42 Damage Localization of Debris Cloud Hypervelocity Impact …
481
In the J-scale, the total energy E of the signal is the sum of the energy of each
sub-bands, that is
E =
2
j −1
k=0
E j,k
(42.2)
The first 10 sub-bands wavelet packet energy are calculated, and the proportion of
each frequency band are obtained, as shown in Fig. 42.6. From the results we can see
that with the increase of the initial velocity, the energy of each sub-band gradually
becomes uniform [17].
In order to describe this characteristic quantitatively, the concept of entropy, which
is commonly used in information theory, is introduced to deal with the signals.
Entropy represents the amount of information output by the source, which is a
measure of the degree of signals confusion. The more concentrated the signal distribution in each frequency band, the smaller the entropy value; otherwise, the more
uniform the signal distribution in each frequency band, the greater the entropy value.
Shannon entropy is defined as follows:
H (X ) = −
L
j=1
p j log( p j )
(42.3)
where, p j ∈ [0, 1][0, 1] is the eigenvalue of the signal; L is the number of
eigenvalues of the signal, when p j = 0, p j log( p j ) = 0.
According to the spectrum characteristics of the signals, A 0 mode lamb wave is
concentrated in the frequency band lower than 100 kHz, so after 8-layer wavelet
packet decomposition, the first 2-order sub-bands can better reflect the A 0 mode
characteristics. Five eigenvalues are obtained by summing the decomposed sub-bands
energy percentages one by one in Fig. 42.6.
p j = E i, j /E( j = 1 − 5)
(42.4)
These eigenvalues are related to the signals below 500 kHz, as the high frequency
part are also an important factor to reflect the damage characteristics, the proportion
of energy in other frequencies is summed as another eigenvalue,
p 6 = 1 −
5
j=1
p j
(42.5)
The energy entropy of the signals are calculated by substituting the six eigenvalues
into (42.3). According to the definition of entropy, when the six value is the same,
the entropy is the largest. For comparison purposes, the entropy value is normalized.
The wavelet packet energy entropy of debris cloud impact AE signal is defined as
481
In the J-scale, the total energy E of the signal is the sum of the energy of each
sub-bands, that is
E =
2
j −1
k=0
E j,k
(42.2)
The first 10 sub-bands wavelet packet energy are calculated, and the proportion of
each frequency band are obtained, as shown in Fig. 42.6. From the results we can see
that with the increase of the initial velocity, the energy of each sub-band gradually
becomes uniform [17].
In order to describe this characteristic quantitatively, the concept of entropy, which
is commonly used in information theory, is introduced to deal with the signals.
Entropy represents the amount of information output by the source, which is a
measure of the degree of signals confusion. The more concentrated the signal distribution in each frequency band, the smaller the entropy value; otherwise, the more
uniform the signal distribution in each frequency band, the greater the entropy value.
Shannon entropy is defined as follows:
H (X ) = −
L
j=1
p j log( p j )
(42.3)
where, p j ∈ [0, 1][0, 1] is the eigenvalue of the signal; L is the number of
eigenvalues of the signal, when p j = 0, p j log( p j ) = 0.
According to the spectrum characteristics of the signals, A 0 mode lamb wave is
concentrated in the frequency band lower than 100 kHz, so after 8-layer wavelet
packet decomposition, the first 2-order sub-bands can better reflect the A 0 mode
characteristics. Five eigenvalues are obtained by summing the decomposed sub-bands
energy percentages one by one in Fig. 42.6.
p j = E i, j /E( j = 1 − 5)
(42.4)
These eigenvalues are related to the signals below 500 kHz, as the high frequency
part are also an important factor to reflect the damage characteristics, the proportion
of energy in other frequencies is summed as another eigenvalue,
p 6 = 1 −
5
j=1
p j
(42.5)
The energy entropy of the signals are calculated by substituting the six eigenvalues
into (42.3). According to the definition of entropy, when the six value is the same,
the entropy is the largest. For comparison purposes, the entropy value is normalized.
The wavelet packet energy entropy of debris cloud impact AE signal is defined as