Intelligent location of simultaneously active acoustic
emission sources:
Part I
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— The intelligent acoustic emission locator is described
in Part I, while Part II discusses blind source separation,
time delay estimation and location of two simultaneously active
continuous acoustic emission sources.
The location of acoustic emission on complicated aircraft frame
structures is a difficult problem of non-destructive testing. This
article describes an intelligent acoustic emission source locator.
The intelligent locator comprises a sensor antenna and a general
regression neural network, which solves the location problem
based on learning from examples. Locator performance was
tested on different test specimens. Tests have shown that the
accuracy of location depends on sound velocity and attenuation
in the specimen, the dimensions of the tested area, and the
properties of stored data. The location accuracy achieved by
the intelligent locator is comparable to that obtained by the
conventional triangulation method, while the applicability of the
intelligent locator is more general since analysis of sonic ray paths
is avoided. This is a promising method for non-destructive testing
of aircraft frame structures by the acoustic emission method.
INTRODUCTION
Acoustic emission (AE) concerns non-destructive testing
methods and is used to locate and characterize developing
cracks and defects in material. In non-destructive testing of
aviation frame structures, acoustic emission is a well accepted
method [8]. The location problem is usually solved by various
triangulation techniques based on the analysis of ultrasonic ray
trajectories [10], [1], [3]. Solving and programming the related
equation is rather cumbersome and cannot be simply per-
formed if the structure of the tested specimen is geometrically
complicated. Acoustic emission testing of aircraft structures
is a challenging and difficult problem. The structures involve
bolts, fasteners and plates, all of which move relative to one
another due to differential structural loading during flight. The
complex geometry of the airframe results in multiple mode
conversions of AE source signals, compounding the difficulty
of relating the source event to the detected signal.
In order to avoid difficulties with equation solving and
programming of the triangulation procedure, several empirical
approaches based on learning from examples have already
been proposed [5]. We developed an intelligent locator capable
of learning from examples which we therefore called an
intelligent locator. The purpose of developing the intelligent
Manuscript generated: January 31, 2007
locator is to replace information obtained from the analysis
of sonic ray trajectories by information obtained directly from
simulated AE events on the specimen under test. In this way,
the calibration procedure, which has to be performed anyway,
could be generalized to the training of the intelligent locator.
The development of such an intelligent locator has been
described elsewhere [4]. In the locator developed a general
regression neural network (GRNN) is employed [9], which
acquires data about the detected AE signals and parameters
of their sources during learning. The GRNN uses these data
in testing when estimating the unknown source position from
detected AE signals. For this purpose, associative GRNN
operation is utilized. The basis of such operation is statistical
estimation determined by the conditional average [6]. Conse-
quently, the accuracy of the intelligent locator also depends on
the learning procedure, and must be examined before testing.
This article describes the results obtained by testing the
intelligent locator on experimental continuous AE sources. The
purpose of this study was to test and examine the advantages
of the intelligent locator compared to a conventional locator.
as described in Part I. In Part II an experiment will be
explained in which an intelligent locator was used to locate
two simultaneously active continuous AE sources generated
by leakage air flow. Location of more than one source at the
same time on the test specimen is a new approach in acoustic
emission testing, and is a very promising method for aircraft
and airspace structural testing.
When preparing the experiments, we focused on locating
evolving defects in stressed materials and constructions, and
leakage of vessels. We therefore performed location exper-
iments on four different specimens with three different AE
sources. The specimens comprised bands, plates, rings, and
vessels, while the AE sources were simulated by rupture of a
pencil lead (pen test), material deformation during tensile test,
and leakage air flow through a small hole in a sample. The
positions of AE sources used in testing were well specified.
Actual positions were compared with estimated ones, and
the discrepancy was used to describe the inaccuracy of the
locator. In this article, only the experiment with leakage air
flow through a small hole in a sample is explained. In Part I,
location of one continuous AE source is explained. This Part
is intended for better understanding of Part II and comparison
of results. In Part II, a new approach to the location of two
http://arxiv.org/abs/0704.0047v1
simultaneously active continuous AE sources is explained.
Below, the article first explains the theoretical background
for application of the conditional average to the location
problem, then describes auxiliary AE signal processing, and
finally demonstrates performance of the experimental intelli-
gent locator.
THEORETICAL BACKGROUND
In this section we describe a non-parametric approach to
empirical modeling of AE phenomena and solving the location
problem. This modeling stems from a description of physical
laws in terms of probability distributions. Since it has been
explained in detail elsewhere, we present here just its basic
concepts [6], [5].
The object of empirical modeling is the relationship between
variables which are simultaneously measured by a set of
sensors. In our example the variables are source coordinates
and AE signal characteristics. Let them be represented by a
vector of M components: x = (ξ1, . . . , ξM ). In the empirical
description of an AE phenomenon we repeat the observation N
times to create a database of prototype vectors {x1, . . . ,xN}.
Instead of formulating a relation between the components of x
we instead treat this vector as a random variable and express
the joint probability density function f by the estimator
f(x) =
δ(x− xn) . (1)
Here δ denotes Dirac’s delta function. For the purposes of
modelling, we must also estimate the probability density in
the space between the prototype points. This is achieved by
expressing the singular delta function in Eqs. 1 by a smooth
function, such as for example the Gaussian
wn(x− xn, σ) = exp
−‖x− xn‖
, n = 1, . . . , N .
in which σ denotes the smoothing parameter.
The data vectors determine an empirical model of the
probability density function. Their acquisition corresponds to
the learning phase of the empirical modeling. Let us further
assume that observation of AE phenomenon provides only
partial information that is given by a truncated vector
g = (ξ1, . . . , ξS ; ∅) , (3)
in which ∅ denotes missing components. The problem is
to estimate the complementary vector of missing or hidden
components:
h = (∅; ξS+1, . . . , ξM ); (4)
such that the complete data vector is determined by concate-
nation
x = g ⊕ h = (ξ1, . . . , ξS , ξS+1, . . . , ξM ) . (5)
A statistically optimal solution to this problem is determined
by the conditional average estimator, which is expressed by a
superposition of terms [6]
Bn(g)hn, where (6)
Bn(g) =
w(g − gn, σ)
w(g − gk, σ)
. (7)
The basis functions Bn(g) represent a measure of similarity
between the truncated vector g given by a particular ob-
servation and truncated vectors from the database gn. The
higher the value of Bn(g) the higher the contribution of hn
to the sum 7 estimating ĥ. Hence, estimation of the hidden
vector ĥ resembles associative recall, which is characteristic
of intelligence. The conditional average represents a general
non-parametric regression [6].
During the learning phase of operation an intelligent locator
of AE sources accepts AE signals and source coordinates
and stores prototype data vectors, while during application
it accepts only AE signals and estimates the corresponding
source position. Each of these phases can be performed in a
separate unit which can be interpreted as a layer of a sensory-
neural network.
In order to ensure acceptable properties of the locator,
the smoothing parameter σ must be properly chosen[2]. The
purpose of δ function smoothing is to estimate the probability
density function between the prototype data points. A unique
method for optimal specification of the smoothing parameter
is as yet unknown. In this case, it is numerically simpler to
specify σ by the half distance to the closest neighbor point:
σn = 0.5 min
‖gi − gn‖ , for all i 6= n . (8)
Signal pre-processing
The intelligent locator comprised a sensor antenna, signal
pre-processing unit and source locating unit, as shown in
Fig. 1. The first unit calculates the time delay ∆t from
AE signals y1(t) and y2(t), while the second unit estimates
the source position ẑ from the time delay ∆t. AE signals
y1(t) and y2(t) are detected by sensors and filtered using a
Butterworth bandpass filter. Without the bandpass filter, time
delays cannot be easily mapped to source positions on the
sample band, and therefore the applicability of this method
depends on the proper choice of bandpass filter function H(f).
We found on dispersive specimens that information in the
continuous AE signal about source position is located in a
narrow frequency band. A wave packet with approximately
constant wave velocity along the specimen must be extracted
by this filter. The filter function H(f) is determined during
training procedure of the locator.
PSfrag replacements
y1(t)
y2(t)
y1(t)
y2(t)
Ry1y2 ∆tCross-
correlator
detector
Locator ẑSensor
Sensor
Bandpass
filter
Test specimen
#2 H(f)
Signal pre-processing unit Source location
Fig. 1. AE signal processing by the intelligent locator
Two conventional methods for time delay estimation be-
tween two signals are known: threshold function and cross-
correlation function. Estimation of time delay by the threshold
function is simple, but only applicable in the case of discrete
AE. More general, but also more demanding, is time delay
estimation from the cross-correlation function of AE signals
[11]. The cross-correlation function:
Ry1y2(τ) =
y1(t) y2(t+ τ) , (9)
generally exhibits a peak when parameter τ corresponds to
the time delay ∆t between signals y1(t) and y2(t). The time
delay is thus determined from the position of the peak of the
cross-correlation function. One advantage of the application
of the cross-correlation function is that it does not depend
on the discrete or continuous character of AE signals. This
method for time delay estimation is only applicable when one
AE source is active at the time of detection. In the event of
two or more simultaneously active continuous AE sources, a
different approach should be used which will be discussed in
the Part II.
A filter function is calculated during calibration of the
intelligent locator as follows. During calibration, a set of
prototype sources is generated on the test specimen by a pen
test at a prepared coordinate net[8]. This net in most cases
has linear sections, where the prototype sources are positioned
on a straight line. In this case, we know that time delays
between signals are also linearly dependent. If we have a test
specimen with a complicated geometrical structure, then a pre-
calibration process has to be performed in which we have to
choose a geometrically simple part of the specimen and carry
out a pre-calibration procedure on this part such that time
delays between signals are linearly dependent.
For calibration we used AE signals generated by a pen
test. We obtained 12 pairs of AE signals from two sensors
concatenated with known coordinates of sources. The posi-
tions of simulated sources were uniformly distributed along a
straight line on a specimen. In such cases, time delay ∆t is
linearly related to source position z. This is of advantage for
optimal determination of bandpass filter because the reference
is a straight line. Calculation of time delays on the same set
of prototype AE signals was repeated 70 times. The bandpass
filter of ∆f = 10 kHz was shifted by 1 kHz at each repetition
from 5 to 75 kHz. Time delays were calculated at each
repetition and the distribution obtained was compared with a
straight line, as shown in Fig. 2. The frequency bandwidth was
considered optimal when the root mean square error (RMSE)
was minimal, as shown in Fig. 3(a). The optimal frequency
band for this specimen was 35-45 kHz and the velocity of
elastic waves was 1.7 km s−1. The filter was further used for
pre-processing samples of prototype as well as test sources. As
shown in Fig. 3(b), the pairs (z,∆t), estimated from filtered
signals, fit a straight line, except one outlier, which results
from experimental error.
EXPERIMENT
The intelligent AE source locator is shown schematically
in Fig. 4. It includes an automatic data-acquisition system
−1 0 1
PSfrag replacements
l [m]
5–15 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
45–55 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
45–55 kHz
55–65 kHz
Fig. 2. Distribution of time delays and their linear approximation along
the band specimen. By this procedure an optimal bandpass filter can be
determined.
controlled by computer and a network of AE sensors.
The AE sensors are piezoelectric transducers (pinducers).
The diameter of the transducer active area is 1.3 mm, And so it
can be considered a point-like sensor. The signals from sensors
are fed to a digital oscilloscope where they are digitized and
transferred to a PC. Operation of the intelligent locator is
determined by software in the PC that controls data acquisition
and estimates the position of unknown AE sources.
The locator operates in two different modes:
1) In learning or calibration mode, a set of N pen tests is
performed in which complete information about the AE
phenomenon is acquired. The operator must prepare an
orientation net the shape of which depends on the shape
of the test specimen. The recommended shape is an
equidistant net, since such position of prototype sources
yield a minimum error of the locator. ¿From source
coordinates and time delays between pre-processed AE
signals, the prototype vectors are created and stored in
the memory of the neural network as a data base.
2) In application mode, only time delays between AE
signals are provided. There are then associated in the
neural network with the estimated source coordinates.
In the case of discrete AE, the time delay can visually be
estimated from a marked jump in the burst of the AE signal, or
can be instrumentally determined using a threshold function.
Hence, in the case of continuous AE, time delays cannot
be simply estimated, although a cross-correlation function
has already been used for this purpose. In our approach, we
therefore applied a cross-correlation function. The purpose of
this experiment was to determine the accuracy of location of
continuous AE sources on a one-dimensional specimen.
Two experiments on aluminum band specimen are explained
in this article. We tested the locator on an aluminum band
specimen of dimensions 4000 × 40 × 5mm3. Reflection of
AE signals at the ends of the band specimen was reduced
by sharpening the ends. For testing we selected a test area
15−25 35−45 55−65 75−85
PSfrag replacements
∆f [kHz] - Frequency band
E ∆fopt
−1000 −500 0 500 1000
PSfrag replacements
z [mm] - Actual location
-outlier
Fig. 3. Time delays for prototype and test sources by using the bandpass
filter of frequency 35-45 kHz. a) Deviation of prototype source position from
a straight line for different filter frequency bandwidth. b) Time delays of
prototype and test sources; Legend: + prototype source, ◦ test source
in the middle of the band specimen where 23 holes were
prepared. The distance between holes was 100 mm and the
diameter of holes was 2 mm. Two AE sensors were mounted
100 mm away from the terminal holes. For the purpose of
locator training, we generated 12 prototype sources separated
by 200 mm, while all 23 holes were applied for locator testing.
In this experiment, we calibrate the locator by pen test and
examine it by continuous AE generated by air flow. The air
flow was produced by expansion of compressed air through
nozzle of 1 mm diameter. The nozzle was mounted 1 mm
above the band specimen surface.
Two experiments were performed. In the first experiment,
only one continuous AE source was active on the band
specimen, while in the second experiment two continuous AE
sources were active simultaneously on the band specimen.
Successive simultaneous location of two sources is explained
in Part II.
Signals were processed as shown in Fig. 1. The first step
in processing was calculation of cross-correlation function
of AE signals. The corresponding signal was sent through a
bandpass Butterworth filter of bandpass from 35 to 45 kHz.
Determination of this filter is explained earlier in this article.
RESULTS
The results of locator testing are shown in Fig. 5(a). The
absolute location error for each test source is shown in
Fig. 5(b). Location error in the experiment ranges from 1.3 mm
to 60 mm with average value εa = 20mm (ignoring the
outlier). If we describe the error with respect to the distance
between sensors (2.4 m), the relative value is less than 1%.
Increasing the number of prototype sources can reduce the
error. Despite the complexity of continuous AE signals, the
location problem was solved satisfactorily with respect to The
accuracy required in non-destructive testing. Results also show
that a standard calibration procedure with discrete AE signals
generated by pen test can be used for locator training.
PSfrag replacements
Sensors
Operator
Analog
Signals
#2 Digital
oscilloscope
Parameter set
Computer
Calibration by simulated AE sources
Fig. 4. Experimental setup of intelligent locator
−1000 −500 0 500 1000
−1000
PSfrag replacements
x [mm] - Actual location
-outlier
−1000 −500 0 500 1000
PSfrag replacements
x [mm] - Actual location
-outlier
Fig. 5. Result of continuous AE source location on the band. a) Estimated
versus actual location of test sources; Legend: + prototype source, ◦ test source.
b) Absolute location error; εa - average error.
DISCUSSION AND CONCLUSION
Estimation of source coordinates by the conditional average
is subject to systematic error caused by smoothing of the
delta function [5]. This error can be reduced by increasing
the number of prototype sources. Since it is not always
possible to increase the number of prototype sources due to
the complexity of experiments, a compromise must be found
by trial and error.
Experimental error is acceptable, so we decided to make
additional tests, as will be discussed in Part II.
This study shows that a conventional AE locator operating
on the triangulation method can be successfully replaced by an
intelligent locator that learns from examples. The results show
that the intelligent locator can locate sources with acceptable
accuracy in cases of: (1) discrete AE on band and plate, (2)
continuous AE on band, (3) discrete AE on plate with hole
(ring), (4) discrete AE generated by specimen rupture during
the tensile test, and (5) discrete AE on pressure vessel. Is has
been also shown that the locator can perform zonal locating[7].
Comparing mean errors of all experiments and the distances
between prototype sources, we find that the average error
is always less than 30% of the distance between prototype
sources, while the maximal error is always less than 50% of
the distance between prototype sources. The accuracy of the
locator can be controlled by the number of prototype sources
excited during training. The experimental error of the locator is
a consequence of wave dispersion on a specimen that operates
as a waveguide, reflections from boundaries, and attenuation.
We found for dispersive waves that an optimal wave packet
must be found which has approximately constant velocity
along the test specimen. Estimation of time delay between AE
signals by the cross-correlation function is only applicable for
one active AE source. If there are several simultaneously active
AE sources, then blind source separation should be used, as
will be shown in Part II.
REFERENCES
[1] Chan, Y. T. Ho, K. C. 1994 , A simple and efficient estimator for hy-
perbolic location, IEEE Transactions on Signal Processing 42(8), 1905–
1915.
[2] Cherkassky, V. Mulier, F. 1998 , Leraning from Data: Concepts, Theory,
and Methods, John Wiley & Sons inc., New York.
[3] Friedlander, B. 1987 , A passive localization algorithm and its accuracy
analysis, IEEE Journal of Oceanic Engineering OE-12(1), 234–245.
[4] Grabec, I. Antolovič, B. 1994 , Intelligent locator of AE sources, in
T. Kishi, Y. Mori M. Enoki, eds, The 12th International Acoustic Emission
Symposium, Vol. 7 of Progress in Acoustic Emission, The Japanese
Society for Non-Destructive Inspection, Tokyo, Japan, pp. 565–570.
[5] Grabec, I. Sachse, W. 1991 , ‘Automatic modeling of physical phenomena:
Application to ultrasonic data’, J. Appl. Phys. 69(9), 6233–6244.
[6] Grabec, I. Sachse, W. 1997 , Synergetics of Measurement, Prediction and
Control, Springer-Verlag, Berlin.
[7] Kosel, T. Grabec, I. 1998 , Intelligent locator of discrete and continuous
acoustic emission sources, in J. Grum, ed., Application of Contemporary
Non-destructive Testing in Engineering, The 5th International Conference
of Slovenian Society for Nondestructive Testing, Slovenian Society for
Nondestructive Testing, Ljubljana, Slovenia, pp. 39–54.
[8] McIntire, P. Miller, R. K., eds 1987 , Acoustic Emission Testing, Vol. 5
of Nondestructive Testing Handbook, 2 edn, American Society for Non-
destructive Testing, Philadelphia, USA.
[9] Specht, D. F. 1991 , A general regression neural network, IEEE Trans.
on Neural Networks 2(6), 568–576.
[10] Tobias, A. 1976 , Acoustic emission source location in two dimensions
by an array of three sensors, Non-Destructive Testing 9(2), 9–12.
[11] Ziola, S. M. Gorman, M. R. 1991 , Source location in thin plates using
cross-correlation, J. Acoust. Soc. Am. 90(5), 2551–2556.
	References

  The intelligent acoustic emission locator is described in Part I, while Part
II discusses blind source separation, time delay estimation and location of two
simultaneously active continuous acoustic emission sources.
  The location of acoustic emission on complicated aircraft frame structures is
a difficult problem of non-destructive testing. This article describes an
intelligent acoustic emission source locator. The intelligent locator comprises
a sensor antenna and a general regression neural network, which solves the
location problem based on learning from examples. Locator performance was
tested on different test specimens. Tests have shown that the accuracy of
location depends on sound velocity and attenuation in the specimen, the
dimensions of the tested area, and the properties of stored data. The location
accuracy achieved by the intelligent locator is comparable to that obtained by
the conventional triangulation method, while the applicability of the
intelligent locator is more general since analysis of sonic ray paths is
avoided. This is a promising method for non-destructive testing of aircraft
frame structures by the acoustic emission method.

Intelligent location of simultaneously active acoustic
emission sources:
Part I
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— The intelligent acoustic emission locator is described
in Part I, while Part II discusses blind source separation,
time delay estimation and location of two simultaneously active
continuous acoustic emission sources.
The location of acoustic emission on complicated aircraft frame
structures is a difficult problem of non-destructive testing. This
article describes an intelligent acoustic emission source locator.
The intelligent locator comprises a sensor antenna and a general
regression neural network, which solves the location problem
based on learning from examples. Locator performance was
tested on different test specimens. Tests have shown that the
accuracy of location depends on sound velocity and attenuation
in the specimen, the dimensions of the tested area, and the
properties of stored data. The location accuracy achieved by
the intelligent locator is comparable to that obtained by the
conventional triangulation method, while the applicability of the
intelligent locator is more general since analysis of sonic ray paths
is avoided. This is a promising method for non-destructive testing
of aircraft frame structures by the acoustic emission method.
INTRODUCTION
Acoustic emission (AE) concerns non-destructive testing
methods and is used to locate and characterize developing
cracks and defects in material. In non-destructive testing of
aviation frame structures, acoustic emission is a well accepted
method [8]. The location problem is usually solved by various
triangulation techniques based on the analysis of ultrasonic ray
trajectories [10], [1], [3]. Solving and programming the related
equation is rather cumbersome and cannot be simply per-
formed if the structure of the tested specimen is geometrically
complicated. Acoustic emission testing of aircraft structures
is a challenging and difficult problem. The structures involve
bolts, fasteners and plates, all of which move relative to one
another due to differential structural loading during flight. The
complex geometry of the airframe results in multiple mode
conversions of AE source signals, compounding the difficulty
of relating the source event to the detected signal.
In order to avoid difficulties with equation solving and
programming of the triangulation procedure, several empirical
approaches based on learning from examples have already
been proposed [5]. We developed an intelligent locator capable
of learning from examples which we therefore called an
intelligent locator. The purpose of developing the intelligent
Manuscript generated: January 31, 2007
locator is to replace information obtained from the analysis
of sonic ray trajectories by information obtained directly from
simulated AE events on the specimen under test. In this way,
the calibration procedure, which has to be performed anyway,
could be generalized to the training of the intelligent locator.
The development of such an intelligent locator has been
described elsewhere [4]. In the locator developed a general
regression neural network (GRNN) is employed [9], which
acquires data about the detected AE signals and parameters
of their sources during learning. The GRNN uses these data
in testing when estimating the unknown source position from
detected AE signals. For this purpose, associative GRNN
operation is utilized. The basis of such operation is statistical
estimation determined by the conditional average [6]. Conse-
quently, the accuracy of the intelligent locator also depends on
the learning procedure, and must be examined before testing.
This article describes the results obtained by testing the
intelligent locator on experimental continuous AE sources. The
purpose of this study was to test and examine the advantages
of the intelligent locator compared to a conventional locator.
as described in Part I. In Part II an experiment will be
explained in which an intelligent locator was used to locate
two simultaneously active continuous AE sources generated
by leakage air flow. Location of more than one source at the
same time on the test specimen is a new approach in acoustic
emission testing, and is a very promising method for aircraft
and airspace structural testing.
When preparing the experiments, we focused on locating
evolving defects in stressed materials and constructions, and
leakage of vessels. We therefore performed location exper-
iments on four different specimens with three different AE
sources. The specimens comprised bands, plates, rings, and
vessels, while the AE sources were simulated by rupture of a
pencil lead (pen test), material deformation during tensile test,
and leakage air flow through a small hole in a sample. The
positions of AE sources used in testing were well specified.
Actual positions were compared with estimated ones, and
the discrepancy was used to describe the inaccuracy of the
locator. In this article, only the experiment with leakage air
flow through a small hole in a sample is explained. In Part I,
location of one continuous AE source is explained. This Part
is intended for better understanding of Part II and comparison
of results. In Part II, a new approach to the location of two
http://arxiv.org/abs/0704.0047v1
simultaneously active continuous AE sources is explained.
Below, the article first explains the theoretical background
for application of the conditional average to the location
problem, then describes auxiliary AE signal processing, and
finally demonstrates performance of the experimental intelli-
gent locator.
THEORETICAL BACKGROUND
In this section we describe a non-parametric approach to
empirical modeling of AE phenomena and solving the location
problem. This modeling stems from a description of physical
laws in terms of probability distributions. Since it has been
explained in detail elsewhere, we present here just its basic
concepts [6], [5].
The object of empirical modeling is the relationship between
variables which are simultaneously measured by a set of
sensors. In our example the variables are source coordinates
and AE signal characteristics. Let them be represented by a
vector of M components: x = (ξ1, . . . , ξM ). In the empirical
description of an AE phenomenon we repeat the observation N
times to create a database of prototype vectors {x1, . . . ,xN}.
Instead of formulating a relation between the components of x
we instead treat this vector as a random variable and express
the joint probability density function f by the estimator
f(x) =
δ(x− xn) . (1)
Here δ denotes Dirac’s delta function. For the purposes of
modelling, we must also estimate the probability density in
the space between the prototype points. This is achieved by
expressing the singular delta function in Eqs. 1 by a smooth
function, such as for example the Gaussian
wn(x− xn, σ) = exp
−‖x− xn‖
, n = 1, . . . , N .
in which σ denotes the smoothing parameter.
The data vectors determine an empirical model of the
probability density function. Their acquisition corresponds to
the learning phase of the empirical modeling. Let us further
assume that observation of AE phenomenon provides only
partial information that is given by a truncated vector
g = (ξ1, . . . , ξS ; ∅) , (3)
in which ∅ denotes missing components. The problem is
to estimate the complementary vector of missing or hidden
components:
h = (∅; ξS+1, . . . , ξM ); (4)
such that the complete data vector is determined by concate-
nation
x = g ⊕ h = (ξ1, . . . , ξS , ξS+1, . . . , ξM ) . (5)
A statistically optimal solution to this problem is determined
by the conditional average estimator, which is expressed by a
superposition of terms [6]
Bn(g)hn, where (6)
Bn(g) =
w(g − gn, σ)
w(g − gk, σ)
. (7)
The basis functions Bn(g) represent a measure of similarity
between the truncated vector g given by a particular ob-
servation and truncated vectors from the database gn. The
higher the value of Bn(g) the higher the contribution of hn
to the sum 7 estimating ĥ. Hence, estimation of the hidden
vector ĥ resembles associative recall, which is characteristic
of intelligence. The conditional average represents a general
non-parametric regression [6].
During the learning phase of operation an intelligent locator
of AE sources accepts AE signals and source coordinates
and stores prototype data vectors, while during application
it accepts only AE signals and estimates the corresponding
source position. Each of these phases can be performed in a
separate unit which can be interpreted as a layer of a sensory-
neural network.
In order to ensure acceptable properties of the locator,
the smoothing parameter σ must be properly chosen[2]. The
purpose of δ function smoothing is to estimate the probability
density function between the prototype data points. A unique
method for optimal specification of the smoothing parameter
is as yet unknown. In this case, it is numerically simpler to
specify σ by the half distance to the closest neighbor point:
σn = 0.5 min
‖gi − gn‖ , for all i 6= n . (8)
Signal pre-processing
The intelligent locator comprised a sensor antenna, signal
pre-processing unit and source locating unit, as shown in
Fig. 1. The first unit calculates the time delay ∆t from
AE signals y1(t) and y2(t), while the second unit estimates
the source position ẑ from the time delay ∆t. AE signals
y1(t) and y2(t) are detected by sensors and filtered using a
Butterworth bandpass filter. Without the bandpass filter, time
delays cannot be easily mapped to source positions on the
sample band, and therefore the applicability of this method
depends on the proper choice of bandpass filter function H(f).
We found on dispersive specimens that information in the
continuous AE signal about source position is located in a
narrow frequency band. A wave packet with approximately
constant wave velocity along the specimen must be extracted
by this filter. The filter function H(f) is determined during
training procedure of the locator.
PSfrag replacements
y1(t)
y2(t)
y1(t)
y2(t)
Ry1y2 ∆tCross-
correlator
detector
Locator ẑSensor
Sensor
Bandpass
filter
Test specimen
#2 H(f)
Signal pre-processing unit Source location
Fig. 1. AE signal processing by the intelligent locator
Two conventional methods for time delay estimation be-
tween two signals are known: threshold function and cross-
correlation function. Estimation of time delay by the threshold
function is simple, but only applicable in the case of discrete
AE. More general, but also more demanding, is time delay
estimation from the cross-correlation function of AE signals
[11]. The cross-correlation function:
Ry1y2(τ) =
y1(t) y2(t+ τ) , (9)
generally exhibits a peak when parameter τ corresponds to
the time delay ∆t between signals y1(t) and y2(t). The time
delay is thus determined from the position of the peak of the
cross-correlation function. One advantage of the application
of the cross-correlation function is that it does not depend
on the discrete or continuous character of AE signals. This
method for time delay estimation is only applicable when one
AE source is active at the time of detection. In the event of
two or more simultaneously active continuous AE sources, a
different approach should be used which will be discussed in
the Part II.
A filter function is calculated during calibration of the
intelligent locator as follows. During calibration, a set of
prototype sources is generated on the test specimen by a pen
test at a prepared coordinate net[8]. This net in most cases
has linear sections, where the prototype sources are positioned
on a straight line. In this case, we know that time delays
between signals are also linearly dependent. If we have a test
specimen with a complicated geometrical structure, then a pre-
calibration process has to be performed in which we have to
choose a geometrically simple part of the specimen and carry
out a pre-calibration procedure on this part such that time
delays between signals are linearly dependent.
For calibration we used AE signals generated by a pen
test. We obtained 12 pairs of AE signals from two sensors
concatenated with known coordinates of sources. The posi-
tions of simulated sources were uniformly distributed along a
straight line on a specimen. In such cases, time delay ∆t is
linearly related to source position z. This is of advantage for
optimal determination of bandpass filter because the reference
is a straight line. Calculation of time delays on the same set
of prototype AE signals was repeated 70 times. The bandpass
filter of ∆f = 10 kHz was shifted by 1 kHz at each repetition
from 5 to 75 kHz. Time delays were calculated at each
repetition and the distribution obtained was compared with a
straight line, as shown in Fig. 2. The frequency bandwidth was
considered optimal when the root mean square error (RMSE)
was minimal, as shown in Fig. 3(a). The optimal frequency
band for this specimen was 35-45 kHz and the velocity of
elastic waves was 1.7 km s−1. The filter was further used for
pre-processing samples of prototype as well as test sources. As
shown in Fig. 3(b), the pairs (z,∆t), estimated from filtered
signals, fit a straight line, except one outlier, which results
from experimental error.
EXPERIMENT
The intelligent AE source locator is shown schematically
in Fig. 4. It includes an automatic data-acquisition system
−1 0 1
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l [m]
5–15 kHz
−1 0 1
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l [m]
∆t [ms]
5–15 kHz
15–25 kHz
−1 0 1
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l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
45–55 kHz
−1 0 1
PSfrag replacements
l [m]
∆t [ms]
5–15 kHz
15–25 kHz
25–35 kHz
35–45 kHz
45–55 kHz
55–65 kHz
Fig. 2. Distribution of time delays and their linear approximation along
the band specimen. By this procedure an optimal bandpass filter can be
determined.
controlled by computer and a network of AE sensors.
The AE sensors are piezoelectric transducers (pinducers).
The diameter of the transducer active area is 1.3 mm, And so it
can be considered a point-like sensor. The signals from sensors
are fed to a digital oscilloscope where they are digitized and
transferred to a PC. Operation of the intelligent locator is
determined by software in the PC that controls data acquisition
and estimates the position of unknown AE sources.
The locator operates in two different modes:
1) In learning or calibration mode, a set of N pen tests is
performed in which complete information about the AE
phenomenon is acquired. The operator must prepare an
orientation net the shape of which depends on the shape
of the test specimen. The recommended shape is an
equidistant net, since such position of prototype sources
yield a minimum error of the locator. ¿From source
coordinates and time delays between pre-processed AE
signals, the prototype vectors are created and stored in
the memory of the neural network as a data base.
2) In application mode, only time delays between AE
signals are provided. There are then associated in the
neural network with the estimated source coordinates.
In the case of discrete AE, the time delay can visually be
estimated from a marked jump in the burst of the AE signal, or
can be instrumentally determined using a threshold function.
Hence, in the case of continuous AE, time delays cannot
be simply estimated, although a cross-correlation function
has already been used for this purpose. In our approach, we
therefore applied a cross-correlation function. The purpose of
this experiment was to determine the accuracy of location of
continuous AE sources on a one-dimensional specimen.
Two experiments on aluminum band specimen are explained
in this article. We tested the locator on an aluminum band
specimen of dimensions 4000 × 40 × 5mm3. Reflection of
AE signals at the ends of the band specimen was reduced
by sharpening the ends. For testing we selected a test area
15−25 35−45 55−65 75−85
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∆f [kHz] - Frequency band
E ∆fopt
−1000 −500 0 500 1000
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z [mm] - Actual location
-outlier
Fig. 3. Time delays for prototype and test sources by using the bandpass
filter of frequency 35-45 kHz. a) Deviation of prototype source position from
a straight line for different filter frequency bandwidth. b) Time delays of
prototype and test sources; Legend: + prototype source, ◦ test source
in the middle of the band specimen where 23 holes were
prepared. The distance between holes was 100 mm and the
diameter of holes was 2 mm. Two AE sensors were mounted
100 mm away from the terminal holes. For the purpose of
locator training, we generated 12 prototype sources separated
by 200 mm, while all 23 holes were applied for locator testing.
In this experiment, we calibrate the locator by pen test and
examine it by continuous AE generated by air flow. The air
flow was produced by expansion of compressed air through
nozzle of 1 mm diameter. The nozzle was mounted 1 mm
above the band specimen surface.
Two experiments were performed. In the first experiment,
only one continuous AE source was active on the band
specimen, while in the second experiment two continuous AE
sources were active simultaneously on the band specimen.
Successive simultaneous location of two sources is explained
in Part II.
Signals were processed as shown in Fig. 1. The first step
in processing was calculation of cross-correlation function
of AE signals. The corresponding signal was sent through a
bandpass Butterworth filter of bandpass from 35 to 45 kHz.
Determination of this filter is explained earlier in this article.
RESULTS
The results of locator testing are shown in Fig. 5(a). The
absolute location error for each test source is shown in
Fig. 5(b). Location error in the experiment ranges from 1.3 mm
to 60 mm with average value εa = 20mm (ignoring the
outlier). If we describe the error with respect to the distance
between sensors (2.4 m), the relative value is less than 1%.
Increasing the number of prototype sources can reduce the
error. Despite the complexity of continuous AE signals, the
location problem was solved satisfactorily with respect to The
accuracy required in non-destructive testing. Results also show
that a standard calibration procedure with discrete AE signals
generated by pen test can be used for locator training.
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Sensors
Operator
Analog
Signals
#2 Digital
oscilloscope
Parameter set
Computer
Calibration by simulated AE sources
Fig. 4. Experimental setup of intelligent locator
−1000 −500 0 500 1000
−1000
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x [mm] - Actual location
-outlier
−1000 −500 0 500 1000
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x [mm] - Actual location
-outlier
Fig. 5. Result of continuous AE source location on the band. a) Estimated
versus actual location of test sources; Legend: + prototype source, ◦ test source.
b) Absolute location error; εa - average error.
DISCUSSION AND CONCLUSION
Estimation of source coordinates by the conditional average
is subject to systematic error caused by smoothing of the
delta function [5]. This error can be reduced by increasing
the number of prototype sources. Since it is not always
possible to increase the number of prototype sources due to
the complexity of experiments, a compromise must be found
by trial and error.
Experimental error is acceptable, so we decided to make
additional tests, as will be discussed in Part II.
This study shows that a conventional AE locator operating
on the triangulation method can be successfully replaced by an
intelligent locator that learns from examples. The results show
that the intelligent locator can locate sources with acceptable
accuracy in cases of: (1) discrete AE on band and plate, (2)
continuous AE on band, (3) discrete AE on plate with hole
(ring), (4) discrete AE generated by specimen rupture during
the tensile test, and (5) discrete AE on pressure vessel. Is has
been also shown that the locator can perform zonal locating[7].
Comparing mean errors of all experiments and the distances
between prototype sources, we find that the average error
is always less than 30% of the distance between prototype
sources, while the maximal error is always less than 50% of
the distance between prototype sources. The accuracy of the
locator can be controlled by the number of prototype sources
excited during training. The experimental error of the locator is
a consequence of wave dispersion on a specimen that operates
as a waveguide, reflections from boundaries, and attenuation.
We found for dispersive waves that an optimal wave packet
must be found which has approximately constant velocity
along the test specimen. Estimation of time delay between AE
signals by the cross-correlation function is only applicable for
one active AE source. If there are several simultaneously active
AE sources, then blind source separation should be used, as
will be shown in Part II.
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