PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Room acoustics modeling using a hybrid method with fastauralization with artificial neural network techniques
Roberto A. TENENBAUM1, Filipe O. TAMINATO1, Viviane S.G. MELO2
1State University of Rio de Janeiro, Brazil

2

Federal University of Santa Maria, Brazil

ABSTRACTThis work presents a new technique to produce fast and reliable auralizations with the computer code RAIOS,
a room acoustics simulator, product of research development at the Instrumentation in Dynamics, Acoustics
and Vibrations Lab, State University of Rio de Janeiro. It discusses briefly the hybrid model used in the room
simulation and the binaural room impulse responses generation technique using artificial neural networks,
with a significant reduction in computational cost of around 85%. It is shown that the binaural impulse
responses generated by the classical convolution method and the artificial neural network technique arealmost indistinguishable. In the sequel, the measured and simulated binaural impulse responses for one of
the rooms used in the Round Robin 4 simulation code´s inter-comparison is presented, showing a quite good
agreement.
Keywords: Fast auralization, Room acoustics simulation, Artificial neural networks

1. INTRODUCTION
This work deals with computer simulation of room acoustics and techniques to generateauralization at selected points in the room. In general, the computational simulation of room acoustics
presupposes the requirements of geometric acoustics (1). This means that the sound wavefronts canbe treated as acoustic rays, which leave the sound source and propagate in the room, reflecting on
their internal surfaces (2). There are two main ways of modeling acoustic rays: the ray tracing method(3,4) and the virtual sources method (5). There are also hybrid algorithms that use the virtual sources
method for the calculation of the direct sound and first reflections and the ray tracing met hod for thecomputation of the remaining reflections (6). Some commercial software is essentially based on the
ray tracing method (7), presenting satisfactory results for the monoaural acoustic field. However, as
already pointed out by many authors (8), the diffuse reflection plays an important role in room
acoustics by providing a greater uniformity in the sound field (9), but also essential when it is desired
the auralization for a source-receiver pair. In this case, it seems essential to have a good model to deal
with diffuse reflections, since the ray tracing technique cannot do so . One of the ways to properly
model diffuse reflections is the radiosity technique (10). The most effective implementation of thismodel is to store the portion of sound energy diffusely reflected after each specular reflection in amatrix whose lines correspond to discrete times and whose columns represent the spatial discretizationof the room’s contour surfaces in triangular elements. These so-called transition matrices, then, evolveby transferring diffuse energy between surface elements of the room, according to the solid angle thateach one is seen and, of course, the respective scattering coefficients (11).
Among the most impressive applications of room acoustics computer simulation it is precisely thepossibility of generating auralization (12) the most powerful branch of acoustical virtual reality (AVR).
Reliable auralization  usually to be heard with properly equalized headphones  can provide thelistener with an authentic sense of sound immersion in the simulated environment. This provides theacoustical designer, for instance, with information about the sound quality of the room u nder analysis
that would not be possible by only observing the acoustic quality parameters (AQPs) provided by thesimulator. One could say that the difference between looking to AQPs of a room or alternatively
hearing its auralization from a given anechoic signal is similar to the difference between reading themenu of a good restaurant or tasting its dishes. It is worth noting, however, that the evaluation of anauralization, being subjective, i.e., depending on the human interpretation, is still a subject of researchin progress. Perhaps the most complete work in this area is the spatial audio quality inventory  SAQI
(13).
1 ratenenbaum@gmail.com

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Although 42 different terms in English are considered to qualify the different human sensations
related to an audio content, there was no pretense of finding objective parameters, i.e., a measurable
metric estimated by a number. Some alternatives have been published in this direction, using
articulation scores to evaluate speech intelligibility, comparing actual rooms with their corre sponding
computational auralizations (14-16).
The Instrumentation in Dynamics, Acoustics and Vibrations Lab  LIDAV, State University of Riode Janeiro, Brazil, has been developing a research computational code for room acoustics simulation
aimed at AVR. This code, known as Room Acoustics Integrated and Optimized Software (RAIOS),
uses a ray-tracing method to model the specular reflections and a transition matrix method to computethe diffuse reflections (11). It also produces auralizations for selected source-receiver pairs. In Section
2, a new technique for generating auralizations is presented, replacing the convolution method with amethodology that models the head-related impulse responses (HRIRs) through artificial neuralnetworks (ANNs) (17) of the radial basis functions kind (18) with a very significant computational
gain. In Section 3, the computational cost of the ANN technique is discussed.
In Section 4, a brief discussion on the results obtained for the computation of filtered HRIRs throughthe convolution method and through artificial neural networks, is compared, showing that the two
methods present results that are practically indistinguishable from each other. In Section 5, thesimulation results obtained in one of the rooms used in Round-Robin 4  the 4 th international intercomparison on room acoustics simulation codes, with auralization  with code RAIOS, are comparedwith the measured results, furnished by the competition organizers. Finally, in Section 6, the main
conclusions are presented.

2. FAST AURALIZATION WITH ANN TECHNIQUE
Once the acoustic field in the room simulation step is completed, the goal in sequel consists in thedetermination of the room impulse mono (RIRs) and binaural (BRIRs) responses at selected points.
As regards the calculation of RIRs, it is a question of convert the energy arrival, via Hilbert's transform(19) and the adequate filtering in octave bands, in filtered impulse responses, whose computational
cost is relatively small. In order to compute the BRIRs, however, it is necessary to take into accountthe head-related impulse responses (HRIRs)  or their corresponding in frequency domain, the socalled head-related transfer functions (HRTFs). In the computational codes that generat e auralization,
this is done via convolution procedure. Each wavefront  or acoustic ray  that reaches a given
receiver carries three main information: (a) its spectrum, in octave bands; (b) its direction of arrival,in azimuth and elevation; and (c) its arrival time. Each wavefront, when leaving the sound source, hasa flat spectrum. Nevertheless, due to the several reflections with absorption and scattering at the
room's boundary surfaces, as well as the attenuation due to its propagation in the air duri ng its
trajectory, reaches the receiver with a filtered spectrum. This must then be multiplied by the HRTF of
the direction closest to its arrival direction and to the resulting spectrum an inverse fast Fouriertransform (IFFT) must be applied in order to obtain the filtered HRIR for that wavefront. In the sequel,
every filtered HRIR must be delayed by its arrival time and the sum of all the filtered and delayed
HRIRs that reach the receiver will constitute the BRIR for that source -receiver pair. The procedure isequivalent to the convolution of the acoustic ray with the HRIR of the corresponding direction andhenceforth it is called convolution method (CM), or classical method. Fig ure 1 illustrates theprocedure.
The described procedure has the drawback of its computational cost. In fact, the complex productbetween the HRTF of the considered direction with the spectrum of the wavefront that reaches thereceiver, followed by the fast inverse Fourier transform in two channels to obtain the filtered H RIRspresents a high computational cost, mainly taking into account that the number of wavefronts thatreaches each receiver can be of the order of 10 5, in a good simulation. However, the delay and addition
procedures of the filtered HRIRs for the BRIR calculation demand low computational costs.
The RAIOS computational code uses another technique to generate the BRIRs. The idea is toreplace the HRIRs/HRTFs database with a set of trained and tested artificial neural networks that“learned” previously the HRIRs patterns. In this way, the procedure is all carried out in time domain.
The radial basis function networks have as input the nine wavefront spectral components in octave
bands (between 63 Hz and 16 kHz) that reach the receiver. Ten neurons are used in the hidden network
layer and, at the output, 128 neurons are used, which correspond to the amplitude values of the6386

resulting filtered HRIR. Then, the delay procedure of each filtered HRIR and addition of all thesefunctions to obtain the BRIR is identical to that of the convolution method. However, thecomputational cost of the artificial neural network technique is about 15% of the cost of the
convolution method, as it is showed in next section. Figure 2 illustrates the procedure.

Figure 1 – General procedure to produce a BRIR by the convolution method.

Figure 3 – General procedure to produce a BRIR by the ANN-RBF technique.

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At the bottom of Fig. 3 two previously trained RBF-kind ANNs are displayed, one for each ear, forthe given wavefront direction. In each network besides the nine entries, it is considered anintermediate layer with N 1 and an output layer with 128 neurons, which are the considered time domain
samples of the filtered HRIR.

3. COMPUTATIONAL COST
In order to examine the numerical efficiency of the convolution method (CM) with that of the RBFkind artificial neural network method (ANNM), a comparison is made as to the number of arithmetic
operations that each technique requires. The number of operations in the convolution method tocompute the filtered HRIRs equals the sum of two parts. The first one corresponds to the number ofmultiplications between the ray spectrum (in octave bands) and the HRTF. Note, however, that due tothe HRTF symmetry, only l/2 products, with l being the number of samples, are necessary. The second
one corresponds to the number of operations for calculating the inverse Fourier transform. The total
number of mathematical operations in the convolution method is then given by (21)௟ܱ஼ெ = ൅ ͷ݈ ଶ ݈ Ǥሺͳሻ
ଶIt is worth noting that, since the convolution method deals with Fourier transforms, l = 512 samples
are necessary to preserve information in all octave bands. So, for each filtered HRIR, thecomputational cost in number of arithmetic operations is(2)
OCM = 23,296.
The training and testing procedures of artificial neural networks are known to be computationallycostly. However, the execution phase  particularly the one of the radial basis function networks  isquite efficient. The number of operations of the RBF network during the implementation phase is also
the sum of two parts. The first one is associated to the sum of the number of operations performed tocompute the output of the activation function of each neuron of the intermediate layer. It can be shown(22) that N 0 being the number of input entries of the RBF network, N 1 the number of neurons of theintermediate layer and N the number of retained terms of the Taylor series in which the activation
function is truncated (23), the number of operations of this part is(3)ܱଵ ൌ ܰଵ (3ܰ଴ ൅ ʹܰሻǤThe second one corresponds to the sum of the number of operations to calculate each neuron of
the output layer. Being N 2 the number of neurons of this layer, the number of sums and products ofthis second part isܱଶ ൌ ʹܰଵN 2.
(4)
In addition, it is necessary to take into account the cost of normalizing the inputs and thesubsequent multiplication of the network output by the inverse factor that was used to normalize theinput. These procedures require only N0 + N 2 multiplications. One can conclude than that the total
number of operations to generate the output of the RBF network in the ANN method isܱ஺ேேெ ൌ ܰଵ ሺ͵ܰ଴ ൅ ʹܰଶ ൅ ʹܰሻ ൅ ܰ଴ ൅ ܰଶ Ǥሺͷሻ
Taking now N0 = 9 (nine octave bands), N2 = 128 (minimum acceptable number of time samples)and N = 35 (20) one would haveܱ஺ேேெ ൌ ͵ͷ͵ܰଵ ൅ ͳ͵͹Ǥሺ͸ሻThe computational cost of the artificial neural network method, therefore, is a linear function of
the number of neurons in the intermediate layer of the RBF network, N1 . There is no way other thantrial and error to check the minimum number of neurons in this layer that still provides good binauralroom impulse responses. Several tests were performed with N1 ranging from 2 to 30. The best costbenefit ratio was found for N 1 = 10. That means that the difference between the filtered HRIRs
calculated by the two methods (CM and ANNM) becomes, for that value of the number of neurons in
the intermediate layer of the network, imperceptible. The comparative results presented in Section 4
are computed with N1 = 10. The computational cost in terms of the number of arithmetic operations
for the method of the RBF-kind artificial neural networks is, then,ܱ஺ேேெ ൌ ͵͸͸͹ǡሺ͹ሻwhich corresponds to 15.74% of the number of arithmetic operations calculated in Eq. (2). The main
conclusion is that by working directly in the time domain  and avoiding the convolution procedure ,
the computational gain is approximately 84,3%.

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4. COMPARATIVE RESULTS FOR FILTERED HRIRs
As mentioned, the convolution technique is the classic BRIR generation method and it is present
in all acoustic field simulation software with auralization, to our knowledge. Therefore, in order toverify the reliability of the method of generating the BRIRs with the artificial neural networks of theradial basis function type, a comparison between the two methods is presented in the sequel. Since
once the filtered HRIRs are generated the procedure is identical, involving the delays and theiraddition to generate the BRIR, the comparison between the two methods will be done among thefiltered HRIRs. Figures 3 to 10 indicate the filtered HRIRs computed via the convolution method(CM) compared with the same functions calculated by the artificial neural networks method (ANNM),
for eight randomly chosen directions, each one representative of the eight octants that the sphere canbe divided around the head (φ = azimuth; θ = elevation). In addition to the confrontation of the filtered
HRIRs, in time domain, their counterpart in frequency domain, both in amplitude and phase, are shown.
To evaluate the similarity between the functions, it is adopted the normalized correlation coefficient,r (21). The similarity between the two functions is better as r is closest to 1.

Figure 3 - Filtered HRIRs obtained with CM and ANNM, for φ = 37 0 and θ = 31 0.

Figure 4 - Filtered HRIRs obtained with CM and ANNM, for φ = 12 0 and θ = 450 .

Figure 5 - Filtered HRIRs obtained with CM and ANNM, for φ = 104 0 and θ = 190 .

Figure 6 - Filtered HRIRs obtained with CM and ANNM, for φ = 156 0 and θ = 22 0.

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Figure 7 - Filtered HRIRs obtained with CM and ANNM, for φ = 243 0 and θ = 9 0.

Figure 8 - Filtered HRIRs obtained with CM and ANNM, for φ = 195 0 and θ = 28 0.

Figure 9 - Filtered HRIRs obtained with CM and ANNM, for φ = 331 0 and θ = 550 .

Figure 10 - Filtered HRIRs obtained with CM and ANNM, for φ = 272 0 and θ = 18 0.
It can be seen in Figs. 3 to 10 a significant similarity between the graphs, both in time andfrequency domain, with values of the correlation coefficient very close to one. This indicates that thetechnique of producing filtered HRIRs via artificial neural networks is, aside from faste r, very reliable.

5. MEASURED AND SIMULATED BRIRs IN ROUND ROBIN 4
Round Robin 4 (RR4) was the last international inter-comparison, so far, involving room acoustics
computer simulation codes, and the first one with auralization. It was jointly organized by t heTechnical University of Berlin and the University of Aachen and launched in 2016. In this project,
information was provided on nine rooms, in a total of 25 different configurations, with geometry,6390

materials, absorption and scattering coefficients of internal surfaces. In addition, databases with the
HRIRs of the dummy head used in the binaural measurements, for 45 angular positions of rotation
about the vertical axis of the head above the torso (azimuth) were given. A variable number of soundsources and mono and binaural receivers were provided in each room. A database was also provided
with the directivities (in azimuth and elevation) of two sound sources used. The data are available in(24). In all, 114 RIRs and 949 BRIRs were requested as output. Possibly due to the heavy datarequirement to be calculated in RR4, the number of participant teams (eight) was much lower than in
RR3 (21). In this section, the comparative results between the measured BRIRs  provided by theorganizing staff of RR4, after sending simulation results by all participants  and those simulated by
the LIDAV team using the RAIOS computational code for the room called “chamber music hall” arepresented. Figure 11 shows part of the room with the positions of sources (LS0306) and binaural
receiver (MP6).

Figure 11 – Room called “chamber music hall” of RR4 with its source and receiver positions.
Partial view.
In the sequel, the interaural cross-correlation coefficient, IACC, is computed for both measured(RR4 organizers) and simulated (RAIOS) BRIRs for the pairs LS03-MP6 (Pair 1), LS04-MP6 (Pair 2),
LS05-MP6 (Pair 3) and LS06-MP6 (Pair 4). The results are shown in Table 1.
Table 1 – Interaural cross-correlation coefficient computed for the source-receiver pairs
S-R Pairs

Pair 1

Pair 2

Pair 3

Pair 4

Measured

0.41

0.43

0.36

0.34

Simulated

0.49

0.38

0.29

0.29

Difference

0.08

0.05

0.07

0.07

As can be withdraw from Table 1, the obtained values show to be close (measured versus simulated)with two of them greater for the measured BRIRs and the other two for the simulated ones. In allcases, the percentual error is below 20%.

6. CONCLUSION REMARKS
A new technique was proposed to model the filtered head-related impulse responses, which are thecore of binaural room impulse responses generation with the purpose of auralization production. The
model is based on artificial neural networks of the radial basis functions kind and was implemented
in RAIOS code, resulting in a computational time saving of around 85% in the BRIRs computation.
As in any procedure of room acoustics simulation, there are two blocks of higher computationalcost, namely: The calculation of all acoustic wavefront arriving at each receiver; and the computation

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of the binaural room impulse responses for each receiver. This second computationally costly block
benefited from the modeling through artificial neural networks, with a significant computational timesaving, especially if many receivers are under consideration.
The comparative results between the filtered HRIRs/HRTFs obtained by the classical convolution
method and by the new model using artificial neural networks showed that the functions are, for allpractical purposes, indistinguishable, presenting a normalized cross-correlation coefficient practicallyequal to unity, both in time and frequency domains. Although only eight of the 64,442 directions havebeen shown here, for all of them the comparative results are equally accurate.
The measured and simulated with computational code RAIOS results for one binaural receiver andfour directional sound source positions were compared for one room of RR4. The simulation was
performed with the ANN technique and the comparative data of the inter-aural cross correlation
coefficient show that there is good agreement. Nevertheless, the discrepancies cannot be attributed
specifically to any one of the many uncertainties in the simulation, such as relative positions,scattering and absorption coefficients used, directivity of sources data etc.

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