A Defect Rock Mass Early Warning Method Based on Multifractal Spectrum and Damage Variables

Abstract

This invention discloses a method for early warning of defective rock masses based on multifractal spectrum and damage variables, belonging to the field of rock mass disaster early warning technology. It includes extracting time-varying data sequences of acoustic emission signals from slope rock masses and calculating the dynamically adaptive sliding window length; determining the ringing count time sequence of each sliding window based on the time-varying data sequence, and performing multi-scale deconstruction based on Haar wavelets to calculate the multi-resolution measure of each sub-interval within the sliding window; determining the upper and lower limits of the weights of each multi-resolution measure and calculating the spectral width of the multifractal spectrum for each sliding window; calculating the rock mass damage index and its acceleration at each moment in the rock mass damage history, and establishing a relationship curve between the spectral width of the multifractal spectrum and the damage index; determining the jump points of the damage index acceleration and the jump points of the spectral width of the multifractal spectrum based on the relationship curve; when the two jump points occur at the same moment, that moment is the early warning point for slope failure.

Description

Technical Field

[0001] This invention pertains to slope early warning technology, specifically involving a defect rock mass early warning method based on multiple fractal spectra and damage variables. Background Technology

[0002] As a complex geological medium, rock mass contains numerous initial defects such as joints, pores, and fissures. Under external loads, these defects easily form stress concentration zones, triggering the initiation, propagation, and penetration of secondary cracks. The crack evolution process exhibits both significant size effects and path sensitivity; its dynamic propagation often induces the synergistic effect of multiple cracks, ultimately forming macroscopic fracture zones that severely degrade the structural integrity and bearing capacity of the rock mass. Crucially, the rock mass defect network directly controls slope stability: well-developed joints, fissures, or weak interlayers can combine to form potential slip surfaces or cutting surfaces, limiting the slope failure mode and scale; defects significantly reduce the shear and tensile strength of the rock mass, exacerbating its deformation and failure risk under shear / tensile stress; and, most notably, the spatial distribution, orientation, and connectivity differences of defects dominate the complexity of failure, causing the instability process to often exhibit a progressive pattern of "creep along structural surfaces → local rock bridge tensile-shear failure → fracture zone penetration → overall instability," demonstrating strong heterogeneity and path dependence. Therefore, how to effectively predict the failure of defective rock masses and accurately capture the precursor information of defective rock mass failure has become a technical challenge and research hotspot for defective rock mass early warning.

[0003] Prior art CN 115144269 B discloses a method and apparatus for predicting and forecasting rockbursts based on time-varying multifractal spectra of acoustic emission. The disclosed technique involves: extracting multiple absolute energy data of acoustic emission from a time series using a sliding event window; calculating the multifractal spectrum and singularity index to determine the spectral width of each multifractal spectrum. By comparing the spectral widths of all multifractal spectra, the starting point where the spectral width continues to increase is obtained, and this point is taken as the characteristic point for rockburst prediction; the ratio of the maximum principal stress value of the rockburst test load corresponding to the characteristic point to the uniaxial compressive strength of the rock specimen is taken as the criterion for rockburst prediction.

[0004] Existing rockburst prediction and forecasting methods provide early warnings of rock mass failure and employ multifractal methods to deconstruct acoustic emission time-series parameters. However, multifractal methods based on partition functions have the following drawbacks:

[0005] The Legendre transformation derivative process amplifies the error, affecting the mass function. pass and The linear fit is overly dependent on the scale. The regression residuals are large, which affects the singular spectral width ( The calculation accuracy is low; the physical meaning is ambiguous. It has no direct physical meaning and is difficult to directly correspond to geological elements; the boundary effect is obvious, and the fixed interval division causes the boundary singularities to be evenly distributed.

[0006] The rock mass naturally contains heterogeneous structures such as joints and bedding, which violates the self-similarity assumption and leads to singular spectral widths ( The deviation from the actual damage state causes the early warning to be inaccurate.

[0007] Rock masses are often in a multi-physical field coupled geological environment. The combined effects of groundwater seepage-stress coupling and temperature changes may change the evolution law of rock mass damage. Using a single multifractal method to provide early warning of rock mass failure makes it difficult to accurately determine the occurrence time of time-varying damage in rocks. Summary of the Invention

[0008] To address the aforementioned shortcomings in existing technologies, the defect rock mass early warning method based on multifractal spectrum and damage variables provided by this invention solves the problems of low accuracy in calculating singular spectrum width and low accuracy in early warning of rock mass failure caused by using a single multifractal method.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0010] A method for early warning of defective rock masses based on multifractal spectrum and damage variables is provided, which includes the following steps:

[0011] S1. Extract the time-varying data sequence of acoustic emission signal characteristic parameters in the slope rock mass damage process, and calculate the dynamic adaptive sliding window length based on the maximum local variance of the time-varying data sequence.

[0012] S2. Based on the time-varying data sequence, determine the ringing count time sequence of each sliding window, and perform multi-scale deconstruction based on Haar wavelets to calculate the multi-resolution measure of each sub-interval within the sliding window.

[0013] S3. Determine the upper and lower limits of the weights for each multi-resolution measure. Based on all the upper and lower limits of the weights for each sliding window and the multi-resolution measure, calculate the spectral width of the multifractal spectrum for each sliding window.

[0014] S4. Calculate the rock mass damage index and its damage index acceleration at each moment in the rock mass damage process, and establish the relationship curve between the spectral width of the multifractal spectrum and the damage index through time matching.

[0015] S5. Determine the jump point of the damage index acceleration and the jump point of the spectral width of the multifractal spectrum based on the relationship curve. When the two jump points occur at the same time, that time is the early warning point for rock mass failure.

[0016] Furthermore, the expression for calculating the dynamically adaptive sliding window length is:

[0017]

[0018]

[0019] in, Let be the length of the sliding window at time t; The length of the reference window; As a regulating factor; Local variance of time-varying data series Maximum value; The variance within the window centered at time t; The half-window width used for calculating local variance; This represents the mean of the time series within the sliding window; For time series data located before t Observations per unit of time.

[0020] The beneficial effects of the above technical solution are as follows: This solution adopts the above design, and introduces a local variance dynamic adjustment factor. Fixed window length Reconstructed as time-varying parameters Its working mechanism is that the non-stationarity of the signal leads to the intensity of local fluctuations. The distribution exhibits heterogeneity; traditional fixed windows result in oversmoothing in low-variance regions due to information redundancy, and underfitting in high-variance regions due to insufficient sampling. The scaling mechanism ensures that the window length is strictly positively correlated with the intensity of local singularities, through... Achieve sensitivity modulation, denominator By establishing a global normalization constraint, the window expansion range is ensured to not exceed the system's carrying capacity limit. This approach suppresses boundary effects while focusing computational resources on critical abrupt change periods (such as the rock sample yielding stage), thus avoiding invalid computation in the stable region.

[0021] Furthermore, the expression for calculating the multi-resolution measure of each sub-interval is as follows:

[0022]

[0023]

[0024] in, The sub-interval scale for each window deconstruction; For scale The next Multi-resolution measure of sub-intervals; To take the absolute value; and respectively scale Next The j-th wavelet coefficient; The total number of wavelet coefficients obtained by multi-scale deconstruction of Haar wavelets; and respectively scale Next The observations of the i and i+1 intervals.

[0025] The beneficial effects of the above technical solution are as follows: This solution uses Haar wavelet basis functions To replace traditional manual interval segmentation, a scale-adaptive energy measure is established. Its physical essence lies in: wavelet coefficients The essence is scale. The high-frequency residual components of the signal directly characterize the local fluctuation amplitudes obscured by traditional mean smoothing; global energy normalization of the denominator eliminates scale dependence. Compared to fixed interval difference... Wavelet decomposition achieves cross-scale detail decoupling through orthogonal basis functions, reduces boundary alignment error while preserving energy conservation, and improves the sensitivity to abrupt change points.

[0026] Furthermore, the expressions for the upper and lower bounds of the weights for each multi-resolution measure are determined as follows:

[0027]

[0028] in, and These are the upper and lower limits of the weight, respectively; This is the tolerance parameter.

[0029] The beneficial effects of the above technical solution are: this strategy constructs by measuring the extreme value ratio. and order Its control logic lies in: molecules The quantization signal singularity dispersion reflects the physical dynamic range that needs to be covered; denominator Then through tolerance parameters Implement exponential decay constraints, when When small fluctuations occur due to noise disturbances, inhibition This design minimizes sensitivity and avoids invalid calculations. Range adaptive matching signal essential characteristics (such as high-intensity rock samples) Smaller Automatic reduction can reduce the amount of computation and improve computational efficiency while ensuring computational accuracy.

[0030] Furthermore, the method for calculating the spectral width of the multifractal spectrum for each sliding window, based on all weight upper and lower limits and multiresolution measures for each sliding window, includes:

[0031] S31. Weight each multi-resolution measure according to its upper and lower limits to obtain its maximum and minimum weighted measures:

[0032]

[0033] in, Let q be the weighted measure corresponding to the weight q, where q takes the value of and At that time, the maximum and minimum weighted measures are obtained; For scale The next Multi-resolution measure of sub-intervals;

[0034] S32. Based on the upper and lower bounds of the weights and the maximum and minimum weighted measures, calculate the upper and lower bounds of the singularity index and the eigenvalue index respectively:

[0035]

[0036]

[0037] in, and These are the singular exponent and feature exponent corresponding to the weight q, respectively, where q takes the value of and When the singularity index and the characteristic index are obtained, the upper and lower limits are obtained respectively;

[0038] S33. Calculate the spectral width of the multifractal spectrum for each sliding window based on the upper and lower limits of the singularity index. :

[0039]

[0040] in, and These are the upper and lower limits of the singularity index.

[0041] The beneficial effects of the above technical solution are as follows: In essence, it is the original measure. The result of moment renormalization, when High-measurement region magnification The time-amplified low-measure region; while the regression process uses least squares fitting. The linear relationship with the information entropy term avoids the second-order error amplification effect of the Legendre transformation in previous schemes.

[0042] Furthermore, methods for extracting time-varying data sequences of acoustic emission signal characteristic parameters during rock mass damage processes include:

[0043] The entire time series of acoustic emission characteristic parameters during the rock mass damage process Extracting a portion of the time series , The length of time is ;

[0044] In the time window In the middle, the data collection time interval is Obtain the time window Time-varying data sequences for:

[0045]

[0046] in, For time window The update rate of the time series data; m is the window index, which is a positive integer, m=0 indicates the first window; for The extracted time series.

[0047] The beneficial effects of the above technical solution are: the formula introduces an adjustable step size factor. and fixed time window length The original acoustic emission time series Reconstructed into a dynamic window subset The physical mechanism lies in the fact that non-stationary AE signals exhibit statistical aliasing characteristics on a global scale, while The settings ensure that the signal within the window satisfies the local stationarity assumption, providing a mathematical basis for multifractal spectrum calculation; sliding step size factor The optimal relationship between computational resolution and efficiency is achieved by controlling the window overlap rate, that is, while ensuring... Under the premise of continuous and smooth curves, the computational complexity of traditional point-by-point sliding calculations is reduced; denominator The introduction of this feature ensures that the model strictly satisfies dimensional consistency, avoiding spectral parameter distortion caused by time-domain scaling; ultimately, this design supports... The millisecond-level dynamic tracking successfully captured the critical characteristics of rock mass failure, providing advanced signals for early warning.

[0048] Furthermore, the expression for calculating the damage exponential acceleration of the rock mass at each moment in the rock mass damage process is as follows:

[0049] ,

[0050] in, Let be the damage exponential acceleration at time t; and The rock mass damage index is denoted as t and t-1. The cumulative acoustic emission count represents the total number of times the rock has completely failed. This represents the cumulative ringing count at time t; For time intervals.

[0051] The beneficial effects of the above technical solution are as follows: This relation defines the damage exponent evolution rate as the limit differential operator. ,in A normalized damage metric is constructed. Its physical mechanism lies in: molecules... Essentially, it is a discrete approximation of the damage rate, reflecting the dynamic characteristics of microcrack propagation; denominator As a time scale factor, it eliminates human interference in the sampling interval through limiting operations; As a benchmark for failure state scaling, the damage index Strictly meet The physical boundedness of the material. This design is mathematically equivalent to an explicit discrete solution to the damage constitutive equation, transforming the abstract rock degradation process into observable acoustic emission metrology parameters.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] This scheme uses Haar wavelet multi-scale deconstruction to compute multi-resolution measures, replacing traditional manual segmentation, and reducing the computational complexity of measures from... Down to By combining weighted measures, the chain error of the Legendre transformation is eliminated. The processing speed is significantly improved when dealing with slope monitoring data of tens of thousands of records. Since there is no error caused by the derivative process of the Legendre transformation, the accuracy of the calculated multifractal spectrum's spectral width is guaranteed.

[0054] To address the local heterogeneity of time-varying slope deformation sequences, this scheme dynamically adjusts the sliding window length based on local variance. This results in different window lengths for time-varying data sequences of varying lengths. By dynamically adjusting the window length in this way, the amount of data distributed within the sliding window can be more rationally allocated, thereby ensuring more accurate spectral widths of the multifractal spectra calculated for each sliding window. This provides key technical support for high-frequency data acquisition.

[0055] This scheme uses the above expression to calculate the upper and lower limits of the weights of the multi-resolution measure. It is an adaptive parameter mechanism that can effectively suppress scale truncation error. The dynamic adjustment of the window length can capture the abrupt change signal of slope deformation. It automatically constrains the range of q, suppresses extreme q value fluctuations, and prevents computational redundancy.

[0056] The damage index acceleration is directly related to the constitutive equation of the rock, characterizing the cumulative damage and reflecting the overall instability trend of the slope, i.e., the macroscopic mechanical state, reflecting the overall trend of the failure process. Spectral width characterizes the spatial heterogeneity of microscopic damage; the divergence or synergy between the two time series can identify different failure stages. An increase in spectral width is accompanied by a sharp rise in the damage index, i.e., an early warning signal. This allows for cross-validation of the signal's authenticity, eliminating outliers caused by isolated noise, thereby ensuring the accuracy of the early warning system in this scheme. Attached Figure Description

[0057] Figure 1 This is a flowchart of a defect rock mass early warning method based on multifractal spectrum and damage variables.

[0058] Figure 2 The data obtained from the AE sensor of the four groups of samples in the example were obtained. The curve relating to q.

[0059] Figure 3 The AE sensor data obtained from the four groups of samples in the example were... The curve relating to q.

[0060] Figure 4 The AE sensor data obtained from the four groups of samples in the example were... and The relationship curve.

[0061] Figure 5 This is a graph showing the relationship between the damage index and the loading process.

[0062] Figure 6 The damage index obtained from the AE sensor of the four groups of samples in the example. and The relationship diagram, where gray circles represent The point of sudden leap. Detailed Implementation

[0063] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0064] refer to Figure 1 , Figure 1 A flowchart of a defect rock mass early warning method based on multifractal spectrum and damage variables is shown; for example... Figure 1 As shown, the method S includes steps S1 to S5.

[0065] In step S1, time-varying data sequences of acoustic emission signal characteristic parameters in the slope rock mass damage history are extracted, and the dynamically adaptive sliding window length is calculated based on the maximum local variance of the time-varying data sequences.

[0066] The expression for calculating the dynamically adaptive sliding window length is:

[0067]

[0068]

[0069] in, Let be the length of the sliding window at time t; The length of the reference window; This is an adjustment factor that controls the sensitivity of the window length to local variance. This value should be selected based on the calibration of the measurement area in the field. The present invention selects... ; Local variance of time-varying data series Maximum value; The variance within the window centered at time t; The half-window width used for calculating local variance; This represents the mean of the time series within the sliding window; For time series data located before t Observations per unit of time.

[0070] In implementation, the preferred method for extracting time-varying data sequences of acoustic emission signal characteristic parameters during the rock mass damage process includes:

[0071] The entire time series of acoustic emission characteristic parameters during the rock mass damage process Extracting a portion of the time series , The length of time is ;

[0072] In the time window In the middle, the data collection time interval is Obtain the time window Time-varying data sequences for:

[0073]

[0074] in, For time window The update rate of the time series data; m is the window index, which is a positive integer, m=0 indicates the first window; for The extracted time series.

[0075] In step S2, the ringing count timing of each sliding window is determined based on the time-varying data sequence, and multi-scale deconstruction is performed based on Haar wavelets to calculate the multi-resolution measure of each sub-interval within the sliding window.

[0076] In implementation, this scheme preferably uses the following expression to calculate the multi-resolution measure for each sub-interval:

[0077]

[0078]

[0079] in, The sub-interval scale for each window deconstruction; For scale The next Multi-resolution measure of sub-intervals; To take the absolute value; and respectively scale Next The j-th wavelet coefficient; The total number of wavelet coefficients obtained by multi-scale deconstruction of Haar wavelets; and respectively scale Next The observations of the i and i+1 intervals.

[0080] In step S3, the upper and lower limits of the weights for each multi-resolution measure are determined, and their expressions are as follows:

[0081]

[0082] in, and These are the upper and lower limits of the weight, respectively; This is a tolerance parameter. It is used to avoid errors due to excessively small measurements. If the value is too large, it will waste computation time steps. Therefore, in the implementation of this invention, the following method is selected: ;

[0083] The spectral width of the multifractal spectrum of each sliding window is calculated based on all weight upper and lower bounds and multiresolution measures of each sliding window. The detailed implementation method is as follows:

[0084] S31. Weight each multi-resolution measure according to its upper and lower limits to obtain its maximum and minimum weighted measures:

[0085]

[0086] in, Let q be the weighted measure corresponding to the weight q, where q takes the value of and At that time, the maximum and minimum weighted measures are obtained; For scale The next Multi-resolution measure of sub-intervals;

[0087] S32. Based on the upper and lower bounds of the weights and the maximum and minimum weighted measures, calculate the upper and lower bounds of the singularity index and the eigenvalue index respectively:

[0088]

[0089]

[0090] in, and These are the singular exponent and feature exponent corresponding to the weight q, respectively, where q takes the value of and When the singularity index and the characteristic index are obtained, the upper and lower limits are obtained respectively;

[0091] S33. Calculate the spectral width of the multifractal spectrum for each sliding window based on the upper and lower limits of the singularity index. :

[0092]

[0093] in, and These are the upper and lower limits of the singularity index.

[0094] In step S4, the rock mass damage index and its damage index acceleration at each moment in the rock mass damage process are calculated, and the relationship curve between the spectral width of the multifractal spectrum and the damage index is established through time matching.

[0095] In implementation, this scheme prioritizes calculating the expression for the damage exponential acceleration of the rock mass at each moment in the rock mass damage history, as follows:

[0096] ,

[0097] in, Let be the damage exponential acceleration at time t; and The rock mass damage index is denoted as t and t-1. The cumulative acoustic emission count represents the total number of times the rock has completely failed. This represents the cumulative ringing count at time t; For time intervals.

[0098] The data can be obtained through calibration using indoor triaxial rock mechanics tests or by statistical analysis of historical data. The data was obtained from on-site acoustic emission monitoring.

[0099] In step S5, the jump point of the damage exponential acceleration and the jump point of the spectral width of the multifractal spectrum are determined according to the relationship curve. When the two jump points occur at the same time, that time is the rock mass failure warning point.

[0100] The defective rock mass early warning method of this scheme is described below with reference to specific embodiments:

[0101] This embodiment uses data from a historical case study, specifically a slope adit with a depth of approximately 540m, whose main lithology is granite pegmatite. Indoor triaxial compressive strength tests were conducted on granite pegmatite samples drilled on-site. All samples were processed into standard cylinders with geometric dimensions of Φ50mm × 100mm, and both ends were polished to ensure a non-parallelism error of less than ±0.05mm. The samples were divided into four groups, with three samples in each group serving as controls. The differences between the groups primarily lay in the mineral content of the rock itself, especially the biotite content (a natural defect).

[0102] The loading system used in the experiment was a WHY-1000 electro-hydraulic servo pressure testing machine with a maximum axial load capacity of 1000 kN and a loading rate set at 0.1 mm / min. Throughout the loading process, resistance strain gauges (model: 120-22AA) were used to measure the axial and circumferential displacement of the specimen, and a dynamic and static strain analyzer (TST3828EN) was used to acquire strain data. Simultaneously, a PAC Micro-II acoustic emission system was used to monitor the acoustic emission signals; this system can achieve real-time extraction and acquisition of 16-channel acoustic emission characteristics.

[0103] Four acoustic emission (AE) sensors were arranged around each specimen, and petroleum jelly was applied as a coupling agent at the connection between the sensors and the specimen. The loading and acoustic emission systems were calibrated at the start of each experiment to ensure the validity of the acoustic emission signals. Acoustic emission data acquisition and loading were performed simultaneously until the specimen was destroyed.

[0104] Steps S1 to S5 of this scheme were executed on the data collected from the four sets of samples, and the results were calculated during the defect rock mass early warning process. , q, , , and And based on these parameters, the graphs of the four AE sensors were plotted. The relationship curve with q (reference) Figure 2 ), The relationship curve with q (reference) Figure 3 ), and Relationship curve (reference) Figure 4 ) and damage index and Relationship diagram (reference) Figure 6 ); Figure 5 This is a graph showing the relationship between the damage index and the loading process.

[0105] According to multifractal theory, a linear curve indicates that the scale invariance assumption fails, making it impossible to analyze the inherent heterogeneity of the signal. Figure 2 The curve morphology shows significant nonlinear characteristics (rather than an ideal straight line), verifying the effectiveness of the multifractal calculation process described in this invention for deconstructing acoustic emission signals. Furthermore, this method, through wavelet multi-resolution measures and adaptive parameter mechanisms, enables… By strictly satisfying the convexity condition, the nonlinearity of the output curve is ensured. This phenomenon empirically demonstrates the universality of this technical solution in non-stationary acoustic emission signal processing.

[0106] Figure 3 express The relationship with q is that the q-value is used to decompose the time series, and each q represents a subset with similar probabilities. It is a feature description of a subset. It is the fractal dimension of the subset; furthermore, q should be confined to a certain range. If the computational range of q is too large, the computational efficiency will be low. When q exceeds a certain threshold (confined to ±40 in this invention), changes in q will not lead to... Changes have occurred. Through Figure 3 This invention demonstrates that by dynamically limiting the moment order search boundary through the measure of the extreme value ratio, it can eliminate the truncation error and computational redundancy caused by the traditional fixed interval, thus enabling... The relative error is reduced in the extreme value range.

[0107] Figure 4 The multifractal spectrum representing the acoustic emission time series shows a right-hook-shaped distribution. Empirically, the output of this method conforms to the physical essence of rock damage evolution: ① Small event dominance: The frequency proportion of low-energy acoustic emission events (microcrack propagation) is higher than that of corresponding high-energy events (macroscopic fracturing), which is consistent with the progressive failure mechanism of rocks; ② Right-hook morphology specificity: The right skewness of the spectrum is directly related to the damage localization process, providing a quantitative criterion for the identification of failure stages; Figure 4 The curve can characterize the progressive damage process of rock fracture, where microcracks accumulate to a certain extent to form macrocracks, leading to the destruction of the sample.

[0108] Figure 5The graph illustrates the relationship between the damage index and the loading process. The black dots represent the peak points of the damage index acceleration, marking the entry of the rock mass into the accelerated damage stage. These acceleration peak points are accurately captured using the real-time differential algorithm of this invention, transforming the abstract damage state into a monitorable dynamic parameter.

[0109] Figure 6 The correlation between the spectral width and damage index of the multifractal spectrum is described. The curve in the first half of the gray circle in the figure is relatively flat without large-scale fluctuations, while a sudden jump occurs in the gray circle area, where both the spectral width and damage index acceleration reach their peaks simultaneously. This synergistic rock mass response mechanism has been identified as the core criterion for rock mass disaster early warning. The small-scale fluctuations before the warning point in the figure originate from outliers caused by isolated noise. The calculation process proposed in this invention does not trigger alarms for these outliers, effectively avoiding [the occurrence of such outliers]. Abnormal fluctuations, but the rock mass has not entered the accelerated damage stage, resulting in a false alarm.

Claims

1. A method for early warning of defective rock masses based on multifractal spectrum and damage variables, characterized in that, Including the following steps: S1. Extract the time-varying data sequence of acoustic emission signal characteristic parameters in the slope rock mass damage process, and calculate the dynamic adaptive sliding window length based on the maximum local variance of the time-varying data sequence. S2. Based on the time-varying data sequence, determine the ringing count time sequence of each sliding window, and perform multi-scale deconstruction based on Haar wavelets to calculate the multi-resolution measure of each sub-interval within the sliding window. S3. Determine the upper and lower limits of the weights for each multi-resolution measure. Based on all the upper and lower limits of the weights for each sliding window and the multi-resolution measure, calculate the spectral width of the multifractal spectrum for each sliding window. S4. Calculate the rock mass damage index and its damage index acceleration at each moment in the rock mass damage process, and establish the relationship curve between the spectral width of the multifractal spectrum and the damage index through time matching. S5. Determine the jump point of the damage index acceleration and the jump point of the spectral width of the multifractal spectrum based on the relationship curve. When the two jump points occur at the same time, that time is the early warning point of rock mass failure. The expression for calculating the dynamically adaptive sliding window length is: in, Let be the length of the sliding window at time t; The length of the reference window; As a regulating factor; Local variance of time-varying data series Maximum value; The variance within the window centered at time t; The half-window width used for calculating local variance; This represents the mean of the time series within the sliding window; For time series data located before t Observations per unit of time.

2. The method for early warning of defective rock masses according to claim 1, characterized in that, The expression for calculating the multi-resolution measure for each subinterval is: in, The sub-interval scale for each window deconstruction; For scale The next Multi-resolution measure of sub-intervals; To take the absolute value; and respectively scale Next The j-th wavelet coefficient; The total number of wavelet coefficients obtained by multi-scale deconstruction of Haar wavelets; and respectively scale Next The observations of the i and i+1 intervals.

3. The method for early warning of defective rock masses according to claim 2, characterized in that, The expression for determining the upper and lower bounds of the weights for each multi-resolution measure is as follows: in, and These are the upper and lower limits of the weight, respectively; This is the tolerance parameter.

4. The method for early warning of defective rock masses according to claim 3, characterized in that, Methods for calculating the spectral width of the multifractal spectrum for each sliding window, based on all weight upper and lower bounds and multiresolution measures for each sliding window, include: S31. Weight each multi-resolution measure according to its upper and lower limits to obtain its maximum and minimum weighted measures: in, Let q be the weighted measure corresponding to the weight q, where q takes the value of and At that time, the maximum and minimum weighted measures are obtained; For scale The next Multi-resolution measure of sub-intervals; S32. Based on the upper and lower bounds of the weights and the maximum and minimum weighted measures, calculate the upper and lower bounds of the singularity index and the eigenvalue index respectively: in, and These are the singular exponent and feature exponent corresponding to the weight q, respectively, where q takes the value of and When the singularity index and the characteristic index are obtained, the upper and lower limits are obtained respectively; S33. Calculate the spectral width of the multifractal spectrum for each sliding window based on the upper and lower limits of the singularity index. : in, and These are the upper and lower limits of the singularity index.

5. The method for early warning of defective rock masses according to any one of claims 1-4, characterized in that, Methods for extracting time-varying data sequences of acoustic emission signal characteristic parameters in rock mass damage processes include: The entire time series of acoustic emission characteristic parameters during the rock mass damage process Extracting a portion of the time series , The length of time is ; In the time window In the middle, the data collection time interval is Obtain the time window Time-varying data sequences for: in, For time window The update rate of the time series data; m is the window index, which is a positive integer, m=0 indicates the first window; for The extracted time series.

6. The method for early warning of defective rock masses according to any one of claims 1-4, characterized in that, The expression for calculating the damage exponential acceleration of the rock mass at each moment in the rock mass damage history is as follows: ， in, Let be the damage exponential acceleration at time t; and The rock mass damage indices are at time t and time t-1, respectively. The cumulative acoustic emission count represents the total number of times the rock has completely failed. This represents the cumulative ringing count at time t; For time intervals.

Images