Damage Identification in Concrete Using Instantaneous Dominant Frequency of Acoustic Emission Signals

Abstract

The real-time assessment of structural damage in concrete structures using the acoustic emission (AE) technique presents substantial challenges. Traditional AE parameters often fail to effectively quantify the extent of concrete damage in real time. To address this limitation, an Instantaneous Dominant Frequency (IDF) method is proposed for identifying critical damage in concrete. This method leverages empirical mode decomposition (EMD), a self-adaptive time-frequency analysis approach, to process AE signals. By identifying the primary intrinsic mode function (IMF) and extracting the instantaneous frequency with the largest amplitude—termed the IDF—this method captures the dominant frequency characteristics of complex damage sources. The variation in IDF values provides insights into the progression of structural damage. In this study, AE signals obtained from uniaxial compression and four-point bending tests were analyzed using the IDF method. The results show that when the IDF value exceeds 300 kHz, significant damage, such as critical damage, occurs. These findings suggest that the IDF method offers an effective and reliable approach for identifying critical damage and determining the structural damage state during the failure process.

1. Introduction

Acoustic emission (AE) has been extensively utilized as a distinctive non-destructive testing method in structural health monitoring and material performance analysis, with a research history spanning over 60 years in concrete engineering [1]. However, the inherent complexity of concrete materials and the diverse forms of structural configurations introduce considerable uncertainty into AE signals. This diversity creates significant challenges in conventional damage detection using AE parameters.

In early AE studies, the damage identification of structures was performed through parametric analysis [2]. Initially, AE signals were analyzed by extracting certain parameters from the signal waveform (e.g., hit count, amplitude, duration, energy, etc.) [3]. The extraction grabbed a certain feature and discarded other information. Therefore, a comprehensive analysis of multiple parameters is always required in practical AE monitoring. Additionally, due to the influence of various factors, such as the shape and size of hydraulic concrete components, material properties, loading conditions, and stress states, AE parameters exhibit significant dispersion [4]. Furthermore, the acquisition of AE signals is influenced by factors such as the AE system and sensor installation, making it difficult to predefine a failure criterion based on AE parameters. Hence, identifying damage states using conventional AE parameters, especially in determining whether a structure has reached a critical state, remains challenging. An alternative approach is to search for new parameters that can more reasonably express the material’s damage characteristics, which often requires waveform analysis [5,6].

Some researchers initiated theoretical developments of quantitative techniques based on waveform analysis in the late 1980s and early 1990s [7,8]. Balázs et al. [9] employed the coherence function to evaluate the similarity between two different AE signals, using frequency as the primary descriptive parameter. This evaluation was beneficial, as similar frequency content implied similar source mechanisms. However, this frequency was an average value, and the calculation disregarded the effects of the medium and sensor characteristics, which prevented accurate reflection of the source properties. With the advent of broadband, high-sensitivity AE sensors, AE waveforms began to be fully recorded, enabling true waveform analysis. Subsequently, more AE studies incorporated spectrum analysis to obtain the frequency characteristics of signals [10,11,12]. However, spectral analysis methods are suitable for processing stationary signals [13], providing only the overall frequency characteristics of the signal. Since AE signals are typically non-stationary, key damage information may be easily overlooked. The development of frequency characteristic analysis has been rapid, making it an indispensable tool. Basic frequency parameters include dominant frequency (sometimes referred to as peak frequency), initial frequency, average frequency, reverberation frequency, and frequency centroid [14]. Clearly, AE waveforms carry more comprehensive damage information, from which parameters that better reflect damage characteristics can be identified and extracted. Alternatively, waveforms can be directly used for comparison, classification, and assessment.

A comprehensive review of the literature reveals that the dominant frequency (DF) is more extensively utilized than other frequency parameters in AE analysis [15]. The DF of an AE signal is defined as the frequency associated with the peak amplitude in a two-dimensional spectrogram [16], providing essential insights for microcrack characterization [17]. Luo et al. [18], through an analysis of AE’s DF, observed that “silent periods” within AE signals and the transition of DF distribution from discrete to continuous serve as indicators of interface crack propagation in roller-compacted concrete, marking the shift from stable to unstable crack growth. By employing wavelet decomposition, they identified frequency bands with maximal energy, which facilitated the determination of primary damage modes throughout each fracture stage. Further, Xu et al. [19] used a combination of DF and Continuous Wavelet Transform (CWT) to detect microstructural alterations in asphalt mixtures. This approach leveraged DF characteristics and AE waveform time-frequency distributions, resulting in a quantitative index based on Discrete Wavelet Transform (DWT) and fractal theory for assessing damage states. Similarly, Wang et al. [20] examined DF distributions and their progression during rock bursts, establishing correlations with entropy variations throughout rock failure. Their findings suggest that peak frequency entropy values serve as critical precursors for predicting rockburst events and identifying imminent instability.

The dominant frequency is derived from the Fourier transform of the signal; however, this approach is limited in that it does not accommodate the non-stationary characteristics typically present in acoustic emission signals. In recent years, researchers have increasingly employed advanced time-frequency analysis methods better suited to capture the instantaneous frequency variations within signals. Notable among these methods are the short-time Fourier transform (STFT) [21], wavelet transform (WT) [22], and Hilbert-Huang transform (HHT) [23]. These techniques offer improved adaptability for analyzing complex, non-stationary signals by providing detailed time-frequency information.

In comparison to the Fourier transform, WT and HHT are more effective for analyzing nonlinear and non-stationary signals [24], making them widely applicable in hybrid analysis approaches. Among these, the EMD method within HHT has gained considerable attention in the field of AE due to its adaptive nature, as it does not require the pre-selection of a wavelet basis function, unlike WT. EMD introduces the concept of instantaneous frequency, which bypasses fixed frequency and time resolutions, thus serving as a highly effective analytical tool. This approach enables the accurate extraction of instantaneous amplitude and frequency components, facilitating precise estimation of system characteristics and capturing nonlinear signal behavior [25].

However, waveform analysis can be time-consuming, making it less suitable for real-time analysis of large volumes of signals in the health monitoring of large structures [26]. Therefore, both the parameter method and the waveform method have their advantages and disadvantages and are currently applied effectively.

In recent years, numerous researchers have integrated parameter-based and waveform-based methods in AE analysis, combining the strengths of both approaches. Yang Ling et al. [27] applied wavelet analysis to AE signals generated from rocks under dynamic compression, extracting the time-frequency spectrum of crack-related AE signals and comparing it with the conventional AE parameter method RA-AF. This combined approach enabled the identification of rock failure modes and provided insights into their evolutionary stages throughout the destruction process. Jiang et al. [28] utilized HHT for spectral analysis of rock samples and found that the frequency characteristics of AE signals closely correlate with the energy released during pure tensile fracture events. While these studies primarily focus on the comparison and integration of multiple methods, they have yet to achieve a fully hybridized approach. Extracting the frequency characteristics of primary AE sources through waveform analysis offers a promising path toward a true hybrid method. This approach allows for the precise extraction and parameterization of critical information, thereby meeting the real-time monitoring demands of large-scale structural systems.

This study introduces a hybrid analysis method that integrates waveform analysis and parameter analysis to continuously evaluate all AE signals using the HHT. A new AE parameter termed the Instantaneous Dominant Frequency (IDF), is proposed to enhance the understanding of damage evolution in concrete structures. The study investigates the relationship between IDF variation patterns and damage states. Unlike the conventional DF method, the IDF approach leverages EMD, enabling a more effective capture of primary source characteristics. The HHT method further provides instantaneous frequency information at each time point, imparting greater physical significance to the extracted IDF and offering a more accurate representation of the frequency characteristics associated with various damage states. Through uniaxial compression and four-point bending tests, the IDF method was systematically compared with traditional parameter-based approaches to analyze the relationship between IDF variation patterns and damage states. The results confirm the effectiveness and practicality of the IDF method, highlighting its superior ability to characterize damage evolution in comparison to conventional techniques. The IDF approach offers a straightforward and efficient means of identifying critical damage in online monitoring systems, presenting a novel framework for real-time health monitoring of concrete structures using AE technology.

2. Method for Extracting IDF

In this section, IDF is defined as the frequency corresponding to the maximum instantaneous amplitude obtained from the IMF components using EMD. This parameter represents the primary frequency component of the signal and has the capacity to reflect the characteristics of the AE source.

2.1. Empirical Mode Decomposition

EMD is the fundamental part of the HHT method, which was introduced by Huang et al. [29]. To establish the upper and lower envelopes of the signal $u(t)$, one must connect all local maxima and minima using cubic spline interpolation, ensuring that these envelopes encompass all data points between them. The mean of these envelopes is defined as $m_1$. The difference between the signal $u(t)$ and $m_1$ is denoted as the first component $h_1$.

$$h_1=u(t)-m_1$$

(1)

If $h_1$ meets the definition of an IMF, it is classified as the initial IMF of the dataset, denoted as $c_1$. By separating $c_1$ from the other data, we can obtain

$$u(t)-c_1=r_1$$

(2)

In which the residual r₁ is regarded as new data and the process is repeated n times to estimate n modal functions c_i of u(t). It is employed to sequentially decompose a signal u(t) into n IMFs c_i and a residual $r_n$ as

$$u(t)={\displaystyle \sum _{i=1}^n{c}_i+r_n}$$

(3)

For each order of the IMF, the Hilbert transform can be utilized to construct an analytic signal

$$z_i(t)=c_i(t)+j{\widehat{c}}_i(t)=a_i(t)e^{j{\varphi }_i(t)}$$

(4)

where ${\widehat{c}}_i(t)$ represents the Hilbert transform (HT) of the IMF, $a_i(t)=\sqrt{c_i^2(t)+{\widehat{c}}_i^2(t)}$ is the amplitude function, ${\varphi }_i(t)=\arctan {\displaystyle \frac{{\widehat{c}}_i(t)}{c_i(t)}}$ is the phase function. Thus, the instantaneous frequency ${\omega }_i(t)$ is given by

$${\omega }_i(t)={\displaystyle \frac{\mathrm{d}{\varphi }_i(t)}{\mathrm{d}(t)}}$$

(5)

Finally, the Hilbert spectrum, which shows the time-frequency distribution of the amplitude, is obtained

$$H(\omega ,t)=\mathrm{Re}{\displaystyle \sum _{i=1}^n{a}_i(t)}{e}^{j{\displaystyle \int {\omega }_i(t)\mathrm{d}t}}$$

(6)

In the EMD process, if certain IMFs exhibit noise characteristics—typically manifesting as high frequency and non-decaying traits—they can be removed from the original signal. This constitutes a denoising method based on EMD decomposition.

2.2. Dominant Frequency

In acoustic emission analysis, the dominant frequency is defined as the frequency corresponding to the maximum amplitude in the spectrum of an AE signal. The procedural steps for determining the dominant frequency are as follows:

(1)

Waveform Acquisition: Capture the waveform data generated by the acoustic emission event.

(2)

Frequency Transformation: Apply a Fast Fourier Transform (FFT) to the waveform data to convert the signal from the time domain to the frequency domain.

(3)

Peak Identification: In the frequency spectrum obtained through the FFT, identify the frequency associated with the highest amplitude.

(4)

Dominant Frequency Definition: Assign this frequency, corresponding to the maximum amplitude in the spectrum, as the dominant frequency.

This method provides a straightforward approach to characterizing the primary frequency component of AE signals.

2.3. Instantaneous Dominant Frequency

In concrete members, damage manifests as the initiation, propagation, and interconnection of internal micro-cracks, ultimately compromising the macroscopic mechanical properties of the material. The onset of significant damage is typically accompanied by numerous secondary phenomena, such as friction and material crushing. These secondary sources contribute to the increased complexity of AE signals. However, the energy released by secondary sources is significantly lower than that of the primary source, and their impact on overall damage progression is correspondingly limited. Therefore, focusing on the primary signal characteristics while minimizing the influence of secondary factors offers a straightforward and effective approach for analyzing damage in concrete structures.

Once the Hilbert spectrum $H(\omega ,t)$ is obtained through Equation (4), the maximum instantaneous amplitude can be identified for focused analysis. This amplitude generally reflects the most critical information within the signal, indicating that the corresponding IMF component likely represents the primary damage mechanism. Frequency parameters are effective tools for characterizing the signal source, leading to the introduction of the IDF.

Aligned with the principles outlined above, a detailed implementation of the proposed method is presented. The process for extracting the IDF from continuously monitored AE signals is depicted in Figure 1. The method comprises the following primary steps:

Step 1: The AE waveform data collected during experimental testing is segmented into individual AE signals using a fixed time window and a specified voltage amplitude threshold. This segmentation eliminates noise and irrelevant events below the threshold, thereby improving the accuracy and efficiency of subsequent signal processing.

Step 2: Each AE signal segmented in Step 1 is processed using empirical mode decomposition to obtain its intrinsic mode functions. The Hilbert Transform is then applied to each IMF to generate the analytic signal, which retains only the positive frequency components of the original IMF while eliminating negative frequency components. Using the Hilbert-Huang Transform, the analytic signals of each IMF are analyzed to determine the instantaneous frequency and amplitude distributions.

Step 3: The maximum instantaneous amplitude among the IMFs derived in Step 2 is identified, and the corresponding frequency is designated as the IDF.

Step 4: By applying the procedures outlined in Steps 2 and 3 to all segmented AE signals, the IDF values and their distribution throughout the entire acoustic emission process are obtained.

These steps form a systematic approach for extracting and analyzing IDF, enabling a detailed characterization of the frequency dynamics in AE signals.

3. Experimental Setup

The experiments are comprised of two parts: the uniaxial compression test on plain concrete specimens and the four-point bending test on reinforced concrete beams. These tests represent two of the most common loading conditions for concrete components in engineering applications. The study aims to investigate the AE characteristics associated with damage during the experiments, with particular emphasis on examining the variations in IDF throughout the process.

3.1. Uniaxial Compression

For this test, a cylindrical specimen with a diameter of 100 mm and a height of 200 mm was used. The specimen was fabricated with concrete aggregate having a particle size range of 5–10 mm and was designed to achieve a strength grade of C25. The specimen was loaded using a microcomputer-controlled electromechanical universal testing machine (SUNS, Shenzhen, China). The test employed a displacement-controlled loading method with a loading rate of 0.6 mm/min.

A comprehensive AE signal monitoring system was utilized to record the AE signals generated during the test. Six sensors were positioned on the surface of the specimen, with three sensors at each end arranged at 120° intervals, located 30 mm from the top and bottom surfaces. The sensors were secured in place with elastic bands to prevent them from detaching during the test. The sensors used were of the RS-2A model, with a working frequency range of 50 kHz to 400 kHz.

Figure 2 illustrates the concrete specimen, loading system, and AE acquisition system.

3.2. Four-Point Bending Test

A reinforced concrete beam with dimensions of 1400 mm × 250 mm × 150 mm was used for the four-point bending test. The concrete mix ratio for this beam was as follows: cement 360 kg/m³, water 195 kg/m³, sand 610 kg/m³, aggregate 1235 kg/m³, and water reducer 0.7 kg/m³. The beam was placed in a curing box and cured under standard conditions for 28 days, achieving a target strength grade of C35. The reinforcement configuration is depicted in Figure 3. The longitudinal reinforcement consists of HRB400 steel bars with a diameter of 12 mm. The measured yield strength of the reinforcement is 547.68 MPa, and its tensile strength is 668.06 MPa. Eight sensors (Beijing Soft Island Times Technology Co., Ltd., Beijing, China) were positioned on the beam to monitor the failure conditions in the pure bending region. After applying a coupling agent, the sensors were securely fastened with external adhesive tape to prevent any loosening during the test.

A 500 kN self-balancing vertical load reaction system was used to apply loads (Hengle, Jinan, China) to the reinforced concrete beam. The test followed a staged loading method in accordance with the Standard for Testing Methods of Concrete Structures (GB/T 50152-2012) [30].

4. Results and Discussion

During the experiment, the occurrence of damage was accompanied by the generation of a substantial amount of AE signals. A comparative analysis was conducted between the conventional AE parameters, and the IDF proposed in this study. This analysis aimed to explore the variation patterns of both types of parameters and assess their applicability in actual damage monitoring. By correlating these parameters with the observed damage states, the study seeks to determine the effectiveness of IDF as a more reliable indicator for monitoring damage progression in concrete structures.

4.1. Analysis of Conventional AE Parameters

In the AE technique, there are several commonly used parameters for analyzing discontinuous signals in concrete materials, such as amplitude, energy, and ring count. Among these, energy and ring count show a strong correlation. Therefore, this study primarily focuses on the analysis of amplitude and energy parameters. Compared to other parameters, these two are less sensitive to threshold values and demonstrate good stability in practical applications.

In the uniaxial compression test, the relatively small size of the specimen and the proximity of the sensors to the damage location resulted in a larger overall amplitude. As a result, some signals reached the system’s upper limit early in the test, which affected the further assessment of the damage level, as shown in Figure 4a. The energy parameter, on the other hand, did not have an upper limit, allowing it to reflect damage progression in the post-experiment analysis. During severe damage events, continuous energy release will manifest as significantly high AE energy values. Consequently, the energy parameter, illustrated in Figure 4b, effectively reflects the damage condition of the concrete material. However, in practical testing, it remains unclear what level of damage corresponds to the various energy peaks; this good correlation can only be established at the conclusion of the test.

In the four-point bending test, the amplitude did not reach its limit, which can reflect the strength relationship between the signals. As the loading progressed incrementally, the damage gradually increased, leading to the emergence of high amplitude values that exhibited an upward trend (Figure 5a). Clearly, the amplitude shows a good correlation with the level of damage. Similarly, the energy parameter effectively reflects the damage condition of the concrete material (Figure 5b). Notably, the significant energy spike observed at 855 s indicates that noticeable damage has occurred (Figure 6), with the applied load being 45% of the maximum value.

However, both the amplitude and energy parameters still face the challenge of not being able to quantitatively determine the degree of damage; this assessment can only be made after the completion of the experiment. This limitation underscores the need for more reliable metrics that can provide real-time insights into damage progression during testing.

4.2. DF Analysis

The DF analysis reflected the frequency characteristics of AE signals but was unable to reliably detect critical damage. Figure 7 illustrates the variations in DF of AE signals for two types of tests. As seen in the figure, the DF distribution is banded, with most signals having a DF below 300 kHz and a small number of high-frequency signals ranging from 300 to 500 kHz.

In the uniaxial compression test (Figure 7a), high-frequency signals appeared early on, which is consistent with the amplitude parameters. Therefore, the damage state cannot be determined in real time. In the four-point bending test (Figure 7b), high-frequency signals began to emerge at 862 s, with a DF of 422 kHz and a load at 45% of the maximum value, which aligns with the energy parameters. When the DF first approached 500 kHz, the load was at 58% of the maximum value. This indicates that the DF method can identify certain key damages, but it cannot reliably identify critical damages.

Moreover, neither of the DF plots shows the so-called silent period before imminent failure, nor was any significant change in a particular frequency band observed to indicate a specific damage pattern. This method does not offer a significant advantage for real-time damage identification; instead, it requires support from other methods for comprehensive analysis or post-event statistical analysis.

4.3. IDF Analysis

Just as DF does, IDF also assesses the state of damage from a frequency perspective. Furthermore, IDF simplifies the evaluation by using the dominant frequency of the primary mode obtained through EMD as a basis for judgment, making it more intuitive.

In the IDF analysis from the uniaxial compression test, the IDF values of the AE signals predominantly fell below 300 kHz, with a particular concentration in the 100–200 kHz range. Higher IDF signals emerged in the later stages of the experiment, as illustrated in Figure 8a, indicating that more significant damage is associated with higher IDF values. A similar trend was observed in the four-point bending test shown in Figure 8b.

Based on these observations, signals with IDF values reaching or exceeding 300 kHz warrant special attention, as this typically signifies that the component has experienced considerable damage.

In Figure 8a, the first signal exceeding 300 kHz was recorded at 267 s, with an IDF of 345 kHz. Although no significant surface cracks were observed at this point, the load had reached 73% of the ultimate load, and the loading curve exhibited a slight inflection, indicating that noticeable internal damage had already occurred. At 303 s, two consecutive high IDF points were noted, with an IDF of 326 kHz. At this time, a visible crack appeared on the specimen’s surface (Figure 9a), and the load had increased to 85% of the ultimate load. Subsequently, as multiple cracks emerged, the damage to the specimen progressed rapidly until complete failure occurred (Figure 10a).

In Figure 8b, the first signal exceeding 300 kHz was detected at 1322 s, with an IDF of 338 kHz. The load at this moment was 72% of the ultimate load. Compared to the previous damage state, a new crack appeared on the right side at this point (Figure 9b). Unlike the four previous cracks (shown in Figure 6), this crack was located outside the pure bending region and gradually developed into a significant crack in the later stages (Figure 10b).

Notably, four cracks had already formed at 855 s before the key signals associated with the above-mentioned cracks were detected. The energy parameter analysis at that time provided corresponding judgments regarding damage. In the IDF analysis, it was also observed that while the IDF signal had not yet exceeded 300 kHz, some values were very close to this threshold. This indicates that IDF values approaching 300 kHz in the four-point bending test should also be monitored closely.

5. Discussion

Based on the observed variations in AE parameters during the experiments, it is evident that traditional AE parameters correlate well with the damage states of concrete components. Notably, post-event relative quantitative analyses, such as the relative changes in AE energy, effectively reflect the extent of damage in the components. However, as previously discussed, accurately assessing the degree of damage using AE technology during real-time monitoring remains challenging due to the absence of predefined damage standards for AE parameter values.

DF analysis provides insight into the frequency characteristics of AE signals to some extent; however, since it relies on overall frequency rather than instantaneous frequency, it lacks the precision needed to accurately identify hazardous damage.

Higher IDF signals are typically associated with more complex damage events, where multiple damage sources are active simultaneously. These complex AE signals, generated by various sources, can be influenced by factors such as propagation direction, waveform transformation, material degradation, and nonlinear superposition. Further application of Empirical Mode Decomposition to extract the dominant frequency may lead to an increased IDF value.

In the uniaxial compression test, the relatively small plain concrete specimens experienced significant damage early in the loading process. This was accompanied by signals characterized by high amplitude and high IDF values. Notably, some IDF values reached approximately 300 kHz even during the initial stages of loading.

During the four-point bending test, the reinforcement effectively delayed the damage and failure of the concrete during the beam’s bending deformation process, resulting in relatively few AE signals in the initial stage of the test. Subsequently, cracks first appeared in the tensile side of the concrete, but the presence of reinforcement inhibited crack propagation, so the IDF value of the signals did not reach a severe level. Typically, the structure enters a more severe damage stage only after multiple cracks have developed in the tensile zone at the bottom. In this experiment, the highest IDF value was observed only when diagonal cracks were initiated. Therefore, based on the mechanical characteristics of reinforced concrete members, it can be inferred that most significant damage signals prior to the critical IDF value are primarily associated with concrete cracking, while reinforcement yielding begins only after the critical IDF value is reached.

In this study, an IDF of 300 kHz is considered the critical threshold for identifying the onset of significant damage. However, in practice, this value depends on the characteristics of the AE sensors employed. For instance, in another four-point bending test, several PAC-WDI-AST wideband sensors(PAC, Houston, TX, USA) were used, offering an operating frequency range of 200–900 kHz and enabling the detection of a broader frequency spectrum. While most signal IDF values remained below 300 kHz—primarily due to the inherent properties of concrete—a substantial number of signals fell within the 300–500 kHz range, with some signals near the ultimate load exceeding 500 kHz (Figure 11). Therefore, in practical applications, the critical IDF threshold should be experimentally determined after selecting suitable sensors. This threshold can then serve as a benchmark for identifying critical damage during structural health monitoring.

6. Conclusions

The IDF method is primarily based on waveform analysis, filtering out intrinsic modes that reflect major damage from complex signals and then extracting the dominant frequency parameters. This approach facilitates real-time health monitoring of large structures. The practicality of the IDF method has been validated through uniaxial compression and four-point bending tests, leading to the following conclusions:

• Traditional AE parameters and DF analysis are correlated with damage evolution in components but cannot provide real-time assessments of the damage status.
• The IDF method, based on the empirical mode decomposition (EMD) of signals and the extraction of the dominant frequency from intrinsic mode functions (IMFs), effectively captures the key characteristics of a signal. When severe damage occurs, the appearance of high IDF values acts as an indicator, enabling the reliable and stable identification of critical damage. In this study, an IDF value of 300 kHz was used to determine the occurrence of critical damage.
• Different models of AE sensors capture signals with varying frequency characteristics, leading to differences in the critical IDF values. Therefore, for actual engineering health monitoring, preliminary experiments are required to determine these values.

The IDF method based on EMD proposed in this paper provides a more effective and reliable approach for monitoring the damage state of concrete structures. It fully leverages the advantages of acoustic emission technology for real-time monitoring. However, this study also has some limitations. The critical IDF value under practical conditions needs to be determined through preliminary experiments, and its theoretical basis requires further mechanistic research. Additionally, the selection of the IDF threshold may lead to changes in the chosen signals and their quantity, which could affect the accuracy of detecting severe damage. Therefore, determining the appropriate IDF threshold will also be an important focus of future research and is crucial for further expanding the applicability of this method in practical engineering applications.