Neural Network Processing of Audible Sound Signal Parameters for Sensor Monitoring

1
Advanced signal processing used in the monitoring
systems of machining processes based on acoustic
emission sensors
E.M. Rubio1, R. Teti2 and I.L. Baciu2 1Dept. of
Manufacturing Engineering, National Distance
University of Spain 2Dept of Materials and
Production Engineering, University of Naples
Federico II
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INDEX INTRODUCTION SIGNALS
PROCESSING Continuous Transforms Fourier
Transform Gabor transform Continuous
Wavelet Transform Discrete Transforms Statist
ical analysis Amplitudes distribution method
Entropic distance method MAIN WORKS
SUMMARY
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INTRODUCTION
The acoustic emission (AE) can be described as a
set of elastic pressure waves generated by the
rapid release of energy stored within a
material This energy disipation is, basically,
due to Dislocations Phase transformations Fricti
on processes Formation and growth of cracks One
feature of the AE waves is that they do not
travel through the air but only through a
material
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INTRODUCTION
The AE signals can be classified into two types
Continuous Burst The continuous-type AE
signals
are associated with the plastic
deformation in ductile materials The burst-type
ones
are observed during
cracks growth within a material, the impact
against it or its breakage
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INTRODUCTION
During the cutting processes the main sources of
AE that appear are 1) Primary shear zone 2)
Secondary shear zone and craterization by
friction 3) Third shear zone and wear flank face
by friction 4) Crack grown by tool tip-workpiece
contact 5) Chip plastic deformation 6) Chip-tool
collision.
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INTRODUCTION
Cutting processes are not easy to management due
to the great account of effects involved in
them However, AE signals provide the
possibility of Identifying the tool wear state

which is essential for
predicting the tool life Detecting some
malfunctions in the cutting process
chip tangling, chatter vibrations and
cutting edge breakage
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INTRODUCTION
Using adequately the AE signals, it will be
possible to develop monitoring systems for
different aspects involved
in the machining processes AE signals
usually are
extracted by measurement
chains
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SIGNAL PROCESSING

• The aim of the AE signal processing is
• Detecting and characterising the bursts that
  evidence the abrupt emissions of elastic energy
  produced inside the material
• Estimating their time localizations, oscillation
  frequencies, amplitude and phases
• Describing appropriately their overlapping
  structure

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SIGNAL PROCESSING
The extraction of such physical parameters from
an AE signal is one of the most common problems
in its processing This is due to such signals
are non-stationary and often comprise overlapping
transients, whose waveforms and arrival times are
unknown and involve variations in both time and
frequency Often, such events are partially
overlapping in the time domain or affected by
noise, that is, they are interfered with
secondary events, not significant but that affect
their structure
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SIGNAL PROCESSING
Different signal processing methods have been
develpoed to analyse AE signals and to extract
from them features that allow
testing and monitoring machining processes Some
of them are Continuous Transforms Fourier
Transform Gabor transform Continuous
Wavelet Transform Discrete Transforms Statistic
al analysis Amplitudes distribution method
Entropic distance method
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SIGNAL PROCESSING
Continuous Transforms. Fourier Transform
A physic signal usually is represented by a time
function f(t) or, alternatingly, in the
frequency domain for its Fourier Transform (FT),
F(w) where t is the time and w is the angular
frequency
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SIGNAL PROCESSING
Continuous Transforms. Fourier Transform
Both functions contain the same information about
the signal exactly, but from different and
complementary focuses This type of functions is
adequate to represent
stationary and eiwt harmonic waves Like AE
signals are essentially non-stationary, it is
possible to afirm that, in general, the FT pair
does not represent this kind of signals
correctely. However, some works have been carried
out successfully using FT for the AE signal
processing emited by tools with different wear
levels
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SIGNAL PROCESSING
Continuous Transforms. Gabor transform
Gabor Transform is a time-frequency technique
used to deal with non-stationary signals A Gabor
Transform has a short data window centered at
time. Assuming an energy-limited signal, f(t) can
be decomposed by where g(t-t) is called
window function
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SIGNAL PROCESSING
Continuous Transforms. Gabor transform
Gabor Transform implementation for the AE signal
processing is efficient when it is used to locate
and to characterise events with very
defined frequency patterns, not overlapping and
long, relatively to the window
function Against, it is completely
inappropriate to detect details of short
duration, long oscillations associated to the low
frequencies, or to characterise
similar patterns in different scales
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SIGNAL PROCESSING
Continuous Transforms. Continuous Wavelet
Transform
Continuous Wavelet Transform is an alternative to
Gabor Trasform that uses modulated window
functions, this is, with variable dimension
adjusted to the oscilation frequency
Particularly, windows with the same number of
oscillations in its domain This is achieved by
generating a complete family of elementary
functions by dilations or contractions and shifts
in the time, from a unique
modulated window
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SIGNAL PROCESSING
Continuous Transforms. Continuous Wavelet
Transform
Continuous Wavelet Transform is an alternative to
Gabor Trasform that uses modulated window
functions. In particular, with the same number of
oscillations in its domain
This is achieved by generating a complete family
of elementary functions by dilations or
contractions and shifts in the time,
from a unique modulated window where ?(t)
is the mother wavelet funtion and ?a,b(t) a
wavelet funtion, being a?0 and b the scale and
shifted parameters
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SIGNAL PROCESSING
Continuous Transforms. Continuous Wavelet
Transform
Given a limited-energy signal s(t) its Continuous
Wavelet Transform can be define by If the
mother wavelet function is real, s(t) can be
written where C? is a positive constant
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SIGNAL PROCESSING
Discrete Transforms
The implementation of the continuous transforms
is expensive from the point of numeric and
computacional view It is possible to obtain
different Discrete Transforms such as Local
Fourier series Gabor discrete transform
Wavelet one given a T-periodic signal s(t),
from its Fourier series where wk2pk/T are
the angular frequencies and s(wk) the Fourier
coefficients
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SIGNAL PROCESSING
Discrete Transforms
The local Fourier series can be written
by like a signal limited to the interval to,
toT, in the frequencies discrete net w and
multiplied for a constant Given a non-periodic
signal s(t), the idea is segment it using a
window function g(t) of width T and that is
shifted to regular intervals along all the domain
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SIGNAL PROCESSING
Discrete Transforms
Selecting the window function g(t) appropriately
and the displacement step to, next representation
will be obtained being cn,k the Fourier
coefficients of the modulated segment
s(t)g(t-nto) that contain the information in
frequency for each temporary segment The
expression represents a time-frequency discrete
transform called Local Fourier Series that can be
considered as a Gabor Discrete
Transform
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SIGNAL PROCESSING
Discrete Transforms
The design of a Wavelet Discrete Transform
version consists of defining an appropiated set
of parameters (aj bjk) Different types of
sets exist. Among them, it is possible to remark
those orthogonal wavelets bases given by With
this parameters selection the usual expression
for the wavelets
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SIGNAL PROCESSING
Discrete Transforms
Then, assuming a real mother wavelet and a
limited-energy signal s(t) the Wavelet Discrete
Transform is defined by The synthesis formula
will be for appropriate coefficients cjk
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SIGNAL PROCESSING
Statistical analysis. Amplitudes distribution
method
The Amplitudes distribution method tries to
recognise differences among signals through the
study of
the distribution of amplitudes Basically,
such distribution is obtained making a graph of
the frequency with which the different ordinates
of the
signal are given A set of parallel lines to the
axis x is traced and the number of crossings of
such lines with the signal is counted
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SIGNAL PROCESSING
Statistical analysis. Amplitudes distribution
method
If a part of the signal graph has a low slope the
value of the relative frequency in the interval
corresponding to
its ordinates will increase In this way, the
aspect of the curve will be reflected
in the aspect of the
distribution There are two aspects to consider
Range Shape
of the distribution
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SIGNAL PROCESSING
Statistical analysis. Amplitudes distribution
method
The study of the problem through of the
characterisation of textures, similar to the
study of the surfaces profiles has
proven that it is in the shape of the
distribution where the
most important aspects appear The most
comprehensive classification of the distribution
shape can be achieved by means of the central
moments of the distribution function
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SIGNAL PROCESSING
Statistical analysis. Amplitudes distribution
method
In particular, by the third and fourth central
moments called skew and kurtosis respectively and
given by where f is the function of the
probably density of the variable x and s, the
standard deviation
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SIGNAL PROCESSING
Statistical analysis. Amplitudes distribution
method
The skew measures the symmetry of the
distribution about its mean value while the
kurtosis represents a measure
of the sharpness of the peaks A positive
value of the skew generally indicates a shift of
the bulk of the distribution to the weight of the
mean, and a
negative one, a shift to the left A high
kurtosis value implies a sharp distribution peak,
this is, a concentration in a small area while a
low kurtosis value indicates
essentially flat characteristics
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SIGNAL PROCESSING
Statistical analysis. Entropic distance method
The Entropic distance method is based on
comparing the obtained signal with a pattern
signal used as reference So as to make this, the
signals are adjusted to an Auto Regressive (AR)
pattern of order p where et is a gaussian
random variable with , and the
pattern coefficients
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SIGNAL PROCESSING
Statistical analysis. Entropic distance method
All roots mi of the polynomial
satisfy Once the parameters have
been identified with the coefficients
and st, it is possible to write the function
of probability of the
sampling A sampling of reference xR of length
NR is compared with the test sampling xT of
length NT. Then, adjusting both to a
pattern of the same order p it is possible to
calculate the combined
probability as well
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SIGNAL PROCESSING
Statistical analysis. Entropic distance method
Under the hypothesis Ho Both sampling fix the
same pattern it will obtained the parameters sp
and ap and the probability Lo will be
maximum Under the hypothesis H1 Both
sampling fix different patterns it will obtained
two sets of parameters (sR, aR) and (sT, aT)
and then probability L1 will be
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SIGNAL PROCESSING
Statistical analysis. Entropic distance method
Therefore, the coefficient of verisimilitude
is Then the entropic distance is defined
as In normal conditions, d is a non negative
number and is zero only if and .
This is, if the patterns are the same Variations
in the amplitudes of the signal will modify the
value of but without modifying the
polynomial coefficient. However, variations in
the frequencies will affect the whole pattern
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MAIN WORKS
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CONCLUSIONS
The work describes some of the most diffused
advanced signal processings used in the
monitoring systems of the machining processes
based on AE sensors Particularly, it is focused
in the continuous and discrete transforms of
Fourier, Gabor and Wavelet, and in the
statistical analysis methods such as the
amplitude distribution method and the entropic
distance one Besides, some works showing the
mentioned signal processing methods have been
shown as well
34
Advanced signal processing used in the monitoring
systems of machining processes based on acoustic
emission sensors
E.M. Rubio1, R. Teti2 and I.L. Baciu2 1Dept. of
Manufacturing Engineering, National Distance
University of Spain 2Dept of Materials and
Production Engineering, University of Naples
Federico II