A method for reducing vibration in underground medium-deep hole blasting

Abstract

The present application relates to a kind of underground medium-deep hole blasting vibration reduction method, belong to the technical field of mine blasting method.The technical scheme of the present application is: collecting blasting vibration signal, analyzing main frequency attenuation characteristics, combining with bayesian statistical modeling quantization uncertainty, according to distance partition design optimal delay time, and select key vibration direction to implement control, and compare the effect of vibration reduction through industrial test.The beneficial effects of the present application are: by based on frequency attenuation and bayesian statistics, for the vibration characteristics of different distance partitions to achieve accurate vibration control, especially suitable for the complex scene that the relative distance of blast area and sensitive area dynamically changes, improve the stability and reliability of vibration reduction effect.

Description

Technical Field

[0001] This invention relates to a vibration reduction method for underground medium-deep hole blasting, belonging to the technical field of mining blasting methods. Background Technology

[0002] Deep-hole blasting in underground mines is a core technology for efficient mining of metals, but the vibrations it induces pose a significant threat to the safety of adjacent projects and the surface environment. Traditional vibration reduction methods rely on the Sadovsky formula to predict peak particle velocity (PPV) and design a fixed delay time, but they do not consider the distance attenuation characteristics of blasting vibration frequency and the changes in the relative distance between the blasting zone and the monitoring area during dynamic mining, resulting in unstable vibration reduction effects.

[0003] Specifically, the limitations of traditional methods are reflected in:

[0004] 1. The attenuation characteristics of blasting vibration frequency during propagation in the rock mass and its crucial impact on waveform superposition are ignored. The rapid attenuation of high-frequency components causes changes in the dominant frequency and waveform of vibration waves from different boreholes at the monitoring point. Relying solely on PPV peak shifting makes it difficult to accurately control energy superposition, resulting in unstable effects.

[0005] 2. Due to the dynamic mining process, the relative distance between the blasting area and the monitoring area continuously changes, leading to alterations in parameters such as the vibration wave propagation path, rock mass characteristics, and frequency attenuation rate. Fixed delay time schemes cannot adapt to the waveform superposition patterns at different distances. At close ranges, insufficient delay may result in energy concentration, while at long ranges, excessive delay may cause low-frequency vibration accumulation, leading to fluctuating control effects or even failure.

[0006] While existing research has made progress in the field of vibration reduction delay time, such as introducing high-frequency secondary cycles, calculating electronic detonator parameters, and conducting orthogonal experiments, there is still room for improvement in integrating the dynamic frequency decay law, spectral adaptability for multi-target protection scenarios, and the statistical reliability of small samples. Therefore, developing a vibration reduction method that can accurately adapt to frequency decay characteristics and dynamically adjust the delay time is of significant engineering importance. Summary of the Invention

[0007] The purpose of this invention is to provide a vibration reduction method for underground medium-deep hole blasting. By using frequency attenuation and Bayesian statistics, it achieves precise vibration reduction control for vibration characteristics of different distance zones. It is especially suitable for complex scenarios where the relative distance between the blasting zone and sensitive areas changes dynamically, thereby improving the stability and reliability of the vibration reduction effect and effectively solving the above-mentioned problems in the background technology.

[0008] The technical solution of this invention is: a method for vibration reduction in underground medium-deep hole blasting, comprising the following steps:

[0009] 1) Blasting vibration signal acquisition: In the sensitive area around the underground medium-deep hole blasting operation, monitoring points are set up according to the gradient of the distance from the blast center to form a distance zone monitoring profile. The three-dimensional particle vibration velocity time history curves in different distance zones are collected simultaneously, and the peak particle velocity and the main vibration frequency data in the X, Y and Z directions are extracted.

[0010] (2) Analysis of the attenuation characteristics of the main frequency: The collected main frequency data is divided into distance zones according to the distance from the center of the explosion. The mean, variance, standard deviation, coefficient of variation and interquartile range of the main frequency in each zone are calculated to quantify the attenuation law and discrete characteristics of the main frequency with the propagation distance in different distance zones.

[0011] (3) Bayesian statistical modeling: Based on Bayes' theorem, a prior distribution of the mean of the dominant frequency is set for each distance partition, a partition likelihood function is constructed, the dominant frequency parameters of each partition are estimated by the posterior distribution, and the significance of the difference in dominant frequency between different distance partitions is verified by Bayes factor.

[0012] (4) Delay time calculation: Based on the principle of phase-shifting vibration reduction, the optimal delay time is calculated according to the average main frequency of each distance zone, and the coupling relationship of "distance zone - frequency attenuation - delay time" is established.

[0013] (5) Optimal delay time direction selection: The optimal delay time direction is determined by considering the engineering influence weight of the vibration direction, the stability of the main frequency attenuation law of each distance zone, and the adaptability of the delay time to the vibration control requirements.

[0014] (6) Engineering verification: Through on-site industrial tests, the vibration reduction effect of this method and the traditional method in each distance zone is compared to verify the effectiveness of the distance zone delay time design.

[0015] In step (1), the monitoring points are set up to meet the following requirements: linearly distributed along the main direction of the propagation of the blasting seismic wave, recording the relative height difference between each measuring point and the blast source, covering the near-field vibration enhancement zone and the far-field attenuation characteristic zone, and the distance from the blast center is 300-800 meters.

[0016] In step (1), a TC-4850 high-precision blasting vibration meter is used, with a sampling frequency of 8000Hz, to simultaneously collect vibration signals in the X, Y, and Z directions, i.e., horizontal radial, horizontal tangential, and vertical directions.

[0017] In step (2), the distance between the explosion center and the explosion point is divided into three distance zones: 300~400 m, 400~700 m and 700~800 m. 21, 42 and 6 sets of effective main frequency data are collected for each zone to form a complete zone data sequence.

[0018] In step (2), the formula for calculating the coefficient of variation is:

[0019]

[0020] in: Standard deviation is the mean of the dominant frequency, and CV is the coefficient of variation;

[0021] The formula for calculating the interquartile range is:

[0022]

[0023] in: This is the upper quartile, or 75th quartile. The lower quartile, or 25th percentile, is represented by the interquartile range (IQR).

[0024] In step (3), the prior distributions for each distance partition are set as follows: the dominant frequency of the 300~400 m partition follows a normal distribution N(70,10²); the dominant frequency of the 400~700 m partition follows a normal distribution N(60,10²); and the dominant frequency of the 700~800 m partition follows a normal distribution N(45,8²). The prior standard deviation ensures that the observed data plays a dominant role in the posterior distribution.

[0025] In step (3), the likelihood function expression for each distance partition is:

[0026]

[0027] in: The mean of the dominant frequency in the k-th distance interval (k=1, 2, 3 correspond to 300~400 m, 400~700 m and 700~800 m respectively); The total variance; For the i-th observation; The sample size of the k-th interval ( , , ).

[0028] In step (3), the Bayesian factor JZS BF 10 To verify the hypothesis that "there are significant differences in the main frequency of partitions with different distances", when JZS BF 10 When the value is greater than 100, it is determined that the hypothesis is strongly supported, confirming the rationality of the distance partitioning.

[0029] In step (4), the optimal delay time calculation formula for each distance partition is as follows:

[0030]

[0031] in, The vibration reduction coefficient is set to 0.6. This represents the average frequency of each distance zone, in Hz.

[0032] In step (5), the optimal delay time direction is selected as the Z direction, which has the largest frequency attenuation amplitude in each distance partition and the Bayesian factor (JZS BF). 10 =2.952×10 19 The value was significantly higher than that in the X and Y directions, and it had the strongest correlation with the vibration response of surface structures.

[0033] The beneficial effects of this invention are: by using frequency attenuation and Bayesian statistics, it achieves precise vibration reduction control for vibration characteristics of different distance zones, which is especially suitable for complex scenarios where the relative distance between the explosion zone and the sensitive area changes dynamically, thereby improving the stability and reliability of the vibration reduction effect. Attached Figure Description

[0034] Figure 1 This is a schematic diagram showing the spatial location of the blasting zone and monitoring points in this invention;

[0035] Figure 2 These are charts of blasting vibration observation data from this invention;

[0036] Figure 3 This is a graph showing the relationship between the X-direction explosion center distance and the dominant frequency in this invention.

[0037] Figure 4 This is a graph showing the relationship between the Y-direction explosion center distance and the dominant frequency in this invention;

[0038] Figure 5 This is a graph showing the relationship between the Z-direction explosion center distance and the dominant frequency in this invention.

[0039] Figure 6 This is the X-direction dominant frequency ladder diagram of the present invention;

[0040] Figure 7 This is the Y-direction dominant frequency ladder diagram of the present invention;

[0041] Figure 8 This is the Z-direction main frequency ladder diagram of the present invention. Detailed Implementation

[0042] To make the purpose, technical solutions, and advantages of the invention's embodiments clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only a small part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0043] A method for vibration reduction in underground medium-deep hole blasting includes the following steps:

[0044] 1) Blasting vibration signal acquisition: In the sensitive area around the underground medium-deep hole blasting operation, monitoring points are set up according to the gradient of the distance from the blast center to form a distance zone monitoring profile. The three-dimensional particle vibration velocity time history curves in different distance zones are collected simultaneously, and the peak particle velocity and the main vibration frequency data in the X, Y and Z directions are extracted.

[0045] (2) Analysis of the attenuation characteristics of the main frequency: The collected main frequency data is divided into distance zones according to the distance from the center of the explosion. The mean, variance, standard deviation, coefficient of variation and interquartile range of the main frequency in each zone are calculated to quantify the attenuation law and discrete characteristics of the main frequency with the propagation distance in different distance zones.

[0046] (3) Bayesian statistical modeling: Based on Bayes' theorem, a prior distribution of the mean of the dominant frequency is set for each distance partition, a partition likelihood function is constructed, the dominant frequency parameters of each partition are estimated by the posterior distribution, and the significance of the difference in dominant frequency between different distance partitions is verified by Bayes factor.

[0047] (4) Delay time calculation: Based on the principle of phase-shifting vibration reduction, the optimal delay time is calculated according to the average main frequency of each distance zone, and the coupling relationship of "distance zone - frequency attenuation - delay time" is established.

[0048] (5) Optimal delay time direction selection: The optimal delay time direction is determined by considering the engineering influence weight of the vibration direction, the stability of the main frequency attenuation law of each distance zone, and the adaptability of the delay time to the vibration control requirements.

[0049] (6) Engineering verification: Through on-site industrial tests, the vibration reduction effect of this method and the traditional method in each distance zone is compared to verify the effectiveness of the distance zone delay time design.

[0050] In step (1), the monitoring points are set up to meet the following requirements: linearly distributed along the main direction of the propagation of the blasting seismic wave, recording the relative height difference between each measuring point and the blast source, covering the near-field vibration enhancement zone and the far-field attenuation characteristic zone, and the distance from the blast center is 300-800 meters.

[0051] In step (1), a TC-4850 high-precision blasting vibration meter is used, with a sampling frequency of 8000Hz, to simultaneously collect vibration signals in the X, Y, and Z directions, i.e., horizontal radial, horizontal tangential, and vertical directions.

[0052] In step (2), the distance between the explosion center and the explosion point is divided into three distance zones: 300~400 m, 400~700 m and 700~800 m. 21, 42 and 6 sets of effective main frequency data are collected for each zone to form a complete zone data sequence.

[0053] In step (2), the formula for calculating the coefficient of variation is:

[0054]

[0055] in: Standard deviation is the mean of the dominant frequency, and CV is the coefficient of variation;

[0056] The formula for calculating the interquartile range is:

[0057]

[0058] in: This is the upper quartile, or 75th quartile. The lower quartile, or 25th percentile, is represented by the interquartile range (IQR).

[0059] In step (3), the prior distributions for each distance partition are set as follows: the dominant frequency of the 300~400 m partition follows a normal distribution N(70,10²); the dominant frequency of the 400~700 m partition follows a normal distribution N(60,10²); and the dominant frequency of the 700~800 m partition follows a normal distribution N(45,8²). The prior standard deviation ensures that the observed data plays a dominant role in the posterior distribution.

[0060] In step (3), the likelihood function expression for each distance partition is:

[0061]

[0062] in: The mean of the dominant frequency in the k-th distance interval (k=1, 2, 3 correspond to 300~400 m, 400~700 m and 700~800 m respectively); The total variance; For the i-th observation; The sample size of the k-th interval ( , , ).

[0063] In step (3), the Bayesian factor JZS BF 10 To verify the hypothesis that "there are significant differences in the main frequency of partitions with different distances", when JZS BF 10 When the value is greater than 100, it is determined that the hypothesis is strongly supported, confirming the rationality of the distance partitioning.

[0064] In step (4), the optimal delay time calculation formula for each distance partition is as follows:

[0065]

[0066] in, The vibration reduction coefficient is set to 0.6. This represents the average frequency of each distance zone, in Hz.

[0067] In step (5), the optimal delay time direction is selected as the Z direction, which has the largest frequency attenuation amplitude in each distance partition and the Bayesian factor (JZS BF). 10 =2.952×10 19 The value was significantly higher than that in the X and Y directions, and it had the strongest correlation with the vibration response of surface structures.

[0068] In practical applications, this invention collects blasting vibration signals through a system, analyzes the attenuation law of the dominant frequency, quantifies uncertainties by combining Bayesian statistical modeling, designs the optimal delay time based on distance partitioning, and selects key vibration directions for control. The specific steps are as follows:

[0069] 1. Acquisition of blasting vibration signals:

[0070] Monitoring points were deployed according to the gradient of the blast center distance in the underground deep-hole blasting area and surrounding sensitive areas to form a radial monitoring profile. A TC-4850 high-precision blasting vibration meter was used, with a sampling frequency of 8000 Hz, to simultaneously acquire the time history curves of particle vibration velocity in three directions: X (horizontal radial), Y (horizontal tangential), and Z (vertical). Parameters such as the horizontal distance, vertical distance, and maximum charge per segment were recorded for each measuring point. After signal processing, the power per volt (PPV) and dominant frequency were extracted.

[0071] 2. Analysis of main frequency attenuation characteristics:

[0072] (1) Based on the distribution of the dominant frequencies in the X, Y and Z directions, the monitoring data is divided into three intervals: 300~400 m, 400~700 m and 700~800 m according to the distance from the explosion center. The mean, variance and standard deviation of the dominant frequencies in the X, Y and Z directions of each interval are calculated respectively.

[0073] (2) The coefficient of variation (CV) and interquartile range (IQR) are used to quantify the frequency dispersion:

[0074] Coefficient of Variation (CV): Quantifies the relative dispersion of the core frequency of each partition, and the formula is as follows: ,in Standard deviation, It is the mean of the main frequency.

[0075] Interquartile Range (IQR): Reflects the dispersion range of the middle 50% of the data in each partition's main frequency. The formula is... ,in It is the upper quartile (75th percentile). It is the lower quartile (25th percentile).

[0076] (3) Analyze the distribution characteristics of the dominant frequency in each interval, clarify the law that the high frequency component decays rapidly with distance and the low frequency component dominates the vibration in the far region. The study found that the dominant frequency in the near region (300~400 m) is concentrated in 60~80 Hz, which is dominated by geometric attenuation; the dominant frequency in the middle region (400~700 m) drops to 45~75 Hz, which is affected by the filtering effect of the strata; and the dominant frequency in the far region (700~800 m) further drops to 38~55 Hz, which is dominated by the inelastic absorption of the rock mass.

[0077] 3. Bayesian statistical modeling

[0078] (1) Prior distribution setting: Based on engineering experience, weak information prior is set for the mean of the dominant frequency of each distance zone to ensure that the observation data dominates the posterior estimation: the interval of 300~400 m follows N(70,10²), the interval of 400~700 m follows N(60,10²), and the interval of 700~800 m follows N(45,8²).

[0079] (2) Likelihood function construction: Assume that the dominant frequency observations of each partition follow a normal distribution. The likelihood function expression is:

[0080]

[0081] in: : is the sample size of the k-th interval ( , , );

[0082] (3) Posterior distribution estimation: The posterior distribution is calculated by Bayes' theorem to obtain the mode, mean, variance and 95% confidence interval of the dominant frequency mean of each partition, and to quantify the uncertainty of the parameters.

[0083] (4) Difference verification: ANOVA test and Bayesian factorial analysis (JZS BF) were used. 10 ) Verify the significance of the difference in main frequency between different distance partitions, when JZS BF 10 When the value is greater than 100, the partition is deemed reasonable.

[0084] 4. Calculation of extension time

[0085] Based on the principle of phase-shifted vibration reduction, the optimal effect of vibration wave peak-valley superposition occurs when the delay time is 0.6 times the half-cycle corresponding to the main frequency of the target zone. (Main cycle) The formula for calculating the partition delay time is:

[0086]

[0087] Based on the average dominant frequency of each distance interval, the optimal delay time in the X, Y, and Z directions is calculated to form a correspondence between "distance partition - direction - delay time".

[0088] 5. Optimal Delay Time Direction Selection

[0089] Choose the optimal direction based on the following factors:

[0090] (1) Engineering impact weight: Z-direction vibration is directly related to the structural response of surface structures. Low-frequency energy in the far region is mainly propagated vertically, and the hazard control priority is the highest.

[0091] (2) Zoned attenuation stability: The maximum attenuation amplitude of the main frequency in the Z direction across all distance zones is 40.7%, with a Bayesian factor of 2.952 × 10⁻⁶. 19 It is significantly higher than in the X and Y directions, and has the strongest statistical reliability.

[0092] (3) Zonal adaptability: The Z-direction delay time in each zone (9 ms, 12 ms, 15 ms) is more in line with the vibration characteristics of the zone, balancing the vibration reduction effect and construction efficiency.

[0093] 6. Engineering Verification

[0094] The vibration reduction effects of this method and the traditional method in different distance zones were compared through industrial tests. Data were collected using the same vibration measurement equipment, and the PPV vibration reduction rate was calculated to verify the effectiveness of the distance zone delay time design.

[0095] Example:

[0096] I. Acquisition of Blasting Vibration Signals

[0097] Taking a certain underground iron mine as the research object, the mining operation is distributed at six horizontal elevations from -110 m to -230 m. The surface elevation of the adjacent village is +205 m, with a maximum elevation difference of 435 m. The maximum charge for a single-stage detonation is limited to 80 kg.

[0098] Four monitoring points (numbered 1 to 4) were set up in the sensitive area of ​​the village, covering a distance of 300 to 800 m from the epicenter. The spacing between the monitoring points met the requirements of linear distribution along the main propagation direction, recording relative elevation differences, and covering the near-field and far-field characteristic areas.

[0099] A TC-4850 vibration meter was used for three-dimensional synchronous acquisition at a sampling frequency of 8000 Hz to record the three-dimensional particle vibration velocity time history curves during the blasting process, and to extract the PPV and the dominant frequency.

[0100] II. Analysis of Main Frequency Attenuation Characteristics

[0101] 1. Interval division: 300~400 m (21 sets of data), 400~700 m (42 sets of data), 700~800 m (6 sets of data).

[0102] 2. Partition statistics parameters:

[0103] (1) Parameters of each zone in the X direction:

[0104] (2) Parameters of each partition in the Y direction:

[0105] (3) Parameters of each partition in the Z direction:

[0106] 3. Calculation of interquartile range:

[0107] 300~400 m: IQR=10 Hz (Q1≈65 Hz, Q3≈75 Hz)

[0108] 400~700 m: IQR=20 Hz (Q1≈50 Hz, Q3≈70 Hz)

[0109] 700~800 m: IQR=12 Hz (Q1≈40 Hz, Q3≈52 Hz)

[0110] 4. Zonal attenuation characteristics:

[0111] 300~400 m zone: High frequency dominant (60~80 Hz), low dispersion (CV<3%), geometric attenuation is the main factor.

[0112] 400~700 m zone: low to medium frequency transition (45~75 Hz), increased dispersion (IQR=20 Hz), enhanced formation filtering effect.

[0113] 700~800 m zone: low frequency dominates (38~55 Hz), with the highest dispersion (CV=6.75%), dominated by inelastic absorption of rock mass.

[0114] III. Bayesian Statistical Modeling

[0115] 1. Zonal Prior Distribution: As described in the technical solution, ensure that the observed data dominates the posterior.

[0116] 2. Partition Likelihood Function: Constructed based on the assumption of normal distribution, by substituting sample data from each partition.

[0117] 3. Estimation of the posterior distribution of the partition:

[0118] (1) Posterior statistics for each partition in the X direction:

[0119] (2) Posterior statistics for each partition in the Y direction:

[0120] (3) Posterior statistics for each partition in the Z direction:

[0121] 4. Difference Verification:

[0122] ANOVA test: The sum of squares between groups in the X, Y, and Z directions was much greater than the sum of squares within groups, with F values ​​of 37.345, 30.313, and 116.066, respectively, and p < 0.001, indicating that the interval differences were extremely significant.

[0123] Bayesian factor: X direction JZS BF 10 =722081647.0, Y direction JZS BF 10 =23397182.41, Z direction JZS BF 10 =2.952×10 19 All values ​​are >100, strongly supporting the conclusion that the frequency difference between intervals is significant.

[0124] IV. Calculation of Zone Delay Time

[0125] According to the formula Calculate the delay time for each partition in the X, Y, and Z directions:

[0126] 1. X-direction

[0127] 2. Y direction

[0128] 3. Z direction

[0129] In actual blasting operations in mines, due to limitations in the manufacturing process of traditional detonators and the safety and controllability requirements of engineering practice, the delay time accuracy is usually measured in integer milliseconds. Therefore, the optimal delay times for each distance interval in the X direction are adjusted as follows: 9 ms for 300-400 m; 10 ms for 400-700 m; and 16 ms for 300-400 m. The optimal delay times for each distance interval in the Y direction are adjusted as follows: 9 ms for 300-400 m; 11 ms for 400-700 m; and 14 ms for 300-400 m. The optimal delay times for each distance interval in the Z direction are adjusted as follows: 9 ms for 300-400 m; 12 ms for 400-700 m; and 15 ms for 300-400 m.

[0130] V. Optimal Delay Time Direction Selection

[0131] The Z direction was chosen as the optimal direction due to the following advantages:

[0132] 1. Engineering impact: Directly related to the response of surface structures, with the control of low-frequency vibration hazards in distant areas having the highest priority.

[0133] 2. Attenuation stability: It has the largest attenuation amplitude, the highest Bayes factor, and the strongest statistical reliability.

[0134] 3. Adaptability: The delay time design takes into account both vibration reduction effect and construction efficiency. The delay time (15ms) in the 700~800m range is better than that in the X direction (16ms).

[0135] VI. Engineering Verification

[0136] Industrial trials comparing the vibration reduction effects of this method with traditional methods in different zones:

[0137] The results show that the proposed method has a significant and stable vibration reduction effect in each distance zone, with a particularly prominent advantage in the far zone, thus verifying the effectiveness of the method.

[0138] The present invention has the following beneficial effects:

[0139] 1. Precise zone control: Through distance zoning design, the frequency attenuation characteristics of the near, middle and far zones are specifically adapted, solving the adaptability problem of traditional fixed solutions under dynamic distance. The vibration reduction rates of each zone reach 25.0%, 26.7% and 28.6%, respectively.

[0140] 2. High statistical reliability: Bayesian modeling based on distance partitioning integrates prior information and measured data, and can still provide reliable parameter estimates even in small sample partitions (such as only 6 sets of data in 700-800 m). Uncertainty quantification provides fault tolerance space for engineering decision-making.

[0141] 3. The project is highly targeted: the Z direction is clearly defined as the core control direction for each distance zone, and the focus is on preventing and controlling the hazards of low-frequency vibrations in the far zone to surface structures, thereby improving the safety level of the project.

[0142] 4. High scalability: Establish a standardized process of "distance partitioning - frequency attenuation - Bayesian optimization" to provide a replicable technical paradigm for vibration reduction in medium and deep hole blasting in different mines.

[0143] This invention constructs a dynamic delay time design method for each distance zone by integrating frequency attenuation laws and Bayesian statistics, thus solving the adaptability problem of traditional methods at different distances. Engineering practice shows that this method can significantly improve the vibration reduction effect of each distance zone, providing a precise and reliable technical solution for vibration control in underground medium-deep hole blasting, and has significant engineering application value.

Claims

1. A method for vibration reduction in underground medium-deep hole blasting, characterized in that... Includes the following steps: (1) Acquisition of blasting vibration signals: In the sensitive area around the underground medium-deep hole blasting operation, monitoring points are set up according to the gradient of the distance between the blast center to form a distance zone monitoring profile. The time history curves of the three-dimensional particle vibration velocity in different distance zones are collected simultaneously, and the peak particle velocity and the main vibration frequency data in the X, Y and Z directions are extracted. (2) Analysis of the attenuation characteristics of the main frequency: The collected main frequency data is divided into distance zones according to the distance from the center of the explosion. The mean, variance, standard deviation, coefficient of variation and interquartile range of the main frequency in each zone are calculated to quantify the attenuation law and discrete characteristics of the main frequency with the propagation distance in different distance zones. (3) Bayesian statistical modeling: Based on Bayes' theorem, a prior distribution of the mean of the dominant frequency is set for each distance partition, a partition likelihood function is constructed, the dominant frequency parameters of each partition are estimated by the posterior distribution, and the significance of the difference in dominant frequency between different distance partitions is verified by Bayes factor. (4) Delay time calculation: Based on the principle of phase-shifting vibration reduction, the optimal delay time is calculated according to the average main frequency of each distance zone, and the coupling relationship of "distance zone - frequency attenuation - delay time" is established. (5) Optimal delay time direction selection: The optimal delay time direction is determined by considering the engineering influence weight of the vibration direction, the stability of the main frequency attenuation law of each distance zone, and the adaptability of the delay time to the vibration control requirements. (6) Engineering verification: Through on-site industrial tests, the vibration reduction effect of this method and the traditional method in each distance zone is compared to verify the effectiveness of the distance zone delay time design.

2. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (1), the monitoring points are set up to meet the following requirements: linearly distributed along the main direction of the propagation of the blasting seismic wave, recording the relative height difference between each measuring point and the blast source, covering the near-field vibration enhancement zone and the far-field attenuation characteristic zone, and the distance from the blast center is 300-800 meters.

3. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (1), a TC-4850 high-precision blasting vibration meter is used, with a sampling frequency of 8000 Hz, to simultaneously collect vibration signals in the X, Y and Z directions, i.e., horizontal radial, horizontal tangential and vertical directions.

4. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (2), the distance between the explosion center and the explosion point is divided into three distance zones: 300~400 m, 400~700 m and 700~800 m. 21, 42 and 6 sets of effective main frequency data are collected for each zone to form a complete zone data sequence.

5. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (2), the formula for calculating the coefficient of variation is: ， in: Standard deviation, is the mean of the dominant frequency, and CV is the coefficient of variation; The formula for calculating the interquartile range is: ， in: This is the upper quartile, or 75th quartile. The lower quartile, or 25th percentile, is represented by IQR, which stands for interquartile range.

6. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (3), the prior distributions for each distance partition are set as follows: the dominant frequency of the 300~400 m partition follows a normal distribution N(70,10²); the dominant frequency of the 400~700 m partition follows a normal distribution N(60,10²); and the dominant frequency of the 700~800 m partition follows a normal distribution N(45,8²). The prior standard deviation ensures that the observed data plays a dominant role in the posterior distribution.

7. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (3), the likelihood function expression for each distance partition is: ， in: The mean of the dominant frequency in the k-th distance interval (k=1, 2, 3 correspond to 300~400 m, 400~700 m and 700~800 m respectively); The total variance; For the i-th observation; The sample size of the k-th interval ( , , ).

8. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (3), the Bayesian factor JZS BF 10 To verify the hypothesis that "there are significant differences in the main frequency of partitions with different distances", when JZS BF 10 When the value is greater than 100, it is determined that the hypothesis is strongly supported, confirming the rationality of the distance partitioning.

9. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (4), the optimal delay time calculation formula for each distance partition is as follows: ， in, The vibration reduction coefficient is set to 0.

6. This represents the average frequency of each distance zone, in Hz.

10. The method for vibration reduction in underground medium-deep hole blasting according to claim 1, characterized in that: In step (5), the optimal delay time direction is selected as the Z direction, which has the largest frequency attenuation amplitude in each distance partition and the Bayesian factor (JZS BF). 10 =2.952×10 19 The value was significantly higher than that in the X and Y directions, and it had the strongest correlation with the vibration response of surface structures.

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