A rock mass instability cross-scale early warning method fusing renormalization group and critical slowing down

Abstract

The application provides a rock mass instability cross-scale early warning method fusing renormalization group and critical slowing down, comprising: obtaining acoustic emission or microseismic monitoring data, reconstructing a single-scale event energy field into a multi-scale scale spectrum through spatial gridding; calculating a composite index, a renormalization critical slowing down factor (RCSD), which fuses long-range correlation (DFA fluctuation function) and memory effect (autocorrelation coefficient), on different coarse-grained scales, and automatically locking the optimal early warning scale matched with the characteristic scale of the rock mass damage connected cluster by finding the fixed point of the factor changing with the scale; and finally, establishing an adaptive hierarchical threshold system based on the statistics of the reference period on the optimal scale, realizing the cross-scale and physically-based rock mass instability early warning.

Description

Technical Field

[0001] This invention relates to the field of engineering rock mass safety monitoring and early warning technology, specifically to a cross-scale early warning method for rock mass instability that integrates renormalization groups and critical slowing. Background Technology

[0002] Rock mass instability (such as rockburst, rock burst, landslide, and pillar collapse) is one of the most serious hazards in rock engineering projects such as mines, tunnels, and hydropower slopes. Currently, mainstream monitoring and early warning methods primarily rely on capturing elastic wave (acoustic emission or microseismic) signals released during rock fracturing. By analyzing parameters such as the quantity, energy, and magnitude of these signals and their changes, the evolution of damage within the rock mass is inverted, and early warning is issued based on this analysis. Another common method focuses on macroscopic mechanical responses such as displacement and deformation. However, these mainstream methods have revealed significant shortcomings in practice. The most prominent problem is the severely insufficient warning time; traditional methods, even under optimal conditions, typically only issue warnings a few minutes before macroscopic failure of the rock mass, which is insufficient to meet the safe evacuation requirements for personnel and large equipment.

[0003] To identify earlier signs of instability, the academic community has introduced the critical slowing-down theory. This theory describes the universal behavior of complex dynamic systems approaching a critical phase transition point, specifically manifested as a slower rate of equilibrium recovery after disturbance, an increase in the variance (amplitude) of state fluctuations, and enhanced autocorrelation (memory effect) of time series. Applying this theory to rock mass monitoring involves continuously calculating the energy variance or autocorrelation coefficient of acoustic emission / microseismic signals; a significant increase in these values ​​is identified as a precursor to instability.

[0004] However, existing early warning methods based on the critical slowing-down theory have a fundamental flaw: they assume the entire rock mass being analyzed is homogeneous and are calculated and analyzed on a single, fixed spatial scale (e.g., using signals from a single sensor or statistical signals within a fixed-size spatial grid). This is completely inconsistent with the objective physical process of rock mass failure. Rock mass instability is a multi-scale cascading process that begins at the microscopic level and develops at the macroscopic level. Microcracks first initiate and propagate in local weak areas, then connect to form interconnected clusters, eventually developing into macroscopic fracture surfaces. In this multi-scale evolution process, the critical behavior of damage is most significant at a specific scale, and this characteristic scale is closely related to the size of the interconnected microcrack clusters. Existing single-scale analysis methods cannot capture this feature, resulting in low early warning sensitivity, late warning time, or false alarms due to local noise. Furthermore, threshold setting relies entirely on experience and lacks a physical basis. Therefore, a new method with a physical basis for early warning of rock mass instability is urgently needed. Summary of the Invention

[0005] To address the problems of existing critical slowing early warning systems being single-scale, having delayed warnings, and lacking a physical basis for their thresholds, this invention provides a cross-scale early warning method for rock mass instability that integrates renormalization groups and critical slowing, comprising the following steps: Step S1: Multi-scale data reconstruction Acoustic emission or microseismic events within the monitoring area are acquired, and their occurrence time, spatial coordinates, and energy parameters are extracted. The monitoring area is discretized into a spatial grid with an initial side length, and the cumulative energy of each grid within a fixed time window is statistically analyzed to form an energy field sequence at the initial scale. The initial energy field sequence is subjected to renormalization group coarsening processing with stepwise block transformation, and a series of coarse-grained energy fields at different scales are generated according to the scale recursion relationship to form a multi-scale energy field dataset.

[0006] Step S2: Calculate the composite critical slowing index At each spatial scale, detrended fluctuation analysis is performed on the energy time series to obtain the fluctuation function reflecting the fluctuation amplitude; the lag autocorrelation coefficient of the energy time series is calculated to obtain the autocorrelation index reflecting the memory effect; by multiplying and fusing the fluctuation function and the autocorrelation index, and normalizing it using the original scale fluctuation function, the renormalized critical slowing factor RCSD is defined to comprehensively characterize the critical slowing behavior.

[0007] Step S3: Automatically identify the optimal early warning scale The relative rate of change of the critical slowing factor (RCSD) of renormalization between adjacent spatial scales is calculated, and the spatial scale corresponding to the minimum value of the relative rate of change is determined as the optimal warning scale. This optimal warning scale corresponds to a fixed point under the renormalization group transformation, indicating the characteristic scale of the damage connectivity cluster in the rock mass.

[0008] Step S4: Execute adaptive hierarchical early warning Monitoring data from a stable rock mass stage were selected as the baseline period. The statistical characteristics of the critical slowing factor (RCSD) for renormalization, including the mean and standard deviation, were calculated at the optimal warning scale. Using the mean and standard deviation, graded warning thresholds were constructed according to the safety factor ratio. During real-time monitoring, the critical slowing factor (RCSD) for renormalization at the optimal warning scale was continuously calculated. When it met the preset threshold conditions and showed an upward trend, the corresponding level of instability warning was triggered.

[0009] Furthermore, in the coarse-graining process, the scale recursion relationship is as follows: ; Where b is the scale magnification factor and k is the coarsening level. The initial mesh edge length is used; the coarsening rule is to... Each lower-level small grid is merged into an upper-level large grid. The energy of the new grid is the sum of the energies of its lower-level grids, where d is the spatial dimension.

[0010] Furthermore, the critical slowing factor (RCSD) for renormalization is defined as: ; in Let be the detrended fluctuation function at the k-th scale. The value of the wave function at the original scale. Let be the autocorrelation coefficient at the k-th scale. These are the weighting coefficients.

[0011] Furthermore, the optimal warning scale is determined by calculating the relative rate of change of RCSD between the k-th and k+1-th scales. ; And will make The scale for obtaining the minimum value It was determined to be the optimal early warning scale.

[0012] Furthermore, the tiered early warning thresholds are set as follows: ; in and These represent the mean and standard deviation of the RCSD under the optimal early warning scale within the baseline period, respectively. The safety factor is selected based on the importance of the project, corresponding to different warning levels; and the warning triggering conditions include RCSD exceeding the corresponding threshold and its time derivative being positive.

[0013] Compared with the prior art, the present invention has the following beneficial effects: This invention automatically identifies the optimal early warning scale that matches the characteristic scale of rock mass damage penetration clusters by fixing points in the renormalization group, and monitors at this scale. The critical slowing behavior is most significant at this characteristic scale and is not affected by local minor noise. Therefore, it can capture reliable precursor signals in the early penetration stage before macroscopic failure occurs, significantly increasing the early warning lead time from the conventional minute level to tens of minutes or even hours.

[0014] The composite index RCSD defined in this invention requires the simultaneous occurrence of two independent critical slowing phenomena: increased volatility and enhanced autocorrelation. Single noise or random disturbances are unlikely to cause false alarms. Furthermore, the warning threshold is set based on the statistical distribution of baseline data, using statistical confidence levels. This transforms warning decisions from empirical judgments to rigorous statistical inferences with probabilistic significance, thereby significantly reducing false alarms and missed alarms.

[0015] The optimal early warning scale of this invention is not preset by humans, but is automatically obtained through data-driven renormalization flow analysis. It can determine appropriate characteristic scales for rock mass structures of different sizes and types (such as tunnels, slopes, and indoor rock samples) based on their respective monitoring data. This method can adapt to multi-scale engineering objects without relying on manual adjustments, demonstrating good universality and adaptability.

[0016] The technical approach of this invention is rooted in the theory of phase transitions and critical phenomena in statistical physics. By constructing renormalization group transformation and critical slowing factor, the abstract concept of rock mass damage evolution process is transformed into calculable physical indicators, so that the early warning threshold and optimal scale have clear physical meaning, which is convenient for understanding and application in engineering practice. Attached Figure Description

[0017] Figure 1 This is a map showing the location of the tunnel monitoring points according to the present invention; Figure 2 This is a distribution map of microseismic events according to the present invention; Figure 3 This is the RCSD-t curve for predicting rockburst in hard rock tunnels according to the present invention; Figure 4 This is the RCSD-t curve diagram for predicting slope instability in open-pit mines according to the present invention; Figure 5 This is a schematic diagram of the deformation-based slope instability early warning system of the present invention, which triggers a first-level early warning 6 hours before instability. Figure 6 This is the RCSD-t curve of rock fracture prediction during the indoor rock mechanics test process of this invention; Figure 7 This is a graph showing the relationship between acoustic emission ring count and energy versus strain in this invention. Figure 8 This is a graph showing the relationship between acoustic emission ringing count and cumulative count and strain in this invention. Figure 9 This is a graph showing the relationship between acoustic emission energy and cumulative energy and strain in this invention. Figure 10 This is a graph showing the relationship between the variance of the acoustic emission parameters of this invention and time. Figure 11 This is a graph showing the relationship between the autocorrelation coefficient of the acoustic emission parameters of this invention and time. Figure 12 This is a flowchart of the method of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] Step S1: Multi-scale data reconstruction Rock fracture signals are acquired in real time using an array of acoustic emission sensors deployed on the rock surface or a network of microseismic detectors within boreholes. The raw waveforms are then filtered, denoised, and the events are identified and located. The following parameters are extracted for each acoustic emission / microseismic event: Time of occurrence t i Unit: s; Three-dimensional spatial coordinates (x) i ,y i ,z i ); Unit: m; Energy Ei; Unit: J or mV·ms; Magnitude M i (Optional).

[0020] The monitoring area is discretized into a region with a side length of... The problem involves a 3D cubic mesh (a 2D problem could use a square mesh). Statistics are calculated for each mesh within a fixed time window. The accumulated acoustic emission energy within the space constitutes the energy field sequence at the initial scale: ; in, The initial grid side length is determined based on the sensor spacing and positioning accuracy, and is generally taken as 0.5~5m; Let p be the center position vector of the p-th grid. This is the center moment of the q-th time window; Q represents the total number of valid grid cells; Q represents the total number of time windows.

[0021] The initial energy field obtained from the aforementioned steps is subjected to a stepwise bulk transformation to generate a series of energy fields at a coarse-grained scale.

[0022] The scale recursion relationship is as follows: ; Where b is the scale magnification factor, usually taken as b=2 or b=3; K is the maximum number of coarsening layers, determined by... The size should not exceed half the minimum size of the monitoring area.

[0023] Coarsening rule: Transform adjacent... The smaller grids are merged into a new larger grid (d is the spatial dimension, d=2 or d=3), and the energy of the new grid is the sum of the energies of the original grids: ; Where b is the scale magnification factor, controlling the resolution change factor between adjacent scales; k is the coarse-grained hierarchy index, k=0 represents the original scale; R n The center position of the nth large grid in the kth layer; r n,j It is the center position of the j-th small grid belonging to the n-th large grid in the (k-1)-th layer.

[0024] Step S2: Calculate the composite critical slowing index For each scale Energy time series Calculate its critical slowdown characteristic index.

[0025] Step S2.1: Detrended Fluctuation Analysis (DFA) DFA is used to quantify the long-range correlation of time series and is a sensitive tool for detecting critical slowing down.

[0026] Calculate the cumulative deviation of the sequence: ; in, This represents the time average of the energy sequence at the k-th scale.

[0027] Will Divided into There are three non-overlapping sub-intervals, each with a length of s (called a time window). A p-order polynomial fit (usually p=1 or p=2) is performed on each sub-interval to obtain the local trend. .

[0028] Calculate the wave function: ; Where s is the length of the DFA time window, reflecting the time scale of the fluctuation analysis; p is the order of the fitting polynomial, p=1 for linear fitting, and p=2 for quadratic fitting. Let be the value of the fluctuation function at the k-th scale and time window s.

[0029] The autocorrelation coefficient measures the degree of correlation between a time series and its lagged version; it approaches 1 at critical slowing.

[0030] Calculation lag The autocorrelation coefficient of the step: ; in, The lag factor; is the lag autocorrelation coefficient at the k-th scale.

[0031] Next, the critical slowdown factor (RCSD) of the renormalization is calculated.

[0032] Define a composite indicator RCSD that considers both volatility and memory effect: ; in, The original DFA fluctuation function value is used as the normalization benchmark. These are the weighting coefficients for the autocorrelation terms. Recommended ; is the renormalization critical slowing factor at the k-th scale, which is dimensionless.

[0033] Step S3: Automatically identify the optimal early warning scale Calculate the relative rate of change of RCSD between adjacent scales: ; The criterion for determining a fixed point is: if there exists a certain Make The corresponding scale This is the optimal early warning scale.

[0034] The physical meaning is that at this scale, the critical behavior of the system is least sensitive to scale transformations, i.e., it reaches the fixed point of the renormalization group transformation. This corresponds to the characteristic scale of damage connectivity clusters in rock mass—at this scale, microcracks have formed through-paths sufficient to cause macroscopic instability.

[0035] Step S4: Execute adaptive hierarchical early warning Step S4.1, Base Period Statistics Calculate the optimal scale by taking monitoring data from a stable rock mass stage (such as immediately after excavation or a period after reinforcement). Statistical characteristics of the RCSD factor: Mean: ; Standard deviation: ; in, The number of monitoring data samples within the baseline period. For the first One sample.

[0036] Step S4.2, Setting the Early Warning Threshold ; in, The safety factor is selected based on the importance level of the project, as follows: Level 1 Warning (Attention): This corresponds to a 99.7% confidence level; Level 2 Warning (Alarm): This corresponds to an extremely high confidence level; Level 3 Warning (Emergency): This corresponds to a deterministic early warning.

[0037] Step S4.3, Real-time Early Warning Logic Continuous monitoring of the optimal scale The RCSD factor below will trigger a warning at the corresponding level when the following conditions are met: Level 1 Warning: ; Level 2 warning: ; Level 3 Warning: .

[0038] The following describes specific embodiments.

[0039] Example 1: Rockburst Early Warning in Hard Rock Tunnel This embodiment uses a deep tunnel in the Dunde lead-zinc-iron mine as an example, with granodiorite as the surrounding rock. The tunnel has a cross-sectional size of 4m × 4m and is mined using the pillarless caving method. Due to the tunnel crossing multiple fault fracture zones during excavation, its stability is poor, necessitating long-term stability monitoring. Eight microseismic sensors are deployed on the roof and both sides to form a monitoring network, with a sensor spacing of approximately 2m. The monitoring point locations are as follows: Figure 1 As shown.

[0040] Step S1: Multi-scale data reconstruction The monitoring area is discretized into a region with a side length of... An initial square grid was used, resulting in P=128 valid grid cells. A time window was then set. The sampling frequency was 500 kHz, and the threshold value was 45 dB. Three-dimensional localization and energy calculation were performed on microseismic events within the window. The cumulative energy of each grid within each time window was statistically analyzed to construct an energy field sequence at the initial scale. A total of M=156000 microseismic events were recorded over 72 consecutive hours, generating energy field data for Q=4320 time windows. The distribution of microseismic events is as follows: Figure 2 As shown.

[0041] With a scale magnification factor of b=2, spatial dimension d=2, and maximum coarsening layer number K=4, five spatial scales are generated: , , , , The coarsening rule is as follows: merge four adjacent lower-level grids into one upper-level grid, and the energy of the upper-level grid is equal to the sum of the energies of the lower-level grids it contains.

[0042] For example, at a certain moment, four The grid energy is 25.3 × 10⁻⁶. -3 J, 18.7×10 -3 J, 32.1×10 -3 J and 14.9×10 -3 J, then the corresponding The energy of the grid is the sum of their values, which is 88 × 10⁻⁶. -3 J.

[0043] Step S2: Calculate the composite critical slowing index The DFA time window is set to s=30, the polynomial fitting order to p=1, and the autocorrelation weighting coefficient is [not specified]. Taking the monitoring period of 2 hours before the disruption (t=66h~68h) as an example, the detrending fluctuation function at each scale was calculated. and autocorrelation coefficient And based on this, the critical slowing factor for renormalization is calculated. The result is as follows Figure 3 And as shown in Table 1 below:

[0044] by Taking scale as an example, the detailed calculation process is as follows: normalized fluctuation is Autocorrelation enhancement term is ;final .

[0045] Step S3: Automatically identify the optimal early warning scale Calculate the relative rate of change of RCSD between adjacent scales. : ; ; ; ; in The minimum, therefore the optimal early warning scale is Physically, this scale coincides with the tunnel span, indicating that the size of the damaged connectivity cluster has reached the characteristic scale of the engineering structure, and the system is in a critical state.

[0046] Step S4: Execute adaptive hierarchical early warning The stable period of 24 to 48 hours after tunnel excavation was selected as the baseline period for calculation. Statistical characteristics of RCSD: mean Standard deviation .

[0047] Set three warning thresholds: Level 1 Warning: ; Level 2 warning: ; Level 3 Warning: ; The real-time monitoring results (critical period before damage) are shown in Table 2 below:

[0048] Real-time monitoring results show that at t=67h, The initial warning threshold was not reached; at t=67.3, the threshold was exceeded for the first time and continued to rise, triggering a Level 1 warning; at t=67.7, the value reached 1.41, triggering a Level 2 warning; at t=68, the value reached 1.92, triggering a Level 3 emergency warning; finally, at t=68.5, the RCSD surged to 3.81 before a rock eruption occurred. This invention's method issues a preliminary warning 1.2 hours before the event, providing ample time for on-site emergency response.

[0049] Example 2: Landslide Early Warning in Open-Pit Mine Slopes Step S1: Multi-scale data reconstruction This example uses microseismic monitoring data from the final slope of the eastern slab of the Beizhan Iron Mine in Hejing County, Xinjiang. The slope height is 280m, the step height is 15m, and the monitoring area covers 200m × 150m. A total of 16 microseismic geophones were deployed on the slope surface and in deep boreholes, with a sampling frequency of 1kHz and a positioning accuracy of ±5m. During the 30-day rainy season monitoring period, the time window... There are a total of Q=8640 time windows, with an initial grid side length of... With an effective grid number of P=300, a total of 8900 microseismic events were recorded.

[0050] Multi-scale coarsening uses b=3 and d=2 to generate four spatial scales. , , , The coarsening rule is to divide adjacent 3 2 =9 small grids are merged into 1 large grid.

[0051] Step S2: Calculate the composite critical slowing index The DFA parameters are set to s = 24 (corresponding to 2h) and p = 2 to eliminate the influence of rainfall trend. The autocorrelation weighting coefficient is taken as... .

[0052] Step S3: Automatically identify the optimal early warning scale Taking the monitoring data from 3 days before the landslide (days 27 to 30) as an example, the RCSD calculation results at various scales are as follows: Figure 4 And as shown in Table 3 below:

[0053] by For example, scale: The normalized fluctuation is 84.7 / 158.3 = 0.552. Autocorrelation term: 1 + 1.5 × 0.74 = 2.110

[0054] Calculate the rate of change at adjacent scales ; ; ,in The minimum, therefore the optimal early warning scale is This scale is close to twice the step height (6×15m), indicating that the sliding surface has penetrated multiple steps, forming a large-scale connected area of ​​damage, and the risk of landslide has increased sharply. This is consistent with the typical characteristics of actual open-pit mine slope failure (a penetrating sliding surface along multiple steps).

[0055] Step S4: Execute adaptive hierarchical early warning Taking the previous 10 days of the dry season stability period as the baseline, the calculation is as follows: , .

[0056] The Level 3 warning threshold is set as follows: , , The threshold increases monotonically, which is consistent with the logic of the warning level.

[0057] During the experiment, the rainy season began on day 27. The infiltration of rainfall caused an increase in pore water pressure, leading to the gradual expansion of internal rock cracks. Real-time calculations were performed. The results were compared with a preset threshold, and the real-time monitoring results are shown in Table 4 below:

[0058] After the rainy season begins, The RCSD (Regulated Radiation Slowing) began to climb from 0.86 on day 27, reaching 0.97 on day 28.3 (1.5 days before failure), triggering a Level 1 warning, earlier than the traditional energy count rate method (which usually only triggers a few hours before failure); it reached 1.84 on day 29.5 (0.3 days before failure), triggering a Level 3 emergency warning; finally, the landslide occurred after the RCSD rose to 2.91 on day 29.8. The entire warning process had no missed reports and no false alarms, perfectly matching the S-shaped critical slowdown characteristics of the RCSD curve. This invention's method issues warnings approximately 1.5 days before a landslide, about 18 hours earlier than traditional deformation monitoring warnings.

[0059] Example 3: Instability Early Warning in Indoor Uniaxial Compression Rock Acoustic Emission Test Step S1: Multi-scale data reconstruction This embodiment uses a uniaxial compression test of a standard granite specimen in an indoor laboratory as an example. The specimen has a diameter of 50 mm, a height of 100 mm, and a height-to-diameter ratio of 2:1. Both ends of the specimen are ground flat, with a parallelism better than 0.02 mm. An electro-hydraulic servo rigid press is used to load the specimen at a constant displacement rate of 0.005 mm / s until failure. The acoustic emission monitoring system uses six Nano30 resonant AE sensors, symmetrically arranged on the side surface of the specimen, in two layers along the height direction (three sensors per layer, circumferentially spaced at 120° intervals). For specific test results, please refer to [link to relevant documentation]. Figures 7-11 The resonant frequency is 300kHz, the sampling rate is 5MHz, the threshold value is 40dB, and three-dimensional time-difference positioning is used, with a positioning accuracy of ±2mm. The time window is set to... The sample volume (50mm in diameter × 100mm in height) is discretized into a sample with a side length of... The cube-shaped mesh element.

[0060] The total volume of the sample is: ; The volume of each grid cell is: ; Total number of valid grid cells (excluding invalid grid cells outside the boundary): ; in, The fill factor for the inscribed cube mesh within the cylinder. The initial grid side length is approximately 1 / 10 of the sensor spacing to ensure sufficient spatial resolution; The time window width is approximately the time required to generate a 0.0025 mm axial displacement at a loading rate of 0.005 mm / s, which can capture the rapidly changing fracture process; P=1100 is the total number of effective grids, ensuring that there are sufficient statistical samples in each grid.

[0061] A total of M=28500 acoustic emission events were recorded during the entire experiment.

[0062] Taking the last 10 seconds before peak stress (the critical stage before failure) as an example, the cumulative energy of each grid within each time window is calculated: Let a certain grid r p In time window t q Internal records If there are AE events, and each event has energy Ej, then the cumulative energy of the grid within this time window is: ; Typical data segments (5 seconds before corruption, t=195.0s~1995.0s) are shown in Table 5 below:

[0063] We set the scale magnification factor b=2, the spatial dimension d=3 (three-dimensional coarsening), and the maximum number of coarsening layers K=4.

[0064] Grid side lengths at various scales: ; The details are shown in Table 6 below:

[0065] because Since the sample diameter is close to 50 mm, it is impossible to form an effective complete mesh. Therefore, the actual effective number of coarse-grained layers K=3.

[0066] Coarse-grained example (with) (For example) Eight adjacent 5mm small grids (2³ = 8) are merged into one 10mm large grid. Let the energies of the eight small grids within the time window tq be: E1=12.5, E2=0, E3=38.2, E4=5.1, E5=89.7, E6=0, E7=215.3, E8=76.1 (unit: mV·ms).

[0067] The coarsened energy is the sum of the energies of the aforementioned eight smaller grids within the time window tq, which is 410.9 mV·ms. Step S2: Calculation of the critical slowing factor DFA parameter settings: Time window: Total sequence length Q = 20 samples, sub-interval length s = 10 samples (approximately 5 seconds); Fitting order: p=1 (linear fitting); Autocorrelation weighting coefficient: α = 1.0.

[0068] Calculation process (in) (Taking the scale and the 10 seconds before the damage as an example) Take the energy sequence of a representative grid at this scale (located slightly above the middle of the specimen; since the testing machine indenter is on top, the failure zone is expected to occur first in the upper part of the specimen) within 10 seconds before failure: {45.2,62.8,58.1,103.5,187.3,210.6,168.4,325.1,412.7,389.3,510.2,478.6,623.4,587.1,702.8,659.3,812.5,768.4,903.7,856.2} (Unit: mV·ms) The sequence length Q = 20.

[0069] Calculate the mean: ; DFA fluctuation function: Will Divide into m = 20 / 10 = 2 subintervals, each with a length s = 10.

[0070] A linear fit was performed on the first sub-interval j=1~10 to obtain the trend line. a=125.3, b=-231.7.

[0071] Calculate the sum of squared residuals: ; Similarly, for the second subinterval j=11~20: ; Wave function: ; Autocorrelation coefficient: Lag The autocorrelation coefficient of the step: ; RCSD factor: ; in The wave function at the original scale within the same time window is calculated as follows: ; Substituting the values ​​into the equation: ; RCSD calculation results at each scale (10 seconds before failure) are as follows: Figure 6 And as shown in Table 7 below:

[0072] Step S3: Automatically identify the optimal early warning scale Calculate the rate of change of RCSD at adjacent scales: , , .

[0073] in The minimum, therefore the optimal early warning scale is .

[0074] The 40mm scale is close to 80% of the specimen diameter (50mm), indicating that the damage connectivity cluster has expanded to almost the entire size of the specimen, and the system is in a global critical state—which is completely consistent with the failure characteristics of the macroscopic fracture surface penetrating the entire specimen under uniaxial compression.

[0075] Base period statistics and threshold setting: Reference period selection: Monitoring data from the initial loading stage (stress level below 30% of peak stress, i.e., the elastic stage) were used, totaling T... base =600 time windows (corresponding to 300 seconds).

[0076] Optimal scale within the reference period The following are RCSD statistics: Mean: ; Standard deviation: ; Step S4: Execute adaptive hierarchical early warning A three-level early warning threshold is set using the method of "mean + multiple × standard deviation": Level 1 Warning (Low Risk): ; Level 2 Warning (Medium Risk): ; Level 3 Warning (High Risk): .

[0077] The entire experiment was monitored continuously, and the RCSD value was updated every 0.5 seconds.

[0078] Key time points (with the peak stress time as the baseline at t=0) are shown in Table 8 below:

[0079] The warning effect is as follows: A level one warning is triggered approximately 84 seconds before the peak stress, at which point the stress level is about 70% of the peak stress, indicating the early stage of unstable crack propagation.

[0080] A level 2 warning is triggered 60 seconds before the peak stress, at a stress level of 72%, and the crack begins to propagate at an accelerated rate.

[0081] A level 3 warning is triggered 15 seconds before the peak stress, at a stress level of 88%. At this point, the acoustic emission energy increases exponentially, and the sample is about to be destroyed.

[0082] Example 4: Comparison and verification with traditional methods To verify the superiority of this invention, two traditional early warning methods were compared using the same set of experimental data: Method A: Early warning of sudden changes based on acoustic emission counts and acoustic emission energy (traditional method) Warning threshold: When the count rate exceeds the mean of the baseline period plus 3 standard deviations or when there is a sudden increase in the count; Warning time: Approximately 17 seconds before the peak.

[0083] Method B: Based on single-scale critical slowdown early warning (without renormalization group optimization), the acoustic emission parameters are selected as ring count, energy, peak frequency, and rise time-to-average frequency ratio.

[0084] Warning threshold: Sudden jumps in variance or autocorrelation coefficient; Warning time: Approximately 48 seconds before the peak.

[0085] Method of the present invention: Warning times: 84 seconds before peak (Level 1), 60 seconds before peak (Level 2), and 30 seconds before peak (Level 3). See Table 9 below for a detailed comparison.

[0086] Conclusion: Compared with traditional methods, the method of this invention increases the early warning lead time by nearly 5 times (84 seconds vs 17 seconds) and has no false alarms, significantly improving the timeliness and reliability of instability early warning in indoor rock tests.

[0087] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any equivalent substitutions or improvements made based on the technical concept of the present invention should be considered as falling within the scope of protection of the present invention.

Claims

1. A cross-scale early warning method for rock mass instability integrating renormalization groups and critical slowing, characterized in that, Includes the following steps: Step S1, Multi-scale data reconstruction: Acquire acoustic emission or microseismic events within the monitoring area, extract their temporal, spatial and energy parameters, discretize the monitoring area into a spatial grid of initial scale, statistically analyze the cumulative energy of each grid within a fixed time window to form an initial energy field, and generate a series of coarse-grained energy fields at a coarse scale through renormalization group coarsening processing of stepwise block transformation, forming a multi-scale energy field dataset. Step S2: Calculate the composite critical slowing index: At each coarse-grained scale, perform detrended fluctuation analysis on the energy time series to obtain the fluctuation function, and calculate the autocorrelation coefficient characterizing the sequence memory effect. Use the fluctuation function and the autocorrelation coefficient to construct the composite renormalization critical slowing factor. Step S3: Automatically identify the optimal warning scale: Calculate the relative rate of change of the renormalization critical slowing factor between adjacent spatial scales, and determine the scale corresponding to the minimum value of the rate of change as the optimal warning scale; Step S4: Execute adaptive graded early warning: Select the monitoring data of the rock mass stability stage as the baseline period, calculate the statistical mean and standard deviation of the critical slowing factor of renormalization under the optimal early warning scale, and construct graded early warning thresholds accordingly. In real-time monitoring, when the real-time critical slowing factor of renormalization under the optimal early warning scale meets the preset threshold conditions and shows an upward trend, the corresponding level of instability early warning is triggered.

2. The method according to claim 1, characterized in that, In the multi-scale data reconstruction step, the scale recursion relationship is as follows: , where b is the scale magnification factor, which takes the value of 2 or 3; K is the maximum number of coarsening layers; The initial grid side length is set to 0.5–5 m, depending on the sensor spacing and positioning accuracy; this ensures that the side length of the Kth layer grid is... It should not exceed half the minimum size of the monitoring area.

3. The method according to claim 2, characterized in that, The coarsening rule for the step-by-step block transformation is: [The text abruptly shifts to a different topic] ...adjacent to the previous level... Each grid is merged into a new grid, and the energy of the new grid is equal to the sum of the accumulated energy of its parent grids within the corresponding time window, where d is the spatial dimension, d = 2 or 3.

4. The method according to claim 3, characterized in that, The renormalization critical slowing factor is defined as: ； in Let be the fluctuation function value at the k-th scale within the DFA time window s. The fluctuation function value at the original scale is used as the normalization benchmark. Let be the autocorrelation coefficient at the k-th scale, lagged by one step. α is the weighting coefficient of the autocorrelation term, with a value range of 0 ≤ α ≤ 2.

5. The method according to claim 4, characterized in that, The fluctuation function is obtained in the following way: The cumulative deviation of the energy time series relative to its mean is calculated. The cumulative deviation series is divided into non-overlapping sub-intervals, and a polynomial fit is performed on each sub-interval to remove the trend. The root mean square value of the residuals after detrending of all sub-intervals is calculated as the fluctuation function. The length s of the sub-interval is set according to the monitoring object.

6. The method according to claim 4, characterized in that, The autocorrelation coefficient Lagging The autocorrelation coefficient of the step is calculated by the ratio of the covariance to the variance of the sampled values ​​at adjacent time points in the energy time series.

7. The method according to claim 1, characterized in that, The determination of the optimal early warning scale includes: Calculate the relative rate of change of the critical slowing factor for renormalization between the k-th and (k+1)-th scales: ； Comparison at different k , will the smallest The corresponding scale This was determined to be the optimal early warning scale.

8. The method according to claim 1, characterized in that, The graded early warning threshold Constructed using the following formula: ； in This represents the time average of the renormalization critical slowing factor under the optimal early warning scale during the baseline period. For the corresponding standard deviation, The safety factor is selected based on the importance level of the project.

9. The method according to claim 8, characterized in that, The safety factor The values ​​are 3, 4, and 5, which correspond to Level 1, Level 2, and Level 3 warnings, respectively.

10. The method according to claim 8, characterized in that, The triggering condition for the real-time warning is: The renormalization critical slowing factor at the optimal early warning scale calculated in real time is greater than the corresponding graded early warning threshold, and its time derivative is greater than zero.

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