James, Dalenback - Computer Modelling With Catt-Acoustic.pdf - Akustyka - dnbdbstp

COMPUTER MODELLING WITH CATT-ACOUSTIC Î

THEORY AND PRACTICE OF DIFFUSE REFLECTION AND

ARRAY MODELING

Adrian James, Adri an James Acoustics, UK (adrian@adrianjamesacoustics.co.uk)

Bengt-Inge Daenbck, CATT, Sweden (bid@catt.se)

Amber Naqvi, IoSR University of Surrey and Adrian James Acoustics, UK

(amber@adrianjamesacoustics.co.uk)

1. INTRODUCTION

This paper describes the room acoustics prediction and auraisation software CATT-Acoustic. It

concentrates on topics reevant to prediction quaity rather than on features such as use of coour

and simiar that instead wil be exempified during the presentation. Athough important for the user,

abundant features are of imited vaue if the underying prediction agorithms fail to predict wel in

many important cases. Specificay, the paper wil focus on the handing of frequency dependent

diffuse refection and oudspeaker array modeing. Frequency-dependent diffuse refection is

essential for the prediction of fundamental parameters such as the reverberation time (RT), whie

handing the sometimes very ong nearfieds are as essential for the prediction of sound from

arrays.

2. SOFTWARE BACKGROUND

To serve as a backdrop for the prediction method discussion beow, the software background is

briefy outined in this section.

The initial DOS-based software was written in 1989 and was used a combination of the image

source model (ISM) for eary refections and gobal ray-tracing for the ate decay. Aready in the

initial versions frequency-dependent diffuse refection was taken into account. In 1990 the first

auraisation impementation, using Lake DSP hardware, was finished [1]. During the years 1990-94

features were added but no major method changes took pace.

In 1995 a software convover was incuded so that the compete auraisation process coud be

performed on a standard PC, athough the cose reationship with Lake DSP continued with head-

tracked auraisation [2] and Ambisonic repay options. Essentiay the same method was used up to

and incuding the first 16-bit Windows version in 1996 (v.6.0), and was successful in the first

international round-robin on room acoustics prediction [3] where CATT was one of ony three

programs that were judged to give reiabe and useful resuts. Of these three, 5 of the 8 predicted

measures were best evauated by CATT-Acoustic. With v.6 aso cassical ray-tracing [4] was added

for audience area coour mapping. However, during 1990-95, B-I Daenbck aso worked haf-time

in the Chalmers Room Acoustics Group [5] deveoping a more advanced prediction and auraisation

method resuting in a Ph.D. thesis [6].

In 1998, v.7 for 32-bit Windows was reeased introducing Randomised Tai-corrected Cone-tracing

(RTC), a simper but more robust variant of the research method. The RTC, detaied beow, is a

very general method useful for prediction of acoustic parameters as wel as for auraisation, and

remains the main prediction method in CATT-Acoustic. Aso reeased in 1998 was a fundamental

functionaity reated to array modeing: the DLL Directivity Interface (DDI) that enabed run-time

array-modeing incuding handing of the nearfied and DSP-settings for beam-steering.

Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi

3. DIFFUSE REFLECTION

Before the prediction methods empoyed are described a question has to be answered. Why is

diffuse refection so important in room acoustics prediction? For the answer it is useful to

characterise rooms according to:

their mixing properties : i.e. basicay to what degree the room shape and surface

orientations are such that rays risk being ocked into particuar directions (e.g. between

parael was).

their absorption distribution : i.e. if al surfaces have simiar coefficients, or if some

surfaces are hard whie other are very absorbent.

First we have the simpe cases: rooms where the shape acts as mixing and where the absorption

distribution is even. Here cassical Sabine theory works very wel and prediction using specuar-

ony methods can be quite successfu. Then we have the other extreme: rooms that are non-mixing

and with uneven absorption distribution. In these rooms Sabine wil dramaticay under-estimate the

actual RT whie specuar-ony methods wil dramaticay over-estimate the RT. To iustrate this a

case from consutant practice is used, see Figure 1.

Figure 1 Sports hal 43 x 23 x 7 m 3 . The ceiing is mosty covered with high-absorbing materia,

remaining surfaces are hard. T Sabine @ 1 kHz was 1.9 s whie the actuay measured T 30 was 5.7 s.

The acoustic consutant invoved [7] recommended pacing high-absorbing material between every

second beam pair in the ceiing (ca. 50% coverage giving an effective ceiing absorption coefficient

of 0.43 @ 1 kHz) and additional high absorption on at east one end wal and one side wa.

However, to save money the contractor instead chose to use ony the ceiing absorption and to

eave the rest basicay as concrete. With ony the ceiing used for absorption T Sabine @ 1 kHz was

1.9 s but when the RT was actuay measured it was 5.7 sec. This is a cear case of a non-mixing

shape where handing of diffuse refection is absoutey necessary. Tabe 1 ists the RT predictions

at 1 kHz using various methods and room modes.

Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi

Method/model

Scattering coefficient

(s @ 1 kHz)

RT @ 1 kHz (T 30 )

Sabine, detaied model 1 N/A

1.9 s

Sabine, simpe model 2 N/A

2.1 s

Measured

N/A

5.7 s

Detaied model 1

s beams = 0.22 3 , s rest = 0.08 5.1 s (10% error)

Simpe model 2

s ceiing = 0.80, s rest = 0.08 5.9 s (3% error)

Detaied model 1

specuar-ony, s = 0 13.0 s

Simpe model 2

specuar-ony, s = 0 12.0 s

Table 1 Predicted and measured RTs forthe sports hall. 1 with beams as in Fig.1, 2 flatceiling with high

diffusion, 3 auto edge diffusion (see below).

An interesting note here is that the sports hal project (ca.1995) was initiay cacuated with CATT-

Acoustic v.6 as wel as the consutants own in-house ray-tracing software, which aso handed

diffuse refection. The resuts were very simiar to those in Tabe 1, which were modeed in CATT

v.7.2. However, the frequency dependence of diffuse refection has not yet been addressed since

the exampe above ony hods for 1 kHz. Generay the frequency dependence has to be incuded

for purey physical reasons, and Figure 2 schematicay iustrates why. For a more general

discussion about diffuse refection in computerised prediction, see [8].

Figure 2 Schematic description ofhow the ratio between surface roughness (D) and wavelength (l)

determines the diffusion.a) l << D :geometricalmixing (effectively acts as diffusion),b) l = D :high

diffusion,complex actualbehavior,c) l >> D :low diffusion.

4. PREDICTION METHODS

With the exampe in the previous section in mind, we can now ook at the two main prediction

methods empoyed by CATT-Acoustic ; ray-tracing and randomised tai-corrected cone-tracing.

RAY-TRACING FOR AUDIENCE AREA MAPPING

Audience area mapping is based on cassical ray-tracing with fixed-sized spherical receivers paced

in a grid over defined audience areas. Frequency-dependent diffuse refection using the Lambert

distribution [4] is taken into account by randomising the directions of those rays which are

determined to refect diffusey off a surface (as dependent on the scattering coefficient). An

Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi

exception is that direct sound is handed deterministicay without rays. When frequency-dependent

diffuse refection is taken into account (and ony when it is taken into account) ray-tracing is a very

robust prediction method. However, the echogram from ray-tracing is difficut to use for auraisation

since, unike with the RTC, the refection density growth over time is unnatura. Hence, ray-tracing

is ony used for mapping of measures such as C 80 but not for auraisation or a detaied echogram.

However, room acoustical measures predicted in CATT using frequency-dependent diffuse ray-

tracing are virtuay identical to those predicted by the more eaborate RTC.

RANDOMISED TAIL-CORRECTED CONE-TRACING FOR DETAIL AND

AURALISATION

The unique RTC is a combination of three different methods, compensating and correcting for

weaknesses in each of these three methods. The program uses scattering coefficients which are

normay estimated based on general guideines and input by the user in the same way as

absorption coefficients, but an automatic edge diffusion can aso be used. For hard smooth objects

ike tabes and refectors, a size- and frequency- dependent scattering coefficient is optionay

cacuated automaticay

1) Image Source Model (ISM) for 1 st and 2 nd order specuar refection so that the most important

eary refections are aways incuded independent of how many rays are used. A weakness of

the ISM is its inefficiency for high-order refections, but up to 2 nd order it is aways fast.

2) Direct diffuse radiation for 1 st order diffuse refection. Many smal diffusey radiating surface

sources are distributed over each diffusing surface. From the actual sound source, vectors are

drawn to each diffuse surface source and from each of those to the receivers (taking occusion

into account). To give the highest geometrical accuracy where it is needed, the number of

these surface sources is increased for surfaces with ow absorption coefficients and high

scattering coefficients.

3) Randomised cone-tracing for higher order refections where ray directions are randomised ike

in ray-tracing so that, unike with specuar cone-tracing, diffuse refection can be taken into

account.

A weakness of ray-tracing is that the receiver sphere must be fairy arge and the eary part detail

therefore suffers. The use of cone-tracing and the ISM compensates for this ack of detai. Cone-

tracing aso gives a refection density which grows with t 2 (t=time) which makes the resuting

echograms we-suited for natura-sounding auraisation. On the other hand, a weakness of cone-

tracing is a ray-density dependent ate refection oss and that is corrected for by an automatic

refection growth extrapoation [6]. However, the more rays/cones that are used the ess the

extrapoation needed.

5. ARRAY MODELLING INCLUDING THE NEARFIELD

The methods described above perform very wel for estimation of refected sound and thus the ful

echogram. However, with non-simpe sound sources the directivity aso needs to be handed in

sufficient detai. Manufacturers and researchers are now measuring ful space directivity at ever-

increasing resoutions, going from 10» and 1/1-octaves to 5» and 1/3-octaves. In some cases even

higher resoutions incuding phase is discussed.

However, with this focus on higher resoutions a fundamental property of oudspeaker arrays

appears to have been forgotten even in dedicated sound system software: the extended nearfied.

The now very popuar ine arrays (e.g. Duran Audio Inteivox and Target systems, L-Acoustics

V-DOSC/dV-DOSC, JBL VERTEC and several other under deveopment) are essentiay cyindrical

Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi

1/r-radiators up to very arge vaues of r (often > 100 m). Many commercial sound-system

modeing programs stil treat these as spherical 1/r 2 -radiators. In other words, these programs take

the farfied directivity of the array and appy it in the nearfied. This method may work for singe

speakers but can give widy incorrect resuts for arrays such as coumn oudspeakers or arge

central custers. To remedy this, in 1998 CATT deveoped a "DLL Directivity Interface" (DDI) that

did not just create an equivaent far-fied baoon from coherent summation of the array eements but

where the summation was done ÐiveÑ during run-time at each distance, azimuth and eevation

required, thus aso handing the nearfied.

Since a DLL is an actual program it can aso hande beam-steering. The first commercial ine array

that used the DDI was the Duran Audio Inteivox where DSP-settings for AZIMUTH , FOCUSDISTANCE

and OPENINGANGLE simpy can be seected in the CATT DLL interface, in much the same way as

they are seected on site when the oudspeaker is programmed. Even if farfied-ony modeing of

such an array worked, it woud be extremey cumbersome to create an equivaent baoon for al

possibe DSP settings since each of the three parameters can be seected in very fine increments

(0.1 unit steps). Figure 3 shows a comparison of predicted poar diagrams at different distances for

an Inteivox 2c. Note that not ony the on-axis evel (as compared to 1/r 2 ) changes with distance but

aso the shape of the baoon. Figure 4 shows a vaidation of the modeing as compared to an

outdoor measurement.

axis

3 m

7 m

10 m

20 m

Figure 3 Duran Audio Intellivox 2c,27 m long DSP-controlled column array.DSP settings: AZIMUTH = -1»,

FOCUSDISTANCE = 40 m, OPENINGANGLE = 6».Polars are plotted at2»resolution,10 dB/div.

120

Measured

115

Simulated (DuranAudio)

110

Simulated (CATTDDI)

105

100

dB spl

1/r 2 ¼ -6 dB/distance-

doubling

> 10 dB difference

100

distance (m)

Figure 4 Validation ofDuran Audio Intellivox 2c DDIprediction at1 kHz,free-field on-axis.

James, Dalenback - Computer Modelling With Catt-Acoustic.pdf

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