**1. Introduction**

Standard in situ methods to obtain airborne sound insulation in building elements are based on sound pressure measurements (ISO 16283-1) [1] and on sound intensity measurements (ISO 15186-2) [2].

The method described in ISO 16283-1 [1] states that the acoustic field generated at the emitting room must be diffuse, stationary, and spectrally flat, at least for the frequency range under consideration (100–3150 Hz). Acoustic field and reverberation time measurements are averaged in space and time to ensure low statistical spread.

The apparent sound reduction index (*R'*) is one of the parameters used to express the acoustic behavior, and it stems from Eq. (1):

$$R'\text{ [dB] = } \boxed{L\_1 \text{--} L\_2} \text{ 10 } \log \frac{S}{A} \tag{1}$$

$$A\left[m^2\right] \ = \ \frac{0.16V}{T} \tag{2}$$

where


The main difference in the measurement procedure ISO-15186-2 [2] regarding to ISO 16283-1 [1] is that reverberation time measurement is not required, and in the receiving room, the measured parameter is the acoustic intensity normal to the surface of the partition element being assessed, whether by scanning or by grid techniques, depending on the resolution required. In this case, the acoustic behavior is defined by the apparent sound reduction index by intensimetry *R'I*, which is different from the index obtained by acoustic pressure and is calculated according to Eq. (3):

\*[c1] : 
$$R\_l \text{ [dB] } = \left[ \overline{L\_{pl}} - 6 + 10 \log \frac{S}{S\_0} \right] - \left[ \overline{L\_{ln}} + 10 \log \frac{S\_M}{S\_0} \right] \tag{3}$$

where


The procedure described in ISO-15186-2 [2] provides a partial assessment of the sound insulation of each surface present in the partition element. Nevertheless, the final evaluation of the acoustic behavior depends strongly on the resolution defined throughout the measurement procedure and is closely related to a high density of

**181**

range.

*In Situ Detection of Leakages in Partition Elements through SONAH and Beamforming Techniques*

measuring points. The validity range of this technique is determined through the calculation and the monitoring of the so-called field indicators (*F2*, *F3*, *F4*) according to ISO 9614-1 [3], which allow to ascertain whether the acoustic intensity

After the examination of the measurement procedures, it is noticed that the main advantages of the pressure method [1] are its standardization and the reduced time required to take the measurement; its main disadvantages are the incapability of detecting leaks and areas with a poor insulation level, and, additionally, it does not reject the possible indirect transmissions. On the contrary, the technique based on intensity measurements [2], identifies leakages or weakened areas; its resolution, however, depends on the density of points of the measuring grid and hence, on the measuring time for each test. In order to achieve intensity data with high resolution in terms of space and frequency, a highly dense (every 5–10 cm) point grid must be

A new measurement procedure is proposed to unify the advantages of both methods mentioned above: quickness and detection of leaks. This new procedure is based on beamforming and accompanied by SONAH; its main aim is the identifica-

algorithm, which consist of the sum of the delayed signals from the array microphones with different delays in order to put all the signals in phase. With this, the signal of interest is reinforced against the noise and other signals propagating in

In the statistically optimal near-field acoustic holography (SONAH) method [6], the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all the propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy. The main advantage of SONAH is the fact that it does not use the discrete spatial Fourier transform used in the classical NAH procedure. Therefore, undesir-

SONAH [6] and beamforming [8] techniques use a measurement system based on specially designed geometrical configurations of microphone arrays [9], which help to understand the acoustic field at a given distance from the acoustic source, using various signal processing algorithms. These techniques are mainly used to

Besides the different array geometries [11] and algorithms [5] used, the main differences in practical applications between SONAH and beamforming techniques

• The distance between the array and the acoustic field—SONAH technique requires near-field measurements close to the surface [6], whereas beamform-

Using only one of these two methods—beamforming or SONAH—would not suffice to cover the whole frequency range of interest (100–3150 Hz), since beamforming shows poor resolution in low-frequency range and SONAH requires a large number of microphones to attain good resolutions at high frequency [13]. Therefore, a combination of both methods can be applied throughout the desired

ing technique does the measurements in the far field [12].

• In the use of references, which are mandatory in SONAH.

Beamforming is performed, in its simplest approach, through the delay-and-sum

tion of the areas with weak insulation in one shot measurement [4].

measurement conditions fulfill or not the minimal requirements.

*DOI: http://dx.doi.org/10.5772/intechopen.82352*

designed, which leads to long measuring times.

able spatial leakage effects are avoided [7].

• In the covered surface of study.

locate acoustic sources [10].

reside in:

other directions [5].

### *In Situ Detection of Leakages in Partition Elements through SONAH and Beamforming Techniques DOI: http://dx.doi.org/10.5772/intechopen.82352*

measuring points. The validity range of this technique is determined through the calculation and the monitoring of the so-called field indicators (*F2*, *F3*, *F4*) according to ISO 9614-1 [3], which allow to ascertain whether the acoustic intensity measurement conditions fulfill or not the minimal requirements.

After the examination of the measurement procedures, it is noticed that the main advantages of the pressure method [1] are its standardization and the reduced time required to take the measurement; its main disadvantages are the incapability of detecting leaks and areas with a poor insulation level, and, additionally, it does not reject the possible indirect transmissions. On the contrary, the technique based on intensity measurements [2], identifies leakages or weakened areas; its resolution, however, depends on the density of points of the measuring grid and hence, on the measuring time for each test. In order to achieve intensity data with high resolution in terms of space and frequency, a highly dense (every 5–10 cm) point grid must be designed, which leads to long measuring times.

A new measurement procedure is proposed to unify the advantages of both methods mentioned above: quickness and detection of leaks. This new procedure is based on beamforming and accompanied by SONAH; its main aim is the identification of the areas with weak insulation in one shot measurement [4].

Beamforming is performed, in its simplest approach, through the delay-and-sum algorithm, which consist of the sum of the delayed signals from the array microphones with different delays in order to put all the signals in phase. With this, the signal of interest is reinforced against the noise and other signals propagating in other directions [5].

In the statistically optimal near-field acoustic holography (SONAH) method [6], the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all the propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy. The main advantage of SONAH is the fact that it does not use the discrete spatial Fourier transform used in the classical NAH procedure. Therefore, undesirable spatial leakage effects are avoided [7].

SONAH [6] and beamforming [8] techniques use a measurement system based on specially designed geometrical configurations of microphone arrays [9], which help to understand the acoustic field at a given distance from the acoustic source, using various signal processing algorithms. These techniques are mainly used to locate acoustic sources [10].

Besides the different array geometries [11] and algorithms [5] used, the main differences in practical applications between SONAH and beamforming techniques reside in:


Using only one of these two methods—beamforming or SONAH—would not suffice to cover the whole frequency range of interest (100–3150 Hz), since beamforming shows poor resolution in low-frequency range and SONAH requires a large number of microphones to attain good resolutions at high frequency [13]. Therefore, a combination of both methods can be applied throughout the desired range.

*Acoustics of Materials*

where • ¯

• ¯

• *S* [m2

• *A* [m<sup>2</sup>

• *V* [m3

to Eq. (3):

where • ¯

• S [m<sup>2</sup>

• SM [m<sup>2</sup>

• S0 (1 m<sup>2</sup>

• ¯

*RI*

the receiving room.

The apparent sound reduction index (*R'*) is one of the parameters used to

*L1 − ¯*

*A*[*m***<sup>2</sup>**] = \_\_\_\_\_ 0.16*<sup>V</sup>*

*L1* [dB] is the average sound pressure level at the emitting room.

*L2* [dB] is the average sound pressure level at the receiving room.

*L2* + 10 log*\_\_S*

] is the total surface of the common partition element between both rooms.

] is the equivalent acoustic absorption area at the receiving room. It is

*<sup>S</sup>0*] <sup>−</sup> [

*LIn* [dB] is the average sound intensity level, normal to the measuring surface/s in

The procedure described in ISO-15186-2 [2] provides a partial assessment of the sound insulation of each surface present in the partition element. Nevertheless, the final evaluation of the acoustic behavior depends strongly on the resolution defined throughout the measurement procedure and is closely related to a high density of

¯

*LIn* + 10 log\_\_\_

*SM*

*<sup>S</sup><sup>0</sup>* ] (3)

The main difference in the measurement procedure ISO-15186-2 [2] regarding to ISO 16283-1 [1] is that reverberation time measurement is not required, and in the receiving room, the measured parameter is the acoustic intensity normal to the surface of the partition element being assessed, whether by scanning or by grid techniques, depending on the resolution required. In this case, the acoustic behavior is defined by the apparent sound reduction index by intensimetry *R'I*, which is different from the index obtained by acoustic pressure and is calculated according

*<sup>A</sup>* (1)

*<sup>T</sup>* (2)

express the acoustic behavior, and it stems from Eq. (1):

*<sup>R</sup>*′ [*dB*] <sup>=</sup> *¯*

obtained using the Sabine Eq. (2).

′ [*dB*] <sup>=</sup> [

) is the reference surface.

¯

*Lp1* − 6 + 10 log\_\_*<sup>S</sup>*

*Lp1* [dB] is the average noise pressure level at the emitting room.

] is the surface of the partition element under study.

] is the total surface of the measuring surface/s.

] is the volume of the receiving room.

• *T* [s] is the reverberation time in the receiving room.

**180**
