**2. Methodology**

All the recommendations laid down in measurements based on pressure [1] and intensity [2] standards have been interrelated regarding the execution of the beamforming and SONAH measurements.

In the emitting room, two omnidirectional sound sources, one placed close to a corner generating white noise and the other one in the center of the room generating pink noise, are independently triggered and equalized to generate an acoustic field diffuse, stationary, and spectrally flat (90–95 dB approx.) with no tonalities over the desired frequency range.

At the receiving room measurement positions are defined based on the features of the surface under study, the instrumentation, and the technique used.

Beamforming technique states that the measuring distance between the array and the source, to cover the whole area of interest at the partition element, must be the minimum value required according to Eq. (4) [14]:

$$L = \mathbf{1.15x} \tag{4}$$

where


Nevertheless, the bigger the distance of Beamforming measurement is, the lower the resolution will be, and therefore, the more difficult will be to locate the maximum sound radiation areas. The resolution can be calculated according to Eq. (5):

$$R = \mathbf{1}.\mathbf{Z}\mathbf{2}\left(\frac{\mathbf{z}}{D}\right)\lambda\tag{5}$$

where


Taking this into account, in the measurements, distances from the partition element should be chosen in such a way that the array can be placed at a distance that allows to fully cover the surface under study, carefully combining the values for calculation distance, covered surface, and expected resolution.

When the measurements have been taken, to process the data, the calculation points are defined over a flat grid. This grid should have an x/y axis spacing as dense as possible in order to allow an accurate identification of leaks, fissures, or sealing defects.

Once defined the calculation grid, the simplest algorithm that can be used is the delay-and-sum one. With this algorithm, it is possible to define the minimum working frequency for a 30° opening angle as [12].

$$\,\_{L}f\_{\min}\left(\mathbf{30}^{\circ}\right) = \frac{c}{D} \tag{6}$$

**183**

and

where

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

)=\_\_ 4

In the case of SONAH measurements, the instrumentation setup is configured to carry out the measurements in the near field. The calculation grid is limited by the array dimensions (although we can take more measurements to synthesize a larger grid [21]). Depending on the array dimensions and the possibility of synthesizing a

• Over smaller characteristic areas, made with different materials, where there

The use of references is compulsory in SONAH. They are selected according to the features of the sound field at the receiver (microphone references) [22] or to the vibration level at the partition elements (accelerometer references) [14], which could be related to sound insulation by the pressure and intensity calcula-

For SONAH measurements, the working frequency range is determined by

• *dx* [m] is the average spacing between array microphone positions.

Once the array-based measurements are performed and processed, results are displayed in color maps where the areas of the studied surface with higher pressure

The frequency range obtained can be used for the case of the beamforming delay-and-sum algorithm and could be increased if other algorithms (such as minimum variance or Capon [15], clean-SC [16], DAMAS [17], beamforming through using eigenvalues and eigenvectors [18], MUSIC [19], or orthogonal beamforming

<sup>3</sup> *fT*, (7)

<sup>2</sup>*<sup>D</sup>* (8)

<sup>2</sup>*dx* (9)

The highest frequency is defined according to the sidelobe level as

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

• *c* the speed of sound (344 m/s)

*fmax*(30°

• Over the whole partition element

tions obtained by these techniques.

might be suspicions fissures or leakages

*fmin* [*Hz*] = \_\_\_*<sup>d</sup>*

*fmax* [*Hz*] = \_\_\_*<sup>c</sup>*

• *c* is the speed of sound (344 m/s).

• *D* [m] is the diameter of the array.

being *fT* [Hz] the sidelobe threshold frequency [12].

large grid, the measurements can be performed in two manners:

• D [m] the array diameter

with

[20]) are used.

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

with

*Acoustics of Materials*

**2. Methodology**

where

where

• *<sup>λ</sup>* [*m*] <sup>=</sup> *<sup>c</sup>* [

• R [m] is the resolution.

\_\_ *m s* ] \_\_\_\_\_\_\_\_\_\_ *f* [*Hz*]

• D [m] is the array diameter.

ing frequency for a 30° opening angle as [12].

beamforming and SONAH measurements.

over the desired frequency range.

• *z* [m] is the measuring distance.

• *L* [m] is the length of the sound source.

*R*=1.22(

is the wavelength.

calculation distance, covered surface, and expected resolution.

All the recommendations laid down in measurements based on pressure [1] and intensity [2] standards have been interrelated regarding the execution of the

In the emitting room, two omnidirectional sound sources, one placed close to a corner generating white noise and the other one in the center of the room generating pink noise, are independently triggered and equalized to generate an acoustic field diffuse, stationary, and spectrally flat (90–95 dB approx.) with no tonalities

At the receiving room measurement positions are defined based on the features

Beamforming technique states that the measuring distance between the array and the source, to cover the whole area of interest at the partition element, must be

*L*=1.15*z* (4)

Nevertheless, the bigger the distance of Beamforming measurement is, the lower the resolution will be, and therefore, the more difficult will be to locate the maximum sound radiation areas. The resolution can be calculated according to Eq. (5):

\_\_*z*

Taking this into account, in the measurements, distances from the partition element should be chosen in such a way that the array can be placed at a distance that allows to fully cover the surface under study, carefully combining the values for

When the measurements have been taken, to process the data, the calculation points are defined over a flat grid. This grid should have an x/y axis spacing as dense as possible in order to allow an accurate identification of leaks, fissures, or sealing

Once defined the calculation grid, the simplest algorithm that can be used is the delay-and-sum one. With this algorithm, it is possible to define the minimum work-

)=\_\_*<sup>c</sup>*

*fmin*(30°

*<sup>D</sup>*)<sup>λ</sup> (5)

*<sup>D</sup>* (6)

of the surface under study, the instrumentation, and the technique used.

the minimum value required according to Eq. (4) [14]:

**182**

defects.


The highest frequency is defined according to the sidelobe level as

$$f\_{\max} \left( \mathbf{30}^{\circ} \right) = \frac{4}{3} f\_{Tt} \tag{7}$$

being *fT* [Hz] the sidelobe threshold frequency [12].

The frequency range obtained can be used for the case of the beamforming delay-and-sum algorithm and could be increased if other algorithms (such as minimum variance or Capon [15], clean-SC [16], DAMAS [17], beamforming through using eigenvalues and eigenvectors [18], MUSIC [19], or orthogonal beamforming [20]) are used.

In the case of SONAH measurements, the instrumentation setup is configured to carry out the measurements in the near field. The calculation grid is limited by the array dimensions (although we can take more measurements to synthesize a larger grid [21]). Depending on the array dimensions and the possibility of synthesizing a large grid, the measurements can be performed in two manners:


The use of references is compulsory in SONAH. They are selected according to the features of the sound field at the receiver (microphone references) [22] or to the vibration level at the partition elements (accelerometer references) [14], which could be related to sound insulation by the pressure and intensity calculations obtained by these techniques.

For SONAH measurements, the working frequency range is determined by

$$f\_{\min} \text{ [Hz]} = \frac{d}{2D} \tag{8}$$

and

$$f\_{\text{max}}\,\,\text{[Hz]} = \frac{c}{2d\text{x}}\tag{9}$$

where


Once the array-based measurements are performed and processed, results are displayed in color maps where the areas of the studied surface with higher pressure or intensity levels can be identified. These areas, therefore, corresponding to leaks, fissures, or sealing defects, are those with higher sound transmission.
