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Experiments with Epidaure: The CSTB Room Acoustics Computer
Model System
Ref
,
~ e r J ' . . - I
National Research Cansbll national
*
Couheii Canada de recherche. Canada Institute for InstitUt deResearch in recherche en Construction cOnstruction
EXPERIMENTS WITH EPIDAURE:
The CSTB Room Acoustics Computer
Model System
J.S. Bradley
Internal Report No. 563
Date of issue: January 1988
This is an internal report of the institute for Research in Construction. Although not intended for general distribution, it may be cited as a reference in other publications.
INSTITUTE FOR RESEARCH IN CONSTRUCTION NATIONAL RESEARCH COUNCIL OF CANADA
INTERNAL REPORT
EXPERIMENTS
WITH
EPIDAURE:
The CSTB
Room Acoustics Computer Model System
by:
2
TABLE OF CONTENTS
1. Introduction
2. Description of the CSTB Ray and Cone Tracing Programs 2.1 Introduction
2.2 RAYDEF: Data Entry Program
2.3 RAYREV/ANAREV: Ray Tracing Program to SpeciMc Receivers 2.4 RAYCAL2/ANARES: Cone Tracine Promam to S ~ e c i n c ~ -~ ~ ~~~ Receivers 2.5 RAYF&C/AZIAREC: Program to ~alcul%e ~onto;r Plots
2.6 RAYREFL/ANAREFL: Program to Analyze Prlnclpal Reflections 3. Critique of Epidaure 3.1 Introduction 3.2 Measurement Philosophy 3.3 Efficiency 3.4 Accuracy 3.5 Details 3.6 Conclusions
4. Comparison With Measurements in the National Arts Centre, Ottawa 4.1 Introduction
4.2 Comparison of Mean Values
4.3 Comparison by Microphone Position 4.4 Stage Area Modifications
4.4. lLateral Reflectors
4.4.2 Varied Stage Shell Diflusion
4.4.3 Varied 125 Hz Stage Shell Absorption 4.5 Conclusions
Acknowledgements References
Appendix 1. Variation of Diflusion and Absorption Coefficients Appendix 2. Summary of Geometrical Studies
1.0 INTRODUCTION
The science of designing and evaluating rooms for speech and music is currently in a state of change. Sweral types of new acoustral measures have become accepted as important correlates of subjective evaluations of the acoustical properties of a hall. While there are still many gaps in our knowledge, it is clear that we have to learn to design and evaluate halls in terms of these newer quantities.
There are four types of new quantities that we must now consider: (1) the overall strength or level.
(2) measures of the balance between clarity and reverberance such as early to late sound ratios,
(3) decay times, and
(4) measures of the relative strength of early lateral reflections.
In general, these quantities are influenced by particular strong early reflections in the impulse response and hence vary from seat to seat within a hall. They are also quantities that are influenced by the geometry of the hall and therefore any method for predicting their values must consider in detafl the shape of the room.
A number of research groups have developed methods for measuring these new quantities in rooms, and work a t IRC has concentrated on learning how to use these measurements to diagnose acoustical problems in existing halls. In order to predict these new quantities at the design stage. it is necessary to be able to calculate impulse responses for particular source and receiver positions in the planned hall. This has been attempted using computer models to geometrically trace rays or using the method of image sources. In either case these types of computer models are based on geometrical acoustics and do not inherently include wave acoustics effects such as diffraction and scattering. Thus they would only approximate conditions in the corresponding real room at higher frequencies where sound would be expected to behave in a ray-like manner. While several attempts to produce computer models have been reported in the literature, very few of these models are complete enough to attempt to calculate values of particular acoustical measures.
The Epldaure ray and cone tracing computer models developed at CSTB Grenoble France are initially based on geometrical acoustics concepts but also include approximations to the non-specular reflections that occur at most real surfaces. The programs do calculate a number of the newer auditorium acoustics measures and are thought to be the most advanced room acoustics models that exist today.
It seems clear that the continued development of such computer models is the way of the future and represents a potentidly accurate and cost effective approach to designing rooms for speech and music. More experience is needed with such computer models to more fully understand their uses and their limitations, as well as to contemplate their future development. The present study was carried out to gain an understanding of the present llmitatlons of the best currently available computer model, and to waluate the potential uses of this developing technology as both a research and a design tool. Because Epidaure represents the best available technology. it was also intended to evaluate in more detail both the concepts on which it is based and the way in which these were implemented. Where problems were identified, recomrnendatlons for an improved approach are made or the need for further development is described.
A s Epidaure is continuing to wolve, it is hoped that any comments and criticisms will be of use to CSTB as well as to others in both Canada and France who are contemplating developing similar computer models.
The report contains first a brief description of the system of programs that constitute Epidaure. This is followed by some comments and criticisms of the programs as they eldsted in the summer of 1987, based on the author's experiences as a user of the programs over a period of several months. Comparisons of measured and predicted values of several acoustical quantities in the Opera of the National Arts Centre in Ottawa, Canada are then presented. This is a large and very complicated multi-purpose hall and modeling this hall represents a quite severe test of the programs. Some further studies are included in the Appendices that illustrate how such computer models are very useful to increase our basic understanding of the acoustical properties of room.
2.0 DESCRIPTION OF THE CSTB RAY AND CONE TRACING PROGRAMS 2.1 Introduction
There are a group of programs that together are known a s "Epidaure" after the ancient Greek theatre. Each calculation tends to be broken into two parts, so that the time consuming tracing of rays or cones can be performed over-night a s a batch job or even over the weekend. There are two basic types of processes: tracing of rays and tracing of cones. Tracing rays is essentially a statistical process. Although it might be theoretically possible to trace a large enough number of rays to never 'gust miss" the microphone this is not really practical. To ensure a large enough number of hits, the microphone is required to be quite large, (i.e.. 1 or 2 meters in diameter). Tracing cones produces an exact image sources impulse response. (Of course all of the restrictions of geometrical acoustics remain.) Diffusion is approximated by two difTerent techniques of different complexity. There are programs that trace rays or cones to specific receivers. and also a program that produces contour maps of acoustical quantities for a particular surface. Finally there is a program that produces a simplified impulse response for a limited order of reflections so that the paths of individual reflections can be identified and plotted on drawings of the room. The programs are running on a VAx 750 using TeMronix colour graphics terminals and printers. There is no printed output of acoustical quantities in numeric form, only contour plots. Impulse responses and decay curves can be plotted out (in colour).
The programs are described separately below. RAYDEF must be run first; it permits the entry of geometrical data describing the room. its materials, source, and receiver positions. RAYREV is a ray tracing program that produces impulse responses at specific receivers. and from which acoustical quantities can be determined. RAYCAL2 is a cone tracing program and again produces impulse responses at specific microphone locations. RAYREC is a cone tracing program that produces contour plots of acoustical quantities. RAYREFL is a ray tracing program that produces simplified impulse responses at specific receiver locations so that individual reflection paths can be identified. Figure 2.1 is a flow chart illustrating how the programs are interrelated.
2.2 RAYDEF: Data Entry Program
This program permits the entry of the description of the room. The coordinates of all comers of surfaces are first entered. Surfaces then are described by the numbers of the coordinate comers associated with the surface. A maximum of 512 sets of coordinates and 256 surfaces are the current limits of the system. A material is associated with each surface, and there is a maximum of 16 different allowed materials. Each material is defined by octave band absorption and diffusion coenicients. It is possible to include an angular dependence on the absorption coefficients. One source position and up to 16 receiver positions can be entered. The directivity of the source can be defined by the reduction in level at 10 degrees away from on-axis. Thus at present the possible directivlty is symmetrical around the axis of the source. The number of rays is selected by choosing the angle between rays. The following equation relates the number of rays to this angle b.
EPIDAURE FLOWCHART OF PROGRAMS AND FILES
...
...
RAYDEF7
1
( r a y s ) ( c o n e s ) ( c o n t o u r maps) I I I RAYREFLI
ANARESI
I
ANARECI
/
ANAREBLI
( w h e r e "xxx" i s a t h r e e c h a r a c t e r room name.)
where N is the resulting number of rays. (This is not quite the same a s the number of rays printed out by the program. In one case the program gave N = 10.316 for b = 2 degrees, compared to 11,370 rays calculated from the above equation for the same 2 degree angle.)
Other information is also entered that is only required for one or another of the calculation programs and is not used by all of them. Since the cone program is also intended to produce an accurate impulse response that can be convolved with music for subjective listening analyses. a sampling frequency and related maximum frequency are specified. For a sampling rate of 32.000 Hz results are obtained in the octave bands from 63 to 8000 Hz, and a 256 ms long impulse response is produced. By halving the sampling rate, a 512 ms impulse response is obtained with information in the octave bands from 3 1 to 4000 Hz.
This program verifies that each set of points associated with a surface are indeed co-planar, and draws the room design on the screen in various ways. Separate receiving surfaces are also specified for the program that plots contours of measures. These surfaces have no effect on the propagation of the rays or cones.
2.3 RAYREV / ANAREV: Ray Tracing Program to Specific Receivers
RAYREV traces rays and includes a relatively simple approximation for diffusion effects. ANAREV is used to analyze the impulse responses that RAYREV produces. The angle between rays from the source determines the number of rays traced. Using 10,316 rays corresponding to an angle of 2 degrees between rays is quite adequate for good results. Measurements for this number of source rays were made using a microphone diameter of 2 meters. Rays are reflected geometrically at incidence with each surface. If the coefficient of Muston is zero. the amount of geometrically reflected energy is determined by the specified absorption coefficients of the surface. When diffusion is included, the angle of the reflected ray is chosen randomly from a gaussian distribution centred about the normal to the surface and with a standard deviation of / 4 multiplied by the diffusion coefficient. Although diffusion coefficients are specified separately for each octave band. this program only uses an average coefficient. RAYREV can run as a batch job and includes results for the average of all microphone positions.
Program ANAREV pennits one to obtain various forms of output from the calculated impulse responses. It is an interactive program. and is relatively time consuming to run. One must analyze the impulse response at each microphone octave by octave. With 7 octaves of data at 8 microphone positions plus the average response of all microphones one has to analyze 63 m e r e n t impulse responses (7 x 9). To do this, one can view the impulse response on the screen, look at the energy build up versus time, or view various decay curves. Each screen can be printed out on a colour printer if desired. It takes approximately 2 minutes per screen to print colour copies. To avoid the problems of a truncated impulse response, the program first requires the user to perform the steps to estimate the steady state level to infinity. This is done with the aid of the display showing the build up of sound energy. Apparently this estimation is based on calculations including only 2 points, and can at times give quite varied results for the associated estimated reverberation time. Once the steady state level and
associated reverberation time have been estimated, one then proceeds to the Schroeder integrated decay curve display. One calculates a reverberation time. RT, from the slope of the curve between two points selected by cursor. The EDT is calculated between two points which are: the start of the decay and the flrst point that is -10 dB or greater. It does not fit a straight line to determine the mean slope of the first 10 dB. Clarity, CEO, and definition. D50, are also calculated as well a s the sound level, Lp. with a source having a level of 90 dB at 1 meter. The source can be white or pink, and the overall level can be A-weighted or a flat response according to the input specifications given when using RAYDEF.
2.4 RAYCAL2 / ANARES: Cone Tracing Program to Specific Receivers
These programs are used in a very similar way to the ray tracing programs above. but the principles of the calculations performed are quite different. RAYCAL2 traces cones rather than rays. At each reflection the cone is reflected from the surface where the largest portion of the cone is incident. Thus near comers and adjacent surfaces errors occur because some of the cone should really be reflected by the other surface a s well. This error can be minimized by choosing a small enough angle between the rays from the source. Ifa receiver is found within the cone the exact ray path from the source to the receiver is calculated. and an impulse added to the impulse response with exactly the correct time of arrival. The result is an exact geometrical impulse response rather than a statistical result. Thus, this program should give results in good agreement with image source programs such as proposed by Borish [I].
The inclusion of diffusion is more complicated than in RAYREV. If "a" is the energy absorption coefficient and "6" is the energy diffusion coefficient, then the portion of energy that is geometrically reflected at a surface is given by,
and the portion of energy that is diffusely reflected is given by.
where Ei is the incident energy, Eg is the geometrically reflected energy and Ed is the diffusely reflected energy. The diffuse energy is emitted as a train of decaying impulses having a decay time given by the estimated reverberation time entered with RAYDEF. That is, you have to estimate the reverberation time before you can run RAYCALZ. The diffuse impulses are separated by the mean free path of the room with a small random variation. The diffusely reflected energy is assumed to follow a cosine reflection law and the energy is traced directly to each microphone from each point of reflection. Thus the diffusely reflected energy arriving at a microphone would have an energy proportional to:
where 0 is the angle between the diffusely reflected ray and the surface normal. and r is the distance from the point of M u s e reflection.
Because the program produces an "exact" impulse response. it can be convolved with anechoic music to demonstrate the effect of the hall on musical signals. For good quality audible results a 32.000 Hz sampling rate is used. This pennits measures to be calculated to 8 kHz, but limits the duration of the impulse response to
256 ms. For calculations of acoustical measures, a better compromise is to use a 16,000 Hz sampling rate that gives a 512 ms impulse response with results up to the 4 lcHz octave band. This is still quite short for determining the reverberation time in a large hall. RAYCAL2 produces an output file for each microphone position and does not produce an average response, because this would not be possible with this type of response. These responses are filtered into octave band results using the program RAYFIL. The details of the desired filters are first specified by the program FILOCT.
Program ANARES is used to obtain output from the impulse responses calculated by RAYCAL2. It functions essentially the same as the program ANAREV. One can view the impulse response directly and zoom in on a particular portion of it. Figure 2.2 is an example of an impulse response produced by this program. The energy build curve, see Figure 2.3, must flrst be extrapolated to infinity, and an associated reverberation time calculated. The final results are then obtained from the Schroeder integrated decay curve. Figure 2.4 is an example of the Schroeder decay curve showing the best fit straight line to the portion of the curve that was selected by the operator. The vertical scale in this display is not calibrated and the user does not know how many decibels of decay is shown until after a particular point is selected with the cursor. D50. C80. Lp, EDT. and RT are calculated a s for ANAREV. The energy build up and decay curves tend to be more irregular than with the ray program. Each screen can be copied with the colour printer, but output is not provided in any other form.
2.5 RAYREC / ANAREC: Program to calculate contour plots
Program RAYREC calculates simplified energy responses at a grid of receivers from which contour plots of various acoustical measures can be calculated. A
1 metre grid is typically used. The energy responses are calculated with 16 ms windows and a total of only 16 such time windows are included. The program traces cones rather than rays, but does not include any estimation of diffusion effects.
ANAREC pennits the user to plot out coloured contour plots on the screen and to copy them with a colour printer. Seven different colours are used, to give seven different levels of each measure. The program will plot contours of broad band values of: (11 (2) (3) (4) 15) 16) (7) (8) (9)
the total energy level, the direct sound level.
the ratio of total to direct sound energy. the lateral efficiency.
clarity, C80, definition. D50.
the Lochner and Burger signal/noise ratio. the early decay time. EDT.
and total energy level in octave bands.
Figure 2.5 is an example of the contour plots that can be produced. In this case it shows the variation of C80 values in a rectangular room. This is the only program that calculates any measure related to the relative strength of lateral reflections. Apparently the lateral energy fraction is calculated with a cosine angular dependence rather than the cosine squared a s occurs in most measurements. The lateral energy is integrated from 25 to 80 ms. It is not clear how the 25 ms starting point is determined with only 16 ms time windows. Due to the limited duration of the energy response at each point there are definite limitations to the results. In particular. if the room is quite reverberant, the EDT cannot be correctly calculated. (because it uses only two points,
and cannot find a -10 dB point). and the total energy level and clarity will not be correct. The advantage of the program is that it gives an instant impression of overall conditions in the entire room.
2.6 RAYREFL / ANAREFL: Program to analyze principal reflections
RAYREFL traces rays in a strictly limited manner
so
that simplified impulse responses of the principal reflections can be obtained, It is then possible with ANAREFL to identify the paths of these principal reflections at each microphone position. When running RAYREFL the user specifies limits on the duration of each ray, the minimum amplitude to be considered for each ray, and the maximum order of reflections to be calculated.ANAREFL uses the same routines to draw the hall on the screen a s RAYDEF. Thus if you wish to change the orientation of the hall you must go back to RAYDEF and do it there. The program ANAREFL always draws the hall on the screen before proceeding to plot the simplified impulse response at the specmed microphone. One can then identify particular reflections with the cursor and alternate between displays of the simplified impulse response and drawings of the hall with particular ray paths drawn on them. Unfortunately with a complicated hall it is a little slow to redraw the hall each time.
The program is very useful to veriry: the location of microphones, the correct orientation of reflecting panels. or to discover the paths of particular reflections. Again the contents of the screen displays can be copied using a colour printer.
3.0 CRITIQUE OF EPIDAURE
3.1 Introduction
While many have dreamed of advanced computer models for predicting the acoustical properties of auditoria, EPIDAURE is a reality and is being used to solve acoustical problems in a wide range of types of rooms. EPIDAURE obviously represents the result of a n enormous effort which has taken computer modeling from crude ray tracing programs to a sophisticated computer model capable of predicting the currently accepted major acoustical quantities. Although a great effort has already been expended, the programs are still developing and so the following criticisms and suggestions are made in a positive manner in hope that they may be of use in this evolutionary process.
The comments can be grouped under three headings: 11) questions concerning the accuracy of the predictions, (2) questions concerning the efficiency of the programs, and (3) more detailed comments.
One would like the most accurate predictions possible. but it is also important to be able to perform these calculations with a minimum of effort. There is also a question of measurement philosophy which relates back to both the accuracy and the efficiency of the predictions. With the current very rapid changes in computer technology, the optimum approach to calculating expected quantities is also subject to change, and better solutions to some of the problems may soon become available.
3.2 Measurement philosophy
A good measurement should be the result of some systematic procedure that is exactly repeatable. In other words there must be a set of precise rules that define how the measurement is made, and anyone following these rules should arrive at the same result each time the same situation is measured. This also means that the measurement can be automated and incorporated in a computer program that can run without human intervention. If human intervention is required. different people will
make different judgments and the results will be biased: that is. each person will obtain different results. This is then not an ideal measurement system. It also makes it a less emcient measuring system, because humans are usually much slower than computers at making decisions. EPIDAURE now includes critical points where the operator must make decisions that can have a considerable influence on some of the results. Completely automating the programs would not only greatly improve the repeatability of the predictions, but also would lead to considerable improvements in overall efficiency.
3.3 Efficiency
In analyzing impulses calculated either with the rays program (RAYREV), or the cones program (RAYCAL2). it is possible to spend several hours performing the extrapolations to infinite time, and the calculation of reverberation times and the other measures. While it is certainly often desirable to see individual impulse responses to better understand them, it is not necessary and not desirable to perform these calculations interactively. Ways should be sought to completely automate the analyses. and the results should be printed to a file for printout and further manipulation.
Having to write down results from the screen with pencil and paper is a waste of time, a source of errors, and not in keeping with the up to date use of computers in other aspects of the programs. The results should be in a file. probably in ASCII. so that they can be readily transferred to personal computers where a wealth of software exists to pennit the easy calculation of means and other desired statistics, as well as plotting graphs of various quantities.
The current, labour intensive approach, forces the user to focus on the details at a relatively small number of microphone positions. One should strive to get a more global picture of the room by obtaining results from a larger number of combinations of sources and receivers. This would only be practical if the analysis programs (ANAREV. and ANARES). were completely automated. The programs for producing contour plots of measures (RAYREC and ANAREC). also offer the possibility of a more global look at the properties of a room, but a s discussed below they produce results of more limited accuracy.
The entry of room coordinates and other information is also a difficult and time consuming problem. It would seem probable that the entry of room coordinates could be most easily improved by making use of available CAD software. Such programs might allow the user to construct the room on the screen perhaps with the aid of a dgitlzing pad. Writing such software oneself would be a n enormous task. and it would probably be better to spend some time searching for appropriate commercially available software. This is obviously not a simple problem, but it must be considered to make the overall process more efficient. The more efficient and easy to use the process is, the more it will be used, and hence the more valuable it would be.
3.4 Accuracy
The programs seem to have dimculty predicting reverberation times, partly because the calculated impulse response is often only a small portion of the duration of the complete reverberation time. This problem is currently solved by extrapolattng the integrated energy bufld up to infinity to represent a steady state level. This extrapolation to infinity is apparently only based on
an
exponential curve fit to two points. It is one of the critical weak links in the analysis programs. Even at intermediate frequencies, the estimated reverberation time associated with this extrapolation to infinity can vary enormously. At low frequencies it is worse and the program encounters calculation errors and at times cannot estimate a reverberation time. As an example. Figure 3.1 is the integrated energy bufld up at 500 Hz for a model of the National Arts Centre. Ottawa. Although the curve looks reasonably smooth, it was possible to obtain estimated reverberation times varylng from 0.95 to 2.88 seconds. Thus. the range of estimated reverberation times corresponds to the range of possible reverberation times for almost all large auditoria. Unfortunately this estimated reverberation time has a very strong influence on the final calculated value. If the estimated reverberation time is too short. then the resulting Schroeder decay curve is curved downward in a n unnatural manner and the user can readily guess that his choice is probably not ideal. However, if the estimated reverberation time is too long, the user has no way of knowing. Thus. there is a tendency for a bias towards calculating longer reverberation times than should occur.While the problem is easy to identify. the solution is not as easy to find. Perhaps a better procedure for fitting an exponential curve to the integrated bufld up curve would improve the situation. Alternatively. one could consider other approaches for calculating the reverberant tail of the impulse response. One suggestion that has
been made is to trace cones for the first part of the response, to obtain the correct detail for the initial reflections. and then to use a Markov process for the reverberant tail of the decay. Perhaps there are also other possible ways for adding the correct reverberant tail to the initial impulse response.
It seems preferable to calculate early decay time. EDT. from the slope of a best fit straight line to the first 10 dB of the decay. This should produce a more stable and more precisely repeatable measure. There are always small irregularities in decay curves and to calculate the EDT based on the single point that is 10 dB below the starting point is to invite these irregularities to introduce unpredictable variations into the results. Thus calculating the EDT from a best fit to the initial slope should produce a more repeatable measure. In addition, surely the subjective effect heard by the ear is not determined by the value of the decay curve at a single point, but is more closely related to the average effect of the initial decay.
Diffusion is a problem that requires a large amount of further work. It is not very satisfactory to have to completely guess at diffusion coefficients, that have different effects in the two different impulse calculation programs (RAYREV, and RAYCAL2). (See Appendix 1 for results of tests to demonstrate the effects of varied absorption and diffusion coefllcients in a simple hall using both RAYREV and RAYCAL2.1 This is further complicated by the practical need to simplify the structure of most rooms. Thus in some cases one may include the details of a beam. while in other cases, one may estimate the effects of a beam by giving the attached surface larger diffusion coefficients. The required diffusion coefficients for the two cases would presumably be quite different. In view of the compleldty of various theoretical approaches to explaining diffusion. this is probably a problem that could best be solved by extensive systematic series of comparisons between the model results and very simple rooms. One could imagine starting with a simple rectangular box. and perhaps flrst adding one beam. By examining the impulse responses for such cases in detail, one should be able to derive a practical procedure for including the effects of diffusion into the programs. After one had empirically determined such a procedure, one would still have to attempt to measure diffusion c o a c i e n t s for a range of materials and structures a s a function of frequency.
The combination of RAYREC and ANAREC offers the potential for a very useful analysis tool permitting the user to have a more global impression of the acoustical characteristics of the room. Unfortunately these programs are a little too limited. No attempt to model diffusion is included and the duration of the simplilled impulse responses that are calculated is too short to produce accurate results in a typical large auditorium with reverberation times approaching 2 seconds. For example. when reverberation times are long, EDT values are incorrectly determined by the maximum duration of the impulse response rather than the point that is 10 dB below the first point of the decay curve. At the same time the overall level and late arriving energy levels will be underestimated leading to errors in several quantities. Including diffusion would presumably have a significant effect on lateral energy fractions. LE. and because this is the only program to calculate this quantity there is at present no really satisfactory prediction of LE values. Only broad band LE values are calculated. LE is an
important quantity that is relatively easy to calculate and it should be included in the other programs.
3.5 Details
There seems to be a problem with rays properly penetrating into narrow openings such as under balconies. Calculating simplified impulse responses with the programs RAYREFL/ANAREFL indicated that if the angle between adjacent rays from the source was too large 1e.g.. 5 degrees), the direct sound might be completely missed at seats under a balcony. With a small movement of the microphone towards the source, the direct sound was again calculated. Decreasing the angle between rays from the source to 1 or 2 degrees also caused the direct sound to be calculated correctly. However with the cone tracing program. RAYCAL2, impulse responses were produced with an apparently very weak direct sound at these locations with
a
2 degree angle between rays from the source. When the microphones were moved slfghtly towards the source, the problem again appeared to disappear. Because the balcony opening, a s seen from the source. formed an angle of only 5 or 6 degrees, it is not completely surprising that such limitations occur.Using a 2 degree cone width at the source and the resulting total of 10.316 rays seems like a large number of rays, but this may not be adequate to correctly describe impulses arriving with longer delays. With a 2 degree cone angle the cone is 12 metres in diameter after 0.5 seconds, 6 metres in diameter after 0.25 seconds. and greater than 2 metres in diameter after only 85 ms. The cone is reflected only from the surfaces that the centre line of the cone encounters. Thus when the cone strikes a surface near an edge a significant amount of energy is actually reflected off the other adjacent surface. This is fgnored in the present version of the program, and hence a number of reflections are not included in the calculated impulse response that would occur in the actual room. It is not clear how these errors would effect the calculated acoustical criteria, because although some of the energy is not reflected from the correct surface the energy is reflected from the adjacent surface and continues to travel around the room.
In general there seems to be a need to better document how the programs should be used, and their limitations. There are now a number of points that one must discover by experience.
There are some cases where the programs could be more efficient if unnecessary steps were removed. The program ANAREFL seems to be the least "user friendly". It first unnecessarily draws the complete room on the screen. With a complex room this takes enough time to be annoying. In addition. because it is not possible to change microphone position within the program, each time you wish to change to the results of a different microphone you again have to wait for the room to be drawn on the screen. ANAREFL is interrelated with the drawing software in RAYDEF. Thus ANAREFL displays the room a s last displayed using RAYDEF. You must exlt from ANAREFL to RAYDEF to change the form of the drawing. It would be more convenient if the form of the drawing could be changed within ANAREFL.
RAYDEF permits the entry of data for all of the analysis programs. It is easy to make mistakes by forgetting to enter certain information. In some cases RAYDEF could include checks to determine whether data had been entered for at least some quantities. For example if you forget to enter the room volume, some programs will work, but the cone tracing program, RAYCAL.2, will not. It would be very simple for RAYDEF to check that a volume value had been entered.
3.6 Conclusions
Perhaps the two largest problems that must be solved in developing a sophisticated room acoustics computer model, are to produce a sdiciently accurate approximation to diffuse wave-acoustics effects, and to develop sophisticated software for the efficient entry and modification of room data. EPIDAURE has achieved considerable success in both these areas but further advances are desirable. Automating the analysis of impulse responses would dramatically improve the overall efficiency of the calculations and would aermit one to aerform a larger number of more
-
precisel; repeatable measurements in each modeled room.4.0 COMPARISON WITH MEASUREMENTS IN THE NATIONAL ARTS CENTRE OTTAWA
4.1 Introduction
Program RAYCAL2. that traces cones. was used to calculate impulse. responses for a computer model of the National Arts Centre Ottawa. Half of the room was entered as 321 coordinates and 292 separate surfaces. The hall was thus assumed to be laterally symmetrical, the centre line boundary was made perfectly reflecting, and the source was on the centre line. Further points and surfaces were added for the receiving surfaces used by the contour plot programs. RAYREC/ANAREC. and for additional experimental reflecting panels not present in the real hall. A total of 16 measurement positions were used corresponding to locations where measurements had been made. Of these, two were on the stage. Figures 4.1 and 4.2 show the room and the microphone positions a s used by the computer program.
Results are presented for different material absorption and diffusion coefncients. Changes to these coefficients were made in a n attempt to improve the agreement between measured and calculated acoustical quantities. The first set of material values, referred to as CONES-6, corresponded to the initial material coefficient values. These values are given in TABLE 4.1. For the second case. referred to as CONES-7. 0.15 was added to all diffusion coefficients. For the final condition, CONES-8, absorption was added to the hall, mostly to the ceiling, in an attempt to improve the agreement between measured and calculated reverberation times. The diffusion coefficients were the same as for the CONES-7 data. This added absorption was an attempt to represent the effect of the suspended catwalks, lighting and decorative flags that exist in the real hall. The material coefficients for the second and third cases are found in Tables 4.2, and 4.3.
4.2 Comparison of Mean Values
Comparisons were first made between the measured and calculated means of the values at 14 measurement positions in the audience seating area of the hall. Figure 4.3 compares measured and calculated reverberation times for the 3 different calculations. The initial calculation. CONES-6, gave reverberation times that were consistently higher than the measured values
at
all octave band frequencies. When diffusion was added to the surfaces, (CONES-71, only small changes in reverberation time values occurred and there was not a large improvement in the agreement between measured and calculated values. When further absorption was added. (CONES-8). there was almost perfect agreement at the lowest two octave band frequencies, but only small improvements at other frequencies.Comparisons for the mean EDT values over the same 14 audience measurement positions are shown in Figure 4.4. The initial condition. (CONES-6). gave good agreement wlth measured values in the 250 and 500Hz octave bands. The CONES-6 data under estimated the measured values at lower frequencies. (125 Hz].
and over estimated them at higher frequencies, (1000 to 4000 Hz). Adding diffusion, (CONES-7). shifted the calculated values upwards so that the frequency of best agreement with measured values became 250Hz. When absorption was added. (CONES-8). the calculated curve was lowered and agreement with measured values was best at higher frequencies. 1000 to 4000 Hz. None of the three calculation conditions produced good agreement at all 6 octave band frequencies. Because the calculated values are measured from only two points on the decay curve they would be expected to
Table 4.1
Material Absorotion and DLffuslon CoefRcfmts, Condltlon CONES-6
(a) Octave Band Absorption Coefficients Material
1) Audience/seating 2) Concrete
3) Plaster/gypsum board 4) Glass doors/windows 5) Reflecting centre line 6) Stage floor
7) Stage ceiling 8) Orchestra shell 9) Hall ceiling
(b) Octave Band Diffusion CoeMclents
Material 63 125 250 500 1000
1) Audience/seating 0.15 0.15 0.20 0.25 0.30 2) Concrete 0.20 0.20 0.25 0.25 0.30 31 Plaster/gypsum board 0.25 0.25 0.30 0.30 0.35 4) Glass doors/windows 0.20 0.20 0.25 0.25 0.30 5) Reflecting centre line 0.00 0.00 0.00 0.00 0.00 6) Stage floor 0.15 0.15 0.20 0.25 0.30
7) Stage ceiling 0.20 0.20 0.25 0.25 0.30 0.30 0.35 81 Orchestra shell 0.20 0.20 0.25 0.25 0.30 0.30 0.35 9) Hall ceiling 0.20 0.20 0.25 0.25 0.30 0.30 0.35
Table 4.2
Material Absomllon and Diffusion Coefncimts. Condition CONES-7
(a) Octave Band Absorption CoetZicienta
Material 63 125 250 500 1000 2000 4000
1) Audience/seating 0.25 0.39 0.57 0.85 0.99 0.93 0.87 2) Concrete 0.03 0.03 0.04 0.06 0.09 0.09 0.11 31 Plaster/gypsum board 0.18 0.16 0.13 0.10 0.07 0.07 0.06 41 Glass doors/windows 0.29 0.21 0.21 0.24 0.09 0.07 0.06 5) Reflecting centre line 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6) Stage floor 0.17 0.12 0.13 0.08 0.09 0.09 0.11 71 Stage ceiling 0.33 0.23 0.19 0.16 0.18 0.18 0.21
8) Orchestra shell 0.28 0.23 0.13 0.16 0.09 0.09 0.11 9) Hall ceiling 0.18 0.16 0.13 0.10 0.07 0.07 0.06
(b) Octave Band Diffusion Coefflciente
Material 1) Audience/seating 2) Concrete
3) Plaster/gypsum board 4) Glass doors/windows 5) Reflecting centre line 6) Stage floor
7) Stage ceiling 8) Orchestra shell 9) Hall ceiling
Table 4.3
Materfal Absomtlon and Diffusion Coefflcfents, Condition CONES-8
[a) Octave Band Absorption CoeEicients
Material 63 125 250 500 1000
1) Audience/seating 0.25 0.39 0.57 0.85 0.99 2) Concrete 0.03 0.03 0.04 0.06 0.09 3) Plaster/gypsum board 0.18 0.16 0.13 0.20 0.10 4) Glass doors/windows 0.29 0.21 0.21 0.24 0.09 5) Reflecting centre line 0.00 0.00 0.00 0.00 0.00 61 Stage floor 0.17 0.12 0.13 0.08 0.09 7) Stage ceiling 0.33 0.23 0.19 0.16 0.18 81 Orchestra shell 0.28 0.23 0.13 0.16 0.09 91 Hall ceiling 0.20 0.30 0.35 0.35 0.40
(b) Octave Band Diffusion Coefficients
Material 63 125 250 500 1000
1) Audience/seating 0.30 0.30 0.35 0.40 0.45
2) Concrete 0.35 0.35 0.40 0.40 0.45
3) Plasterlgypsum board 0.40 0.40 0.45 0.45 0.50
4) Glass doors/windows 0.35 0.35 0.40 0.40 0.45 0.45 0.50 5) Reflecting centre line 0.00 0.00 0.00 0.00 0.00 0.00 0.00 61 Stage floor 0.30 0.30 0.35 0.40 0.45 0.45 0.45 7) Stage ceiling 0.35 0.35 0.40 0.40 0.45 0.45 0.50 81 Orchestra shell 0.35 0.35 0.40 0.40 0.45 0.45 0.50 91 Hall ceiling 0.35 0.35 0.40 0.40 0.45 0.45 0.50
2.5 2 RT, s 1.5 1 125 250 500 1000 2000 4000 FREQUENCY, Hz
Figure 4.3 Comaprison of calculated and measured reverberation times.
-
Measured*
cones-6*
cones-78
cones-8 2.5 2 EDT, s 1.5 1 125 250 500 1000 2000 4000 FREQUENCY,Hz
be a Uttle more variable and to give different EDT values than the measured values which were calculated from the mean slope of the first 10 decibels of the decay curve. If
the initial part of the decay curve were concave the measured EDT values, obtained from straight h e fits to the actual decay, would have shorter EDT values than the calculated values. If the degree of curvature of the initial part of the decay curve varied with frequency, then the agreement between measured and calculated values would vary with frequency a s observed in Figure 4.4.
Figure 4.5 compares measured and calculated definition. D50, values. The initial calculation (CONES-6). gave reasonable agreement with measured values. "1O0h, from 500 Hz to 4000 Hz. Adding diffusion (CONES-71, lowered D50 values and degraded the agreement with measured values at 1000 Hz. Adding absorption (CONES-8). considerably raised the D50 values and degraded the agreement between measured and predicted values, In all cases the calculated results did not reflect the very marked decrease in D50 values at low frequencies (125 and 250 Hz). This dip in the measured D50 values is most llkeiy due to the seat dip effect caused by the attenuation of grazing incidence sound propagating over the seating areas. Unfortunately the computer models do not attempt to model this effect.
Clarity values. C80, are compared in Figure 4.6. The results were very similar to those for Dm values. A s the absorption and diffusion was changed the calculated values increased and decreased indicating that it was possible to obtain reasonable agreement between measured and predicted values for frequencies between 500 and 4000 Hz. Again the computer predictions do not attempt to predict the seat dip effect and thus there was very poor agreement between measured and calculated values at low frequencies (125 and 250 Hzl.
While it may be possible to adjust material coefficients so that measured and calculated average reverberation time values are in good agreement. it seems unlikely that all of the other quantities would also be in good agreement. The condition that gave the best agreement for reverberation time values, CONES-8. was much less satisfactory for the other quantities. With 9 different types of materials it would be a very long task to systematically vary the properties of each material individually to search for better agreement. If this were done it might eventually lead to improved agreement between measured and calculated values. It is perhaps more instructive to first consider the comparison of measured and calculated values at individual microphone positions.
4.3 Comparison by Microphone Position
Comparisons were made at individual microphone positions by plotting octave band results as a function of the microphone location for each of the measured and calculated conditions. The microphone locations were generally arranged so that in going from left to right along the horizontal axis of the graph, one is moving away from the source. Thus the first two positions (from the left) were on the stage, the next 6. F1 to W34 were on the main floor. MD1 and MD34 were in the first balcony. AD1 and AD34 were in the second balcony. BD1 and BD34 were in the third balcony. and BX16 and BX22 were boxes at the second balcony level. The last two positions did not follow the general trend and were not the farthest from the source. The actual seat locations were included on Figures 4.1 and 4.2.
-
Measured
9c
Cones-6
*
Cones-7
8
Cones-8
20 1 I II
125 250 500 1000 2000 4000FREQUENCY.
HzFigure
4.5Comparison of calculated and measured definition values.
500 1000
FREQUENCY. Hz
Figures 4 . 7 to 4 . 1 2 plot octave band C80 values versus seat position for the octaves from 125 to 4000 Hz respectively. Each plot compares measured values and the three sets of calculated values. It was seen from the mean C80 values in Figure 4.6
that calculated C80 values at low frequencies considerably over estimated measured values at low frequencies. Thus it is not surprising that the 125 H z calculated values in
Figure 4 . 7 are also much higher than the measured values. There was best agreement for seats in the third balcony (BD1, and BD34). The agreement was best when diffusion was added [CONES-71, and the added absorption (CONES-81, did not improve the agreement with measured values. The comparison of 2 5 0 Hz C80 values is found in Figure 4 . 8 . The average agreement between measured and calculated values was better than for the 125 H z results, and the added diffusion case (CONES-7), again generally gave the best agreement with measured values. The largest differences between measured and predicted values occurred for the main floor seats, again probably due to the grazing incidence seat dip effect.
At 5 0 0 Hz the results shown in Figure 4 . 9 indicate good agreement between measured and calculated C80 values with added diffusion (CONES-7). Measured and predicted values agreed within approximately 2 dB or less for the main floor seats, but the agreement was generally a little inferlor for the balcony locations where the largest difference at seat AD1 was approximately 5 dB.
The 1 0 0 0 Hz results shown in Figure 4 . 1 0 continue the trend for improved agreement between measured and calculated C80 values with increasing frequency. The added diEusion calculation (CONES-7). again seemed to give the best overall agreement, but in many cases there were not large differences between the three calculations.
Figure 4.11. showing the 2 0 0 0 Hz comparisons. again indicates that the added diffusion calculations. CONES-7, gave generally the best agreement, but the areas of best agreement were different than in the previous octave. For the 2 0 0 0 Hz octave, agreement between measurement and calculation was generally better for seats in the first and second balconies than for the closer main floor seats.
Figure 4 . 1 2 indicates that the best overall agreement between measured and calculated C 8 0 values occurred in the 4000 H z octave band, and that the added diffusion case (CONES-7). was generally in closest agreement with measured values. While excellent agreement occurred for most seats. in the second and third balconies differences of 2 to 3 dB or more occurred.
Comparisons of measured and calculated values of other criteria by receiver position are presented only for the 1 0 0 0 Hz octave band. Figure 4 . 1 3 compares measured and calculated 1 0 0 0 Hz D 5 0 values. For most positions agreement was best between measured and the added diffusion case (CONES-7). where the differences were usually less than 10%.
Figure 4 . 1 4 compares measured and calculated 1000 Hz EDT values. While the three different sets of calculated values gave similar EDT values, there was a trend for
a
systematic difference between measured and predicted values. The measured 1 0 0 0 Hz EDT values tended to decrease relative to the calculated values with increasing distance from the source. Results at the two receivers in the third balcony were exceptions to this overall trend. This same trend was not evident in the C80, and D 5 0 results and was not found in the reverberation time results that follow. The tendency for the measured EDT values to decrease towards the rear of this hall andSEAT
Figure 4.7 Comparison of calculated and measured 125
Hz
clarity values.-10
STG POD F1 F34 0 1 0 3 2 W1 W34 MD1 MD34 AD1 AD34 ED1 ED34 ABX16 A8X22
SEAT
20
-
Measured 15 10 5 0STG POD F1 F34 0 1 0 3 2 W1 W34 MD1 MD34 AD1 AD34 ED1 BD34 ABX16 ABX22
SEAT
Figure 4.9 Comparison of calculated and measured 500 Hz clarity values.
1
STG POD F1 F34 0 1 0 3 2 W1 W34 MDl MD34 AD1 AD34 BD1 ED34 ABX16 ABX22
SEAT
-10
r
ISTG PO0 F1 F34 0 1 0 3 2 W1 W34 MDl M034 AD1 A034 BD1 BD34 ABX16 ABX22
SEAT
Figure 4.1 1 Comparison of calculated and measured 2000 Hz clarity values.
-5
5
-1 0
STO P O 0 F1 F34 0 1 0 3 2 W l W34 MDl MD34 AD1 AD34 BO1 8034 ABX16 ABX22
SEAT
other halls had prevfousiy 121 been explained as due to a lack of diffusion of the early sound field. If this is a correct explanation, then this lack of agreement may indicate a basic flaw in the modeling of diffusion in the program.
The comparison of measured and calculated 1000 Hz RT values in Figure 4.15 shows larger seat to seat variations in the calculated RT values than occurred for the measured values. Such large seat to seat variations are not reasonable and suggest that the program does not accurately predict reverberation times. The average results of Figure 4.3 indicated that the CONES-8 calculations gave the best average agreement with measured values. but that it tended to over predict the measured results. The same overall trend was seen in the results of Figure 4.15, but the differences at individual seats varied from 0 to over 0.4 seconds. More experimentation wlth the program would be required to determine whether these large seat to seat variations are repeatable. or are more dependent on the individual operator's use of the program.
4.4 Stage Modification Studies
The programs were also used to explore the effects of modifications to the stage area of the room. on the resulting acoustical properties of the room. Due to time limitations, calculations were only performed for 8 microphone locations. These were the 6 seats on the main floor. F1 to W34. and the 2 seats in the first balcony. MD 1 and MD34. Three types of modifications were considered:
(a) large lateral reflecting panels were added above the stage and front of the hall,
(b) the diffusion of the stage shell was varied, and (c) the 125 Hz absorption of the stage shell was varied.
These tests were selected as representing practically useful evaluations of possible modifications to the real hall. They gave further opportunities to evaluate the programs' abilities to solve realistic practical problems.
4.4.1 Lateral Reflectors
Tests in the Opera of the National Arts had led to the conclusion that this hall is lacking in early lateral reflections. The program was used to model the expected results of a large array of reflecting panels intended to increase the level of early lateral reflected energy. It was intended that this would both give an indication of the potential success of such a solution and would also evaluate how useful the programs were to test such solutions. Figure 4.16 shows a drawing of the hall with 8 reflecting panels added. Also shown are the 8 microphone positions that were used in all the calculations of Section 4.4.
As the program pair RAYREC / ANAREC provided the only means of calculating lateral energy fractions, LE, the results were obtained in the form of contour plots. Figure 4.17 and Figure 4.18 show the plots of LE contours for the main floor audience area of half of the hall. for the cases of no reflectors and with added reflectors respectively. Values were read off these contours at a grid of 12 points. The mean LE
values were 34.8% without reflectors and 35.2% with reflecting panels added. Thus, on average the fraction of early lateral energy was not greatly increased. From the contour
-
Measured9C
Cones-6 80*
Cones-78
Cones-8x
ST0 POD F1 F34 0 1 0 3 2 W1 W34 MD1 MD34 AD1 AD34 BD1 B D U ABX16 ABX22
SEAT
Figure 4.13 Comparison of calculated and measured 1000 Hz definition values.
2 1.5 EDT, s 1
-
Measured 0.5 0STG POD F1 F34 0 1 0 3 2 W1 W34 MDl MD34 AD1 AD34 BDl BD34 ABXl6 ABX22
SEAT
RT, s 1
-
Measured*
Cones-6 0.5*
Cones-78
Cones-8 0STG POD F1 F34 0 1 032 W1 W34 MD1 MD34 AD1 AD34 BDl 81334 ABX16 ABX22
SEAT
plots the largest increases are seen to occur towards the stage in the centre of the room. For the 4 points of the 12 point grid that fell in this area LE values were increased from 24.5% to 32.8%. Thus reflecting panels did effectively increase LE values in a specific area where early lateral energy was initially weakest.
These results seem to indicate that the program is potentially a very effective means of inexpensively and quantitatively estimating the effect of such modifications. The programs would also be useful to fine tune the design and position of such reflecting panels. It is disappointing that the program does not now calculate
LE values in a manner directly paralleling measurement techniques, and that it only produces broad band LE values. It would be much more satisfactory if the program RAYCAL2. that traces cones, was expanded to calculate LE values that could be more accurate than the RAYREC contour plots.
For comparison. Figures 4.19 and 4.20 show contour plots of Cm values without and then with added reflecting panels respectively. As with the LE values the major changes occur in the area close to the stage and near the centre line of the hall. In this area C80 values seemed to increase by about one contour or approximately 1 dB. This is similar in magnitude to the increase in LE values in this area from 24.5 to 32.8%.
4.4.2 Varied Stage Shell Diffusion
Program RAYCAL2 was used to examine the influence of varying the diffuseness of the surfaces making up the stage shell. This was again looked upon as both a test of a possible modification to the real hall and
an
evaluation of the program as a tool to perform such tests. Results were obtained at the same 8 receiver positions shown in Figure 4.16.Figure 4.21 gives mean C80 values from results at these 8 receivers for the material properties of the CONES-8 case detailed in Table 4.3 and also with the properties of the orchestra stage shell changed to have dflusion coefficients of 0 and 0.99 to represent the full possible range of this variable. Figure 4.21 shows a systematic trend for C80 values to decrease with increased diffusion. The only exception was at 63 Hz where decreasing the diffusion coemcient to 0 did not change the C80 value. When these C80 values at 1000 Hz are plotted versus seat position, as shown in Figure 4.22, the same systematic effect is seen in all but one case. Here at seat W34. (on the main floor but to the side and under the balcony). increased difTusion increased rather than decreased the C80 value. Thus. in almost all cases. increased diffusion of the stage shell surfaces led to decreased C80 values in the hall. It appears that added diffusion causes energy to effectively be shifted from the early to the late time period and hence decreases C80 values.
Figure 4.23 illustrates the mean D50 values versus frequency for the three conditions of stage shell diffusion. Although the trend is not quite as clear. the results are generally the same a s for C8O values. That is, increased diffusion of the stage shell surface led to decreased D50 values. In this case decreased diffusion did not ahvays increase D50 values at lower frequencies, and the changes in D50 values were smaller than the changes found in C80 values. For example, at 1000 Hz increased diffusion decreased D50 values by less than 2% while for the same situation C80 values decreased by approldmately 1 dB, a much larger change.
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