Creation and calibration method of acoustical models for historic virtual reality auralizations

Abstract

Virtual reality provides the possibility for interactive visits to historic buildings and sites. The majority of current virtual reconstructions have focused on creating realistic virtual environments, by concentrating on the visual component. However, by incorporating more authentic acoustical properties into visual models, a more realistic rendering of the studied venue is achieved. In historic auralizations, calibration of the studied building’s room acoustic simulation model is often necessary to come to a realistic representation of its acoustical environment. This paper presents a methodical calibration procedure for geometrical acoustics models using room acoustics prediction programs based on geometrical acoustics to create realistic virtual audio realities, or auralizations. To develop this procedure, a small unfinished amphitheater was first chosen due to its general simplicity and considerable level of reverberation. A geometrical acoustics model was calibrated according to the results of acoustical measurements. Measures employed during the calibration of this model were analyzed to come to a methodical calibration procedure. The developed procedure was then applied to a more complex building, the abbey church Saint-Germain-des-Prés. A possible application of the presented procedure is to enable interactive acoustical visits of former configurations of buildings. A test case study was carried out for a typical seventeenth-century configuration of the Saint-Germain-des-Prés.

Appendices

Appendix 1: Details of amphitheater calibration

This section details steps 4–6 of the calibration procedure for the amphitheater. Table 2 shows the absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$ used in the first iteration, and the associated surface areas which were concluded from the material search as proposed in step 1.

Table 2 Absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$ (mm) as the single value which was inserted into Eq. (1), and surface area (m$^2$) used in the initial iteration of the amphitheater

Curve initial in Fig. 14 shows the average T20 and C50 which resulted from the use of the material properties presented in Table 2. Subsequently, the absorption coefficients of the Aluminum (walls) and aluminum (ceiling), the materials most used in the amphitheater, were iteratively adjusted to arrive at [0.168, 0.150, 0.099, 0.072, 0.080, 0.072], bringing EDT and T20 within 1 JND, as depicted by Curve step 4 in Fig. 14.

Fig. 14

Evolution of mean T20 and C80 during the calibration procedure as compared to the mean measured ($\pm 1$ JND) values

Curve step 4 in Fig. 14 shows that the mean C50 was $\Delta$[$-0.49$, +0.21, +0.33 +0.32, +0.60, 0.50 dB].⁸ Since Fig. 6 showed that increasing the scattering resulted in a lower clarity, the ${\mathrm{char}}_{\mathrm{depth}}$ of the aluminum (walls) was increased to 55 mm, the ${\mathrm{char}}_{\mathrm{depth}}$ of the plaster board was increased to 10 mm, the ${\mathrm{char}}_{\mathrm{depth}}$ of the concrete (floor and wall) was increased to 20 mm, and the ${\mathrm{char}}_{\mathrm{depth}}$ of the concrete (ramp) was increased to 20 mm. To raise the mean C50 in the 125-Hz octave band, the scattering in this octave band of these surfaces was set to 5 %. Furthermore, the edge diffusion of the objects was omitted, and the metal construction was modeled with edge diffusion. Curve step 5 shows that after these adjustments the mean difference between measured and simulated C50 changed to $\Delta$ [$-0.33$, +0.06, +0.39, +0.20, +0.50, 0.35 dB] which is an improvement across all octave bands except for 1000 Hz.

At the start of step 6, the SD determined over the positions’ difference between measured and simulated T20 was [0.29, 0.18 s] and EDT was [0.44, 0.25 s]. A decrease in these values means a better estimation of the parameters per position. Therefore, a search was conducted for positional differences. It was found that the receivers on the upper mezzanine (R11–15) overestimated the T20 [125, 250 Hz] with $\Delta$[+0.14, +0.02 s], while the receivers on the lower mezzanine underestimated this with $\Delta$[0.15, 0.06 s]. Since the receivers on the upper mezzanine were closer to the objects and plaster boards, their absorption coefficients were raised to arrive at, respectively [0.25, 0.12] and [0.17, 0.12], while the absorption of the aluminum (walls) and aluminum (ceiling) was lowered to [0.156, 0.146] to retain the same mean reverberation and clarity. After these adjustments, the receivers on the upper mezzanine overestimated the T20 by $\Delta$[+0.11, +0.02 s], while the receivers on the lower mezzanine underestimated the T20 by $\Delta$[$-0.11$, $-0.03$ s]. This resulted in a lower SD of the T20 [0.25, 0.15 s] and EDT [0.37, 0.25 s] and therefore a better estimation of these parameters per position. Curve step 6 shows the resulting mean T20 and C50.

With the calibrated GA model, the initially chosen material properties are compared to those used in the final model. The difference between originally and finally modeled absorption coefficients of the aluminum panels is because the initial values were adopted from data concerning nonperforated aluminum panels on a 300-mm airspace measured in a reverberation chamber. However, in the amphitheater, insulation material is installed behind the aluminum panels. Therefore, the actual absorption properties of the aluminum panels differ from the initially simulated values. The absorption of the objects is difficult to estimate due to the uncertainty in used material and possible panel absorbing properties due to their hollow interior. Beside the change in absorption coefficients, the scattering coefficients for the concrete, plaster board, and aluminum panels were decreased in the 125-Hz octave band, and those of the aluminum (walls), concrete, and plaster board were increased. As the concrete, plaster board, and aluminum panels are large flat surfaces and consequently the surface size is large in relation to the wavelength, it is justified to adopt a scattering of 5 % in the 125-Hz octave band. Furthermore, raising the ${\mathrm{char}}_{\mathrm{depth}}$ of the aluminum (walls) can be justified by the metal construction in front of the wall which makes the wall more diffusing in the higher octave bands than initially assumed, and increasing the ${\mathrm{char}}_{\mathrm{depth}}$ of the concrete and plaster board is justified by the objects in front these which makes it more diffusing than originally assumed. Additionally, probably for similar reasons, we note that the general guidelines in the CATT-Acoustic manual recommend that it is better to overestimate scattering coefficients than to underestimate them (Dalenbäck 2011, p. 111) (Table 3).

Table 3 Absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$ (mm) as the single value which was inserted into Eq. (1), and assigned surface area (m$^2$) used in the calibrated model of the amphitheater

Appendix 2: Details of Saint-Germain-des-Prés calibration

This section details steps 4–6 of the calibration procedure for the Saint-Germain-des-Prés. Table 4 depicts the absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$, and surface area assigned to these materials, in first iteration. Curve initial in Fig. 15 shows the average EDT and C80 of the first iteration.

Table 4 Absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$ (mm) as the single value which was inserted into Eq. (1), and surface area (m$^2$) used in the initial iteration of the Saint-Germain-des-Prés

Fig. 15

Evolution of mean EDT and C80 during the calibration procedure as compared to the mean measured ($\pm 1$ JND) values

The average T20 and EDT were brought within 1 JND of the measured value by adjusting the absorption coefficient of the painted plaster to [0.010, 0.019, 0.028, 0.032, 0.038, 0.037], since this material represents the largest surface area and therefore has a principal influence on the acoustic response. Curve initial in Fig. 15 shows the average EDT came within one JND after the absorption coefficient was lowered, concluding step 4.

Figure 8 shows that by increasing the scattering, the clarity parameters in the octave bands 500–4000 Hz became lower and vice versa. Curve step 4 in Fig. 15 shows that at this stage the C50 differed $\Delta$[$-1.35$, 0.25, $-0.26$, 0.98, 1.60, 0.52] from the measurements. Since the clarity in the higher octave bands needed to decrease, the ${\mathrm{char}}_{\mathrm{depth}}$ was increased to 300 mm for the columns, to 10 mm for the floor, to 55 mm for the walls, and to 55 mm for the ceiling. Additionally, the absorption coefficients of the painted plaster in octave band 2000 Hz was lowered to 0.035. Furthermore, since Fig. 8 did not give an answer how to raise the C50 in the lower octave bands, iteratively adjusting various parameters resulted in finally adding edge diffusion to the columns and raising the absorption of the painted plaster [125, 250, 500 Hz] to [0.013, 0.022, 0.032]. Curve step 5 in Fig. 15 shows that the combination of these measures resulted in a C50 $\Delta$[$-1.01$, 0.03, $-0.29$, 0.87, 1.43, 0.43], which better estimated the measurement across all octave bands, except in the 500 Hz where it remained approximately the same.

The main adjustments in the GA model’s surface properties were the adjustment of the plaster surfaces’ absorption coefficient as well as the raising of the ${\mathrm{char}}_{\mathrm{depth}}$ of the limestone and plaster surfaces. Various reasons can explain the difference between the initial and final modeled absorption coefficients of the plaster surfaces. In the initial iteration, these values were adopted from the material Concrete block, plastered; in the calibrated model, the absorption coefficient more resembles the material Walls, hard surface average (brick walls, plaster, hard floors) [0.02, 0.02, 0.03, 0.03, 0.04, 0.04] found in Vorländer (2008). Since these are both reasonable choices for the absorption coefficient, it can be stated that these fall within the range found in step 1 of the methodological calibration. There are additional reasons why absorption coefficients can differ from the databases: Materials may have experienced transformations due to aging (Garcia et al. 2014). Additionally, probably because the size of elements high in the Saint-Germain-des-Prés is difficult to gauge during a visual inspection, these were underestimated in the initial iteration. This has influenced the estimation of the ${\mathrm{char}}_{\mathrm{depth}}$ of the plaster wall, limestone, plaster arch, and plaster ceiling, which were underestimated in the initial iteration, explaining the increased ${\mathrm{char}}_{\mathrm{depth}}$. Furthermore, because the plaster column has a small size in relation to the wavelength, the addition of the edge diffusion is justified (Table 5).

Table 5 Absorption coefficients, ${\mathrm{char}}_{\mathrm{depth}}$ (mm) as the single value which was inserted into Eq. (1), and surface area (m$^2$) used in the final iteration of the Saint-Germain-des-Prés