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Y. Luo et al.
the AF-value is on the contrary. In the initial loading stage, tensile cracks are the main
fracture mode of the specimen. With the increase of stress level, there is a transition
from tensile to shear fracture, so that large macroscopic shear cracks occur until
the late plastic stage. After entering the peak stress, because the carbon block still
has a certain bearing capacity, the interaction of macroscopic cracks and the friction
between aggregate particles in the block lead to more tensile fractures. As shown
in Fig. 50.3b, the distribution characteristics of the cathode carbon block with high
AF-value and low RA-value are relatively significant under uniaxial compression
loads, indicating that the fracture mode is mainly tensile fracture.
50.3.2 Cluster Analysis of AE Parameters
50.3.2.1 The k-Means Clustering Algorithm
As mentioned above, AE parameters such as rise time, ringing counts, duration,
energy, amplitude and peak frequency can all identify the crack evolution process of
cathode carbon block during the fracture process to a certain degree. However, it is
not clear which parameter of AE signal is sufficiently representative. Therefore, in
order to deeply understand the characteristics of fracture signals of cathode carbon
blocks in the whole process of failure, k-means clustering method is adopted to
conduct multivariate analysis of AE signals, so as to identify the crack types of AE
signals [16, 17].
Commonly, AE counts and hits reflect the number of cracks and the degree of
damage, amplitude and energy are used to describe the strength of the AE signals
which is associated with the scale of cracks, peak frequency has close relationship
with crack type, duration and rise time can be used for waveform identification
[18]. Thus, according to the relationship between AE characteristic parameters and
fracture mechanism, the rise time, duration time, ringing counts, amplitude and peak
frequency were selected as sample variables. Before clustering, these parameters
were normalized to the range of [0,1] to construct the pattern vector so as to eliminate
the influence of physical dimension on classification, its principle is to convert data
into the interval of [0,1]. For any variable, row i and column j can be expressed as
x
i j =
x i j − x j min
x j max − x j min
(50.1)
where x
i j and x i j are the standardization and original parameters of AE signals,x j max
and x j min
are the maximum and minimum values of column j, respectively.
The k-means algorithm randomly selects k coordinate points from the standardized
data as the initial cluster coordinates, calculates the distance from each AE signal
point to these cluster centers according to the Euclidean distance formula (refer to
50.2), and classifies them into the class corresponding to the nearest cluster center
Y. Luo et al.
the AF-value is on the contrary. In the initial loading stage, tensile cracks are the main
fracture mode of the specimen. With the increase of stress level, there is a transition
from tensile to shear fracture, so that large macroscopic shear cracks occur until
the late plastic stage. After entering the peak stress, because the carbon block still
has a certain bearing capacity, the interaction of macroscopic cracks and the friction
between aggregate particles in the block lead to more tensile fractures. As shown
in Fig. 50.3b, the distribution characteristics of the cathode carbon block with high
AF-value and low RA-value are relatively significant under uniaxial compression
loads, indicating that the fracture mode is mainly tensile fracture.
50.3.2 Cluster Analysis of AE Parameters
50.3.2.1 The k-Means Clustering Algorithm
As mentioned above, AE parameters such as rise time, ringing counts, duration,
energy, amplitude and peak frequency can all identify the crack evolution process of
cathode carbon block during the fracture process to a certain degree. However, it is
not clear which parameter of AE signal is sufficiently representative. Therefore, in
order to deeply understand the characteristics of fracture signals of cathode carbon
blocks in the whole process of failure, k-means clustering method is adopted to
conduct multivariate analysis of AE signals, so as to identify the crack types of AE
signals [16, 17].
Commonly, AE counts and hits reflect the number of cracks and the degree of
damage, amplitude and energy are used to describe the strength of the AE signals
which is associated with the scale of cracks, peak frequency has close relationship
with crack type, duration and rise time can be used for waveform identification
[18]. Thus, according to the relationship between AE characteristic parameters and
fracture mechanism, the rise time, duration time, ringing counts, amplitude and peak
frequency were selected as sample variables. Before clustering, these parameters
were normalized to the range of [0,1] to construct the pattern vector so as to eliminate
the influence of physical dimension on classification, its principle is to convert data
into the interval of [0,1]. For any variable, row i and column j can be expressed as
x
i j =
x i j − x j min
x j max − x j min
(50.1)
where x
i j and x i j are the standardization and original parameters of AE signals,x j max
and x j min
are the maximum and minimum values of column j, respectively.
The k-means algorithm randomly selects k coordinate points from the standardized
data as the initial cluster coordinates, calculates the distance from each AE signal
point to these cluster centers according to the Euclidean distance formula (refer to
50.2), and classifies them into the class corresponding to the nearest cluster center