COMPUTER ASSISTED METHODS AND ACOUSTIC QUALITY:

RECENT APPLICATION CASES

From MCHA95, Tokyo, Japan 

 

Alessandro Cocchi *, Angelo Farina**, Massimo Garai*, Lamberto Tronchin*

 

* Nuclear, Energetics and Environmental Control Engng. Dept., University of Bologna,

Viale Risorgimento 2, 40136 BOLOGNA (Italy)

** Industrial Engineering Dept., University of Parma, Via delle Scienze, 43100 PARMA (Italy)

 

 

I. INTRODUCTION

 

While planning a new concert hall the architect is generally free from any cultural constrain and can design looking only at the best compromise between architecture and acoustics; the peculiar characteristic of restoration works is that quite always the shape is already defined and sometimes also the architectural look cannot be changed.

However, when the restoration of an existing concert hall has to be undertaken, the architect has, in general, some choices whose acoustic performances are difficult to evaluate. In the most recent years a number of numerical simulation programs has been realised, making it possible to obtain the most useful acoustic parameters from a 3D CAD model of the room. However, the good practice demands for an initial calibration of the numerical model based on experimental measurements, from which a reliable estimation of the effects produced by the proposed modification can then be obtained.

In this work a prediction numerical method specially fitted for working on existing halls will be presented together with the results obtained in four cases related to different kinds of restoration:

The results show that this method can produce useful informations in a reasonably little time, provided that measurements are carried out with the most advanced digital techniques and that a fast computation model is used: in this case the MLSSA measuring system and pyramid tracing or cone tracing programs were used.

For each hall, the study has been carried out by the following steps:

The results of these comparisons and the influence of the right configuration of some parameters in impulse response prediction by pyramid and/or cone tracing are here explained.

 

II. Measurement technique

 

The measuring system has been used basically to obtain the binaural impulse responses in each listening point. For this, an omnidirectional loudspeaker was used, being fed with the Maximum Length Signal produced by a MLSSA board, installed in a portable PC. The signal period was 65535 samples, and the sampling rate varied between 22.05 kHz and 44.1 kHz. The acoustic signal was sampled through a dummy head (Sennheiser MKE2002set), connected with the MLSSA board through a wireless system (NADY VF-701). The measure was repeated for each ear, thus enabling the computation of the Inter Aural Cross Correlation (IACC) through a dedicated post-processing program, in addition to the wide range of other acoustical parameters computed by the MLSSA software. Fig. 1 shows a scheme of the measuring system.

 

 

Fig 1 - The measuring system

III. NUMERICAL SIMULATION PROGRAMS

 

In the first case presented, two commercial room acoustics programs have been employed. The first, used for the three cases presented, is a pyramid tracing code [1], suited both for noise evaluation in workplaces, for the simulation of loudspeaker coverage and for concert hall acoustic quality evaluation. The particularity of this program is the fact that it is not hybrid: each pyramid is followed (without split-up) for the whole time length of the impulse response. Then a multiplicative correction is applied to the response of each receiver, enabling the study also of non Sabinian spaces with a little number of pyramids (typically 256). However, till now some problem rises for very regular spaces: considering always specular reflections also for high order reflections, the late part of the tail becomes very uneven as clearly shown by Dalenback [2].

The second program, used for comparison in one of the three cases, is an hybrid cone tracing [3], in which initially the cone tracing is used for evaluating deterministically the early reflections (by identifying the corresponding image sources), and then a reverberant tail is appended, computed by an advanced statistics on the history of the rays. It can handle also diffuse reflections, producing smooth late tails, provided that a number of cones high enough is employed.

In the case where both programs were used, it was possible to verify the difference between the results obtainable with the two different approaches, and the sensitivity of the two programs to the variation of the input data (absorption coefficient of the surfaces).

 

 

 

IV. The "S.Lucia" MAIN HALL in Bologna

 

The University of Bologna has its main hall located inside an unused building, an ancient dismissed church originally devoted to "Santa Lucia"; it was restored and was opened to the public in 1988. The aesthetic appearance of the hall is impressive: the architectural complex comprises three naves, a semicircular apse and a high, vaulted roof; the walls and the ceiling are finished with a clear, hard plaster. Lightly upholstered seats occupy the floor of the main nave, surrounded by a wooden balcony. Fig. 2 shows a perspective view of the room, with the proposed acoustic treatment.

Due to the large dimensions of the hall, to its large and empty volume and to the sound reflecting finishing of almost all surfaces, the listening quality in the hall is very poor. Therefore, a thorough acoustical study was undertaken, in order to give to the hall an acceptable acoustical quality, for both speech and music; the experience reported in this paper regards the study oriented toward the second goal (music).

The experimental data clearly showed that the poor acoustic quality is due to the lack of early reflections, to the very slow sound decay (too high reverberation) and to the strong and late reflections from the vaulted roof and from the rear wall.

The proposed acoustic correction, not fully satisfying from the aesthetic point of view but surely useful for the comparison of the two numerical programs, is based on sound reflecting transparent panels which exclude a considerable part of the upper volume, block the negative influence of the lateral naves and redirect the sound energy to the only strong absorbing surface: the seating area.

 

A. Choice of the Calculation Parameters

The measured reverberation time was always smaller than 8 s in each frequency band of interest; therefore the simulations were limited to 8 s.

With an auxiliary procedure of the cone tracing program a volume V = 45900 m3 and a total surface S = 12500 m2 were estimated. Using those data a mean free path l = 14,7 m and an average number of reflections for a ray k =  200 were computed. Thus, it was decided to make the cone tracing program generate 10000 rays to be followed till the 200th reflection. The pyramid tracing program generated 8000 pyramids (this number must be a multiple of 8× 2n, n integer), followed until the time limit.

The diffusion coefficient required by the cone tracing program was set to 1 as suggested [3], and the transition order from deterministic to statistic reflections was set to 5.

 

B. Validation of the Models

In order to evaluate the accuracy of the two models, a comparison was made between the computed values of some acoustical criteria and the corresponding experimental values.

The variations of the criteria with the position in the hall was taken into account selecting an array of eight reference points distributed along the main nave. The choice of the most suitable criteria for the task was restricted to those common to both programs: SPL, EDT, C80 and centre time ts. The validation was made in two steps:

The first step was only a matter of shifting the resulting SPL, in a straightforward and simplified way, because the cone tracing allowed the assignement to the source model of a global sound power level, but not of a spectrum shape according to the actual source.

The second step involved only the EDT because, among the above mentioned criteria, this is the most sensitive to the sound absorption of the hall. The measured EDT values are very close to those of T15 and T20.

It should be noted that the values of C80 computed with both programs are very different from the measured ones, although their spatial variation is close to the reality. This suggests that at present, even with a room model more accurate than in current practice, the clarity is not a reliable criterion for acoustic simulations, because the geometrical simplifications and the physical approximations needed to make the program work affect too much the clarity values.

In practice, the validation procedure was based on the variation of the sound absorption coefficient of the plaster, which is by far the most common material inside the room. Table 1 reports the initial, intermediate and final values used in the two programs.

For every acoustic criterion x (in the present case the EDT), if xs,i is the value computed during the simulation for the i-th point and xm,i is the corresponding measured value, the prediction error is

 

Tab. 1. Plaster sound absorption coefficient in three validation runs of the programs.

Values for 1/1 octave bands.

Plaster sound absorption coefficient for 1/1 octave bands

 

125

250

500

1000

2000

4000

         
Cone Tracing 1

0,03

0,03

0,03

0,02

0,03

0,02

         
Cone Tracing 2

0,05

0,03

0,01

0,02

0,02

0,02

         
Cone Tracing 3

0,05

0,03

0,018

0,018

0,018

0,02

         
Pyramid Tracing 1

0,04

0,035

0,03

0,02

0,03

0,04

         
Pyramid Tracing 2

0,045

0,04

0,02

0,02

0,03

0,05

         
Pyramid Tracing 3

0,045

0,035

0,02

0,02

0,03

0,06

         

 

 

(xs,i - xm,i); therefore as an index of the accuracy of the model the RMS value of the prediction error over the eight reference points was taken. Fig. 3 shows the RMS error values affecting the results obtained with the two programs at the end of the iterative adjusting procedure.

 

 

Fig. 3 - RMS error of the parameter EDT for the two computer models

 

As it can be seen, with the Cone Tracing a reasonable accuracy can be obtained, except of in the 125 Hz octave band (probably a lower diffusion coefficient should be selected at low frequency). On average, Pyramid Tracing achieves a better accuracy than Cone Tracing, with the exception of the 4000 Hz octave band, where a bias error occurs in the computation of the sound absorption of air.

Anyway, the absolute error values are little, as it can be seen in fig. 4: the optimising values of the absorption coefficient are such that almost exact correspondence between the computed values of EDT and the experimental ones occurs.

 

 

Fig. 4 - Comparison of experimental EDT with values computed with Pyramid Tracing before and after the treatment

 

C. Design of the Acoustic Correction

The visual analysis of the ray paths, possible with the cone tracing program, confirmed the strong non-Sabinian behaviour of the hall and revealed the different (and critical) role of: the high vaulted roof, the lateral naves, the vertical wall in front of the apse. The suggested acoustic correction was then designed in three steps.

At first, a sound reflective ceiling was introduced over the audience, at a height considerably smaller than that of the vaulted roof (see fig. 2); this reflector shall send many sound rays toward the sound absorbing seating area and shall "cut-out" the reverberating effect of the upper volume. The material should be optically transparent, in order to not change the appearance of the hall.

In the second step, the coupling with the lateral naves was prevented by inserting heavy curtains in the communication openings. Their sound absorbing surface help to keep the reverberation as low as possible. It should be noted that, during the simulations, the lateral naves act as "traps" for the sound rays, which often remain segregated in a little lateral volume and find the exit only after a relatively long time; this effect, typical of rays rather than of waves, could lead to an overestimation of the negative role of the lateral naves.

The third step was the covering of the rear wall with a sound absorbing plaster, in order to avoid echo effects.

Optically transparent reflectors were also inserted over the apse and oriented in order to reinforce the early reflections perceived by the orchestra.

The overall effect of the proposed treatment is noticeable: in fig. 4 the new EDT values are shown to become significantly lower than in the actual case (however the reduction of T20 is not so large). In fig. 5 the contour maps of RASTI, computed with the Pyramid Tracing program, are compared; the improvement is on average good. However a strong focalisation effect in the center of the apse can still be observed, which was not reduced by the proposed treatment.

 

 

Fig. 5 - Contour map of RASTI before (left) and after (right) the proposed treatment

 

V. The "S.DOMENICO" church IN foligno

 

 

The city of Foligno (PG) does not have a concert hall suitable for large ensemble performances with a wide number of listeners. For this reason an ancient church, no more used for religious tasks, was re-adapted and restored. However it was not possible to reduce the enormous volume, and so it was necessary to study an acoustic treatment of the room, with the aim of reducing the reverberation time, to increase the clarity and intelligibility and to eliminate some echoes and focalisations actually present.

Fortunately in this case the main nave is narrow and long, and the side walls produce a lot of strong lateral early reflections, so the spatial impression is very good. The reverberation time was a bit lower than in the previous case, and it was possible to add some sound absorbing plaster on the walls, so that the reverberation can be controlled to reasonable values in this case, Then a reflector was added over the orchestra pit, to avoid echoes and focalisations from the apse, and to send the reflected sound energy towards the rear part of the main nave, where the direct waves arrive attenuated by the grazing incidence over the long seating area. Figure 6 shows the modelled geometry of the church with the proposed acoustic treatment, which actually is already partially executed.

 

A. Choice of the Calculation Parameters

In this case an accurate calibration of the computation parameters having an important role in the tail correction, as explained in [1], was performed, enabling very fast computation with just 256 pyramids. First a preliminary test was conducted, based on the comparison between the results obtained with two different runs with a different number of pyramids: 256 and 2048. Then, by a least squares best fitting, "optimal" values were found, able of minimising the difference between the two sound decays.

In this way it was found that the field has a perfectly Sabinian character in this room, as the number of reflections increase with the square of the time; it resulted also that the mean free path is lower than 4·V/S, due to the shape of this room, very narrow compared to its length, and to the presence of some lateral chapels and other minor spaces. It must be noted, however, that this effect could also be caused by the lack of diffusion artificially introduced by the specular reflection assumption mantained for all the reflections: in this sense the adjustment of the relevant parameters makes it possible to compensate for this bias error, removing one of the limits of the actual implementation of Pyramid Tracing.

For the simulation an impulse response length of 5 s and a time resolution of 10 ms were chosen.

 

B. Validation of the Model

After the proper choice of the relevant parameters, many computations were performed, changing the absorption coefficient of the plaster, in such a way to obtain computed values of the reverberation time T20 close as much as possible to the experimental values. This was possible as the computation time was only 4 minutes on a i486 DX2-66 PC, launching 256 pyramids for each simulation. The advantage of using a reduced number of pyramids, among the speed obtained, is also that the tail correction algorithm corrects the late part of the tail, producing a numerical "diffusion" effect, that is useful to avoid the oddities sometimes found in the simulation of long impulse responses with a "specular-only" simulation code, as reported by Dalenback [2].

Fig. 7 shows the results of the validation process: the computed T20 values are perfectly corresponding to the experimental values. At the lower frequencies the reverberation is very high, but it must be noted that the room was considered empty, and 1200 peoples will add considerable absorption particularly in the low frequency zone.

Fig. 7 - comparison of experimental EDT with computed values before and after the treatment

 

C. Design of the Acoustic Correction

The acoustic correction of the room is based on three steps: installation of sound absorbing plaster on the walls of the apse and transepts, large velvet panels suspended from the top of the laterals walls and realisation of an acoustic reflector over the orchestra pit. All these modifications are shown in fig. 6. It must be noted, however, that these solutions are effective only at medium and high frequency; low frequency absorption could be obtained by the people seating in the stalls, but probably it will be necessary to add some vibrating panels on the back wall, to control the low end of the spectrum. This can be shown in fig. 7: the reduction of the reverberation time is noticeable at medium and high frequencies, but it is little at low frequency.

Fig. 8 shows the comparison between the RASTI maps computed in the actual state and after the proposed treatment: there is a relevant improvement of the speech intelligibility, that will probably be beneficial also for music reproduction. The effect on music was anyway evaluated by listening to convoluted music samples, obtained using the convolution software Aurora [5,6] and anechoic samples coming from the DENON PG-6006 CD. Three convolutions were obtained for each sample, the first with experimental impulse responses, the second with the simulation in the original state (which resulted almost identical to the first) and the third after the treatment; the latter exhibit a better clarity, lower reverberation and wider spatial impression. A subjective validation of the auralisation system was conducted including the comparison of the first two samples, as reported in [6]; although the simulated sample resulted often distinguishable from the sample obtained by convolution with the experimental impulse response, the average subjective scores for the four most important parameters were not significantly different.

 

Fig. 8 - Comparison between computed RASTI before (L) and after (R) the proposed treatment

 

VI. The "Teatro Comunale" in Gradisca d’Isonzo

 

The town of Gradisca D’Isonzo (GO) has a municipal theatre, located in the main square. Actually the building is dismissed and is under restoration.

The architectural complex comprises three order level of seats, one at the mail level and two semicircular floors, as shown in fig. 9.

In order to establish the acoustic behaviour of the theatre, and to give to the hall an acceptable acoustical quality, for both speech and music, a thorough acoustical study was undertaken, together with the architectonic designer of the restoration.

 

Fig. 9 - Photographic view of the hall and CAD drawing of the model used for the validation

 

The experimental data clearly showed that the poor acoustic quality was due to the lack of early reflections, to the slow sound decay (too high reverberation) and to the lack of loudness in the farthest seats. The proposed acoustic correction is based on sound reflecting panels which redirect the sound energy to the only strong absorbing surface: the seating area.

All curved surfaces were modelled with several planes; in particular, the thickness of the walls and of the columns cannot be neglected. Also the seating areas were modelled with a realistic detail in the seat drawing, even if this caused an inevitable slowing of the program.

 

Fig. 10 - Ando’s total preference index

 

A. Choice of the Calculation Parameters

The measured reverberation time was always smaller than 4 s in each frequency band of interest; therefore the simulations were limited to 4 s.

The computer code generated 16384 pyramids, followed until the time limit, so it was possible to model the environment without any other hypothesis. The program always requires to set in advance the time resolution for the impulse response computation: it was set to 10 ms.

 

B. Validation of the Model

In order to evaluate the accuracy of the model, a comparison was made between the values of some acoustical criteria, either measured or resulting from the simulations.

The variations of the criteria with the position in the hall was taken into account selecting the calculation points distributed along the whole theatre. The choice of the most suitable criteria for the task were restricted to EDT, C80 and centre time ts [4]. The validation procedure has been the same as described above.

At the end of the iterative procedure, the values of EDT obtained from the simulation resulted very close to the measured ones, as shown in fig. 11.

Fig. 11 - Comparison of experimental EDT with computed values before and after the treatment

 

 

C. Design of the Acoustic Correction

The acoustic correction was simulated in two steps.

At first, a set of reflective glasses was introduced over the proscenium; this reflectors shall redirect many sound rays toward the sound absorbing seating area.

Fig. 12 - Proposed solution: rendered view (left) and wireframe CAD model (right)

 

The second step was the covering of the ceiling and the rear wall with a sound absorbing plaster, in order to avoid echo effects, and obtain a smaller reverberation time; in fact the goal of the acoustic correction was to establish an equal behaviour of the theatre either for music than for speech.

Fig. 11 also shows the reverberation time values obtained with the proposed acoustic treatment. Fig. 12 shows the final appearance of the room with the proposed acoustic reflectors. Fig. 13 shows the improvement in STI obtained with the proposed treatment.

Fig. 13 - Comparison of STI map before (left) and after (right) the proposed restoration

 

VIi. The "DANTE ALIGHIERI" THEATRE IN RAVENNA

 

A. Introduction

In many Italian theatres it is still possible to find semi cylindrical cavities under the orchestral pit [7]. Many European old opera houses had this cavity too, but almost all has been destroyed so making place to some kind of mechanical system that makes possible to change the configuration of the stage in few minutes against half a day as requested for hand-made modifications.

In the "Teatro Alighieri" of Ravenna this wood cavity has a linear axis, and it was built by venetian carpenters. In this case, at first the subjective response of both performers and musically educated people, to the same musical program performed twice, first with the empty cavity and then with the same full of sawdust, was tested. From these responses, it seemed that something in clarity and in spatial distribution of preference was changed, but the results was probably influenced both on the listening and the performers, who adapted their performance to the acoustic response of the pit.

 

 

Fig. 13 - Impulse responses in point n.4, with empty and filled hole, for the right channel

B. Experimental Measurements

In order to quantify the effectiveness of the cavity to qualify the acoustics of the theatre, a set of experimental measurements with empty and polystyrene filled cavity was performed.

The study has been carried out by the upmentioned steps, i.e.:

 

C. Results of the Experimental Measurements and Outwiev

From the experimental measurements, it was clear that the main value of the parameters, referring to the conditions with empty cavity and filled cavity behave in the following way:

 

Fig. 14 - Ando’s total preference index: empty (left) and filled (right) cavity, for Mozart’s music.

 

The spatial distributions of the Ando’s preference parameters, passing from the condition of filled cavity to that of empty cavity, are changed in this way:

 

Fig. 15 - Comparison of experimental T15 with empty and filled cavity

 

Fig. 16 - Spatial distribution of center time with empty (left) and filled (right) cavity

 

In the condition of empty cavity, the sound is reinforced, so the listening level and reverberation time preference indices are better, but the spatialisation in the near seats of the hall is worse.

 

Fig. 17 - Comparison of experimental SPL with empty and filled cavity

The results of the objective measurements are very closed to subjective evaluations already given from a large number of musicians in an other psychoacoustic research, in which the need of "warmth" and "liveness" was expressed.

Using the numerical technique already described, it will be possible to define the acoustic characterisation of the theatre in order to validate the possibility of using an acoustic chamber for a better enjoyment of the hall.

 

*****

Work partially supported by the Ministry of University, Scientific & Technologic Research (MURST 40%).

 

VIII. REFERENCES

 

1 A. Farina -"RAMSETE - a new Pyramid Tracer for medium and large scale acoustic problems", Proc. of "Euro-Noise 95", Lyon, France, 21-23 march 1995.

2 B.I. Dalenback - "The importance of diffuse reflection in computerized room acoustic prediction and auralization", Proc. of "Opera and Concert Hall Acoustics Conference", IOA, pp.27-34, London Gatwick, February 1995.

3 G. Naylor, "Odeon Room Acoustics Program - Version 2.0 User Manual", The Acoustics Laboratory, Lyngby, Denmark (1992).

4 Y.W. Lam "On the modelling of auditorium acoustics, part II: the validation of an hybrid computer model", submitted for publication in JASA, December 1993.

5 A. Farina - "An example of adding spatial impression to recorded music: signal convolution with binaural impulse responses" - Proc. of "Acoustics and Recovery of Spaces for Music", Ferrara (Italy) 27-28 ottobre 1993.

6 A. Farina - "Auralization software for the evaluation of the results obtained by a Pyramid Tracing code: results of subjective listening tests" - Proc. of "ICA95", Trondheim, Norway, 26-30 June 1995.

7 A. Cocchi, M Garai, L. Tronchin - "Influenza di cavità risonanti poste sotto la fossa orchestrale:il caso del teatro Alighieri di Ravenna" - Atti di "Musei a Convegno", Ferrara, 1 Aprile 1995.