Treble simulation of a coupled space (CR1 from BRAS)
ABSTRACT
Treble’s hybrid algorithm outperforms conventional energy-based geometrical acoustics (GA) software in simulating single reflections (BRAS - RS1), diffraction from a finite object (BRAS - RS6), diffraction from a large barrier (BRAS – RS6), and medium to large rooms (CR2-CR4) by directly solving the wave equation. This study also shows Treble’s excellent performance in coupled rooms, namely, BRAS – CR1. Such a coupling between two rooms through a door opening should be a very challenging yet interesting case to showcase Treble’s hybrid algorithm combining wave-based and pressure-based GA methods.
1. Introduction
Accurate room acoustic simulations fundamentally rely on accurate simulation of all wave phenomena, including individual reflections off the surfaces, diffraction, and scattering due to obstacles and furniture. It has been shown that Treble accurately captures the reflections and diffraction for various BRAS RS conditions. This study investigated a scenario of coupled rooms, BRAS scene CR1 is chosen. The two rooms are basically rectangular, 122 m3 reverberation chamber and 104 m3 laboratory room. Imported into Treble, the coupled room volume of 225 m3 is correctly estimated, as can be seen in the lower right corner of Figure 2.
Figure 1. Sketchup model of CR1 [1].
Figure 2. Treble model [3].
2. Measurement setup
In this case, a dodecahedron and a Genelec8020 were used as sound sources and the receivers were B&K 4134 omni-directional microphones. In this study, the Treble simulation with an omni-directional source and omni-directional microphone is compared to the measurement. The transition frequency is 710 Hz, covering up to the 500 Hz octave band, the acoustic condition is simulated by discontinuous Galerkin finite element method (DGFEM). The measurement was conducted with a three-way dodecahedron source having low-, mid-, and high-frequency units. However, Treble allows only one source position, so the location of the mid-frequency unit is used: Two source positions are used in Treble simulations: LS1 (1.5, -2.23 0.77) [all in m in what follows] in the reverberation chamber which is the larger and more reverberant space and LS2 (-1.77, -2.28, 0.72) in the laboratory room, which is much more damped and somewhat smaller. The high-frequency unit is located at a height of 1.023 m, while the low-frequency unit has a height of 0.462 m according to the general documentation of BRAS. Both receivers MP1 (-1.21, 0.68, 1.24) and MP2 (-4.35, 0.7, 1.24) are located in the laboratory room, which will experience a double sloped energy decay due to the coupling from the bigger and more reverberant chamber.
The absorption coefficients in the BRAS database (fitted absorption) are shown as follows: Table 1. The absorption coefficient from BRAS database
| Freq. (Hz) | 63 | 125 | 250 | 500 | 1000 | 2000 | 4000 | 8000 |
|---|---|---|---|---|---|---|---|---|
| Concrete | 0.06 | 0.12 | 0.06 | 0.05 | 0.04 | 0.03 | 0.03 | 0.03 |
| Painted concrete | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 |
| Table | 0.02 | 0.06 | 0.17 | 0.26 | 0.27 | 0.25 | 0.25 | 0.25 |
| Absorber | 0.04 | 0.06 | 0.2 | 0.26 | 0.47 | 0.47 | 0.43 | 0.4 |
| Door (not specified) | 0.18 | 0.16 | 0.12 | 0.1 | 0.09 | 0.09 | 0.09 | 0.09 |
One transfer function (TF) comparison for LS1MP1 is shown in Fig. 3 up to 100 Hz to demonstrate low frequency room modes. Note that the source is in the reverberation chamber, and the microphone is in the laboratory. There is a good agreement between the Treble and BRAS measurement, in particular, the location of the room modes. As a comparison, another commercial energy-based GA software’s result for the same source-receiver LS1MP1 pair is shown. The other GA software’s result is far from the measured BRAS TF.
Figure 3. Transfer function comparisons for LS1MP1. Upper: Treble, Lower; GA.
The ISO 3382 parameters are compared in Fig. 3. The ISO 3382 parameters are grouped according to the source and then the averages over the two receivers are plotted. First, early decay time (EDT) is a reverberation parameter of which the accuracy is mainly dominated by the early reflections.
Figure 4. EDT comparisons, Left: LS1 (the source and receiver in different rooms) Right: LS2 (the source and receiver in the same room).
EDTs with the source in the reverberation chamber, LS1, (Fig. 4 left) are much longer compared to LS2 (Fig. 4 right), because of the substantial amount of energy coming from the more reverberant chamber. In particular, the Treble EDT curve is more accurate due to the correct amount of diffraction around the opening. When both the source and the receivers are in the laboratory room (LS2, right), which has a large amount of absorbers inside, the EDT gets lower than 2 s for most frequencies –Treble predicts the EDT more accurately than the other commercial GA.
Figure 5. T30 comparisons, Left: LS1 (the source and receiver in different rooms), Right: LS2 (the source and receiver in the same room).
Due to a non-negligible coupling (a larger door opening angle of about 30 degrees in this case), T30 differs significantly from EDT, particularly for LS2 (Figure 5 right). This indicates that the rate of the energy decay at later times differs from the slope for the early energy decay. The Treble simulation is more accurate at low frequencies for both sources. The average percentage error of T30 across the frequency and source-receiver pair for Treble is 14%, while the GA error is 16 %. For EDT, the error is 17% and 41% for Treble and GA, respectively.
Figure 6. Center time (Ts) comparisons, Left: LS1 (the source and receiver in different rooms), Right: LS2 (the source and receiver in the same room).
We see a similar trend in the center time. Treble is generally more accurate at lower frequencies for LS1 (Fig. 6 left). The average percentage error of Ts over the frequency for Treble is 21%, while the other commercial GA error is 26%.
Figure 7. Clarity (C80) comparisons, Left: LS1 (the source and receiver in different rooms), Right: LS2 (the source and receiver in the same room).
The match between clarity values C80 is not as good as for the other parameters. The average difference (not the percentage error) between Treble and measurement is -2 dB, while the difference for the GA simulation is -2.4 dB.
3. Conclusions
This study investigates how the Treble simulation methods perform in simulating the acoustics of coupled volume spaces. Treble’s acoustic parameter predictions agree well with the measurement data, evidently better than the energy-based purely-GA methods, illustrating the importance of the wave-based solver to handle crucial low frequency effects. Specifically, Treble can capture the significant variations within EDT and T30 parameters due to double sloped decays in both rooms.
References
[1] Benchmark of Room Acoustical Simulation (BRAS) database CR1: https://depositonce.tu-berlin.de/items/38410727-febb-4769-8002-9c710ba393c4