On the accuracy of the sound absorption measurement with an impedance gun

Applied Acoustics 158 (2020) 107039

Contents lists available at ScienceDirect

Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

Technical note

On the accuracy of the sound absorption measurement with an impedance gun Antonio Pedrero, María Ángeles Navacerrada ⇑, Daniel de la Prida, Luzis Iglesias, Alexander Díaz-Chyla Grupo de Investigación en Acústica Arquitectónica, Escuela Técnica Superior de Arquitectura, Universidad Politécnica de Madrid, Avda. Juan de Herrera, 4, 28040, Madrid, Spain

a r t i c l e

i n f o

Article history: Received 11 July 2019 Received in revised form 6 September 2019 Accepted 13 September 2019

Keywords: In situ absorption coefficient Impedance gun Accuracy Metrology

a b s t r a c t The measurement of the sound absorption coefficient is clearly described in the ISO 10534 series of standards as well as in the ISO 354:2003 standard. However, the methods described in these standards are intended for laboratory testing under certain controlled conditions. There are situations where measurements have to be carried out in situ, as the material to be characterized cannot be transferred to the laboratory. To overcome this issue, the impedance gun, a device comprising a small spherical loudspeaker and a PU probe, can be very useful. However, several questions regarding the accuracy of this method remain open. The purpose of this paper is to determine, quantitatively and statistically, the accuracy of this in situ measurement system. To this end, an experiment was carried out in which the sound absorption of a sample of rock wool was measured. The sound absorption coefficient measurement of the specimen was carried out in several environments, at different specimen – impedance gun distances and using different calculation models (i.e. mirror source model (M), plane wave model (P) and Q-term model (Q)). In this way, the effect of each of these factors on the accuracy of the measurement could be evaluated. In addition, the results of these in situ measurements were compared with those of an impedance tube intercomparison for the same material sample. The evaluation of accuracy was performed by adapting the method described in the ISO 5725 series of standards, regarding the precision of measurements in terms of repeatability and reproducibility, to this case study. The main findings were that significant differences were found between the different calculation models and, therefore, cannot be considered equivalent. In addition, some calculation models were more sensitive to the influence of other factors such as specimen - impedance gun distance and the measuring environment. Finally, it was found that in situ measurement methods provide comparable results to impedance tube measurements for frequency bands above 500 Hz. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Several factors can interact in the measurement of the sound absorption coefficient and may, therefore, affect the accuracy of the results. These factors are well described and taken into account in laboratory measurements of the sound absorption coefficient, either through the impedance tube method described in ISO 10534-2:1998 [1] or by the reverberation room method described in ISO 354:2004 [2]. Much research has been done on the accuracy of laboratory measurements, mainly because intercomparisons

⇑ Corresponding author. E-mail address: [email protected] (M.Á. Navacerrada). https://doi.org/10.1016/j.apacoust.2019.107039 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved.

must be performed regularly [3]. Thanks to this, the precision of the laboratory methods for obtaining the absorption coefficient is known. However, in situations where the material to be characterized cannot be taken to the laboratory, and the sound absorption coefficient has to be determined under in situ conditions with an impedance gun [4–6], the influence of several factors can have a significant effect on the accuracy. Even though the effect of these factors has not been addressed widely, some research has been conducted to assess the effect of the distance between the sample and the impendance gun [6], the size of the sample to be measured [7] and the measuring environment [8]. The main issue of these studies is, however, that none of them followed a rigorous methodology from the metrological point of view. For this reason,

2

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039

no conclusions could be drawn from them regarding the accuracy and the uncertainty of the measurement. In this work, the results of an experimental procedure aimed to obtain the accuracy of the in situ measurement of the sound absorption are presented. First, the effect of the different factors influencing the measurement, such as the calculation method, which is the mathematical approximation used for the calculation of the sound absorption coefficient from the PU probe measurements, the distance between the specimen and the impedance gun and the measuring environment are addressed. Then, a precision analysis is carried out for three different calculation methods following the series of ISO 5725:1994. Finally, the results of the in situ measurement for the three calculation models are compared to those obtained for the same specimen, under laboratory conditions, following the impedance tube procedure described in ISO 10534-2:1998 [1]. This allows metrologically robust conclusions to be drawn, in terms of trueness (difference between the measured values) and precision (repeatability, reproducibility and intermediate precision).

2. Material and methods In this section, the material sample and instrumentation used, as well as the method of analysis used to extract the results, are described. 2.1. Sample material For all the tests, a rock wool sample was used as specimen. In particular, a sample of rock wool type 231.652 from the Rockwool Company was used. This specimen had a thickness of 50 mm and a declared density of 70 kg/m3. Only one sample was used, whose dimensions were 1.2
0.6 m2. These dimensions were chosen to ensure that edge problems were negligible during the measurements [6,8]. 2.2. Measurement setup 2.2.1. Instrumentation An impedance gun of Microflown Technologies was used to carry out the in situ measurements. This impedance gun consists of a small spherical loudspeaker, a PU probe, as well as a handheld bracket that allows the user to handle the entire structure and, at the same time, keep a constant distance of 27 cm between the probe and the loudspeaker. The measuring frequency range is set between 200 Hz and 10 kHz. The lower limit is determined, among other factors, by the loudspeaker behaviour, whose small dimensions do not allow the range to be extended to lower frequencies. On the other hand, the upper limit is established by the difficulty in calculating the phase of the impedance above this frequency, which could reduce the reliability of the results. The handheld device is connected, through a Microflown MFSC2 signal conditioner, to a laptop computer, which is in charge of collecting all the measured signals and performing all the required calculations for the absorption coefficient from the measurements. This calculation is carried out by means of the ‘‘In situ absorption” package of the Velo software of the same company. Regarding the laboratory measurements, an impedance tube inter-laboratory exercise was carried out, involving the participation of nine laboratories with different instrumentation. This intercomparison exercise was organized by the Laboratory Society ACUSTILAB under EUROLAB-Spain. The details of this exercise can be found in [9].

2.2.2. Procedure To perform an in situ measurement of the sound absorption coefficient, the PU probe should be aimed at the material as orthogonal as possible, while trying to minimize any change in the distance between the impedance gun and the specimen. Once the gun is correctly placed, the measurement can be started. At this point, the loudspeaker emits a broadband noise and the PU probe up both the pressure and velocity signals. With this information, the Velo software is able to carry out the necessary calculations to obtain the absorption coefficients. This calculation can be performed through different mathematical models. In particular, this software allows calculations to be carried out using the P model (Plane wave model), the M model (Mirror source model) and the Q model (Q-term model). The particularities and differences between each of these methods are beyond the scope of this technical note. Further information on this regard can be found in [10]. Measurements for different distances, calculation models and environments were addressed in the experiment. For each particular configuration, the measurement was repeated five times. For the laboratory measurements, the sound absorption coefficient was calculated both in 1/3 octave bands and as a single weighted evaluation index obtained according to ISO 11654 [11]. 2.2.3. Influence of factors According to the previous section, factors such as the measuring environment, the distance between the PU probe and the specimen and the calculation model can affect the value of the sound absorption coefficient. Since, as explained in the introduction, one of the purposes of the experiment was to determine their influence on the results, measurements were carried out with different variations or levels of these factors. The different levels of each of the evaluated factors are described below. Environment. In order to be able to address the influence of the environment on the in situ measurement of the sound absorption coefficient, the same measurement was carried out in different environments regarding the background noise and the reverberation time. In particular, five different enclosures were used, whose reverberation time and background noise are presented in Table 1.  E-1: Anechoic chamber.  E-2: Empty room with absorbent materials on the walls (50 m3)  E-3: Ordinary room with office furniture and computers running (175 m3)  E-4: Empty room (50 m3)  E-5: Reverberant room PU probe - specimen distance. The distance between the PU probe and the specimen can also affect the calculation of the sound absorption coefficient. It is therefore interesting to assess to what extent differences in the distance change the result. The measurements were carried out at seven different distances between the probe and the specimen, as shown in Table 2. Calculation model. Three different calculation models were used to compute the sound absorption coefficient for each of the environment and distance combinations. The Plane Wave Model (Model P), the Mirror Source model (Model M) and the Q-term Model (Model Q). 2.3. Analysis of the results Two different methods were used for the analysis of the results. First, the significance of the different factors was addressed by the analysis of variance (ANOVA). Then, the accuracy of each combination of distance, measuring environment and calculation model

3

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039 Table 1 Reverberation time (T), measured in seconds, and background noise level (LB), measured in dB, of the different environments. Frequency (Hz)

Environments E-1

250 500 1000 2000 4000

E-2

E-3

E-4

E-5

T

LB

T

LB

T

LB

T

LB

T

LB

0.40 0.28 0.12 0.08 0.06

9.8 4.8 5.7 6.0 7.2

0.54 0.67 0.62 0.60 0.53

14.7 14.3 7.9 6.6 6.7

0.61 0.59 0.60 0.65 0.60

38.8 44.5 38.0 29.4 27.1

1.12 1.34 1.41 1.31 1.00

19.5 19.4 14.7 12.9 9.9

4.77 5.06 4.15 2.35 2.20

13.2 10.9 10.2 11.1 10.5

Table 2 Distance between the PU probe and the specimen, in centimeters. Distance (cm)

D1

D2

D3

D4

D5

D6

D7

0.2

0.5

1.0

1.5

2.0

2.5

3.0

was obtained by applying the ISO 5725 series of standards procedure. In this section, both these methods are explained briefly.

2.3.1. ANOVA (analysis of variance) Different methods of analysis can be used to evaluate whether the means of several samples of data can be considered significantly different from each other, among which Student’s t-test and ANOVA are the most used. While Student’s t-test have some restrictions regarding the number of means to be compared, as it only allows to compare means two by two at the same time, ANOVA imposes no restrictions regarding the number of means [12]. Given that all the factors to be evaluated in this research article have more than two levels, ANOVA is preferred. ANOVA is based on the assumptions of equal homogeneity of variance, normality and independence of the observations. Having these assumptions in mind, the base of this method is on checking whether the null hypothesis that the means of the different data samples are the same can be rejected. The ANOVA analysis provide both figures and tabulated results. On one hand, the figures show together the main statistics of each of the levels of a factor, so that the degree of difference between levels can be easily observed. On the other hand, the summary table ANOVA presents several parameters among which the parameter ”Prob>F” is particularly noteworthy, which determines if differences in the levels of a certain factor have significant importance in the result.

2.3.2. ISO 5725:1994: Accuracy The precision analysis was carried out by means of the criteria described in ISO 5725:1994. In the first place, given that this standard is aimed at intercomparisons, some correspondence had to be made between the definitions of the standard and those existing in the experiment. In this regard, ‘‘Laboratory”, which in the standard refers to the different treatments used for the same experiment (i.e. the different laboratories), was each possible combination of distance between specimen and probe and environment in the experiment. Also, the definition ‘‘Level” had correspondence with each of the 1/3 octave frequency bands on the experiment. Given that significant differences were obtained among the different calculation models, a different precision analysis was carried out for each of them. Quantitatively, precision in expressed in terms of the standard deviation of repeatability (sr), standard deviation of reproducibility (sR). However, in practice, the limits of repeatability (r) and reproducibility (R) are used, generally assuming a 95% confidence interval.

For this experiment, for each treatment and level, the mean value (a) and the estimated variance (s2 w ) of the absorption coefficient was calculated from the five measured repetitions. Then, for each level, the overall mean of the absorption (a) was calculated as the average of a for all the treatments at a same level. Also, the estimated variance of repeatability (s2 w for all the treatments at a same level. Regarding the value of the estimated variance of reproducibility (s2 R ) it can be calculated following the Eq. (1):

s2R ¼ s2L þ s2r

ð1Þ

where S2 L is the intercell variance calculated as the interlaboratory variance in ISO 5725-2 [13]. The limits of repeatability (r) and reproducibility (R) can be computed following Eq. (2):

x ¼ 2:8sx

ð2Þ

where x can take the values r or R depending on whether the repeatability or the reproducibility is to be calculated. The intermediate standard deviation (sI) allows addressing the effect of each of the factors (i.e. the environment and the distance specimen-probe) in each treatment on the precision. To obtain this intermediate value, Eq. (3) have to be applied to t different groups of data split from the pooled data, each of these groups containing the results of n different variations. In particular, n are the levels of the factor whose intermediate standard deviation is to be studied and t are the levels of the other factor in the combination.

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u t X n X u 1   sI ¼ t y  yj tðn  1Þ j¼1 k¼1 jk

ð3Þ

where yj is the mean value of the results of group j, for each level and yjk is a result of the measurement of group j obtained for the factor k. For the comparison, in terms of trueness, between the mean absorption coefficients obtained by the impedance tube interlaboratory test and those of the measurements carried out in situ, ISO 5725-6:1994 [14] was used. In this standard it is stated that the means of two methods A and B are significantly different if Eq. (4) is met.

  y  y   A B  > 2:0   s  with s ¼

ð4Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 s2 RA ð11=nA Þs2 RA B Þs RB where yA and yB are the þ s RB ð11=n pA pB

overall mean absorption coefficient obtained by methods A and B

4

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039

(i.e. A is the absorption coefficients for any of the calculation models and B is the absorption coefficient obtained by the impedance tube method), s2 RA and s2 RB are the variance of reproducibility of methods A and B, pA is the number of combinations between PU probe - specimen distances and environments and pB is the number of laboratories that participated in the impedance tube intercomparison. Finally, nA and nB are the number of repetitions performed for each method. Also, to address the significance of the differences in terms of precision between the impedance method and the three calculation models, the procedure describe in ISO 5725-6:1994 [14] was used. In this standard it is stated that a method or the other would be more accurate depending on the value of the parameters Fr and FR, for repeatability and reproducibility, respectively, calculated as described in Eqs. (5) and (6).

Fr ¼

s2 rB s2 rA

ð5Þ

FR ¼

s2 RB  ð1  1=nB Þs2 rB s2 RA  ð1  1=nA Þs2 rA

ð6Þ

In particular, if Fx, with x being r or R, fulfills Eq. (7.a), no significant differences between method A and method B can be found regarding repeatability (r) or reproducibility (R). If Fx fulfills Eq. (7.b) then method A can be considered significantly more accurate than B. Finally, if Fx fulfills Eq. (7.c) method B can be considered significantly more accurate than A.

F a=2 ðmxA ; mxB Þ 6 F x 6 F ð1a=2Þ ðmxA ; mxB Þ

ð7:aÞ

F x < F a=2 ðmxA ; mxB Þ

ð7:bÞ

F x > F ð1a=2Þ ðmxA ; v xB Þ

ð7:cÞ

3. Results 3.1. Significance of factors First, an ANOVA (Analysis of Variance) analysis was carried out from the pooled data to address the global effect of the different factors on the result of the sound absorption coefficient. To this end, an ANOVA analysis was computed for each frequency band and all of the factors (i.e. distance, environment and calculation model). This analysis reported p-values 0.001(values of 1010

Fig. 1. Box and whisker plot of the influence of the different factors in the sound absorption coefficient at 1 kHz.

Fig. 2. Mean values of the 1/3 octave Absorption Coefficient for the three calculation models and the impedance tube.

Table 3 Main accuracy values for the three calculation models (M, Q and P columns) and impedance tube intercomparison (I column). Frequency (Hz)

a

250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000

M 0.01 0.17 0.40 0.59 0.71 0.81 0.86 0.89 0.91 0.92 0.94 0.96 0.97 0.98

sr Q 0.08 0.02 0.26 0.50 0.65 0.77 0.84 0.88 0.91 0.93 0.95 0.96 0.98 0.98

P 0.20 0.33 0.50 0.67 0.77 0.85 0.89 0.92 0.93 0.94 0.95 0.97 0.98 0.98

I 0.32 0.41 0.57 0.71 0.79 0.84 0.89 0.91 0.90 0.90 0.90 0.94 0.96 0.97

M 0.07 0.07 0.06 0.05 0.03 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01

sR Q 0.11 0.13 0.08 0.07 0.06 0.05 0.03 0.03 0.03 0.02 0.01 0.01 0.01 0.01

P 0.07 0.07 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.00 0.00

I 0.02 0.03 0.03 0.02 0.01 0.02 0.03 0.03 0.02 0.01 0.01 0.01 0.01 0.01

M 0.11 0.11 0.08 0.05 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.01 0.01 0.01

Q 0.14 0.18 0.13 0.09 0.07 0.05 0.05 0.05 0.04 0.03 0.02 0.02 0.01 0.01

P 0.16 0.14 0.09 0.06 0.04 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0.01

I 0.03 0.05 0.06 0.06 0.04 0.05 0.04 0.03 0.03 0.03 0.03 0.01 0.01 0.01

5

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039

Fig. 3. Standard deviation of repeatability for the three Calculation Models and the impedance tube.

between the specimen and the probe, in different environments and calculated through different methods. The fact that different calculation models (i.e. P-model, Mmodel and Q-model) generate significantly different results is especially relevant. While the level of the factor environment can be determined by the features of the environment where the measurements are to be made, the calculation model method can always be chosen. Therefore, it is interesting to select the method that, on one hand, is less sensitive to differences in the factor of environment while, on the other, being the most accurate. The first of these facts can be evaluated in greater detail using the box and whiskers plots shown in Fig. 1. In this figure, as a matter of example and for the frequency band of 1 kHz, the variability of the levels of the other factors is presented, for the three different levels of the factor calculation model. As it can be seen in Fig. 1, the effect and the influence of the distance on the absorption coefficient may vary from one calculation model to another. In this regard, the absorption coefficient varied significantly in the three models across the different levels of the factor Environment. Regarding the factor of Distance, the differences among Calculation Models were not as big as they were for the factor of Distance. Nonetheless, these differences were significant for all levels in the Models Q and P while they were mainly not significant for the case of Model M. 3.2. Accuracy of results Following the procedure described in the ISO 5725:1994: Accu-

Fig. 4. Standard deviation of reproducibility for the three Calculation Models and the impedance tube.

and below) for the environmental and calculation model factors. Regarding the distance factor, p-values 0.001 were obtained for the 250 Hz frequency band, as well as for the bands between 1600 Hz and 5000 Hz, p-values <0.01(values between 103 and 1010 ) for the bands between 400 Hz and 1250 Hz and a p-value < 0.05 (values between 0.05 and 103 ) for the 315 Hz band. From all of this it can be seen that all the factors were significant in the obtaining of the sound absorption coefficient, for all frequency bands in the studied range. Therefore, it can be stated that the in situ measurement of the sound absorption coefficient may give different results when carried out at different distances

racy section, Table 3 presents the values of a; sr and sR for the three calculation models (M, Q and P columns), as well as their counterparts a; sr and sR for the impedance tube (I column). To ease the comparison, these data are also presented graphically in the Figs. 2–4 for the absorption coefficient, the standard deviation of repeatability and the standard deviation of reproducibility respectively. The data in the Table 4 give important information about the limits of precision of the experiment. r represents the maximum expected difference between the results of two different measurements performed under repeatability conditions. These repeatability conditions include, for this study, measurements carried out at the same distance, using the same Calculation Model, in the same environment, by the same operator and with the same instrumentation. R, on the other hand, represents the maximum difference between two test results under reproducibility conditions. These reproducibility conditions include measurements made at different distances, as well as different environments. Graphically, Figs. 3 and 4, referring to the standard deviations of repeatability and reproducibility respectively, give a good impression of the values

Table 4 Values of the limits of repeatability and reproducibility for the three calculation models (M, Q and P columns) and the impedance tube (I column). Frequency (Hz)

r

250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000

M 0.19 0.20 0.16 0.14 0.07 0.06 0.06 0.06 0.05 0.04 0.03 0.02 0.02 0.02

R Q 0.30 0.35 0.22 0.20 0.17 0.13 0.10 0.08 0.07 0.06 0.04 0.02 0.02 0.01

P 0.20 0.20 0.10 0.09 0.06 0.06 0.06 0.05 0.05 0.03 0.02 0.02 0.01 0.01

I 0.05 0.06 0.07 0.05 0.02 0.04 0.05 0.05 0.04 0.03 0.03 0.01 0.01 0.02

M 0.32 0.31 0.21 0.15 0.08 0.07 0.09 0.10 0.09 0.07 0.05 0.04 0.03 0.03

Q 0.38 0.50 0.35 0.25 0.20 0.15 0.13 0.13 0.11 0.10 0.07 0.05 0.03 0.02

P 0.45 0.38 0.24 0.17 0.12 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.02

I 0.06 0.10 0.13 0.12 0.09 0.10 0.08 0.07 0.07 0.05 0.05 0.02 0.02 0.03

6

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039

Table 5 Resulting values of applying the criteria of standard ISO 5725-6:1994 [14] to mean values of absorption coefficient calculated by two methods: impedance tube and each of the calculation models (M, P, Q) of the PU probe. Frequency (Hz)   yA yB   s 

250

315

400

500

630

800

1000

1250

1600

2000

2500

3150

4000

5000

M

2.6

2.0

1.7

1.5

1.5

0.6

0.5

0.4

0.3

0.6

1.1

0.9

0.6

0.4

Q P

2.9 0.7

2.4 0.5

2.2 0.7

2.0 0.5

1.7 0.3

1.0 0.1

0.8 0.1

0.5 0.3

0.2 0.9

0.6 1.3

1.3 1.7

1.2 1.7

1.0 1.3

0.6 0.9

Table 6 Best method regarding the with-in laboratory precision (BWLP), for each frequency band, following ISO 5725-6:1994 [14]. ‘‘T” stands for ‘‘Impedance tube”, ‘‘P” stands for ‘‘PU Probe” and ‘‘S” stands for ‘‘same”, when no significant differences can be found. Frequency (Hz) BWLP

M Q P

250

315

400

500

630

800

1000

1250

1600

2000

2500

3150

4000

5000

T T T

T T T

T T T

T T T

T T T

S T S

S T S

S S P

S T S

S T S

P S P

S S S

S S P

P P P

Table 7 Best method regarding the overall precision (BOP), for each frequency band, following ISO 5725-6:1994 [14]. ‘‘T” stands for ‘‘Impedance tube”, ‘‘P” stands for ‘‘PU Probe” and ‘‘S” stands for ‘‘same”, when no significant differences can be found. Frequency (Hz) BOP

M Q P

250

315

400

500

630

800

1000

1250

1600

2000

2500

3150

4000

5000

T T T

T T T

S T S

S S S

S T S

S S S

S S S

S S S

S S S

S S S

S S S

S S S

S S S

S S S

presented in Table 4, given that the values of r and R are no more than scaled versions of sr and sR , following Eq. (2). Although the values presented are intrinsic to this case study and cannot be directly extrapolated to other cases, they are of great relevance. Their importance lies in the fact that from them it is possible to know, a priori, which will be the maximum dispersion expected in the results, depending on the conditions of performance. Regarding the mean absorption coefficient, Fig. 2 shows two relevant facts. Firstly, that the three calculation models are not equivalent, yielding to different results. These differences are greater in the lower frequency bands. Secondly, that the results for the three calculation models differ from those of impedance tube for frequency bands below 500 Hz. In these frequency bands, the P model, which uses the same Plane Wave mathematical approach as the impedance tube, is the closest to the actual tube measurements. At frequencies higher than 800 Hz the results obtained for the three calculation models are much more similar to those obtained for the impedance tube. In order to quantitatively evaluate the equivalence between the different calculation models and the impedance tube measurements, the results of applying Eq. (4) are presented in Table 5. As can be seen, the results obtained by the P Model are statistically equivalent to those obtained by the impedance tube method, for all frequency bands. This fact is also true for Model M from the 315 Hz band and for Model Q from 500 Hz. With regard to sr , Fig. 3 shows its behavior for the three calculation models and the impedance tube. Table 6 summarizes the best method, regarding the within-laboratory precision (BWLP), following the Eqs. (5), (7.a), (7.b) and (7.c). As it can be seen, impedance tube shows the best behavior in the low-frequency range. It can also be observed that the Q Model is the one that behaved the worst in a general way. Also, regarding the sR , Fig. 4 shows the differences between the three Models and the impedance tube. Table 7 summarizes the best method, regarding the overall precision (BOP in table), following the Eqs. (6), (7.a), (7.b) and (7.c). Again, as it happened for the standard deviation of repeatability, the Q Model is the one with the worst general behavior. However,

Fig. 5. Standard deviation of intermediate precision for M, P and Q models.

the precision of all methods is mostly equivalent for medium and high frequencies. In the low-frequency range below 400 Hz, the impedance tube method again demonstrated better accuracy. Finally, in order to evaluate the effect of distance and environment factors on the different calculation methods, the intermediate precision was calculated for the distance probe-specimen (sI ðDÞ) and environment (sI ðEÞ) factors, following Eq. (3). Fig. 5 shows the results of the intermediate precision, for each factor and frequency band. Three different sub-figures are presented, one for each Calculation Method. The Q model was the worst in terms of the intermediate precision, as both factors had influence, in the lower frequency range.

A. Pedrero et al. / Applied Acoustics 158 (2020) 107039

The effect of distance was negligible for the M model, while affected both the Q and P models. Also, the environment was less influential for the P model.

4. Conclusions The accuracy of the PU probe was analyzed by means of an accuracy experiment according to the three types of precision conditions (repeatability, reproducibility and intermediate conditions) described in the series of standards ISO 5725. The calculation models (M, Q and P models) used to get the absorption coefficient under in situ conditions, the measuring environment and the distance between the PU probe and the sample were the three factors investigated using a rock wool sample as test specimen. First, the experiment revealed that the three calculation models were not equivalent, and that differences between models were more evident at low frequencies. Also, the factors of environment and distance between the PU probe and the specimen were proved to be significant in the measurement on the sound absorption coefficient. The M model was practically insensitive to changes in the environment and the measurement can be done at any distance considered, while for P model the measurement at shorter distances are recommended. The values calculated by Q model are influenced by both factors, and many absorption coefficient values are negative as such this model is not recommended. In any case, measurements with the PU probe located more than 2 cm away from the sample are not recommended. The study was completed by comparing the results obtained by the PU probe with those obtained for the impedance tube intercomparison. At low frequencies, discrepancies in the values of the absorption coefficient between the two techniques, for all PU probe calculation models, were evident. At intermediate and high frequencies, the methods were less distinguishable from one another. With this in mind, for each calculation model it was established, in terms of repeatability and reproducibility, from which frequency threshold the values are statistically equivalent to those obtained with an impedance tube. Also, the standard deviation of repeatability (sr ) and reproducibility (sR ) were presented for the different calculation models under in situ conditions. These values, allowed the calculation of the parameters known as limits of repeatability (r) and reproducibility (R), presented in Table 4 following Eq. (2). These limits, which are a quantitative determination of the maximum expected dispersion of the measurements, can be of great help so that future research can have some a priori knowledge about how repeatable and reproducible their in situ measurement results can be expected, for each frequency range, depending on the calculation model used.

7

However, it should not be forgotten that these results are not directly extrapolatable to other cases, mainly because they have been obtained by means of a case study in which a single material has been used. Also, because the results presented for the PU probe come from an adaptation of the method to this case study and not from the results of a true intercomparison. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement Funding for this study was provided by the Autonomous Community of Madrid under the programme S2018/NMT-4372 TOP Heritage-CM References [1] ISO 10534-2:1998. Acoustics — Determination of sound absorption coefficient and impedance in impedance tubes — Part 2: Transfer-function method. Geneva: International Organization for Standardization; 1998. [2] ISO 354:2003 – Acoustics – Measurement of sound absorption in a reverberation room. Geneva: International Organization for Standardization. . [3] Wittstock V. Determination of Measurement Uncertainties in Building Acoustics by Interlaboratory Tests. Part 2: Sound Absorption Measured in Reverberation Rooms. Acta Acustica united with Acustica 2018;104 (6):999–1008. [4] Liu Y, Jacobsen F. Measurement of absorption with ap-u sound intensity probe in an impedance tube. J Acoust Soc Am 2005;118(4):2117–20. [5] Tijs E, Druyvesteyn E. An intensity method for measuring absorption properties in situ. Acta Acustica united with Acustica 2012;98(2):342–53. [6] Tijs E. Study and development of an in situ acoustic absorption measurement method. Enschede, The Netherlands: University of Twente; 2013. PhD. [7] Lanoye R, de Bree HE, de Bree HE, Lauriks W, Vermeir G. A practical device to determine the reflection coefficient of acoustic materials in-situ based on a Microflown and microphone sensor. Leuven: ISMA; 2004. [8] Lanoye R, Vermeir G, Lauriks W, Kruse R, Mellert V. Measuring the free field acoustic impedance and absorption coefficient of sound absorbing materials with a combined particle velocity-pressure sensor. J Acoust Soc Am 2006;119 (5):2826–31. [9] EUROLAB-España. AQUS-TUBO IMPEDANCIA 1 – Final Report; 2014. (accessed 04 september 2019). Available from:http://www.arquilav.aq.upm.es/sites/ default/archivos/AQUS_TUBO_IMPEDANCIA_1.pdf. . [10] Brandao E, Tijs E, Lenzi A, de Bree HE. A comparison of three methods to calculate the surface impedance and absorption coefficient from measurements under free field or in situ conditions. Acta Acustica united with Acustica 2011;97(6). [11] ISO 11654:1997 - Acoustics – Sound absorbers for use in buildings – Rating of sound absorption. Geneva: International Organization for Standardization. . [12] Howell DC. Statistical methods for psychology. Cengage Learning; 2009. [13] ISO 5725-2:1994 – Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. Geneva: International Organization for Standardization. . [14] ISO 5725-6:1994 – Accuracy (trueness and precision) of measurement methods and results – Part 6: Use in practice of accuracy values. Geneva: International Organization for Standardization. .