Intelligent location of simultaneously active acoustic emission sources:
  Part II
Intelligent location of two simultaneously active
acoustic emission sources:
Part II
Tadej Kosel and Igor Grabec
Faculty of Mechanical Engineering, University of Ljubljana,
Aškerčeva 6, POB 394, SI-1001 Ljubljana, Slovenia
e-mail: tadej.kosel@guest.arnes.si; igor.grabec@fs.uni-lj.si
Abstract— Part I describes an intelligent acoustic emission
locator, while Part II discusses blind source separation, time
delay estimation and location of two continuous acoustic emission
sources.
Acoustic emission (AE) analysis is used for characterization
and location of developing defects in materials. AE sources
often generate a mixture of various statistically independent
signals. A difficult problem of AE analysis is separation and
characterization of signal components when the signals from
various sources and the mode of mixing are unknown. Recently,
blind source separation (BSS) by independent component analysis
(ICA) has been used to solve these problems. The purpose of
this paper is to demonstrate the applicability of ICA to locate
two independent simultaneously active acoustic emission sources
on an aluminum band specimen. The method is promising for
non-destructive testing of aircraft frame structures by acoustic
emission analysis.
INTRODUCTION
A common goal of many non-destructive testing methods is
to detect defects in materials. Acoustic emission analysis (AE)
is a passive testing method used to locate and characterize
defects which emit sound[10].
There are many ways to deduce the location of an AE
source from electrical signals detected by a chain of sensors.
The corresponding problems may be classified by the type of
acoustic source mechanism as the location of a continuous
emission source, such as that generated by a leak, or as the
location of discrete emission, such as an AE burst caused by a
growing crack. This paper describes a method for processing
continuous AE signals to determine the time delay (T-D)
between signals and thus to provide information for location
of AE sources. It should be pointed out that application of
AE source characteristics, such as count, count rate, ampli-
tude distribution, and conventional time delay measurement,
becomes meaningless when dealing with continuous acoustic
sources.
The basic information for AE source location consists of
T-D between stress waves detected at different positions on
a specimen. In the case of only one active AE source, T-
D of continuous acoustic waves can be estimated using the
cross-correlation function (CCF) of sensor signals described
in Part I of this article[10], [7]. In the case of two (or
Manuscript generated: January 31, 2007
more) simultaneously active AE sources, this method is not
applicable, since analysis of the CCF leads only to the T-D
of the most powerful AE signal. Detection of simultaneously
active independent AE source signals therefore requires a more
sophisticated approach.
The purpose of our study was to find a suitable method for
processing a mixture of two simultaneously active continuous
AE signals to determine the T-D and, related to this, the
coordinates of both AE sources. We found that the Blind
Source Separation (BSS) method solves this problem satisfac-
torily. BSS is a general signal processing method involving
the recovery of the contributions of different sources from
a finite set of observations recorded by sensors, independent
of the propagation medium and without any prior knowledge
of the sources. BSS has already been successfully applied
in medicine, telecommunications, image processing etc[8].
However, it is also a promising method for AE analysis of
aircraft structures, because AE signals are often hidden in a
mixture of signals from various sources. BSS could extract
the specific signature of each AE source, which can further
be used for location and characterization purposes, or to
isolate AE sources from background noise. We conducted
experiments with BSS on an aluminum beam on which two
continuous AE sources were generated simultaneously by air
flow.
METHODS
In this section we explain two different methods for time
delay estimation of AE sources. The first method is based on
analysis of the CCF and is convenient for T-D estimation of
one active continuous AE source as is described in Part I[10],
[7], [12]. The CCF exhibits a peak when the delay parameter
compensates the T-D between the sensor signals [10]. The T-D
is thus determined by the position of the highest peak of the
CCF. The second method is based on BSS algorithm and is
convenient for T-D estimation of two (or more) simultaneously
active continuous AE sources[9]. Location of two simulta-
neously active AE sources was performed by an intelligent
locator based on a general regression neural network[5] as is
described in Part I.
Multichannel Blind Source Separation has recently received
increased attention due to the importance of its potential
http://arxiv.org/abs/0704.0050v1
applications[3]. It occurs in many fields of engineering and
applied sciences, including processing of signals from antenna
array, speech and geophysical data processing, noise reduction,
biological system analysis, etc. It consists of recovering signals
emitted by unknown sources and mixed by an unknown
medium (material where waves propagate), using only several
observations of the mixtures. The only assumptions made
are the linearity of the mixing system and the statistical
independence of original signals.
BSS methods may be classified in several ways. One
possible classification that can be made depends on whether
the mixtures are instantaneous or convolutive [4]. Convo-
lutive mixtures correspond to a mixing system with time
dependent memory. They represent a more general case than
instantaneous mixtures, and they have in particular acoustic
applications. Recently, the principle of independent component
analysis (ICA) was applied in BSS, and it was found to
be a simple and powerful tool[6]. This study deals with the
separation of two convolutively mixed independent continuous
AE signals by ICA and the intelligent locator was used to
locate two independent continuous AE sources based on T-D
The mixing and filtering processes of unknown input signals
sj(t) may have different mathematical or physical back-
grounds, depending on specific applications. In this paper,
we focus mainly on the simplest cases with n signals xi(t)
linearly mixed in n unknown statistically independent, zero
mean source signals sj(t). The composition is expressed in
matrix notation as x = A ∗ s [8], where ‘*’ denotes a
convolution, x = [x1(t), . . . , xn(t)]
T is the vector of sensor
signals, s = [s1(t), . . . , sn(t)]
T is the vector of source signals
and A is an unknown full rank n × n mixing matrix whose
elements are finite inpulse response (FIR) filters. We assume
that only vector x is available. The goal of ICA is to find a
matrix W , by which vector x can be transformed into source
signals u = W ∗ x.
Matrix W is simply the inverse of A. However, when noise
corrupts the signals, matrix W must be found by an optimal
statistical treatment of the inverse problem. The optimal ma-
trix W can be estimated by a feed-forward neural network
operating in the frequency domain. A learning algorithm with
Amari’s natural gradient can be written as[1]: ũ = W̃ · x̃,
W̃ (τ + 1) = W̃ (τ) + α∆W̃ (τ) + η∆W̃ (τ − 1), ∆W̃ =
[I − ỹ · ũH] W̃ , ỹ = tanh(ℜ[ũ]) + ı tanh(ℑ[ũ]), where α is
the learning rate, η is the constant of learning, I is the identity
matrix and the tilde ‘˜ ’represents a frequency domain.
The ICA algorithm runs off-line and proceeds as follows
[11] (Fig. 1):
1) Pre-process the time-domain input signals, x(t): sub-
stract the mean from each signal.
2) Initialize the frequency domain unmixing filters, W̃ .
3) Take a block of input data and convert it into the
frequency domain using the Fast Fourier Transform
(FFT).
4) Filter the frequency domain input block, x̃, through W̃
to get the estimated source signals, ũ.
5) Pass ũ through the frequency domain nonlinearity, ỹ.
6) Use W̃ , ũ and ỹ along with the natural gradient
extension [2] to compute the change in the unmixing
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pre-process initialize
unmixing
filters
filter
update rule
Fig. 1. Block diagram of ICA algorithm
filter, ∆W̃ .
7) Take the next block of input data, covert it into the
frequency domain, and proceed from step 4. Repeat this
process until the unmixing filters have converged upon
a solution, passing several times through the data.
8) Normalize W̃ and convert it back into the time domain,
using the Inverse Fast Fourier Transform (IFFT).
9) Convolve the time domain unmixing filters, W , with x
to get the estimated sources.
EXPERIMENTS
We performed experiments with two independent continu-
ous AE sources on an aluminum band of dimensions 4000×
40× 5mm3. Reflections at the end of the band were reduced
by wrapping the ends in putty. The testing area was on the
longitudinal axis in the middle of the band, where 23 holes of
diameter 2 mm and mutual separation 100 mm were prepared
as shown in Fig. 2.
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φ 2 mm bandl air flow
Fig. 2. AE generation by air flowing through the hole
Two AE sensors were mounted 100 mm away from the
terminal holes, that is 2.4 m from each other. The origin of
the coordinate system was in the middle of the band and the
testing area extended from −1.1m to +1.1m. AE signals
were excited by two independent air jets flowing through
the holes. The source position was arbitrarily selected at
+100mm and +800mm. Air jets were formed by two nozzles
of diameter 1 mm using pressure 7 bar. The experimental set-
up consisted of the test specimen (aluminum band), two AE
sensors (pinducers), two AE sources (air jets), two amplifiers,
a digital oscilloscope (A/D converter) and a computer (BSS
module, locator, plotter) as shown in Fig. 3. Three experiments
were performed : (1) T-D estimation using a CCF of two AE
signals that were not simultaneously active; (2) T-D estimation
using a CCF of two AE signals which were simultaneously
active and (3) T-D estimation of AE signals using ICA.
Location of sources, based on T-D, by the intelligent locator
was performed in all three cases.
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sensor
AE source
locator
plotter
Fig. 3. Experimental set-up
In the first experiment only one air jet was activated for
a particular measurement. In the second experiment both air
jets were activated. Sensor signals were linear convolutive
mixtures of two independent continuous AE sources as shown
in Fig. 4. The auto-correlation R11, R22 and cross-correlation
functions R12, R21 were calculated from sensor signals. Only
one T-D of two signals can be estimated from the highest
peak in both CCF, regardless of the number of independent
AE sources on the test specimen as shown in Fig. 5. This
means that a CCF can not be used for automatic T-D estima-
tion of multiple AE signals on the test specimen. The CCF
exhibits various peaks which belong to various independent
AE sources, but it is ussually impossible to relate these peaks
to corresponding coordinates of AE sources.
0 0.1 0.2 0.3 0.4
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t [ms]
(a) Sensory signal #1
0 0.1 0.2 0.3 0.4
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t [ms]
(b) Sensory signal #2
Fig. 4. Mixtures of two independent continuous AE sources aquired by two
sensors
In the third experiment the ICA algorithm was used to
solve this problem satisfactorily. The ICA algorithm results
in demixing FIR filters which extract the independent source
signals from sensory signals. By inverting the demixing filters
W we obtain mixing filters A. In the case of two independent
0 5000 10000 15000
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Rx1x1
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Rx1x1
Rx1x2
0 5000 10000 15000
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Rx1x1
Rx1x2
Rx2x1
Fig. 5. Auto- and cross-correlation functions of sensory signals; down-arrow
marks the highest peak
AE sources and two sensors, the components of A are four
FIR mixing filters, as shown in Fig. 6. There are two direct
a11, a22 and two cross mixing filters a12, a21. The first index
of the filter represents the number of the sensor, while the
second index represents the number of the source. The position
of the highest peak of the cross FIR filters determines the T-
D between two signals from two sensors. If we substract the
coordinate of the highest peak of a direct mixing FIR filter
a11 from the coordinate of the highest peak of cross filter a21
we obtain the T-D of first independent AE source, since each
of the highest peaks in the FIR filters belongs to different
independent AE signals.
RESULTS
The results of T-D estimation of two continuous independent
AE sources are shown in Fig. 7. Three experiments were done.
In the first experiment, the T-D was estimated by a CCF of two
AE sources which were not active simultaneously as marked
by ‘◦’. Locations of these two sources estimated by the
intelligent locator were +181 mm and +784 mm. The second
experiment was performed with both AE sources active simul-
taneously. T-D were also estimated by a CCF. The highest peak
0 5000 10000 15000
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0 5000 10000 15000
0.5PSfrag replacements
Fig. 6. Mixing filters obtained by ICA of sensory signals; down-arrow marks
the highest peak
position corresponds to the source location marked by ‘− −’
and was +784 mm. The third experiment was performed using
ICA for T-D estimation and location by intelligent locator. The
result is marked by ‘�’. Estimated positions of this two sources
were +179 mm and +784 mm respectively. If we compare the
coordinates of both independent AE sources estimated by
the first experiment and by the third experiment, we find a
good correspondence. If we compare estimated AE source
coordinates with actual coordinates, which were +100 mm and
+800 mm respectively, we observe a slight disagreement due to
experimental error. Experimental error is about 3% regarding
the distance between sensors. Absolute error in this case is
79 mm and 16 mm respectively. The results also depend on
the number and distribution of prototype sources marked by
‘•’, which are essential for operation of the intelligent locator.
If the number of prototype sources is increased, location error
is reduced. In our case the prototype sources were distributed
along the beam from −1.1m to +1.1m separated by 0.1m, so
that systematic error of the locator was set to several procents.
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actual position l [m]
correlation function
Fig. 7. Results of location of two continuous independent AE sources.
Symbols: ‘�’ – AE sources obtained by ICA; ‘◦’ – estimated AE sources
obtained by cross-correlation function in two steps, when just one of two
AE sources was active at time of measurement; ‘− −’ – estimated AE
sources obtained by cross-correlation function when two AE sources were
active simultaneously; ‘•’ – prototype AE sources required for location using
intelligent locator; ‘−’ – distribution of actual sources.
DISCUSSION AND CONCLUSION
CCF is applicable to T-D estimation only in the case of one
active AE source. The goal of our research is to develop a new
method to estimate T-D between AE signals in the case of mul-
tiple simultaneously active continuous AE sources. We have
shown that, for this purpose, ICA is an applicable option. ICA
finds a linear coordinate system (the unmixing filters) such that
the resulting signals are statistically independent. This is an
advantage of ICA over CCF. It represents a new approach to
processing of AE data and further expands the applicability of
AE analysis in the field of non-destructive testing. In machines
or in an industrial environment, multiple sources are usually
active Simultaneously, often representing environmental dis-
turbances. The corresponding complex signals are not directly
applicable to characterization of particular sources. However,
separation of contributions by ICA analysis in fact represents a
kind of filtering, increasing the applicability of filtered signals
to characterization of sources in complex environments. Future
research will be focused on location of multiple AE sources
on two-dimensional and three-dimensional specimens.
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