operation immediately upon specimen failure, while the AE
acquisition system will continue to work for about 5 s to ensure
the comprehensiveness of the AE signals. All data should be
promptly saved and processed. The loading equipment used
is the electro-hydraulic servo material testing machine, as
shown in Figure 1. Additionally, the AE monitoring system (a
multichannel acoustic emission signal acquisition system with
integrated acoustic emission analysis software), as depicted
in Figure 2, is utilized for real-time collection and preliminary
processing of the concrete AE signals throughout the entire
uniaxial tension process.
The arrangement of the complete AE signal acquisition
system designed in this study is shown in Figure 3. Sensors
1 and 2 are placed on both sides of the middle surface of the
specimen using petroleum jelly. The sensors are connected to
an amplifier, which amplifies the AE signals before transmitting
them to the AE acquisition system. Finally, all the AE feature
parameters are read by the computer.
2.3. System Parameter Settings
Reasonable parameter settings are conducive to ensuring the
validity of the AE signals collected during this uniaxial tensile
test. Therefore, based on the characteristics of this experiment
and the features of the AE monitoring and acquisition system,
and after repeated adjustments of the relevant parameters, the
final parameter values shown in Table 1 were determined for
this study.
Figure 1. Loading device.
Figure 2. Acoustic emission (AE) monitoring system.
TA B L E 1
Parameter values of acoustic emission acquisition
system
Parameters Set point
Threshold (dB) 35
Preamplifier gain (dB) 40
Bandpass filter (kHz) 1–3000
Sampling frequency (MSPS) 5
Peak definition time (µs) 50
Hit definition time (µs) 100
Hit lockout time (µs) 300
Sensor 1 Sensor 2
Preamplifier
Data processing
and monitoring
Figure 3. Layout of AE signal acquisition system.
M AY 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 43

3. AE Signal Analysis Method
This section describes in detail the acoustic emission analysis
methodology and the k-means clustering algorithm used in
this study.
3.1. Selection of AE Characteristic Parameters
This study, considering the inherent properties of concrete,
selected 14 AE feature parameters to analyze the damage
signals of concrete under tensile stress. These parameters
include ring count, energy, absolute energy, signal strength,
amplitude, average signal level (ASL), root-mean-square (RMS)
voltage value, rise time, duration, initial frequency, average
frequency, inverse frequency, center frequency, and peak fre-
quency. The AE feature parameters and their corresponding
meanings are shown in Table 2.
3.2. K-Means Clustering Analysis Classification Method
Cluster analysis automatically divides large amounts of data
into multiple categories based on their internal similarity. It
does so without relying on any specific classification criteria,
instead organizing the data based on inherent similarities [24].
The k-means clustering algorithm is designed to partition large
data samples according to their similarities. It offers advan-
tages such as good clustering results and fast convergence
[25], providing a new approach for finding the best method
to classify AE signals, as expressed in the following formulaic
representation.
First, the optimal number of clusters, K, for cluster analysis
is determined using the Davies-Bouldin (DB) criterion [23],
hereinafter referred to as the DB coefficient. The formulaic
definition of the DB coefficient is as follows: ​ ​
(1)​ DB =​ 1
K ​ ​
∑
i=1​
K ​ ​
max​
i≠j​ ​ ​ {​​
di​​​ +​ dj​​​ _​
D​ij​​ ​ }​​​
where​​
di​​​ ​ and ​​ ​ j​​​ represent the average intra-cluster distances for
cluster ​ ​ and cluster ​ ​ respectively, and ​ ​
Dij​​​ ​ indicates the average inter-cluster distance between
cluster ​ ​ and cluster ​ ​ .
Therefore, when the DB coefficient reaches its minimum
value, it indicates that the average intra-cluster distance is
minimized while the average inter-cluster distance is max-
imized, suggesting that the clustering result is optimal. The
corresponding number of clusters, ​ ​ is then regarded as the
optimal number of clusters.
Let the ​ ​ cluster centers be denoted as ​​ ​ 1​​​ ​​ ​ 2​​​ ...,​​ ​ k​​​ The
number of samples contained in each cluster is ​​ ​ 1​​​ ​​ ​ 2​​​ ...,​​ ​ k​​​ ,
and the clustering content in each cluster is ​​ ​ 1​​​ ​​ ​ 2​​​ ...,​​ ​ k​​​ Using
squared error ​ ​ as the objective function, the optimal clustering
result is obtained when ​ ​ is minimized. By calculating the sta-
tionary points of ​ ​ to minimize it, the clustering information ​​ ​ j​​​
for each cluster can be determined as follows: ​ ​
(2)​ J(​u​1​​, ​ ​ u​2​​, …,u​k​​)​ ​ =​ 1
2 ​ ​
∑
j=1​i​=1​
K ​ ​ ∑
N​j​​ ​ ​ ​ (​​ ​ x​i​​ − ​ u​i​​​)​​​​2​​​​ ​ ​
(3)​ ​ ∂ j
∂ ​ u​j​​​
=− 2​∑(​x​
i=1 ​ ​
N​j​​ ​ ​
i​​ − ​ u​i​​)​​​ ​ ​ ​
(4)​ uj​​​ =​ 1
N ​ ​
∑
i=1 ​ ​
N​j​​ ​ ​
x​i​​​​
According to the results of the two-dimensional clustering
of the 14 AE feature parameters in this study, it can be deter-
mined that the number of clustering combinations obtained is
105. To select the optimal clustering combination among them,
this study employs the coefficient of variation [26] to evaluate
the horizontal effectiveness of these cluster combinations, as
illustrated in Equation 5:
ME
|
AXIALTENSION
TA B L E 2
Acoustic emission (AE) characteristic parameters and their meanings
AE characterization parameters Meaning
Ring count Reflects the strength of the AE signal and can evaluate AE activity
Absolute energy, signal strength, energy Reflects the energy of the AE signal
Amplitude Reflects the strength of the AE signal and can help identify
different wave source types
ASL, RMS Evaluates the activity of AE signals and helps identify
the background noise level
Rise time Evaluates the activity of AE signals and helps identify
the background noise level
Duration Distinguishes between different types of AE wave source signals
Initial frequency, average frequency,
inverse frequency, center frequency Reflects the frequency of the AE signal
Peak frequency Distinguishes between different AE sources
44
M AT E R I A L S E V A L U AT I O N • M AY 2 0 2 5