Experimental study on failure precursors of coal and sandstone based on two‐step clustering of acoustic emission characteristics

Accurately determining the precursors of coal and rock failures is crucial for preventing associated risks in coal mines. In this study, based on the values of the four parameters amplitude, duration, counts and energy of acoustic emission (AE) signals, the AE signals of coal and sandstone samples failure were clustered by the two‐step clustering method. And the precursory AE signals of sample failure under uniaxial compression were analyzed and identified. Results show that the peak of AE amplitude is before that of AE duration, counts, and energy. AE signals of both coal and sandstone samples can be classified into five types. Values of the parameters of Types I–IV AE signals of the sandstone sample are lower than that of the coal sample. The duration, counts, and energy of Type V AE signals of the sandstone sample are higher than that of the coal sample. Type V AE signals, which are middle amplitude (hundreds of mV), high duration (hundreds of thousands of μS), high counts (about 10,000), and high energy (tens of thousands of mV*mS), account for the lowest proportion of all AE signals, at approximately 0.1%. And they began to occur at 87% σc of the coal sample and at 97% σc of the sandstone sample, respectively. Type V AE signals can be used as precursors of coal and sandstone samples failure under uniaxial compression.

][15][16] Previous studies have shown that AE signals exhibit obvious responses to the occurrence, extension, and coalescence of cracks during rock failure. 17,18In uniaxial loading-unloading tests, the AE count rates in each cycle display a steadily increasing trend as the test progresses and the rate increases sharply in the last cycle. 19dditionally, the sequence of total AE counts and AE energy under different loading modes appear to be concentrated at the peak stress. 20Wang et al. found that a sudden increase in AE energy was accompanied by a drastic decline or local fluctuations in rock load-bearing capacity. 18More recently, Liu et al. represented the evolution of coal failure by the value of b over a stress range of approximately 60%-80%, such that the number and maximum amplitude of AE signals increased rapidly as the corresponding b-value decreased.They found that the energy of AE signals exhibited a declining trend after being maximized at a stress level of approximately 80%. 21n terms of the study on AE precursors of coal and rock failures.Zhang et al. considered the precursory AE characteristics of coal and rock failure by studying the characteristics of the energy, dominant frequency, and amplitude of AE signals in the process of granite failure under uniaxial compression.The results showed that the gradual disappearance of the intermediate and high frequency low amplitude events and the occurrence of low frequency high amplitude signals can be used as the precursor indicators for granite failure. 9Yang et al. suggested that the high-level AE activity can be viewed as the precursor of the brittle instability of coal, 2 while Su et al. noted that a sudden increase and then decrease in AE hit rate and count rates can be used as precursors to predict the final dynamic instability. 22Additionally, some quiet stages of AE signals before the peak stress, which were suggested as precursors of rock failure, were discovered during the failure processes of different rocks under uniaxial compression in the study of Wang et al. 18 What's more, sudden increases were observed in AE counts and energy with abrupt declines in stress, though in some cases, stress did not decrease abruptly when AE counts and energy sharply increased.Therefore, the development of a rock deformation field may not be in a calm stage during the quiet period of AE signals. 23o date, there has been no unified conclusion on the precursory AE indicators of coal and rock failures.In most existing studies, the fluctuations of AE parameters are used to qualitatively describe the different stages of coal and rock failures and it is difficult to determine an early warning threshold.There is also a lack of classification and analysis of AE waveforms that reflects the type and scale of cracks. 9,24For AE signals of coal and rock failures with big data characteristics, machine learning methods are well suited to deeply mine them to explore the quantitative precursors of coal and rock failures.][27] They can categorize a large amount of data and the basic principle is to quantitatively determine the similarity relationship among samples according to a certain characteristic. 28Zhang et al. stated that the AE signals during granite failure formed three clusters.Among them, one type of AE signals with small number and high energy could be used as precursors for granite failure. 29Zhang et al. later showed that the AE signals of coal failure could be clustered into three types using the K-means algorithm.Based on this algorithm, one type of AE signals with very high energy that corresponds to a significant reduction in the so called "quiet period" of AE signals could be used as a precursor for coal failure. 12It is clear from the above that the characteristics of precursory AE signals in existing studies are inconsistent, and the type of AE signals that are effective precursors of coal and rock failures has not yet been clarified.Therefore, it is necessary to explore the precursory AE signals of coal and rock failures and analyze their unique characteristics.
In this study, AE signals during the failure processes of coal and sandstone samples under uniaxial compression were obtained.The changes of amplitude, duration, counts, and energy of the AE signals over time were analyzed and the two-step clustering method was used to classify the AE signals of different samples according to the values of parameters.The respective precursory AE signals for coal and sandstone sample failure were then identified.Our findings can aid in establishing AE precursors for coal and rock failures and thereby help to improve the safety of mines, tunnels, and other underground projects.

| Sample preparation
Coal and sandstone samples with different physical and mechanical properties were used in this test.According to the recommendations of the International Society for Rock Mechanics, irregular-shaped coal and sandstone samples were processed into standard cylindrical samples (diameter = 50 mm, height = 100 mm) for the uniaxial compression test.Furthermore, the non-parallelism of the samples was controlled under 0.05 mm, and the diameter deviation was limited to less than 0.2 mm.The uniaxial compression experiment was conducted using a precision electronic material testing machine (AG-I 250KN, Shimadzu) equipped with a visual operation system and high-speed data acquisition system.The AE signals of coal and sandstone samples were detected and documented using a DS2-8A holographic acoustic emission signal analyzer (Beijing Softland Times Scientifc & Technology Co. Ltd.).To avoid the influence of the sensor position on AE signals, 30 four AE sensors were positioned around the samples.The complete experimental system is shown in Figure 1.
The test procedure included four stages.(1) Four AE sensors were positioned on the upper and lower parts of the sample such that any two sensors faced each other.
(2) AE sensors, AE amplifiers, and a host computer were connected sequentially.Table 1 lists the parameters of the AE system.The starting mode was set to external triggering.(3) The pressure-loading mode and loading speed were set to displacement loading and 0.05 mm/ min, respectively.The pressure loading head of the testing machine was manually adjusted to connect it to the upper end face of the sample, and to ensure that the loading axis coincided with the sample axis.(4) The testing machine and AE acquisition instrument were started simultaneously and terminated simultaneously after the sample failure.
The parameter category and meaning of the AE waveform are shown in Figure 2. To explore the special characteristics of AE waveforms generated by different cracks, and to avoid the deterioration of classification results caused by the parameter number, four parameters, namely, AE amplitude, AE duration, AE counts, and AE energy, were selected for analysis.Among them, AE amplitude is directly related to the magnitude of the AE signals.AE duration can be used to identify the special wave source type.AE counts are widely used to evaluate AE signals, and AE energy reflects the relative energy and intensity of AE signals. [33]

| Two-step clustering method
The two-step clustering model was used to cluster the AE signals.Compared with other clustering methods, the two-step cluster model can manage both discrete data and continuous data and is suitable for the clustering of big data. 34,35The model includes two steps: (1) Preclustering: The data is clustered into multiple subclasses.
(2) Formal clustering: multiple subclasses defined in the first step are clustered into the desired number of clusters.These calculation steps are explained comprehensively below.

| Preclustering
A leaf node containing all the variable information of the observation value initiated by the root of the tree was constructed according to the first observation of the data set.Distance measurements were used as a similarity criterion to judge whether a new observation should be combined with an existing node or a new node.All observations were placed in a similar manner and developed into a clustering feature tree.
The distance measurement model was based on logarithmic similarity and was calculated as follows: Diagram of the experimental system.(A) AGI-250KN testing machine, (B) AE monitoring system.AE, acoustic emission.
where d i j ( , ) represents the distance between the two clusters of i and j, and the   i j , index represents a new cluster generated by combining the clusters i and j.
where K A represents the number of continuous variables, K B represents the number of categorical variables, N v is the total number of records in cluster v, σ k represents the estimated variance of the kth continuous variable in all data sets, and σ k represents the estimated variance of the kth continuous variable in the cluster v.
where N v represents the total number of recorded datasets in the v cluster.L k represents the number of kth categorical variable.N vkl represents the number of v clusters, and the categorical variable k is divided into l groups.

| Clustering
The leaf nodes were combined using a merge-clustering algorithm to produce clustering schemes with different cluster numbers.The final clustering scheme can be formed not only according to the number of clusters sets but also according to the Bayesian information criterion (BIC) to select the optimal number of clusters.BIC was calculated as follows: where N represents the number of cluster I, represents the maximum value of the likelihood function, and m i represents the number of model parameters.
The observational values in this study represented the corresponding AE signals during the failure of coal and sandstone samples.AE amplitude, AE duration, AE counts, and AE energy represented the variable information from observation values.Further, the leaf node was expressed as a four-dimensional vector as follows:

| AE results
Variations in loading stress and AE parameters during coal and sandstone sample failure under uniaxial compression tests are shown in Figure 3, where C1, C2, C3, and C4 represent the four sensors for the coal sample, and S1, S2, S3, and S4 represent the four sensors for the sandstone sample.σ c is used to represent the uniaxial compression strength of the samples.The AE characteristics varied marginally among different sensors during the failure processes of coal and sandstone samples.Moreover, the AE characteristics differed between the coal and sandstone samples.As shown in Figure 3A, the AE amplitude increases gradually with an increase in the loading stress until the loading stress reaches approximately 75% σ c of the coal sample.Subsequently, the amplitude decreases rapidly.Contrastingly, with an increase in the loading stress, the AE amplitude of the sandstone sample gradually decreases initially, abruptly increases at 66% σ c , and presents a short decline, and then abruptly increases at 89% σ c , followed by a rapid decline (Figure 3B).Additionally, the AE amplitude of the sandstone sample peaked at approximately 89% σ c .As shown in Figure 3C, the AE duration during coal sample failure increases gradually with an increase in the loading stress, and subsequently, sharply increases linearly when the loading stress is approximately 95% σ c .
Figure 3C shows that AE duration slowly increases as the stress grows, followed by a sharp increase at approximately 95% σ c and a decrease before σ c .Regarding the sandstone sample (Figure 3D), the AE duration varies slightly as the stress rises, followed by a sharp linear increase at approximately 99% σ c .As shown in Figure 3E-H, the characteristics of changes in AE counts and AE energy during the failure of coal and sandstone samples are similar to those of AE duration.Notably, the peaks of AE duration, AE counts, and AE energy are after AE amplitude.

| Quality evaluation of clustering results
By comparing the different clustering results, it was found that when the number of clusters was five, the clustering results were evaluated as good.The quality evaluation charts of the clustering results are shown in differed, the clustering results of the data from each sensor were evaluated as good.Figure 4 shows that the silhouette coefficients of the data obtained by different sensors are all greater than 0.5, which suggests that there are unique characteristics among different types of AE signals and the clustering results are reliable.

| Number of different types of AE signals
The five types of AE signals of coal and sandstone samples were arranged in descending order according to their respective quantities (Figure 5).As shown in Figure 5A, the numbers of Types I-V AE signals from the AE sensor C1 for the coal sample are 19136, 3360, 853, 243, and 25, respectively, and accounting for 81.03%, 14.23%, 3.61%, 1.03%, and 0.11%, respectively.
Figure 5B-D show that those values for sensors C2, C3, and C4 are similar to sensor C1.As shown in Figure 5E, the numbers of Types I-V AE signals from the AE sensor S1 for the sandstone sample are 12,995, 3549, 851, 178, and 6, respectively, and accounting for 73.92%, 20.19%, 4.84%, 1.01%, and 0.03%, respectively.Figure 5F-H show that those values for sensors S2, S3, and S4 are similar to sensor S1.
The proportions of different types of AE signals for the sandstone sample are similar to those for the coal sample.However, the total number of AE signals for the coal sample failure process is more than that for the sandstone sample failure process, possibly because of the different physical and mechanical properties of coal and sandstone samples, wherein the coal sample has more original microcracks than the sandstone sample. 36herefore, compared to the sandstone sample, there are more cracks closure and more new cracks generation of the coal sample, especially in the initial crack compression stage and the unstable crack propagation stage, which generates more AE signals.It can be seen from Figure 7A that the first occurrence time of Type V AE signals for sensor C1 was at the 108.6249th second and at 95% σ c .For sensors C2, C3, and C4 (Figure 7B-D), the times were the 101.6826thsecond and at 87% σ c , 101.6823th second at 87% σ c , and 108.6175th second at 95% σ c , respectively.The first occurrence times of Type V AE signals of the four sensors for the coal sample were 11.4251, 18.3674, 18.3677, and 11.4325 s ahead of the time of σ c , respectively.The first Type V AE signals of C2 and C3 likely occurred due to a same crack.Similarly, the first Type V AE signal for C1 and C4 likely occurred due to a same crack.It is worth noting that some Type V AE signals of different sensors responded to the same crack, while others did not.This phenomenon may have been caused by the different positions of sensors.As differences in the distance between the sensors and cracks can lead to differences in the data monitored, this can lead to different clustering results.

| Qualitative characteristics of different types of AE signals
As shown in Figure 7E-H, the first Type V AE signal of the four sensors for the sandstone sample all occurred at 97% σ c .They occurred at the 253.2488th, 253.1514th, 253.3135th, and 253.2145th second, respectively.They were 8.4512, 8.5486, 8.3865, and 8.4855 s ahead of the time of σ c , respectively.Compared with the coal sample, the first occurrence times of Type V AE signals of the sandstone sample were closer to the time of σ c .
Combined with the Sections 3.2.1 and 3.2.2, it is believed that Types I and II AE signals are mainly caused by the closure of micro-cracks and the generation of new cracks.Types III and IV AE signals mainly represent the unstable extension of larger scale cracks.Type V AE signals represent that the deformation of the samples has reached the late yield stage and cracks are rapidly gathering and nucleating, and the final failure will occur immediately.Coal is more plastic and more porous than sandstone, which causes the scale of cracks generated in coal to be larger than those generated in sandstone, and the cracks in coal to expand at a smaller rate and for a longer duration than that in sandstone. 37,38Consequently, the numbers of AE signals of Types I-IV occurred in the coal sample are higher and the average values of the parameters are higher than those of the sandstone sample.Near the final failure, compared with the coal sample, the sandstone sample is more brittle and can store more energy due to its high strength.And the sandstone sample has a shorter yielding phase and quicker crack aggregation, leading to a tight aggregation of the corresponding low-amplitude AE signals.As a result, the Type V AE signals of the sandstone sample show the characteristics of lower number, longer duration, more counts, and higher energy.In contrast, the cracks in the coal sample nucleated at a slower rate during the yielding period, leading to the corresponding low-amplitude AE signals were not as densely grouped as those of the sandstone sample.Consequently, compared with the sandstone sample, the coal sample has a higher number of Type V AE signals with lower values of duration, counts and energy.Figure 8A shows that there are other types of AE signals within the time period containing Type V AE signals of the coal sample.Significantly, the amplitudes of Type V AE signals are very low compared with those of other types.The same goes for the sandstone sample (Figure 8B).As shown in Figure 8C,D, the durations of Type V AE signals of coal and sandstone samples are the highest among all AE signals.Moreover, the same result was obtained for AE counts and AE energy (Figure 8E,F and 8G,H, respectively).Based on the test results and analysis in this paper, it is clear that Type V AE signals are characterized by low amplitude, long duration, high counts, and high energy.In addition, they begin to occur close to the peak stress.Compared with other types of AE signals, the number of Type V AE signals is the lowest, accounting for approximately 0.1% of all signals.
Some tests have indicated that low amplitude AE signals, 9 high energy AE signals, 18,20 and high counts AE signals 39 occur near the peak stress.These results prove the reliability of considering Type V AE signals as precursors for coal and sandstone samples failure in this study.Additionally, Zhang et al. discovered that the energy released during the main fracture stage for most rocks contributed the largest proportion of the total energy released over the entire loading process. 40This is consistent with the phenomenon that the energy of Type V AE signals is approximately 100 times that of other types of AE signals.
There are four stages of coal and rock failures under uniaxial compression: compaction, linear elasticity, plastic yielding, and postpeak damage stages. 32,41Existing study shows that AE signals are quite active in the plastic yield stage, during which the AE counts and AE energy increases rapidly. 31Additionally, Chen et al. discovered that AE activity decays rapidly after the maximum shear stress value. 42Feng et al. found that the concentration of large energy signals before the peak is consistent with the impact failure position after the peak. 43These results are consistent with the results in this study that Type V AE signals begin to occur close to the peak stress and disappear afterward.The Type V AE signals of coal and sandstone samples occurred at approximately 95% and 97% of peak stress, respectively.This is consistent with the results of a previous study. 5

| Precursory AE signals for coal and sandstone sample failure
Numerous existing studies have regarded the abnormal AE signals near the peak stress as the precursors for coal and rock failures, such as the "quiet period" of AE signals, 18 high-level AE activity, 2 and sudden increase in AE counts. 22These conclusions were mostly reached by the analysis of a single factor.There is a lack of detailed analysis combining multiple parameters on AE signals of coal and rock samples.Moreover, it is necessary to develop a detailed explanation for special AE signals based on the physical structure of coal and rock samples.
Coal and rock are primitive heterogeneous materials that contain many structures with different strengths and scales.Among them, structures with high strength (called "locking section") control the stability of the sample. 44During coal and rock failures, the process of macro crack initiation and propagation is a fracture process of "locking sections" in the rock mass. 45The fracture process of every "locking section" experiences a plastic yield process, with the germination, propagation, and nucleation of microcracks.Rock bridge is a type of common "locking section."Chen et al. discovered that AE energy rose suddenly when the rock bridge was AE signals = {amplitude, duration, counts, energy}.(6) SPSS software was used for preparing the two-step clustering model of the AE signals in this study.The number of clusters was set to five.

T A B L E 1 2
Parameters of the AE system.Preamplifier gain (dB) Sampling frequency (MHz) Threshold value (mv) PDT (μs) HDT (μs) HLT (μs) Parameters of AE waveform.AE, acoustic emission.F I G U R E 3 Relationships between different AE characteristics and the loading stress of coal and sandstone samples.(A) AE amplitude of coal samples.(B) AE amplitude of sandstone sample.(C) AE duration of coal samples.(D) AE duration of sandstone samples.(E) AE counts of coal samples.(F) AE counts of sandstone sample.(G) AE energy of coal sample.(H) AE energy of sandstone sample.AE, acoustic emission.
According to the clustering results in Section 3.2.2, the average values of the parameters of each type of AE signals were calculated, as shown in Figure6.The average values of duration, counts, and energy of Type I-IV AE signals are approximately thousands of μS, tens, and hundreds of mV*mS, respectively, and hundreds of thousands of μS, thousands, and tens of thousands of mV*mS for Type V AE signals, respectively.The average values of parameters of AE signals from the four sensors for the coal sample are given in Figure 6E.These different types of AE signals reflect the different scales and types of cracks generated in the failure process of the coal sample.To easily characterize each type of AE signals and explain the meaning of different colors in Figure 6, the values of four AE parameters were categorized as low, lower-middle, middle, higher-middle, and high according to the range of their respective values in this study.Based on this classification, the characteristics of the five types of AE signals are as follows.Type I AE signals of coal sample are characterized with low amplitude, low duration, low counts, and low energy, and Type II AE signals are characterized with lower-middle amplitude, middle duration, middle counts, and lower-middle energy.Type III AE signals are characterized with higher-middle amplitude, middle duration, middle counts, and middle energy.Type IV AE signals are characterized by high amplitude, middle duration, middle counts, and middle energy.And Type V AE signals are characterized by medium amplitude, high duration, high counts, and high energy.

Figure
6J shows that the characteristics of amplitude, duration, counts, and energy of the five types of AE signals of the sandstone sample are similar to that of the coal sample, although the values are different.Notably, the values of the above four AE parameters of Type I-IV AE signals and the AE amplitude of Type V AE signals of the sandstone sample are smaller than that of the coal sample.However, the duration, counts, and energy of Type V AE signals of the sandstone sample are larger than that of the coal sample.The closure of microcracks and the expansion of new cracks of different scales are the reasons for the generation of different types of AE signals.The differences between the AE signals of coal and sandstone samples might be because of the different plasticity and brittleness of coal and sandstone samples.

3. 3 |
Relationship between AE signal types and loading stressThe relationship between the different types of AE signals and loading stress during coal and sandstone samples failure processes are shown in Figure7.Type I and Type II AE signals occurred continuously throughout the uniaxial compression tests.Type III and Type IV AE signals occurred occasionally in the early stages of the test, but their occurrence frequency increased with an increase in loading stress.Significantly, Type V AE signals did not occur in the early stages of the test until the loading stress was close to the peak.And these signals disappeared after the peak stress.

4 | DISCUSSION 4 . 1 |
Characteristics of the Type V AE signalsA comparison of AE parameters between Type V AE signals and others during the failure of coal and sandstone samples is shown in Figure8, taking the data of C2 and S1 sensors as examples.

F
I G U R E 8 AE amplitude between the Type V AE signals and others of coal and sandstone samples.(A) AE amplitude of coal samples.(B) AE amplitude of sandstone sample.(C) AE duration of coal samples.(D) AE duration of sandstone samples.(E) AE counts of coal samples.(F) AE counts of sandstone samples.(G) AE energy of coal samples.(H) AE energy of sandstone sample.AE, acoustic emission.
damaged.42Thus, the appearance of Type Ⅴ AE signals may reflect the fractures of the rock bridges with high strength.In other words, the appearance of the Type Ⅴ AE signals indicate that coal and sandstone samples begin to experience the final failure stage.The length of this time interval is related to the physical properties of coal and sandstone samples.In summary, the Type Ⅴ AE signals can be used as precursors of coal and sandstone samples failure.The sequential occurrences of Type Ⅴ AE signals for different sensors indicate the imminent failure of samples.Compared with other studies that qualitatively described the trends of AE parameters during rock failure, the results in this study put forward a definite precursory index for coal and sandstone samples failure.In this study, AE signals for coal and sandstone samples failure during uniaxial compression were identified.The evolution of the amplitude, duration, counts, and energy of AE signals were analyzed.Thereafter, the two-step clustering method was used to classify these AE signals according to the above four AE parameters.The evolution of AE signals during coal and sandstone sample failure was explored.Precursory AE signals for coal and sandstone sample failure were then defined.The following conclusions are drawn from this study.(1) AE amplitude, AE duration, AE counts, and AE energy increase abruptly and peak near the peak stress during coal and sandstone samples failure.The peak of AE amplitude is before that of AE duration, AE counts, and AE energy during the failure processes of coal and sandstone samples.(2) According to the values of amplitude, duration, counts, and energy, AE signals of the coal and sandstone samples were clustered into five types.Except for amplitude, the duration, counts, and energy of the Type V AE signals are much higher than others.The characteristics of AE signals of the coal sample are similar to those of the sandstone sample.(3) The values of amplitude, duration, counts, and energy of Type I-IV AE signals of the sandstone sample are smaller than those of the coal sample.The duration, counts, and energy of Type V AE signals of the sandstone sample are greater than those of the coal sample.(4) The Type V AE signals in this study, which are middle amplitude (hundreds of mV), high duration (hundreds of thousands of μS), high counts (about ten thousand), and high energy (tens of thousands of mV*mS), accounted for the lowest proportion of all signals, at approximately 0.1%.They began to occur at 87% σ c of the coal sample and at 97% σ c of the sandstone sample.The Type V AE signals of coal and sandstone samples can be used as failure precursors under uniaxial compression.Further research is required on a broader range of rock types, as well as data collected from actual engineering.42.Chen G, Zhang Y, Huang R, Guo F, Zhang G. Failure mechanism of rock bridge based on acoustic emission technique.J Sens. 2015;2015:1-11.43.Feng L, Wang H, Wang X, Zhang Q. Microfracture evolution characteristics and precursor identification of coal impact failure.Chin J Rock Mech Eng.2022;41(7):1440.44.Huang R, Chen G, Tang P. Precursor information of locking segment landslides based on transient characteristics.Chin J Rock Mech Eng.2017;36(03):521-533. 45.Wang X, Wang E, Liu X, Li X, Wang H, Li D. Macro-crack propagation process and corresponding AE behaviors of fractured sandstone under different loading rates.Chin J Rock Mech Eng.2018;37(06):1446-1458.How to cite this article: Zheng M, Liang Y, Li Q, et al.Experimental study on failure precursors of coal and sandstone based on two-step clustering of acoustic emission characteristics.Energy Sci Eng.2023;11:4505-4519.doi:10.1002/ese3.1594