Method for quantifying correlation between coal rock damage charge and stress and determining optimal time window

Abstract

The present application provides a kind of coal rock damage charge and stress correlation quantification and best time window determination method, it is related to coal rock monitoring technical field.First, the stress and charge signal of coal rock damage process is obtained, then the stress signal is decomposed into a series of intrinsic mode function and a residual component using empirical mode decomposition method, the frequency spectrum characteristics corresponding to each intrinsic mode function are determined;According to the frequency spectrum distribution, the low-frequency trend item is removed, and the remaining intrinsic mode function is reconstructed to obtain the de-trended stress signal;Then, using wavelet coherence analysis method, the wavelet coherence coefficient of de-trended stress signal and charge signal is calculated, and the wavelet coherence atlas is output;Finally, the best observation time scale is determined according to the correlation between de-trended stress and charge signal, and the cooperative change rule of stress and charge signal is analyzed in the best observation time scale.The method can realize the quantification of coal rock damage process charge and stress correlation and the determination of best observation time window.

Description

Technical Field

[0001] This invention relates to the field of coal and rock dynamic disaster monitoring technology, and in particular to a method for quantifying the correlation between coal and rock damage charge and stress and determining the optimal time window. Background Technology

[0002] Coal and rock are key research subjects in mineral resource development, and their damage and failure processes directly impact mine safety, geological disaster prevention, and efficient energy extraction. Under external loads, coal and rock undergo an evolutionary process involving the initiation, propagation, and connection of microcracks, culminating in macroscopic instability. This process is accompanied not only by significant changes in the stress field but also by physical phenomena such as the release of electrical charges, electromagnetic waves, and acoustic emissions. In recent years, the electrical charge signal phenomena accompanying coal and rock damage and failure have attracted widespread attention due to their high sensitivity and rapid response, providing a new research direction for identifying precursors of dynamic coal and rock failure. Therefore, a thorough understanding of the intrinsic relationship between electrical charge signals and stress changes during coal and rock damage and failure is of significant theoretical and practical value for developing disaster early warning technologies based on electrical charge monitoring.

[0003] In experimental studies, different loading modes, including uniaxial compression, triaxial compression, shearing, and bending, were applied to coal and rock. High-precision charge monitoring equipment was used to qualitatively describe the correlation between charge signal characteristics and stress, as well as the stages of coal and rock failure. Specifically, during the elastic stage, the charge signal was weak or even non-responsive during the linear increase of stress; the plastic stage was mainly characterized by rapid accumulation of coal and rock damage, with a slower stress increase and high, intermittently fluctuating charge signal amplitude; and during the failure stage, stress rapidly decreased from its peak, while the charge signal exhibited explosive growth. It is evident that the magnitude of stress does not directly reflect the strength of the charge signal. Due to an overemphasis on the relationship between stress magnitude and charge amplitude, the correlation between the changes in these two physical quantities themselves has been neglected. In reality, coal and rock failure is directly related to stress drop, and the magnitude of stress drop is the key factor determining the degree of coal and rock damage. Therefore, changes in stress and changes in charge amplitude should correspond, but currently, there is still a lack of effective methods to quantify this relationship.

[0004] In terms of monitoring technology and application, a coal and rock dynamic damage induction charge monitoring system has been developed for complex underground environments, forming a complete set of technologies and equipment. Combined with stress monitoring technology, it has been used in long-term industrial trials for mines with dynamic disasters such as rockburst and roof pressure, with good early warning effects. However, sometimes the charge signal and stress change characteristics are inconsistent or contradictory, which cannot be effectively explained. The key reasons are: (1) the bottleneck of quantitative characterization between charge and stress has not been broken through; (2) the time window scale is too narrow to describe the correlation between stress and charge signals. If the time window scale is too wide, the correlation coefficient between stress and charge signals will be close to 1, which will mask the changes in the details of the signals and cause distortion. The quantitative relationship between stress and charge is greatly affected by the time window. Therefore, it is necessary to find a suitable time window scale to more accurately reflect the correlation between the two. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method for quantifying the correlation between charge and stress in coal and rock failure and determining the optimal time window, thereby realizing the quantification of the correlation between charge and stress in the coal and rock failure process and the determination of the optimal observation time window.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window, including:

[0007] Acquire stress and charge signals during the coal and rock failure process;

[0008] The Empirical Mode Decomposition (EMD) method is used to decompose the stress signal into a series of intrinsic mode functions (IMFs) and a residual component, and the frequency characteristics corresponding to each intrinsic mode function are determined.

[0009] Based on the spectral distribution, low-frequency trend terms are removed, and the remaining intrinsic mode functions are reconstructed to obtain the detrended stress signal.

[0010] Using wavelet coherence analysis, the wavelet coherence coefficients of detrended stress and charge signals are calculated, and wavelet coherence spectra under different time window scales are output to obtain the correlation between stress and charge signals under different time window scales.

[0011] The optimal observation timescale was determined based on the correlation between the detrended stress and charge signals. Within the optimal observation timescale, the coordinated change law of stress and charge signals was analyzed to verify the effectiveness of the optimal time window.

[0012] Furthermore, the Empirical Mode Decomposition (EMD) method is used to decompose the stress signal into a series of intrinsic mode functions (IMFs) and a residual component. The specific method for determining the frequency characteristics corresponding to each IMF is as follows:

[0013] (1) Calculate the mean value of the upper and lower envelopes of stress;

[0014] Identify all local extrema from the original stress-time curve s(t) corresponding to the stress signal, and connect all the maxima points using cubic spline interpolation to form the upper and lower envelopes s. + (t), s - (t); then calculate the mean m1(t) of the upper and lower envelopes:

[0015] ;

[0016] (2) Calculate the eigenfunctions and residuals;

[0017] h1(t) is obtained by subtracting the mean of the upper and lower envelopes m1(t) from the original stress-time curve s(t):

[0018] ;

[0019] Check whether h1(t) satisfies the two conditions defined by the intrinsic mode function (IMF): the number of extreme points and the number of zero-crossing points do not differ by more than 1; the mean of the upper and lower envelopes at any point is zero; if satisfied, let the first intrinsic mode function be IMF1(t) = h1(t); the first residual be Res1(t) = s(t) - IMF1(t); if not satisfied, take h1(t) as the new signal s(t) and repeat the above steps (1) and (2) until the first intrinsic mode function IMF1 and the residual Res1(t) that satisfy the conditions are obtained;

[0020] Using the residual Res1(t) as a new signal, repeat steps (1) and (2) to calculate the stress mean envelope, eigenfunctions, and residuals of this signal, obtaining the second eigenmode function IMF2 and the residual Res2(t); in this way, the new residual is repeatedly used as a new signal until the k-th order eigenmode function IMF and the residual Res2(t) are obtained. k and the residual Res k Consider it as the final residual component Res;

[0021] (3) Use Fourier transform to determine the frequency distribution of each intrinsic mode function (IMF) and arrange the k IMFs from high frequency to low frequency.

[0022] Calculate the barycenter frequency x for each intrinsic mode function (IMF). c It reflects the dominant frequency position of each intrinsic mode function (IMF).

[0023] Furthermore, based on the spectral distribution, the low-frequency trend term is removed, and the remaining intrinsic mode functions are reconstructed to obtain the detrended stress signal. The specific method is as follows:

[0024] After identifying the low-frequency trend term based on the frequency distribution of each intrinsic mode function (IMF), the IMFs containing the low-frequency trend and the residual component Res in the EMD decomposition results are removed. Then, the other IMFs are reconstructed to obtain the detrended stress fluctuation curve.

[0025] Furthermore, the specific method for calculating the wavelet coherence coefficients of the detrended stress and charge signals using wavelet coherence analysis is as follows:

[0026] The destressed stress signal and the charge signal are respectively subjected to wavelet transform to obtain two wavelet coefficient matrices W. X (s), W Y (s), where s is the scaling factor that controls the scaling;

[0027] The cross-wavelet spectra of the detrended stress signal and the charge signal are calculated to determine the distribution of their common high-energy regions at different time scales;

[0028] The wavelet coherence coefficients of the detrended stress signal and the charge signal are calculated, and the wavelet coherence spectrum is output to reveal the dynamic correlation between the two signals at different time scales.

[0029] Furthermore, the specific method for determining the optimal observation time window scale based on the correlation between stress and charge signals under different time window scale domains is as follows:

[0030] Calculate the skewness S of the wavelet coherence coefficients of the downward stress signal and the charge signal at each time scale. kew ;

[0031] In S kew Select the optimal observation timescale within a timescale greater than 0;

[0032] Calculate the proportion of the duration corresponding to the high correlation coefficient intervals exceeding a set threshold at different time scales to the total loading duration of the coal body. The time scale corresponding to the peak of this proportion is taken as the optimal observation time window, as shown in the following formula:

[0033] ;

[0034] In the formula: P l l´ represents the proportion of the duration corresponding to a certain coherence coefficient interval at different time scales to the total loading duration of the coal body; l´ represents the loading duration of the coal body within a certain coherence coefficient interval at different time scales; l represents the total loading duration of the coal body.

[0035] The time proportion corresponding to a correlation coefficient greater than 0.8 is more statistically significant. The time window corresponding to the peak of this time proportion is taken as the optimal observation scale. The coordinated change law of stress and charge signals is analyzed within the optimal observation time scale to verify the effectiveness of the optimal time window.

[0036] Furthermore, the skewness S of the wavelet coherence coefficients of the detrended stress signal and the charge signal kew As shown in the formula below:

[0037] ;

[0038] In the formula: S kew Indicates the skewness of the coherence coefficient at each time scale; s i denoted by α, which represents the i-th wavelet coherence coefficient that varies with time at each time scale; μ represents the average value of the coherence coefficients at each time scale; and α represents the variance of the coherence coefficients at each time scale.

[0039] The beneficial effects of adopting the above technical solution are as follows: The method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window provided by this invention combines empirical mode decomposition (EMD) with wavelet coherence analysis, filters out the slow stress change trend term and retains high-frequency fluctuation characteristics, and realizes the evolution and quantitative characterization of the coherence coefficient of stress change and charge signal fluctuation under different time window scale domains; secondly, it introduces the coherence coefficient kurtosis and coherence coefficient time period ratio indicators, analyzes the influence law of the time window scale on the correlation results, and proposes for the first time a criterion for determining the optimal time window scale for charge signals, providing a quantifiable scale selection basis for the analysis of similar signals. Attached Figure Description

[0040] Figure 1 A flowchart illustrating the method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window, provided in an embodiment of the present invention;

[0041] Figure 2 The following are curves showing the relationship between stress and charge signals during the coal and rock failure process of four samples provided in this embodiment of the invention: (a) is the curve showing the relationship between stress and charge during the coal and rock failure process of sample B1, (b) is the curve showing the relationship between stress and charge during the coal and rock failure process of sample B2, (c) is the curve showing the relationship between stress and charge during the coal and rock failure process of sample B3, and (d) is the curve showing the relationship between stress and charge during the coal and rock failure process of sample B4.

[0042] Figure 3 The following are the relationship curves between stress and charge signal after the detrending term of four samples provided in the embodiments of the present invention: (a) is the relationship curve between stress and charge signal after the detrending term of sample B1, (b) is the relationship curve between stress and charge signal after the detrending term of sample B2, (c) is the relationship curve between stress and charge signal after the detrending term of sample B3, and (d) is the relationship curve between stress and charge signal after the detrending term of sample B4.

[0043] Figure 4 The wavelet coherence spectrum between stress and charge signals after detrending term is provided in the embodiments of the present invention, wherein (a) is the wavelet coherence spectrum of sample B1, (b) is the wavelet coherence spectrum of sample B2, (c) is the wavelet coherence spectrum of sample B3, and (d) is the wavelet coherence spectrum of sample B4.

[0044] Figure 5 Skewness plots of wavelet coherence coefficients at various time scales for four samples provided in embodiments of the present invention;

[0045] Figure 6 The following are time percentage diagrams for each coherence coefficient segment of four samples at different time scales provided in the embodiments of the present invention: (a) is the time percentage diagram for each coherence coefficient segment of sample B1 at different time scales, (b) is the time percentage diagram for each coherence coefficient segment of sample B2 at different time scales, (c) is the time percentage diagram for each coherence coefficient segment of sample B3 at different time scales, and (d) is the time percentage diagram for each coherence coefficient segment of sample B4 at different time scales.

[0046] Figure 7 The following are detailed feature maps showing the changes in coherence coefficient over time at the optimal time scale for four samples provided in this embodiment of the invention: (a) is a detailed feature map showing the changes in coherence coefficient over time at the optimal time scale for sample B1, (b) is a detailed feature map showing the changes in coherence coefficient over time at the optimal time scale for sample B2, (c) is a detailed feature map showing the changes in coherence coefficient over time at the optimal time scale, and (d) is a detailed feature map showing the changes in coherence coefficient over time at the optimal time scale for sample B4.

[0047] Figure 8 The average coherence coefficient diagram before and after the main failure at the optimal observation scale provided in this embodiment of the invention. Detailed Implementation

[0048] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0049] In this embodiment, the method for quantifying the correlation between coal and rock failure charge and stress, and determining the optimal time window, is as follows: Figure 1 As shown, it includes the following steps:

[0050] Step 1: Obtain stress and charge signals during the coal and rock failure process;

[0051] In this embodiment, the collected raw coal was processed into multiple coal body samples with dimensions of length × width × height = 50 × 50 × 100 mm, and the surfaces were polished to ensure that the unevenness of both ends was less than 0.02 mm. The coal body samples were divided into 4 groups, each consisting of 3 samples, for a total of 12 samples. Then, a displacement loading method was used, with the loading rates of the 4 groups of samples being respectively... , , , The sampling frequency for load and charge signals is 1000 Hz.

[0052] In this embodiment, four representative samples were selected from four loading rates and named B1, B2, B3, and B4 according to the loading rate from smallest to largest. Stress and charge signals of the coal and rock failure process of the four samples were obtained, and the relationship between stress and charge was analyzed. Figure 2 As shown, the stage of drastic change in charge amplitude mainly occurs near the peak and post-peak stages of stress. During this stage, coal body damage is most severe. Each stress drop phenomenon in the loaded sample represents a coal body fracturing event, indicating that the charge signal primarily reflects coal body failure. Therefore, the correlation between charge change and stress change is significant.

[0053] Step 2: Determine the correlation between stress changes and charge signal changes during the coal and rock failure process based on the wavelet coherence method;

[0054] The process of damage and failure of the coal-bearing body can be accompanied by stress fluctuations and changes in charge amplitude. Obviously, the focus should be on analyzing the correlation between stress changes and charge signal changes, rather than considering the macroscopic trend of the stress curve. Therefore, this invention first uses the Empirical Mode Decomposition (EMD) method to decompose the stress signal into a series of intrinsic mode functions (IMFs) and a residual component, determining the frequency characteristics corresponding to each IMF. Subsequently, based on the spectral distribution, low-frequency trend terms are removed, and the remaining IMFs are reconstructed to obtain the detrended stress signal. Finally, wavelet coherence analysis is used to calculate the wavelet coherence coefficients of the detrended stress signal and charge signal, outputting the wavelet coherence spectrum to obtain the correlation between the detrended stress and charge signals. The specific steps include:

[0055] Step 2.1: Using the Empirical Mode Decomposition (EMD) method, the stress signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual component, and the frequency characteristics corresponding to each intrinsic mode function are determined.

[0056] Empirical Mode Decomposition (EMD) is an effective tool for nonlinear signal processing. Its core advantage lies in its ability to adaptively decompose stress signals without pre-setting basis functions. The specific decomposition steps are as follows:

[0057] (1) Calculate the mean value of the upper and lower envelopes of stress;

[0058] Identify all local extrema from the original stress-time curve s(t) corresponding to the stress signal, and connect all the maxima points using cubic spline interpolation to form the upper and lower envelopes s. + (t), s - (t); then calculate the mean m1(t) of the upper and lower envelopes:

[0059] (1);

[0060] (2) Calculate the eigenfunctions and residuals;

[0061] h1(t) is obtained by subtracting the mean of the upper and lower envelopes m1(t) from the original stress-time curve s(t):

[0062] (2);

[0063] Check whether h1(t) satisfies the two conditions defined by the Intrinsic Mode Function (IMF): the number of extreme points and the number of zero-crossing points do not differ by more than 1; and the mean of the upper and lower envelopes at any point is zero. If satisfied, let the first IMF be IMF1(t) = h1(t); and the first residual be Res1(t) = s(t) - IMF1(t). If not satisfied, take h1(t) as the new signal s(t) and repeat the above steps until the first IMF1 and residual Res1(t) that satisfy the conditions are obtained.

[0064] Using the residual Res1(t) as a new signal, repeat steps (1) and (2) to calculate the stress mean envelope, eigenfunctions, and residuals of this signal, thus obtaining the second eigenmode function IMF2 and the residual Res2(t). This process is repeated, using the new residual as a new signal, to obtain IMF1 and Res1(t), until the k-th order eigenmode function IMF and the residual Res2(t) are obtained. k and the residual Res k It is considered as the final residual component Res.

[0065] (3) Use Fourier transform to determine the frequency distribution of each intrinsic mode function (IMF), as shown in equation (3), and arrange the k decomposed intrinsic mode functions (IMF) from high frequency to low frequency.

[0066] (3);

[0067] In the formula: x[n] is the value of each IMF, X[f] is the frequency domain distribution of each intrinsic mode function (IMF), N is the length of each IMF, f is the discrete frequency value of the IMF sequence obtained from the decomposition of the original stress signal, and j represents the imaginary unit, which satisfies .

[0068] Calculate the barycenter frequency x for each intrinsic mode function (IMF). c It reflects the dominant frequency position of each intrinsic mode function (IMF), and the calculation formula is as follows:

[0069] (4);

[0070] Step 2.2: Based on the frequency distribution of each intrinsic mode function (IMF), remove the low-frequency trend term, and then reconstruct the remaining intrinsic mode functions to obtain detrended stress information;

[0071] After identifying the low-frequency trend term based on the frequency distribution of each intrinsic mode function (IMF), the IMFs containing low-frequency trends and the residual component Res in the EMD decomposition results are removed. The remaining IMFs are then reconstructed to obtain a stress fluctuation curve that has been detrended to some extent.

[0072] (5);

[0073] In the formula: D s The stress after detrending is expressed in MPa, k is the number of IMF components into which each stress curve is decomposed, and m represents the threshold of the intrinsic mode function. The sum of the IMF components in columns 1 to m is the detrending stress.

[0074] In this embodiment, the EMD method is used to decompose the four sets of stress-time curves into nine intrinsic mode functions and one residual component. Among all signals, IMF1 to IMF4 reflect high-frequency, rapidly fluctuating signal components, while IMF5 to IMF9, which are lower down, exhibit gentle fluctuations and long periods. Res changes slowly over time, and the oscillation mode is not significant, reflecting the low-frequency trend of the signal.

[0075] To remove trend terms and more accurately capture signals with significant fluctuations, this embodiment employs the FFT transform method to obtain the spectrum of each IMF component. The dominant frequencies of the IMF components of all signals are concentrated in the 0-40 Hz range, especially IMF1 and IMF2. The amplitudes of most IMF components in the high-frequency band (greater than 100 Hz) approach zero, indicating that the stress signal is predominantly low-frequency. The spectra of IMF5-IMF9 components are concentrated in an extremely narrow frequency range, even nearly a single frequency, indicating that the proportion of high-order, high-frequency IMFs in the original stress signal is extremely small and can be eliminated.

[0076] The centroid frequency of each intrinsic mode function (IMF) is the weighted average frequency of the signal energy in the frequency domain, which can be used to further quantify the frequency domain characteristics of each IMF component. From Table 1, the centroid frequencies of IMF5~IMF9 components of samples B1, B3, and B4, and IMF6~IMF9 components of sample B2, are less than 1 Hz, far below the Nyquist limit of 500 Hz, which conforms to the definition of trend components. Therefore, components related to stress change trends mainly exist in these IMF components. Using equation (5), the IMF components after removing the trend term are reconstructed to obtain the detrended stress change curve, which shows good correspondence with the fluctuations of the original stress curve, such as... Figure 3 As shown, while preserving the characteristics of stress fluctuations, the trend component was effectively removed, and the correspondence between the significant locations of stress changes and the fluctuations of the charge signal was more intuitively displayed.

[0077] Table 1. Barycenter frequencies of each eigenmode function

[0078]

[0079] Step 2.2: Using wavelet coherence analysis, calculate the wavelet coherence coefficients of the detrended stress and charge signals, output the wavelet coherence spectrum, and obtain the correlation between the detrended stress and charge signals;

[0080] Wavelet coherence coefficient is a method for analyzing the correlation between two sets of signals in the time-frequency domain, revealing the dynamic correlation between the two signals at different time intervals. This invention uses the Morlet wavelet basis to calculate and analyze the correlation between detrended stress and charge signals. The specific process is as follows:

[0081] Wavelet coherence analysis is based on wavelet transform; therefore, wavelet transforms are performed on the destressed stress signal and charge signal respectively to obtain two wavelet coefficient matrices W. X (s), W Y (s), the calculation formula is shown in (6):

[0082] (6);

[0083] In the formula: For the signal data to be analyzed, s is the scaling factor that controls the scaling, b is the translation factor that controls the translation, and ψ() is the wavelet basis function. The scaling factor s is similar to the window length of the windowed Fourier transform. The larger the scale, the longer the wavelet function is stretched in the time domain, and the overall trend of the signal can be observed. The smaller the scale, the shorter the wavelet function is compressed in the time domain, and transient fluctuations can be captured.

[0084] Then, the cross-wavelet spectra of the detrended stress signal and the charge signal are calculated to study the distribution of common high-energy regions at different time scales. Regions with larger absolute values ​​of the cross-wavelet spectra indicate that there are common high-energy driving factors or causal relationships between the two.

[0085] (7);

[0086] In the formula: W XY (s) represents the cross-wavelet spectrum of the destressed stress signal and charge signals X and Y, W X (s) and W Y (s) represent the wavelet coefficient matrices of the detrended stress signal and charge signals X and Y, respectively. Let Y be the complex conjugate wavelet coefficient matrix of the charge signal Y.

[0087] Finally, the wavelet coherence coefficients of the detrended stress signal and the charge signal are calculated, and the wavelet coherence spectrum is output to reveal the dynamic correlation between the two signals at different time scales.

[0088] (8);

[0089] In the formula: S is the wavelet coherence coefficient and S is the smoothing operator. The value of the wavelet correlation coefficient is in the range of 0 to 1. The larger the value, the better the correlation between the detrended stress signal and the charge signal.

[0090] In this embodiment, wavelet coherence analysis is used to calculate the coherence coefficients of stress and charge signals under different time window scales, and wavelet coherence maps under different time window scale domains are output, such as... Figure 4 As shown, this better reveals the synchronicity of changes in stress and charge.

[0091] Step 3: Determine the optimal observation time scale for charge monitoring based on the correlation between the detrended stress and charge signals. Analyze and verify the coordinated change law of stress and charge signals within the optimal observation time scale to verify the effectiveness of the optimal time window.

[0092] The coherence coefficients of stress and charge in wavelet coherence maps exhibit significant differences across different time scales. The coherence coefficients of stress and charge signals are smaller before the peak and larger after the peak. Overall, the coherence coefficient increases with increasing time scale. At smaller time scales, the coherence coefficients are generally low; if the time scale is too small, it becomes difficult to describe the correlation between stress and charge signals, resulting in low resolution. At larger time scales, the coherence coefficients of stress and charge signals are larger; if the time scale is too large, the coherence coefficients approach 1, masking subtle changes in the signals and causing distortion. Therefore, the coherence coefficients between stress and charge are significantly affected by the time scale, necessitating the search for a suitable time scale to accurately reflect their correlation.

[0093] To determine a suitable range for the time scale domain, this invention introduces the skewness S of the coherence coefficient at each time scale from statistics. kew The formula for calculating this parameter is as follows:

[0094] (9);

[0095] In the formula: S kew Indicates the skewness of the coherence coefficient at each time scale; s i denoted by α, which represents the i-th wavelet coherence coefficient that varies with time at each time scale; μ represents the average value of the coherence coefficients at each time scale; and α represents the variance of the coherence coefficients at each time scale.

[0096] exist Figure 5 In the middle, S kew >0 indicates that, at this time scale, the coherence coefficient is mostly less than the mean, and a few are much greater than the mean. kew A value <0 indicates that, at this time scale, most coherence coefficients are greater than the mean, while a few are much smaller than the mean. Based on this characteristic, the entire time scale domain can be roughly divided into two parts, as shown in Table 2. Skewness S kew The correlation coefficient <0 generally indicates a high correlation between stress changes and charge signals on a large scale, suggesting a sustained and stable relationship. However, the stress-charge signal synchronous response is a short-term, rapid change; therefore, the optimal observation timescale should be within 1 second. kew Selected within a timescale greater than 0.

[0097] Table 2 Time Scale Domain Division for Each Sample

[0098]

[0099] Based on the time proportion of the high coherence coefficient interval, the optimal time scale for the synchronous response of stress-charge signals during coal damage and failure is further determined. This involves calculating the proportion of the duration of a certain coherence coefficient interval at different time scales to the total loading time of the coal body, as shown in the following formula:

[0100] (10);

[0101] In the formula: P l l´ represents the proportion of the duration corresponding to a certain coherence coefficient interval at different time scales to the total duration of coal loading; l´ represents the duration of coal loading within a certain coherence coefficient interval at different time scales; l represents the total duration of coal loading.

[0102] In this embodiment, the time occupancy of each coherence coefficient segment at different time scales is as follows: Figure 6 As shown, at larger time scales, coherence coefficients close to 1 generally account for a high proportion, and on excessively large time scales, the proportion of high coherence coefficients approaches 100%, which is unrealistic and severely distorted. A better time scale should clearly reflect the hierarchical distribution of different coherence coefficients at the same time scale; that is, when stress and charge fluctuate synchronously, the coherence coefficient significantly increases, while at other times, the coherence coefficient remains at a low level. Therefore, a relatively smaller time scale is more realistic, especially the time proportion corresponding to coherence coefficients greater than 0.8, which is more statistically significant. The time scale corresponding to the peak of this time proportion can be taken as the optimal observation scale, i.e., the optimal time scales for the four groups of samples are 5.67 s, 3.53 s, 3.62 s, and 0.89 s, respectively. The coordinated change law of stress and charge signals is analyzed within the optimal observation time scale to verify the effectiveness of the optimal time window.

[0103] In this embodiment, the refined characteristics of the coherence coefficient change over time at the optimal time scale for the above four groups of samples are as follows: Figure 7As shown, besides the area near the peak and the post-peak failure stage, the coherence coefficient also exhibits a short-term increase during the compaction stage. During the compaction stage, the charge signal oscillation amplitudes of samples B1 to B4 remained stable within the ranges of ±0.0053 pC, ±0.0091 pC, ±0.0097 pC, and ±0.0088 pC, respectively. However, sample B1 suddenly dropped to -0.0098 pC at 301.632 s, sample B2 suddenly dropped to -0.0704 pC at 233.825 s, sample B3 jumped to +0.0163 pC at 51.161 s, and sample B4 jumped to +0.0125 pC at 41.278 s. This indicates that deformation and slip friction during the compaction stage also generate minute abrupt changes in charge signals, and the coherence coefficient can effectively capture the correlation between stress and charge. Near the peak value and during the failure stage, coal seam fractures rapidly propagate and penetrate, with both stress and charge signals exhibiting significant fluctuations. Sudden stress drops and high-amplitude charge signals are abundant, and stress and charge signals show a high degree of correlation over a long period, with the coherence coefficient reaching nearly 1. In summary, wavelet coherence coefficients can effectively reflect the synchronous changes in stress and charge signals. Combined with the finding that the average coherence coefficient after the main failure is higher than before failure at the optimal observation timescale for all four groups of samples (see details...), Figure 8 It is not difficult to see that abrupt changes in charge amplitude can effectively reflect changes in stress and are highly correlated with changes in stress.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for quantifying the correlation between coal and rock failure charge and stress, and determining the optimal time window, characterized in that, include: Acquire stress and charge signals during the coal and rock failure process; The Empirical Mode Decomposition (EMD) method is used to decompose the stress signal into a series of intrinsic mode functions (IMFs) and a residual component, and the frequency characteristics corresponding to each intrinsic mode function are determined. Based on the spectral distribution, low-frequency trend terms are removed, and the remaining intrinsic mode functions are reconstructed to obtain the detrended stress signal. Using wavelet coherence analysis, the wavelet coherence coefficients of detrended stress and charge signals are calculated, and wavelet coherence spectra under different time window scales are output to obtain the correlation between stress and charge signals under different time window scales. To determine the optimal observation timescale based on the correlation between stress and charge signals under different time window scales, the coordinated variation law of stress and charge signals is analyzed within the optimal observation timescale to verify the effectiveness of the optimal time window. The specific method is as follows: Calculate the skewness S of the wavelet coherence coefficients of the downward stress signal and the charge signal at each time scale. kew ; In S kew Select the optimal observation timescale within a timescale greater than 0; Calculate the proportion of the duration corresponding to the high correlation coefficient intervals exceeding a set threshold at different time scales to the total loading duration of the coal body. The time scale corresponding to the peak of this proportion is taken as the optimal observation time window, as shown in the following formula: ； In the formula: P l l´ represents the proportion of the duration corresponding to a certain coherence coefficient interval at different time scales to the total loading duration of the coal body; l´ represents the loading duration of the coal body within a certain coherence coefficient interval at different time scales; l represents the total loading duration of the coal body. The time proportions corresponding to correlation coefficients greater than 0.8 are more statistically significant, and the time window corresponding to the peak of this time proportion is taken as the optimal observation scale; The coordinated variation of stress and charge signals within the optimal observation timescale was analyzed to verify the effectiveness of the optimal time window; The skewness S of the wavelet coherence coefficient between the destressed stress signal and the charge signal kew As shown in the formula below: ； In the formula: S kew Indicates the skewness of the coherence coefficient at each time scale; s i denoted by α, which represents the i-th wavelet coherence coefficient that varies with time at each time scale; μ represents the average value of the coherence coefficients at each time scale; and α represents the variance of the coherence coefficients at each time scale.

2. The method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window according to claim 1, characterized in that, The Empirical Mode Decomposition (EMD) method is used to decompose the stress signal into a series of intrinsic mode functions (IMFs) and a residual component. The specific method for determining the frequency characteristics corresponding to each IMF is as follows: (1) Calculate the mean value of the upper and lower envelopes of stress; Identify all local extrema from the original stress-time curve s(t) corresponding to the stress signal, and connect all the maxima points using cubic spline interpolation to form the upper and lower envelopes s. + (t), s - (t); then calculate the mean m1(t) of the upper and lower envelopes: ； (2) Calculate the eigenfunctions and residuals; h1(t) is obtained by subtracting the mean of the upper and lower envelopes m1(t) from the original stress-time curve s(t): ； Check whether h1(t) satisfies the two conditions defined by the intrinsic mode function (IMF): the number of extreme points and the number of zero-crossing points do not differ by more than 1; the mean of the upper and lower envelopes at any point is zero; if satisfied, let the first intrinsic mode function be IMF1(t) = h1(t); the first residual be Res1(t) = s(t) - IMF1(t); if not satisfied, take h1(t) as the new signal s(t) and repeat the above steps (1) and (2) until the first intrinsic mode function IMF1 and the residual Res1(t) that satisfy the conditions are obtained; Using the residual Res1(t) as a new signal, repeat steps (1) and (2) to calculate the stress mean envelope, eigenfunctions, and residuals of this signal, obtaining the second eigenmode function IMF2 and the residual Res2(t); in this way, the new residual is repeatedly used as a new signal until the k-th order eigenmode function IMF and the residual Res2(t) are obtained. k and the residual Res k Consider it as the final residual component Res; (3) Use Fourier transform to determine the frequency distribution of each intrinsic mode function (IMF) and arrange the k IMFs from high frequency to low frequency. Calculate the barycenter frequency x for each intrinsic mode function (IMF). c It reflects the dominant frequency position of each intrinsic mode function (IMF).

3. The method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window according to claim 2, characterized in that, The specific method for removing low-frequency trend terms based on the spectral distribution and then reconstructing the remaining intrinsic mode functions to obtain the detrended stress signal is as follows: After identifying the low-frequency trend term based on the frequency distribution of each intrinsic mode function (IMF), the IMFs containing the low-frequency trend and the residual component Res in the EMD decomposition results are removed. Then, the other IMFs are reconstructed to obtain the detrended stress fluctuation curve.

4. The method for quantifying the correlation between coal and rock failure charge and stress and determining the optimal time window according to claim 3, characterized in that, The specific method for calculating the wavelet coherence coefficients of the detrended stress and charge signals using wavelet coherence analysis is as follows: The destressed stress signal and the charge signal are respectively subjected to wavelet transform to obtain two wavelet coefficient matrices W. X (s), W Y (s), where s is the scaling factor that controls the scaling; The cross-wavelet spectra of the detrended stress signal and the charge signal are calculated to determine the distribution of their common high-energy regions at different time scales; The wavelet coherence coefficients of the detrended stress signal and the charge signal are calculated, and the wavelet coherence spectrum is output to reveal the dynamic correlation between the two signals at different time scales.

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