reflections, leading to a good acoustic experience for the audience.³² Sound Pressure Level (SPL) is another important acoustic index that describes energy distribution and is often evaluated through relative SPL in concert hall design.^33,34 To provide a more normalized evaluation independent of the sound source level, Sound strength (G) is utilized in this study.

To summarize, three acoustic indices were chosen to evaluate room acoustic quality in the early design stage of concert hall design, as shown in Table 1. For T₃₀, the values were the average of all receivers, whereas C₈₀ and G were analyzed individually at each receiver. The target frequencies were the average of 500 and 1000 Hz in this study.³⁵

Table 1.

Selected acoustic indices and target frequencies.

Acoustic index	Definition	Target frequency
T₃₀	The time sound energy decays from 5 to 35 dB, doubled to obtain a linear transformation into T₆₀	Average of 500 and 1000 Hz
C₈₀	The ratio of early and late sound energy, using 80 ms as the boundary.
G	The sound pressure level relative to the free-field level at 10 m from the same source.

Parametric models and boundary conditions

The two parametric models, representing shoebox and surround-type (also known as vineyard-type) concert halls as shown in Figure 2, were simplified from the Großer Musikvereinssaal and the Berliner Philharmonie by adopting similar shape, volume, and overall proportions.^36,37 These parametric models were established in Rhino-Grasshopper to support later acoustic simulations.

Figure 2.

Parametric variations of shoebox and surround-type models.

The geometry variables of the shoebox-type parametric model include length, stage depth, width, height, and lift, resulting in 405 combinations. These variables show the possibilities of shoebox-type concert hall designs, such as wider or taller configurations and the slope of raked auditorium floor. The geometry variables of the surround-type parametric model include the length, width, and height of each section, resulting in 432 combinations. These variables emphasize the boundary and ceiling geometry angles, highlighting the importance of side walls and ceiling design in surround-type concert halls. Both parametric models were simplified and exhibit axial symmetry to reflect conditions during the early design stage.

The absorption coefficients ranged from 0.1 to 0.5 for the walls and ceiling and from 0.5 to 0.9 for the audience. Additionally, the scattering coefficients were set to 0.1 for the walls and ceiling, and 0.7 for the audience, representing a typical case for concert halls.³⁸ The combinations of the two parametric models are summarized in Table 2.

Table 2.

Parameter ranges and search space of shoebox and surround-type models.

Model	Parameter	Range	Variable count
Shoebox-type	Length	23–47 m	5
	Stage depth	6–10 m	3
	Width	10–20 m	3
	Height	10–20 m	3
	Lift	0–1/2 height	3
	Absorption coefficient of stage, stage wall, ceiling, back wall	0.1–0.5	3
	Absorption coefficient of side wall	0.1–0.5	3
	Absorption coefficient of audience area	0.5–0.9	3
	Search Space		10,935
Surround-type	Length of middle	20–35 m	2
	Length of back	10–15 m	2
	Width of middle	35–45 m	2
	Width of back	15–30 m	2
	Height of front and back	15–25 m	3
	Height of middle-F	15–25 m	3
	Height of middle-B	15–25 m	3
	Absorption coefficient of stage, stage wall, ceiling, back wall	0.1–0.5	3
	Absorption coefficient of side wall	0.1–0.5	3
	Absorption coefficient of audience area	0.5–0.9	3
	Search space		11,664

The acoustic simulation was operated using the Pachyderm plug-in for the Rhino-Grasshopper platform automatically. For both parametric models, one omni-directional sound source was placed at the center of the stage at a height of 1.5 m. In the shoebox-type, 9 receivers were evenly distributed, while in the surround-type, a total of 10 receivers were placed, with 1 in the center of each audience area. All receivers were set at a height of 1.5 m. The reflection order was set to three, meaning the calculation of specular reflections considered only the image-source method up to the third order, while the ray-tracing method continuously computed diffuse reflections of all orders. The cut-off time was set to 6000 ms, and the number of rays was set to the Minimum Convergence, where Pachyderm automatically adds rays through an iterative process and converges once the variance of the energy decay stabilizes.

The total search spaces of the two parametric models are 10,935 and 11,664. The simulations were performed separately, recording data on T₃₀, C₈₀, G, and geometry information, based on 1/1 Octave Bands from 63 to 8000 Hz.

Features analysis and rescaling

Architectural design is a phased decision-making process, with architects determining more details as the design is elaborated. Therefore, due to its minimal parameter requirements, Sabine’s equation is widely used to predict reverberation time during the early design stage with limited information as shown in equation (1), where T₆₀ is the time (s) of sound energy decay 60 dB, V is the volume of the room (m³), S is the boundary surface area (m²), and $\bar{α}$ is the average absorption coefficient.

T_{60} = 0.161 V / S \bar{α}

(1)

Although Sabine’s equation is applicable under specific conditions, it lacks the ability to describe the sound source position and the distribution of equivalent absorption areas. Consequently, completely different geometries can result in the same calculated reverberation times. To overcome this limitation, this study proposes a feature extraction method by splitting the model based on the sound source position, respecting the importance of early reflections.³⁹ In acoustic simulation, a point sound source is regarded as having spherical propagation. As shown in Figure 3, the use of the distributed equivalent absorption area allows for capturing the distribution of equivalent absorption areas and sound source positions, which Sabine’s equation ignores due to its uniform absorption assumption.

Figure 3.

Comparison: Sabine’s equation versus distributed equivalent absorption area.

For this research, the interval for model splitting was set to 3.4 m, approximately equivalent to the distance sound travels in 10 ms. Theoretically, smaller intervals provide higher descriptive power for the model. Beranek⁴⁰ suggests that the maximum length of the audience area in a concert hall should be less than 40 m. Considering the depth of the stage, the maximum analysis length was determined to be 51 m, which is approximately equivalent to the distance sound travels in 150 ms. In addition to the distributed equivalent absorption areas, the volume V (m³) and total equivalent absorption area A_T (m²) were also considered as geometric features. Furthermore, since C₈₀ and G are strongly influenced by the distance from the sound source to the receiver (L_SR), this distance was also included as a geometric feature. These geometric features were used for machine learning predictions. However, the differences in the ranges of each feature are significant. To accelerate the process and avoid local convergence, all features were rescaled based on their data domains, as shown in Table 3. Note that the distributed equivalent absorption area beyond 140 ms (A_140~150) of sound propagation length can be inferred from the total equivalent absorption area.

Table 3.

Rescaling ranges of geometric features.

Geometric features	Rescaling range
Volume (V)	0–50,000 m³ to 0–1
Total equivalent sound absorption area (A_T)	0–5000 m² to 0–1
Distributed equivalent sound absorption area (A_0~140)	0–1000 m² to 0–1
Length from source to receiver (L_SR)	0–50 m to 0–1

Machine learning framework

After generating data through the aforementioned methods, these datasets were utilized for machine learning. To better integrate with parametric design, the machine learning process was conducted using the Pug plug-in for Rhino-Grasshopper, which is built on Keras-TensorFlow. Considering the inherent variability in acoustic simulation results, Artificial Neural Network (ANN) were chosen for their capability to learn complex patterns from data and reduce the impact of simulation uncertainties. The hyperparameters settings, as shown in Table 4, are the result of adjustments and improvement in accuracy and convergence speed.

Table 4.

ANN hyperparameter settings.

Hyperparameter	Type/value
Hidden layer	3
Unit per hidden layer	400
Activation function	ReLu
Initializer	HeNormal
Optimizer	Adam
Learning rate	0.001
Bach	32
Epoch	100

Results and discussion

The range and relationship between each feature are highly related to the quality of machine learning, so it is necessary to analyze the distribution of features before applying them to machine learning. To ensure the dataset reflects realistic conditions for concert halls, only cases with a T₃₀ ranging from 1.2 to 3.0 s were kept for the subsequent analysis.³⁷ Consequently, 38.6% of the shoebox-type and 29.1% of the surround-type results were excluded from the dataset. As shown in Figure 4, the surround-type hall contains a larger volume and leads to a higher total equivalent absorption area, further resulting in a higher distributed equivalent absorption area. The shoebox-type hall contains a wider range of L_SR due to the longer maximum length of the audience area. For the simulation results, the shoebox-type shows a lower T₃₀ and a higher C₈₀. This result indicates that T₃₀ is negatively correlated with C₈₀, which agrees with previous studies.⁴¹

Figure 4.

Distribution of features and acoustic indices from shoebox and surround-type models.

The correlation matrix provides another way to analyze the relationship between features: values close to +1 indicate a strong positive correlation, values close to −1 indicate a strong negative correlation, and values near 0 imply almost no correlation. As shown in Figure 5, the relationships between each acoustic index and the distributed equivalent absorption area show that the effect of absorption decays with distance, indicating the impact of early absorption, as well as early reflection. This supports the potential of using distributed equivalent absorption area as a feature to describe a model. In addition, L_SR significantly affects G, which aligns with the general principle that sound energy decreases with distance. The significant effect from the distributed equivalent absorption area starting at A_20~30 rather than A_0~10 may be due to the design of the surround-type parametric model. Since the variable features focus on boundary elements such as side walls and ceilings, the equivalent absorption area near the sound source shows less variation.

Figure 5.

Correlation matrices of acoustic indices and features: (a) shoebox-type and (b) surround-type.

Predictive models evaluation

The evaluation was separated into three parts, using the datasets of shoebox and surround-type respectively for training and validation, as well as an intermixed dataset. To assess the difference between actual and predicted values, the Just Noticeable Difference (JND) was often used as a reference for evaluating accuracy. However, different acoustic indices are suited to different ways of expressing these differences. For example, RT is commonly expressed by percentage difference, while C₈₀ is typically expressed by absolute difference. Therefore, the Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) were selected to assess the accuracy of predictions from the ANN models compared to the actual values obtained from Pachyderm simulations, as shown in equation (2) and equation (3), where $y_{i}$ is the actual value, ${y^{'}}_{i}$ is the predictive value, and $n$ is the size of the dataset.

M A P E = \frac{1}{n} \sum_{i = 1}^{n} | \frac{{y^{'}}_{i} - y_{i}}{y_{i}} |

(2)

R M S E = \sqrt{\sum_{i = 1}^{n} \frac{{({y^{'}}_{i} - y_{i})}^{2}}{n}}

(3)

According to ISO 3382-1:2009,³⁵ the JND of RT is 5%, and for C₈₀ and G are 1 dB. Other studies have reported that the JND of RT ranges from 6% to 39% under different conditions,⁴² and for C₈₀, it is approximately 1.6 ± 0.3 dB.⁴³ The predictive model accuracy was evaluated through fivefold cross-validation to avoid sample selection bias. The results from each fold were overlaid in the subsequent figures for discussion.

Prediction accuracy

The average accuracy of each fold is shown in Table 5, and the overlaid scatter plots of predicted versus actual values for each fold are presented in Figure 6. The MAPE and RMSE for each index are all within 1 JND. To further evaluate prediction accuracy, the results are also presented as the percentage of predictions falling within JND intervals.

Table 5.

Average results of fivefold cross validation using different datasets.

Acoustic		Fivefold cross validation dataset
index		Shoebox type	Surround type	Intermixed
T₃₀	MAPE	3.9%	3.2%	3.7%
	<1 JND	72.88%	81.87%	75.40%
	<2 JND	93.70%	96.57%	94.40%
C₈₀	RMSE	0.3	0.6	0.5
	<1 JND	99.73%	95.92%	97.45%
	<2 JND	99.99%	99.55%	99.68%
G	RMSE	0.2	0.4	0.4
	<1 dBA	100.00%	97.90%	98.85%
	<2 dBA	100.00%	99.65%	99.76%

Figure 6.

Prediction versus actual value scatter plots of fivefold cross validation.

For the T₃₀ prediction, the validation using the surround-type dataset exhibits deviations at shorter reverberation times. This may be due to the dataset boundaries established after data filtering. However, the validation using the intermixed dataset maintains high accuracy, which indicates that the predictive model can identify the two types of halls through overlapping feature distributions within a single framework. Compared with Sabine’s equation, the predictive model shows lower errors relative to the Pachyderm simulation results, which are defined as the actual values in the validation datasets. Sabine’s equation often underestimates the reverberation time, which can be attributed to the assumption of a uniform sound field.

For the C₈₀ and G predictions, the validation using the shoebox-type dataset shows high accuracy, with 100% and 99.73% of the prediction errors falling within 1 JND. This may be attributed to the simple variation in L_SR and the strong relation between C₈₀, G, and L_SR. In contrast, the accuracy of the validation using the surround-type dataset is lower for both C₈₀ and G. This may be caused by the numerous acoustic shadows created by the vertical surfaces in the surround-type audience areas. Without considering the solid angle and the acoustic shadowing effect, the spherical splitting method might lead to overestimating the effective absorption area. Furthermore, the scatter plot of the intermixed dataset demonstrates an overlaid distribution combining shoebox and surround-types. Compared to individual datasets, the intermixed dataset shows several interference deviations. However, most of the overlapping predictions still fall within 1 JND. This indicates that despite the interference, the model can evaluate both hall types.

Conclusion

In this study, a new method for describing acoustic simulation models has been developed. Distributed equivalent absorption areas relative to the sound source were introduced as features for the ANNs model, replacing the commonly used geometric or material parameters in previous studies. This approach integrates the geometric features of shoebox and surround-type concert halls into a single machine learning framework.

In the early design stage, information about the hall is very limited while design proposals change quickly. Most existing methods require detailed data that is not yet available at this stage. However, architects need to approximately evaluate and rapidly eliminate impractical proposals. Although detailed and professional acoustic consultation remains necessary, this study provides a complementary tool for the exploration of architectural design.

By using distributed equivalent absorption areas, geometric features of different hall types could be captured in the same way. As shown in Figure 7, the predicted MAPE and RMSE of the three indices in this study are all under 1 JND for each dataset. Though this accuracy is based on the simulation results of Pachyderm, as an acoustic simulation engine, Pachyderm is replaceable in this framework. Theoretically, the machine learning framework should be adaptable to more advanced simulation or realistic measurement datasets in the future.

Figure 7.

Overall prediction accuracy by JND for Sabine’s equation and ANNs model.

Limitation and future work

In this study, the concert hall geometries were simplified to reflect the exploratory stage of architectural design. However, features such as balconies and reflectors also play crucial roles in real-world conditions. To provide more realistic simulations, integrating these complex geometric elements and sound source configurations, such as a full symphony orchestra, remains a priority for future work.

Furthermore, while the acoustic performance of concert halls was evaluated using three indices: T₃₀, C₈₀, and G, other indices, such as Inter-Aural Cross-Correlation (IACC) and Lateral Energy Fraction (LF), are equally critical for comprehensive auditorium experiences. As these indices are highly sensitive to reflection angles, introducing solid angle parameters from the sound source is a necessary step in future.

Footnotes

ORCID iDs

Yen-Chieh Yu

Yaw-Shyan Tsay

Author contributions

Y.C. Yu and Y.S. Tsay conceived of the presented idea. Y.C. Yu developed the theory and performed the computations. Y.S. Tsay received and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project has received funding from the National Science and Technology Council of Taiwan (NSTC 113-2221-E-006-071-).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Blesser

Salter

LR.

Spaces speak, are you listening? In: Experiencing aural architecture. The MIT Press, Cambridge, MA, 2007, p.232. https://doi.org/10.1121/1.2537427

Cirillo

Martellotta

Worship, acoustics, and architecture. Multi-Science Publishing Company, 2006.

Sabine

WC.

Collected papers on acoustics. Harvard University Press, 1922.

Beranek

LL.

Concert hall acoustics—1992. J Acoust Soc Am 1992; 92(1): 1–39. https://doi.org/10.1121/1.404283

Beranek

Acoustics and musical qualities. J Acoust Soc Am 1996; 99: 2647–2652. https://doi.org/10.1121/1.414808

Badino

Shtrepi

Astolfi

Acoustic performance-based design: a brief overview of the opportunities and limits in current practice. Acoust 2020; 2(2): 246–278. https://doi.org/10.3390/acoustics2020016

Echenagucia

Sassone

Astolfi

, et al. EDT, C₈₀ and G driven auditorium design. Build Acoust 2014; 21(1): 43–54. https://doi.org/10.1260/1351-010x.21.1.43

Boning

Bassuet

From the sound up: reverse-engineering room shapes from sound signatures. J Acoust Soc Am 2014; 136(4_Supplement): 2218. https://doi.org/10.1121/1.4900050

Peters

Nguyen

Omar

Parametric acoustics: design techniques that integrate modelling and simulation. In: Proceedings of euronoise 21 annual congress, Madeira, Portugal, 2021.

10.

van der Harten

. Pachyderm acoustical simulation: towards open-source sound analysis. Archit Des 2013; 83(2): 138–139. https://doi.org/10.1002/ad.1570

11.

Lin

A parametric method in room acoustics simulation with performance verification. In: Proceedings of the 29th international conference of the association for computer aided architectural design research in Asia (CAADRIA) 2024, Singapore,2024, vol. 1, pp. 405–414.

12.

Oldland

Teufl

Mahdavi

Computational and empirical assessment of the acoustic performance of repurposed university spaces. In: E3S Web of Conferences, BuildSim Nordic 2022, Copenhagen, Denmark, 2022, vol. 362, p. 05001. EDP Sciences. https://doi.org/10.1051/e3sconf/202236205001.

13.

Badino

Shtrepi

Astolfi

, et al. An evaluation of geometrical room acoustics simulations in outdoor settings. In: Proceedings of the 10th convention of the European acoustics association forum acusticum 2023, Torino, Italy, 2024, pp. 1451–1456. 2023. https://doi.org/10.61782/fa.2023.0240

14.

Tsay

YS.

Optimizing the shapes of concert halls through parametric design. In: INTER-NOISE and NOISE-CON congress and conference proceedings, Chiba, Japan, 2023, vol. 268, No. 4, pp. 4683–4688. Institute of Noise Control Engineering. https://doi.org/10.3397/IN_2023_0665

15.

Badino

Manca

Shtrepi

, et al. Effect of façade shape and acoustic cladding on reduction of leisure noise levels in a street canyon. Build Environ 2019; 157: 242–256. https://doi.org/10.1016/j.buildenv.2019.04.039

16.

Manesh

Dehnavi

Tahsildoost

, et al. Acoustic design evaluation in educational buildings using artificial intelligence. Build Environ 2024; 261: 111695. https://doi.org/10.1016/j.buildenv.2024.111695

17.

Vlaun

van Waart

Tenpierik

, et al. A sound working environment: optimizing the acoustic properties of open plan workspaces using parametric models. In: SimAUD EU 2016: 7th annual symposium on simulation for architecture and urban design, London, UK, 2016, pp. 239–246. simAUD.

18.

Abarghooie

Zomorodian

Tahsildoost

, et al. A machine-learning framework for acoustic design assessment in early design stages. arXiv preprint arXiv:2109.06459, 2021, https://doi.org/10.48550/arXiv.2109.06459

19.

Shtrepi

Aletta

Aspöck

, et al. Ten questions concerning architectural acoustics. Build Environ 2024; 265: 112012. https://doi.org/10.1016/j.buildenv.2024.112012

20.

Nannariello

Fricke

The prediction of reverberation time using neural network analysis. Appl Acoust 1999; 58(3): 305–325. https://doi.org/10.1016/s0003-682x(98)00081-4

21.

Broyles

Rusk

ZT.

Predicting the reverberation time of concert halls by use of a random forest regression model. In: Proceedings of Meetings on Acoustics, Chicago, 2023, May, vol. 51, No. 1. AIP Publishing. https://doi.org/10.1121/2.0001751

22.

Yeh

Tsay

YS.

Using machine learning to predict indoor acoustic indicators of multi-functional activity centers. Appl Sci 2021; 11(12): 5641. https://doi.org/10.3390/app11125641

23.

Falcon Perez

Götz

Pulkki

Machine-learning-based estimation of reverberation time using room geometry for room effect rendering. In: Proceedings of the 23rd international congress on acoustics, Aachen, Germany, 2019, pp. 7258–7265. http://pub.dega-akustik.de/ICA2019/data/articles/000624.pdf

24.

Borrel-Jensen

Goswami

Engsig-Karup

, et al. Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators. Proc Natl Acad Sci 2024; 121(2): e2312159120. https://doi.org/10.1073/pnas.2312159120

25.

Götz

Tuna

Walther

, et al. Online reverberation time and clarity estimation in dynamic acoustic conditions. J Acoust Soc Am 2023; 153(6): 3532–3542. https://doi.org/10.1121/10.0019804

26.

McGinley

Vestergaard

Jeong

, et al. An OpenBIM workflow to support collaboration between acoustic engineers and architects. In: Journal of physics: conference series, Copenhagen, Denmark, November 2021, vol. 2069, No. 1, p. 012164. IOP Publishing. https://doi.org/10.1088/1742-6596/2069/1/012164

27.

Cerdá

Giménez

Romero

, et al. Room acoustical parameters: A factor analysis approach. Appl Acoust 2009; 70(1): 97–109. https://doi.org/10.1016/j.apacoust.2008.01.001

28.

Skålevik

Reverberation time–the mother of all room acoustic parameters. In: CD proceedings of 20th international congress on acoustic, ICA, Sydney, Australia, 2010, vol. 10.

29.

Campbell

Nilsson

Svensson

The same reverberation time in two identical rooms does not necessarily mean the same levels of speech clarity and sound levels when we look at impact of different ceiling and wall absorbers. Energy Proc 2015; 78: 1635–1640. https://doi.org/10.1016/j.egypro.2015.11.242

30.

Marshall

LG.

An acoustics measurement program for evaluating auditoriums based on the early/late sound energy ratio. J Acoust Soc Am 1994; 96(4): 2251–2261. https://doi.org/10.1121/1.410097

31.

Reichardt

Definition und Messgrundlage eines objektiven Masses zur Ermittlungder Grenze zwischen brauchbarer und unbrauchbarer Durchsichtigkeit bei Musikdarbietung [Definition and measurement basis of an objective measure for determining the boundary between usable and unusable transparency in music performance]. Acust 1975; 32: 126–137.

32.

Jurkiewicz

Wulfrank

Kahle

Architectural shape and early acoustic efficiency in concert halls (L). J Acoust Soc Am 2012; 132(3): 1253–1256. https://doi.org/10.1121/1.4740493

33.

Nagata

Design problems of concert hall acoustics. J Acoust Soc Jpn 1989; 10(2): 59–72. https://doi.org/10.1250/ast.10.59

34.

Barron

Loudness in concert halls. Acust 1996; 82: S–21.

35.

International Standard Organization. (2009). ISO 3382-1:2009(E) Acoustics-Measurement of room acoustic parameters. Part1: Performance spaces.

36.

Beranek

Concert hall acoustics. Archit Sci Rev 2011; 54(1): 5–14. https://doi.org/10.3763/asre.2010.0059

37.

Beranek

LL.

Concert halls and opera houses: music, acoustics, and architecture. Springer, 2004. Vol. 2.

38.

Lam

YW.

On the modelling of diffuse reflections in room acoustics prediction. In Refereed Invited Paper, Proc. BEPAC & EPSRC Conference on Sustainable Building, February 1997, pp. 106–113.

39.

Blauert

Spatial hearing: the psychophysics of human sound localization. MIT press, 1997.

40.

Beranek

LL.

Concert hall design: new findings. In: Proceedings of the Institute of Acoustics, 2014, 36(Pt 3).

41.

Hidaka

Beranek

LL.

Objective and subjective evaluations of twenty-three opera houses in Europe, Japan, and the Americas. J Acoust Soc Am 2000; 107(1): 368–383. https://doi.org/10.1121/1.428309

42.

Blevins

Buck

Peng

, et al. Quantifying the just noticeable difference of reverberation time with band-limited noise centered around 1000 Hz using a transformed up-down adaptive method. In: Proceedings of the International Symposium on Room Acoustics; Toronto, Canada; June 9–11, 2013, 2013.

43.

Vigeant

Celmer

Jasinski

, et al. The effects of different test methods on the just noticeable difference of clarity index for music. J Acoust Soc Am 2015; 138(1): 476–491. https://doi.org/10.1121/1.4922955