PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Impulse source localization with background noise in a reverberant
environment by multiple sensors
Tiangang Wang1, 2; Choy Yatsze2; Jungang Zhang1
1
2

Beijing Institute of Spacecraft Environment Engineering, Beijing, China

Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

ABSTRACTDuring vibration testing of space hardware, breaking sounds can be heard when cracks happen in the structure.
However, much efforts are needed to determine the position of fault in a complex large-scale model such asa satellite with background noise in reverberant environment. This paper focuses on implementing noncontact localization of the sound sources which are attributed to structure failures. In order to achieve thisgoal, a system for fault detection by sound source localization with limited number of sensors under themoderate reverberant environment is established based on the TDOA technology. The low-quefrency filtering
technique is adopted as a dereverberation pre-processing approach to alleviate the reverberation effects dueto the echoes from the reflections of the laboratory. In order to reject the interference sound sources, twocriteria, the geometrical criterion and the cyclical check criterion, are introduced. A series of experiments are
conducted to verify the performance of this system. The results show that this system can localize the cracksources and hitting sources accurately in a short time.
Keywords: Impulse source localization, reverberant environment, TDOA

1. INTRODUCTION
During vibration testing with the input signal of sine-sweeping or random amplitude, breaking
sounds can be heard when cracks happen in the structure. However, it is often a difficult task to
localize the structure failure position in a complex large-scale model with background noise inreverberant environment. Consequently, it often requires much effort for engineers to check over thewhole structure in order to determine the position of fault.
The current work aims at implementing non-contact localization of the sound sources which are
attributed to structure failures. In order to achieve fault detection by sound source localization withlimited number of sensors, the TDOA technique is adopted (1-3). Comparing with another classic
sound source localization technique the beamforming method, the microphones required for
implementing TDOA is much less. At least three omni-direction microphones are capable to obtainthe location of a point source in 2-D case, which is often the case when the fault positions are
considered on the surfaces of the space hardware. However, in the current study, one more microphone
is employed for each surface to enhance the performance of the localization system against theinterference sources and background noise.
By using the TDOA method, an impulse source can be localized accurately with four microphones
for one surface of the test item in a short time in the free-field condition. However, when theenvironment is reverberant as in most application cases, the echoes due to the wall reflections will
significantly degrade the performance of the TDOA method. In order to overcome this problem, thehomomorphic filtering technique is adopted to reduce the reverberation effect. This techniqueeliminates the reverberation contributions by decomposing the original measurement signals into the1

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wangtiangang001209@163.com

minimum-phase components and the all-pass components, and by applying low pass filtering in thequefrency domain on the minimum-phase components. This technique can effectively reduce thereverberation effects in the measurement signals and therefore make the TDOA method more robust
in reverberant environments.
Following the methodology, a prototype of 16-channel structural failure localization system isestablished and tested on a satellite model. The experiments show that this system can localize thecrack sources and hitting sources quickly and accurately.

2. Methodology
As a classic technique for sound source localization, the TDOA technique has been applied in many
fields for its simple principle, less sensors and less computation amount comparing with othertechniques. Many researches have been done on TDOA in recent years (4-7). The TDOA technique isutilized in the localization system established in the current work so as to reduce the complexity ofthe microphone array and to reduce the measurement channels and therefore the economic cost.
Consider the acoustic wave S k(t) emitted from a point source S k. The received acoustic signal by amicrophone j is expressed as:

xj t

4S r jk

1

 sk t  r jk c  n j t

j 1,

,M

(1)

where xj (t) is the received signal by microphone j, r jk is the vector from the location of the jthmicrophone to the source S k, nj (t) is background noise which is considered as incoherent with eachother in each measurement channel, and c is the speed of sound in air.
For a microphone pair consisting the ith microphone and the jth microphone, the time differenceof arrival (TDOA) from the source S k to the two microphones is defined by the following equation:

G ij = r jk  rikc(2)

It can be seen from this equation that if the TDOA δij is found out, the sound source S k is thenconstrained on one branch of a hyperboloid determined by Equation (2) in the 3-D situation. A
convenient way to obtain δij is to evaluate the cross-correlation function (CCF) of the measurement
signals of the microphone pair, which is given by:

Rij W

T

1
lim
xi t  x j t  W
T of T ³
t 0(3)

Equation (3) is the definition of CCF for continuous signals. However, the signals are processed
digitally by computers and therefore sequences are used instead of continuous functions. Consequently,
the following equation take the place of Equation (3) in real applications.

Rij >W @1
N sample

N sample¦ x > n@  x > n  W @
i

j

(4)

n 1

where Nsample is the number of total sampling points of the signals and τ is the possible time shift.
Equation (2) represents one branch of a hyperboloid with the focal points at the positions of the
ith and the jth microphones. In order to determine the location of a point sound source in a 3 -D field,
at least four microphones that are not in the same plane are needed so that three microphone pairs canbe formed. The hyperboloids obtained in each local coordinate system are then transformed into theglobal coordinate system by applying coordinate transformation. The position of the sound source isobtained at the intersection of the three corresponding hyperboloids.
In most real situations, the acoustic signal captured by a microphone contains not only the direct
path signal from the sound source but also multiple echoes reflected by the surfaces of the reverberant
environment as well as the incoherent noise. These echoes can be considered as a series of delayed
and attenuated versions of the direct path signal. In such situations, the measurement signal can be
expressed as the convolution of the source signal and the room impulse response function which
describes how the echoes are delayed and attenuated.
The contribution of the reverberation effect can be reduced using the cepstral dereverberation
method. To apply this technique, first, each measurement signal is transformed into its cepstrum (8).

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Then, the cepstrum is decomposed into two parts, the minimum-phase part and the all-pass part. The
former part is further low-pass filtered to suppress the contribution of the reverberation effects.
Afterwards, the filtered minimum-phase part and the all-pass part are transformed into the frequency
domain and multiplyed with each other to obtain the processed spectrum. And finally, a processedmeasurment signal is obtained by applying the inverse Fourier’s transformation. This technique isadopted in the current work as a pre-processing method of the measurement signals. To get moredetails one can refer to Reference (9-11).

3. Some Consideration of the Structural Failure Localization System
3.1 Optimization of microphone arrangement
The TDOA method determines the position of a sound source according to the intersection ofmultiple hyperboloids which depend on the time difference of arrival between two microphones ineach microphone pair. In order to localize a point source in a 3-D field, at least three microphone pairs
are needed, that is, at least four microphones which are not in the same plane should be used.
However, in the current study, the sound sources of interest are all assumed on the surfaces of thetest item. Typically, the profile of a satellite model can be simplified as a cube. For each side of thecube, the sound sources to be localized are within a known area, that is, the corresponding surface ofthe model. In such situation, two microphone pairs are enough to obtain two hyperboloids. Theintersection line of the two hyperboloids meets the surface at the sound source location. Hence, atleast three microphones on a plane parallel to the corresponding surface of the space hardware should
be utilized.
In many real applications, however, there are often reverberation effects as well as someinterference sound sources such as the sound of air conditioning system, the voices of workers. These
interferences may lead to spurious peaks in the cross correlation functions of th e microphone pairs
and consequently lead to wrong intersection of the hyperboloids. In order to enhance the robustnessof the localization system, another microphone is added in the sub -array for each surfaces of the test
item. Therefore, six microphone pairs are formed and six hyperboloids are obtained using four
microphones in each sub-array. In order to localize the structure failure sound sources on the foursides of a test item, a whole microphone array containing 16 microphones with four sub -arrays are
established. The four microphones of each sub-array are placed near the four corners of the surface tocapture the acoustic signals on each surface.
3.2 Rejection of the interference sound sources
In order to reject the interference sound sources and enhance the localization robustness, twocriteria, the geometrical criterion and cyclical check, are introduced into the current localization
system.
Geometrical criterion
In order to reject the undesired sound sources, a geometrical criterion is introduced. This criterion
constrains the range of the cross correlation function in which the main peak position is consideredas the TDOA of the sound source of interest. According to the geometrical relation between eachmicrophone and the corresponding surface of the test item, the maximum possible TDOA for a soundsource on this surface is the maximum one of the four corners (illustrated in Fig . 1). By comparing
the four TDOAs on the four corners, the maximum possible TDOA δij,max is determined. Therefore,
for the cross correlation function of the microphone pair containing Mic i and Mic j, only the highest
peak within the range -│δij,max │≤ δij ≤│δij,max │ is considered.
By introducing this criterion, the peaks in the cross-correlation function formed by the undesired
sound sources which are out of the surface of the satellite model will not be considered. Therefore,
the interference sound sources are naturally rejected.

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Figure 1 – Illustration of the geometrical criterion
Cyclical check
The TDOA method finds the source position by looking for the intersection point of thehyperboloids. Sometimes a pure quantity of measurement of one microphone will lead to a wrong
TDOA and therefore a wrong hyperboloid. In this situation, the system will fail to localize the true
source position even if the other two hyperboloids precisely correspond to the TDOAs of the
microphone pairs.
In order to determine whether an intersection point is the true source position or not, a cyclicalcheck procedure is introduced to check the time delay relations and to reject the wrong peaks in the
cross-correlation functions of the measurement signals. The judgment is based on the following
relation among the time delays of three microphone pairs that are formed by three microphones. Whenmeasuring the acoustic signal emitted from one single source s with two microphones Mic i and Mic
j, the time delay of the two measurement signals are given by:

G ij = rjk  rik

c W kj  W ki

(5)where τkj=│rjk│/c and τki=│r ik│/c are the propagation time from the source S k to Mic i and Mic j
respectively.
Therefore, for any point source S k and three microphones Mic i, Mic j and Mic n, the following
relation exists:

G ij W kj  W ki
W kj  W kn  W ki  W kn

(6)

G nj  G ni
There are four microphones in each sub-array. Therefore, four three-microphone groups are formed.
Those groups do not make Eq. (6) exist will not be used for localization.

4. Experimental validation
In order to validate the 16-Channel structure failure localization system, a series of experiments
have been conducted.
4.1 Set-up of the experiment
The test set up is shown in Fig. 2. A series of cases are tested to localize impulse sources on thefour vertical surfaces of a satellite model. These surfaces are numbered in such a way: Surface 1 isthe front surface in Fig. 2, Surface 2 is the right surface facing the wall, Surface 3 is the back surface
and Surface 4 is the left surface. Four microphone sub-arrays with four microphones in each one areset surrounding the model. Mic 1~4 facing Surface 1, Mic 5~8 facing Surface 2, Mic 9~12 facing
Surface 3 and Mic 13~16 facing Surface 4. The distance from each surface of the model to thecorresponding microphone array is 0.55 meter. The coordinate system is placed with the origin at thecenter of the first sub-array containing Mic 1~4. The x-axis lies on the horizontal plane pointing to
the right when facing the model. The y-axis is placed horizontally pointing to the model, and the z-

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axis lies vertically pointing upwards to the ceiling. A series of cases are designed to verify theperformance of the system.

Figure 2 – The test set up
4.2

Cases and results

Case 1: Two sources on different surfaces
Two sound sources are designed in Case 1 to verify the performance of this system in localizing
multiple sources in different surfaces. The first source S1 on Surface 1 is generated by hitting thesurface with a small hammer twice and S 2 is a small loudspeaker placed on Surface 4 playing a seriesof transient signals. The coordinates of the microphones as well as the sound sources are listed inTable 1.
Table 1 – The coordinates of the microphones and the sources in Case 1
Mic 1

Mic 2

Mic 3

Mic 4

S1

(-0.25, 0, 0.33)(0.25, 0, 0.33)(0.25, 0, -0.33)(-0.25, 0, -0.33)(-0.1, 0.5, -0.25)

Mic 13

Mic 14Mic 15

Mic 16S2(-0.92, 1.05, 0.33)(-0.92, 0.55, 0.33)(-0.92, 0.55, -0.33)(-0.92, 1.05, -0.33)(-0.42, 0.6, -0.15)

The measurement signals of Mic 1 and Mic 16 are shown in Fig. 3 (a) and (b) respectively. In Fig.
3, the low-frequency noise has been eliminated by a high-pass filter. The two measurement signals
both contain the signals from both sources. The five transient signals which occur periodically every
one second are emitted from S 2 on Surface 4 while the other two impulses are the hitting sound of S1
on Surface 1. Although S 1 is on Surface 1 and Mic 16 is facing Surface 4, the amplitude of the signal
from S 1 is still larger than that from S 2 in the measurement signal of Mic 16 according to Fig. 3(b).

Figure 3 – The measurement signals of: (a) Mic 1, (b) Mic 162672

By default, the system extracts the largest peak which occurs at around 0.92s for localization. This
peak is the first transient signal emitted from S 2 . The localization results are shown in Fig. 4. S2 islocalized at (-0.41, 0.62, -0.17) by Mic 14, Mic 15 and Mic 16. There is no localization result on any
other surface of the test item. S 1 is not found because the extracted time block only contains the signal
from S 2 .

Figure 4 – The localization result for S2
In order to localize S1 , the time-domain signal block at around 1.5s with the duration of 0.3s is
extracted. The localization result is shown in Fig. 5. In this configuration, S1 on Surface 1 is localized
at (-0.07, 0.5, -0.25) and no miscarriage of justice is made on other surfaces.. The localization errors
for S 1 and S 2 are both 0.03m.

Figure 5 – The localization result for S1
Case 2: Two sources on the same surface
Two sound sources are both placed on Surface 1 in Case 2 to verify the capability of this systemin finding multiple sources on the same surface. S 1 is generated on Surface 1 by hitting the surface

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with a hammer and S2 is a loudspeaker placed on the same surface playing a series of transient soundswith the interval of one second. The coordinates of S 1 and S 2 are (0.15, 0.5, 0.2) and (-0.22, 0.5, -0.2)
respectively.
By default, the sound source that is localized first is S 1 which corresponds to the highest peak ataround 2.12s. The localization result is shown in Fig6. S1 is found at (0.16, 0.5, 0.16) by the threemicrophone group of Mic 1, Mic 3 and Mic 4.
In order to localize S2 , the signal segment extraction is reset. The center time is chosen at 2.8s andthe time duration is set of 0.3s. The localization results are shown in Fig. 7. In this situation, S2 islocalized by Mic 1 Mic 2 and Mic 4 at (-0.21, 0.49, -0.17). No miscarriage of justice is made on othersurfaces. The localization errors for S1 and S2 are 0.0412m and 0.0332m respectively.

Figure 6 – The localization result for S1

Figure 7 – The localization result for S2

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5. CONCLUSIONSThis paper aims at establishing a non-contact structure failure diagnosis system by localizing theimpulse sound sources corresponding to the potential structural failures. The CCF method of TDOA
technique is adopted. In order to alleviate the reverberation effect due to the echoes from thereflections, the low-quefrency filtering technique is utilized as a dereverberation pre-processing
approach. By involving this technique, the robustness of the localization system is improved to a great
extent.
A 16-channel structure failure localization system is established thereafter. In order to reject theinterference sound sources, two criteria, the geometrical criterion and the cyclical check criterion, areintroduced. A series of experiments are conducted to verify the performance of this system. The results
show that the system can localize multiple sources on different surfaces, and even multiple sourceson the same surface of the test item accurately (the maximum localization error is about 4cm) in ashort time (less than two minutes in this experiment). The localization results are shown both in theimage format and as the coordinates to help users to find the locations of the structure failures easily.

ACKNOWLEDGEMENTS
The authors would like to acknowledge the funding support from Beijing Institute of Spacecraft
Environment Engineering.

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