PROCEEDINGS of the 22 nd International Congress on Acoustics Isotropy and Diffuseness in Room Acoustics: Paper ICA2016-277 Correction algorithm for sound scattering coefficient measurements Monika Rychtáriková (a)(b), Nicolaas Bernardus Roozen (b), Daniel Urbán (c), Christ Glorieux (d) (a) STU Bratislava, Faculty o Civil Engineering, Dep. of Building Structures, Radlinského 11, 810 05, Bratislava, Slovakia, monika.rychtarikova@stuba.sk (b) KU Leuven, Physics and Astronomy, Soft Matter and Biophysics, Laboratory of Acoustics, Celestijnenlaan 200D, 3001 Leuven, Belgium, bert.roozen@kuleuven.be (c) A&Z Acoustics s.r.o., Repašského 2, 84102 Bratislava, Slovakia, ing.daniel.urban@gmail.com (d) KU Leuven, Physics and Astronomy, Soft Matter and Biophysics, Laboratory of Acoustics, Celestijnenlaan 200D, 3001 Leuven, Belgium, christ.glorieux@kuleuven.be Abstract Scattering coefficient measurements according to ISO 17497-1 are very sensitive to temperature and humidity changes in the reverberant room. Even variations as small as 0.1 K can significantly influence effective reverberation times and lead to wrong results. This phenomenon puts quite stringent limitations on how scattering measurements can be performed. This article elaborates on these limitations and discusses precautions that need to be taken in practical situations. Furthermore, we verify to what extent a stretching algorithm can help to recalibrate impulse responses and improve the quality of measured data in case measurement sequences have been subject to moderate temperature variations. Keywords: sound scattering, measurement accuracy, atmospheric conditions
Correction algorithm for sound scattering coefficient measurements 1 Introduction Although procedures for measurements of surface scattering coefficient have been already developed, validated and standardized [1], quite often the measurement analysis is hampered by effects of changes of the air temperature and humidity in the reverberant room, in spite of the limited time span for performing measurements is kept as prescribed by the standard (i.e., 1 hour). Changes of temperature and humidity throughout a sequence of impulse response measurements typically result in temporal deviations, apparent loss of correlation between the impulse responses, and erroneous (increased) values of the scattering coefficient obtained according to ISO 17497-1. Temperature changes within one hour of measurement can occur because of different reasons. Insufficient insulation of the reverberant room from the outdoor environment, e.g. when the room is not situated in the basement or not enough thermally insulated, leads to temperature drifts as soon as the building facade is exposed to changes in exposure to sunlight. The air inside the room is partially exchanged with room from outside when the door is opened, e.g. when in between measurements the room needs to be entered for checking of fixing the rotating plate. This typically goes along with a change of temperature and humidity. In case of such a situation, the question is if the whole set of measurements needs to be redone from beginning. This article introduces a stretching algorithm that can be applied to correct a measurement data set affected by temperature and humidity changes so that accurate information can be recycled. The algorithm can also be used preventively on data sets measured under strictly kept atmospheric conditions as a quality check. 2 Surface scattering coefficient 2.1 Definition The scattering coefficient s (-) is defined as the ratio between the non-specularly reflected sound energy (1 - E spec ) to the totally reflected amount of sound energy E r. Scattering by a surface of interest in a room is inducing modifications of the impulse response of that room. While bouncing back and forth between the surfaces in a room, each time waves are encountering the irregular surface, their temporal behavior is slighty scrambled. Due to the cumulative nature of this effect, the scrambling of the impulse response is exponentially increasing with time. As a result, the degree of decorrelation between impulse responses I n (t), measured under different object orientation conditions, in the typical case of a noncentrosymmetric object and room geometry is, increasing accordlingly. This results in a decrease of the slope of the logarithmic decay of the average impulse response I average (t), and thus an apparent decrease of the reverberation time and an apparent increase of the absorption coefficient as determined from the average impulse of the room, α spec. Due to the irregularity induced phase shifts of different frequency components being proportional with frequency, the apparent absorption coefficient is frequency dependent. As a consequence of the similarity between the degree of scattering on one hand and the reduction of the apparent absorption of a 2
room as determined from the average over rotation angle impulse responses on the other hand, the surface scattering coefficient s (-) can be estimated as αspec αs s = 1 α s (1) where α s is the average random-incidence absorption coefficient. 2.2 Measurement and simulation The surface scattering coefficient can be measured in diffuse field conditions or simulated in frequency domain by the boundary element method (BEM), in time domain by finite difference methods (FDM), or by similar algorithms. Guidelines on how to measure the random-incidence scattering coefficient is given in the standard ISO 17497-1 [1]. The measurement requires a random-incidence absorption coefficient measurement as described in the ISO 354 [2], followed by two extra measurements [3]. The measurement procedure is shown schematically in Figure 1. According to the norm, impulse response measurements need to be performed for different orientations of the turning table, with and without the sample (diffusor), using phase-locked averaging of 60-80 samples, measured within time span one hour maximum [1]. Figure 1: Graphical description of the determination of different effective reverberation times that make part of the measurement procedure of the scattering coefficient. T 1 and T 2 are determined without, T 3 and T 4 with rotational averaging of the impulse response. T 2 and T 4 are determined with, T 1 and T 3 without sample. In order to determine the reverberation time T 4, (and the effective absorption coefficient based on the average impulse response, α 4), averaging is performed for different angles of orientation of the rotating sample table. Based on the average reverberation time T 2, the non-scattering part of the sample reflectivity and corresponding absorption α 2 is determined. Similarly, T3 and T1 are determined without sample on the baseplate. The scattering coefficient s is then calculated based on α 1,α 2,α 3 and α 4, each obtained, by means of Sabine s expression, from measured reverberation times T 1,T 2,T 3 and T 4 under the conditions described in the Figure 1. V is the room volume in m 3, S is the total area of interior surfaces in m 2, c 1,c 2,c 3, c 4 are the values of the speed of sound and m 1,m 2,m 3 and m 4 the values of the air attenuation coefficient (m -1 ) during the respective measurements. 3
nd 22 International Congress on Acoustics, ICA 2016 st Acoustics for the 21 Century 2.3 Influence of atmospheric conditions It is well known that atmospheric conditions have influence on sound wave propagation. Temperature and relative humidity belong to the most important factors since they directly influence the density and speed of sound of air, and its specific acoustic impedance. The impact of atmospheric conditions on sound propagation is also discussed in the international standard ISO 2533 [4]. Changes in the properties of the air have also impact on the sound amplitude, in a frequency dependent way [5,6]. Acoustic standards therefore recommend, that atmospheric conditions should be carefully noted during measurements. 3 Changes in atmospheric circumstances during ISO 17497 measurements and compensation by stretching algorithm 3.1 Standardized measurement of scattering coefficient This study is based on measurements on a real size sample, and corresponding BEM simulations. Standardized surface scattering measurements according as prescribed in ISO 17497-1 were performed. The experiments were done in diffuse field conditions in a reverberant room at KU Leuven, Belgium (Fig.2) with volume V = 200m3. The measurement results were compared with results of a simulation in AFMG Reflex software, which is based on the BEM. AFMG was typically used for calculation of a reflection, diffusion, and scattering of a sound wave incident onto a defined geometrical structure. Figure 2: Rotating plate without (left) and with sample (right). Figure 3 (right) shows a good fit between measured and simulated data. As the diffusor had rather small elements, scattering was only significant at higher frequencies. Figure 3 (left) shows the results of base plate measurements, as required by the ISO standard. 4
sca$ering*coefficient**s*(/)* random/incidence*sca$ering*coefficient* 1.00# 0.90# Base#Plate#4#measurement# 0.80# Limit#for#the#Base#Plate# 0.70# 0.60# 0.50# 0.40# 0.30# 0.20# 0.10# 0.00# 100# 125# 160# 200# 250# 315# 400# 500# 630# 800# 1000# 1250# 1600# 2000# 2500# 3150# 4000# 5000# 1/3*octave*bands***f*(Hz)* sca$ering*coefficient**s*(/)* random/incidence*sca$ering*coefficient* 1.00# 0.90# Sound#Diffusor#7#measurement# 0.80# Sound#Diffusor#7#BEM#simula@on# 0.70# 0.60# 0.50# 0.40# 0.30# 0.20# 0.10# 0.00# 100# 125# 160# 200# 250# 315# 400# 500# 630# 800# 1000# 1250# 1600# 2000# 2500# 3150# 4000# 5000# 1/3*octave*bands***f*(Hz)* Figure 3: Results of base plate measurements of the scattering coefficient (left) and comparison between measured and simulated values (right). 3.2 Experiment with temperature changes during the measurement In the case of this experiment, impulse response measurements were performed on a same sample as in part 3.1. but with longer time intervals between them. In a first phase, based on impulse response measurements performed every 30 minutes (without rotating the plate), we have checked how much temperature in the room affects the data throughout a day night cycle. Figure 4 (left) shows the time shift of direct sound arrival at half day intervals, from Friday 25 September midnight till Monday noon 29 September. Figure 4 (right) depicts differences of the arriving sound reflections in the impulse response after 0.08s (about 30m of acoustic pathlength) of reverberation, i.e. after it the sound waves have reflected back and forth in the room several times. Figure 4: Illustration of differences in arrival time of the direct wave arrival signal (left) and reflected sound pressure signals after ~ 0.08s of reverberation (right) throughout a weekend, measured with half day intervals. The horizontal time axis is in units of sample periods (sampling frequency 44.1kHz). The impact of changes in air temperature and humidity on the speed of sound in the room is clearly visible. 5
The maximum time shift of about 2±1 sampling periods or (45±23)µs after 1342 sampling periods or 30ms in the direct signal, and 3±1 sampling periods or (68±23)µs after 5020 sampling periods or 114ms in the reflected signal fragment infers a procentual speed of sound change of respectively (0.15±0.07)% and (0.06±0.02)%. In case this change could be attributed fully to a change of temperature (the room not having been opened or entered by people during the period of measurement, humidity changes are unlikely), then it corresponds with a maximum variation in the 0.2-0.4K range. We have also performed a classical set of measurements, in the middle of which a person has entered the reverberant room for a while, introducing a change in atmospheric conditions. Interestingly, the value of the scattering coefficient, obtained in the classical way, was severely overestimating the true one. 3.3 Stretching algorithm The idea of ISO 17497-1 is to exploit the scattering induced decorrelation between impulse responses obtained with different orientations of the sample in order to determine the scattering coefficient. Since atmospherically induced changes of the speed of sound induce a decorrelation-like temporal compression or expansion, the method is very sensitive to such changes, overestimating the scattering coefficient. Unlike the very irregular influence of scattering, provided the temperature field in the room is uniform, the effect of speed of sound changes (c 1 c 2 ) on the impulse response for a given speed of sound c, I c (t), involves a simple, uniform, linear scaling transformation of the time axis, which can be expressed as: c = 2 Ic2() t Ic 1 t c1 (2) Provided the speed of sound ratio η=c 2 /c 1 is known, this transformation effect can be neutralized, and two impulse responses can be made to match, by applying a stretching (or compressing) transformation, with a temporal stretching factor c 1 /c 2 =1/η. In our approach, before averaging impulse responses obtained for different angles of orientation of the sample, we have chosen the first measured impulses response I c0 (t) as reference, and estimated η j =c j /c 0 by minimizing the sum of squared differences between I c0 (t) and I cj (η -1 j t). In this way, the difference between best matching impulse response I cj (η -1 j t) and I c0 (t) was only due to sample surface scattering, and not any more to differences in atmospheric conditions. After having done this stretching correction for each impulse response, the average impulse response was determined, and the ISO 17497-1 calculation was done. Figure 5 shows an example of an improvement of about 50% (compared to no stretching/compressing) of the match between two impulse responses when a temporal stretch factor of 0.9997 is applied. The remaining mismatch between the two impulse responses is due to a difference in scattering field, as a result of a difference in orientation of the sample between the two measurements. 6
4 Conclusions A stretching algorithm that is intended to neutralize the apparent decorrelation effect of atmospherically induced speed of sound changes on the value of the scattering coefficient as determined according to ISO 17497-1 was proposed and validated. Acknowledgments The authors acknowledge VEGA for grant no.1/0286/15 and H2020-MSCA-RISE-2015 for grant no. 690970 PAPABUILD, and express their gratitude to Geert Dierckx for kind contributions to the measurements. References [1] ISO 17497-1: Acoustics - Measurement of the sound scattering properties of surfaces, Part 1: Measurement of the random-incidence scattering coefficient in a reverberation room (2000). [2] ISO 354: Acoustics Measurement of sound absorption in a reverberation room (2003). [3] Vorländer, M.; Mommertz, E. Definition and measurement of random-incidence scattering coefficients. Applied Acoustics Vol 60 (2), 2000, pp 187 199. [4] ISO 2533:1975 Standard Atmosphere [5] Bass, H. E.; Sutherland, L. C.; Zuckerwar, A. J.; Blackstock, D. T.; Hester, D. M. Atmospheric absorption of sound: Further developments. Journal of the Acoustical Society of America Vol 97 (1), 1995, pp. 680 683. [6] Müller-Trapet, M.; Vorländer, M. Uncertainty analysis of standardized measurements of randomincidence absorption and scattering coefficients, Journal of the Acoustical Society of America Vol 63 (1), 2015, pp. 63 74. [7] Mommertz, E. Determination of scattering coefficients from the reflection directivity of architectural surfaces, Appl. Acoust. 60, 201-203 (2000). [8] Kosaka, Y. and Sakuma, T. Numerical study on the behavior of scattering coefficients of wall surfaces, Proc. 18th Int l Cong. Acoust. (2004). [9] Gomes, M. Vorländer M. and Gerges, S. Aspects of the sample geometry in the measurement of the random-incidence scattering coefficient, Proc. Forum Acusticum Sevilla 2002, RBA-06-002-IP (2002) 7