time history analysis. The second cluster has moderate inten-
sity and moderate frequency, indicating moderate damage,
with the primary phenomenon being the expansion of micro-
cracks in the concrete, matching the damage mechanism of
stage D2. The third cluster has low intensity and low frequency,
indicating severe damage, mainly due to the formation of mac-
roscopic cracks in the concrete, which aligns with the damage
mechanism of stage D3. The cumulative hit count time history
curves for the three clusters are plotted in Figure 9, provid-
ing further validation for the classification of damage levels in
concrete.
From Figure 9, it is evident that the cumulative hit count
time history curves for the three clustered results of concrete
acoustic emissions exhibit noticeable differences across the dif-
ferent damage stages. In stage D1, the AE activity represented
by the three time history curves tends to be consistent, indi-
cating a quiet period. In stage D2, the second and third types
of signals begin to show significant growth as the stress level
increases, with signals of moderate and severe damage over-
taking those of mild damage, gradually becoming dominant. In
stage D3, the AE activity of the third type of signal, representing
severe damage, increases significantly, becoming the dominant
signal in this stage.
In summary, the distribution of time history curves for the
three types of signals representing concrete damage levels after
clustering analysis shows dominance in their corresponding
damage stages. This further corroborates that the clustering
analysis results align with the AE characteristics of the three
damage stages described earlier.
4.2.3. JOINT ANALYSIS OF DAMAGE MECHANISMS
To further explore the comprehensive information on concrete
damage mechanisms hidden behind the optimal clustering
results, the study calculates the average values of AE feature
parameters corresponding to each cluster of the ring count–
center frequency combination, as summarized in Table 6.
From Table 6, it can be seen that the average values of the
AE feature parameters for the three types of AE signals have
noticeable numerical differences, confirming that the optimal
clustering combination chosen in this study effectively classi-
fies concrete axial tensile damage information. By examining
the differences in the average values of AE feature parameters,
this study explores the concrete damage mechanism informa-
tion underlying the three levels of damage severity.
In the first type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which repre-
sent signal intensity, are at relatively low levels. At the same
time, the rise time and duration, which represent the signal’s
duration, are at relatively high levels. This indicates that this
type of signal is characterized by low signal intensity and long
duration, typical of the quiet period in concrete axial tensile
damage. During this stage, the primary processes are the
expansion of existing cracks and the initiation of microcracks
in the concrete material. This can be identified as the signal
for the initiation of microcracks in concrete, consistent with
the characteristics of mild damage derived from the clustering
center analysis earlier.
In the second type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which represent
signal intensity, are at moderate levels. Additionally, the rise
time and duration, which indicate the signal’s duration, are also
at moderate levels. This suggests that this type of signal is char-
acterized by moderate signal intensity and duration. Thus, this
signal can be identified as representing the expansion of micro-
cracks in concrete, aligning with the characteristics of moderate
damage derived from the clustering center analysis earlier.
In the third type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which represent
signal intensity, are at relatively high levels. Meanwhile, the rise
time and duration, which indicate the signal’s duration, are
at relatively low levels. This suggests that this type of signal is
characterized by high signal intensity but a rapid rate of signal
decay, typical of strong excitation signals. Thus, this signal
can be identified as representing the cracking of macroscopic
cracks in concrete, consistent with the characteristics of severe
damage derived from the clustering center analysis earlier.
0
10001
5005
15001
D11
D2
D33 2000
2500
0 0.2 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time (normalized)
Category 1
Category 2
Category 3
0
0 2 0 0 3 0 4 0 5 0 6 0 0 8 0 9 0
y
ategory
Figure 9. Normalized time history curve of cumulative impact number
of three types of concrete AE signals.
TA B L E 6
The average values of AE characteristic parameters of concrete optimal cluster center
Clustering results Rise time (µs) Ring count Energy (pV-s) Duration (µs) Signal strength (pV-s) Absolute energy (aJ)
Category 1 36.14 2.36 0.06 473.35 2565.92 3.65
Category 2 14.51 7.02 0.32 65.58 1983.42 15.79
Category 3 8.81 37.02 6.34 39.79 42759.19 6404.17
M AY 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 49
Accumulated
number
of AE
impacts

In summary, the clustering center analysis of the ring
count–center frequency clustering combination selected in
this study, along with the analysis of the AE feature parame-
ters behind each combination, are consistent. These results
achieve accurate categorization and corresponding expla-
nation of concrete damage levels and damage mechanisms.
Among them, the first type of signal represents mild damage
in concrete under axial tensile stress, primarily involving the
initiation of microcracks, which aligns with the damage mech-
anism of stage D1 from the time history analysis. The second
type of signal represents moderate damage, mainly involving
the expansion of microcracks, consistent with the damage
mechanism of stage D2. The third type of signal represents
severe damage, involving the cracking of macroscopic cracks,
consistent with the damage mechanism of stage D3. These
relationships are summarized in Table 7.
4. Discussion
This study systematically investigates the evolutionary laws
and classification mechanisms of concrete damage under
axial tension by integrating AE technology with cluster-
ing analysis. However, as the experiments were conducted
under controlled loading conditions with small specimens
in laboratory settings, the applicability of the results to real-
world engineering structures requires further exploration.
Environmental factors such as temperature and humidity
may significantly influence AE signal characteristics and
damage mechanisms. For instance, temperature fluctuations
could induce thermal stresses within concrete, triggering spon-
taneous microcrack propagation and altering the frequency
and energy distribution of AE signals. High-humidity environ-
ments might accelerate pore-water migration and chemical
corrosion in concrete, affecting crack initiation and propaga-
tion rates. Furthermore, noise interference in complex envi-
ronments (e.g., mechanical vibrations and electromagnetic
disturbances) could mask valid AE signals, reducing moni-
toring accuracy. To address these challenges, future research
could employ multi-sensor fusion technology (e.g., integrating
temperature and humidity sensors) to enable synchronous
environmental parameter acquisition and signal compensa-
tion. The development of adaptive filtering algorithms could
enhance noise suppression capabilities. Additionally, establish-
ing an AE characteristic database under diverse environmental
conditions and incorporating machine learning models for
dynamic correction could significantly improve the robustness
of this methodology.
In practical applications, this methodology must account
for the scale effects and material heterogeneity of engineering
structures. The geometric complexity of large-scale structures
(e.g., bridges and dams) may lead to signal attenuation or scat-
tering during AE propagation, influencing sensor deployment
strategies and signal capture efficiency. To address this, sensor
network layouts should be optimized by adopting array-based
monitoring schemes combined with waveguide technology to
expand coverage. Meanwhile, heterogeneous components such
as steel reinforcements and aggregates in real structures may
generate multimodal AE features, necessitating precise damage
pattern identification through multi-parameter joint analysis
and deep learning models. Although the clustering analysis
results from current research effectively differentiate damage
levels in laboratory specimens, their generalization capabil-
ity in real-world engineering scenarios involving multi-factor
coupling (e.g., dynamic loads, fatigue loads, and material aging
under long-term service) still requires validation. For example,
evolving damage pathways caused by time-dependent factors
demand further integration of time-varying analysis models
and lifespan prediction theories to refine classification criteria.
Despite these challenges, this study provides theoretical
support for intelligent monitoring of concrete structures. By
optimizing algorithm efficiency and hardware integration, this
method could be embedded into real-time monitoring systems
to achieve online damage diagnosis and early warning. Future
research should extend to full-scale components and real
service environments to validate applicability under diverse
working conditions. Additionally, synergistic application with
other nondestructive testing technologies (e.g., fiber-optic
sensing and digital image correlation) should be explored to
establish a multi-scale, multi-dimensional structural health
monitoring framework.
5. Conclusions
This study first divided concrete axial tensile damage into three
stages based on the characteristics of the acoustic emission
time history curves and analyzed the corresponding damage
mechanisms. Next, the k-means clustering technique was used
to determine the optimal number of clusters and the best clus-
tering combination. Based on the optimal clustering results,
concrete axial tensile damage was classified into three severity
ME
|
AXIALTENSION
TA B L E 7
Corresponding relationship between cluster analysis and time history analysis of concrete axial tensile damage
Clustering results Degree of damage Damage mechanism Damage stages defined by time history curves
Category 1 Mild Microcrack initiation D1 (0–20% stress level)
Category 2 Moderate Microcrack expansion D2 (20–75% stress level)
Category 3 Severe Macroscopic crack formation D3 (75–100% stress level)
50
M AT E R I A L S E V A L U AT I O N • M AY 2 0 2 5