Method for obtaining credible blasting vibration dominant frequency and application of obtained credible blasting vibration dominant frequency

Abstract

The invention relates to a method for obtaining credible blasting vibration dominant frequency, which solves the problem of dominant frequency prediction under complex geology through EMD-HHT multi-scale decomposition and statistical confidence interval analysis and is difficult to adapt to dynamically changing construction conditions. EMD decomposition adaptively eliminates low-frequency noise caused by nonlinear response of the rock mass, and the signal-to-noise ratio is increased; a main frequency determination strategy is automatically switched through confidence interval width (RW) to adapt to complex geological conditions; 95% confidence coefficient ensures that a dominant frequency predicted value accords with actual energy distribution; compared with a traditional Samsu formula, the main frequency prediction error is reduced by more than or equal to 40%.

Description

Technical Field

[0001] This invention belongs to the field of vibration control technology in blasting engineering, specifically relating to a method for obtaining a reliable blasting vibration dominant frequency and the application of the obtained reliable blasting vibration dominant frequency. Background Technology

[0002] As one of the most economical and efficient methods for earthwork excavation, the drill-and-blast method is widely used in the construction of underground engineering tunnels or roadways, mining, water conservancy and hydropower projects. Blasting vibration is one of the hazards in blasting engineering practice. Blasting vibration can cause instability of ground buildings, cracking of concrete walls, and severe blasting vibration may cause engineering disasters such as building collapse. Existing methods for predicting the dominant frequency of blasting vibration mostly rely on empirical formulas (such as the Sadovsky formula), but the complexity of geological conditions and blasting parameters leads to insufficient prediction accuracy. Traditional methods rely on linear empirical formulas (such as the Sadovsky formula) and do not consider the nonlinear response of rock mass and the multi-scale characteristics of blasting energy. At present, the most commonly used technical solutions for blasting vibration safety control are concentrated in the following aspects: (1) In blasting engineering, empirical formulas are often used to predict the attenuation law of blasting vibration. Usually, blasting vibration meters are set up before blasting to collect peak velocity data of blasting vibration. Based on the maximum single-end charge Q and the distance between the blasting cores R, the engineering site coefficients K and α are obtained. Based on the collected data, the Sadovsky formula is fitted and then the blasting parameters that meet the vibration safety allowable standard are derived. Due to factors such as equipment and on-site testing environment, test data will produce errors, which may lead to mistakes in guiding actual construction. (2) Arrange blast holes reasonably according to terrain and geological conditions, ensure the conditions of the free face, increase the number of empty holes or adopt multi-stage inclined hole wedge-shaped slotting, etc., to improve the blasting effect and reduce the impact of vibration. By reducing the charge amount per hole or adjusting the number of blast holes detonated at the same time, the maximum charge amount per section can be limited, thereby reducing the intensity of blasting vibration. This method relies too much on the engineer's experience to design and formulate a conservative blasting design scheme.

[0003] Therefore, designing a dominant frequency prediction method that can adapt to complex geological conditions and dynamic construction environments, has high reliability and practicality, and can be widely applied in the field of blasting engineering is an urgent problem to be solved. Summary of the Invention

[0004] To address the above problems, this invention provides a method for obtaining a reliable dominant frequency of blasting vibration, comprising the following steps:

[0005] Step S1: Conduct vibration tests, collect vibration data, and save the data;

[0006] Step S2: Open the .txt file using Matlab software, call the EMD toolbox to perform empirical mode decomposition on the vibration signal, remove low-frequency noise components and residual terms, and retain the IMF component corresponding to the high-frequency vibration signal that is closest to the frequency components of the original signal.

[0007] Step S3: Perform Hilbert-Huang transform (HHT) on the effective IMF components retained in Step S2 to generate a spectrogram;

[0008] Step S4: Collect all the main frequency observations within the main frequency distribution range determined in Step S3 and organize them into a data set; calculate the sample standard deviation;

[0009] Step S5: Obtain the confidence interval width and relative width through the following method, and obtain the reliable blasting vibration main frequency according to the magnitude of the relative width;

[0010]

[0011] In the formula, W is the confidence interval width; S is the sample standard deviation; is the critical value of the t-distribution; n is the sample size. RW is the relative width, dimensionless; is the main frequency mean.

[0012] Based on the above scheme, in Step S5, if RW ≤ 30%, take the median value of the interval as the reliable main frequency;

[0013] If 30% < RW ≤ 50%, take the value with the same and highest occurrence frequency of the main frequency sample frequency. If the sample frequency distribution is too dispersed, take the frequency corresponding to the energy peak in the marginal spectrum as the reliable main frequency;

[0014] If RW > 50%, the reliable main frequency needs to be obtained through calculation and comparison.

[0015] Based on the above scheme, the method for obtaining the reliable main frequency through calculation and comparison is as follows:

[0016] (1) Calculate the total energy

[0017] Perform HHT transform on the denoised IMF components to generate the Hilbert spectrum H(ω,t), and then calculate the marginal spectrum M(ω):

[0018]

[0019] where T is the signal duration, and M(ω) represents the energy accumulation of frequency ω on the entire time axis;

[0020] Segment the marginal spectrum by frequency band, integrate the marginal spectrum for each frequency band ωi to obtain the energy Ei of that frequency band:

[0021]

[0022] The total energy Etotal is the sum of the energies of all frequency bands:

[0023]

[0024] Energy percentage per frequency band:

[0025]

[0026] (2) Starting from the highest energy region, expand outwards to both ends to determine the target frequency band with a cumulative energy >80%;

[0027] (3) Take the median of the target frequency band as the main frequency.

[0028] Based on the above scheme, in step S1, when conducting vibration testing, 3-5 monitoring points are set up, covering different geological conditions and vibration propagation paths; blasting vibration data are collected using a blasting vibration meter at a sampling frequency of not less than 1000Hz.

[0029] Based on the above scheme, in step S1, the collected blasting vibration data is saved in .txt format.

[0030] Based on the above scheme, in step S2, after calling the EMD toolbox to perform empirical mode decomposition on the vibration signal, 10 mode functions (IMF components) and 1 residual are obtained.

[0031] Based on the above scheme, in step S4, the selected confidence level is 95%.

[0032] Based on the above scheme, the method for calculating the sample standard deviation in step S4 is as follows:

[0033]

[0034] In the formula: S is the sample standard deviation; n is the sample size; x i is the i-th value in the sample; μ is the sample mean.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] This invention addresses the problem of dominant frequency prediction under complex geological conditions, particularly when adapting to dynamically changing construction conditions, through EMD-HHT multi-scale decomposition and statistical confidence interval analysis. EMD decomposition adaptively eliminates low-frequency noise caused by the nonlinear response of the rock mass, improving the signal-to-noise ratio. The dominant frequency determination strategy is automatically switched using the confidence interval width (RW), adapting to complex geological conditions. A 95% confidence level ensures that the predicted dominant frequency value matches the actual energy distribution. Compared to the traditional Sachs formula, the dominant frequency prediction error is reduced by ≥40%. Attached Figure Description

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 This is the result of decomposing the blasting vibration signal at measuring point #1 in Example 2;

[0039] Figure 2 The time-frequency spectrum obtained in Example 2;

[0040] Figure 3 This is the boundary map obtained in Example 2. Detailed Implementation

[0041] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0042] Example 1

[0043] This invention provides a method for obtaining a reliable dominant frequency of blasting vibration, comprising the following steps:

[0044] Step S1: Conduct vibration tests, collect vibration data, and save the data;

[0045] Step S2: Open the .txt file using Matlab software, call the EMD toolbox to perform empirical mode decomposition on the vibration signal, remove low-frequency noise components and residual terms, and retain the IMF component corresponding to the high-frequency vibration signal that is closest to the frequency components of the original signal.

[0046] Step S3: Perform Hilbert-Huang Transform (HHT) on the effective IMF components retained in Step S2 to generate a time-frequency spectrum.

[0047] Step S4: Collect all dominant frequency observations within the dominant frequency distribution interval determined in Step S3, and organize them into a dataset; calculate the sample standard deviation;

[0048] Step S5: Obtain the confidence interval width and relative width using the following method, and obtain the reliable blasting vibration dominant frequency based on the size of the relative width;

[0049]

[0050] Where W is the confidence interval width; S is the sample standard deviation; is the critical value of the t-distribution; n is the sample size. RW is the relative width, dimensionless; is the mean of the main frequency.

[0051] As a specific implementation, in step S5, if RW ≤ 30%, take the median of the interval as the reliable main frequency;

[0052] If 30% < RW ≤ 50%, take the value with the same and highest occurrence frequency of the main frequency samples. If the sample frequency distribution is too dispersed, take the frequency corresponding to the energy peak in the marginal spectrum as the reliable main frequency;

[0053] If RW > 50%, the reliable main frequency needs to be obtained through calculation and comparison.

[0054] As a specific implementation, the method for obtaining the reliable main frequency through calculation and comparison is as follows:

[0055] (1) Calculate the total energy

[0056] Perform HHT transform on the denoised IMF components to generate the Hilbert spectrum H(ω,t), and then calculate the marginal spectrum M(ω):

[0057]

[0058] where T is the signal duration, and M(ω) represents the energy accumulation of frequency ω on the entire time axis;

[0059] Segment the marginal spectrum by frequency band, integrate the marginal spectrum for each frequency band ωi, and obtain the energy Ei of this frequency band:

[0060]

[0061] The total energy Etotal is the sum of the energies of all frequency bands:

[0062]

[0063] The energy proportion of each frequency band:

[0064]

[0065] (2) Start from the highest energy area and expand towards both ends to determine the target frequency band with cumulative energy > 80%;

[0066] (3) Take the median of the target frequency band as the main frequency.

[0067] Specifically, in step S1, when conducting the vibration test, arrange 3 - 5 monitoring points, and the monitoring points cover different geological conditions and vibration propagation paths; use a blasting vibration instrument to collect blasting vibration data at a sampling frequency not lower than 1000Hz.

[0068] As a specific implementation plan, in step S1, the collected blasting vibration data is saved in .txt format.

[0069] Specifically, in step S2, after calling the EMD toolbox to perform empirical mode decomposition on the vibration signal, 10 mode functions (IMF components) and 1 residual are obtained.

[0070] Specifically, in step S4, the selected confidence level is 95%.

[0071] Specifically, in step S4, the method for calculating the sample standard deviation is as follows:

[0072]

[0073] In the formula: S is the sample standard deviation; n is the sample size; x i is the i-th value in the sample; μ is the sample mean.

[0074] Example 2

[0075] Based on the method of Example 1, this invention conducts vibration testing and predicts the dominant frequency of blasting vibration in the open-pit mine of Moergou Bluestone Plant in Dongdi Town, Gongxian County, Yibin, Sichuan Province. The method includes the following steps:

[0076] Step S1: Conduct vibration tests on the blasting vibration of the open-pit mine at Moergou Bluestone Plant in Dongdi Town. The mine blasting scheme adopts deep-hole blasting with a borehole diameter of 90mm. The design adopts a single-row arrangement of boreholes with a depth of approximately 17.5m. The 4m blasting zone of the plugging section uses Class III mining emulsion explosives and ammonium nitrate explosives. The emulsion explosive used is 70mm thick, and the total amount of explosives used in a single blast is 64kg. The first 5 boreholes are reserved as test holes and numbered sequentially as 1, 2, 3, 4, 5, and 6. Vibration meters are arranged sequentially in the opposite direction to the boreholes at distances of 8m, 14m, 22m, 35m, 55m, and 80m. One TC-4850 blasting vibration meter and a triaxial accelerometer connected to the blasting vibration meter are set up at each measuring point. The blasting vibration is recorded according to the borehole number and the blasting vibration velocity and frequency are recorded. The collected vibration data is saved in .txt format, as shown in Table 3.

[0077] Table 3 Vibration monitoring data

[0078]

[0079] Vibration velocity is inversely proportional to distance, but vibration frequency analysis of triaxial vibration data cannot yield a regular summary. It is necessary to re-examine these data using scientific methods (HHT) to convert the time-domain signals into frequency-domain signals, and then conduct a reasonable analysis of the frequencies.

[0080] Step S2: Open the .txt file using Matlab software, call the EMD toolbox to perform empirical mode decomposition on the vibration signal, remove low-frequency noise components and residual terms, and retain the IMF component corresponding to the high-frequency vibration signal that is closest to the frequency components of the original signal.

[0081] like Figure 1 As shown, the blasting vibration signal at measuring point #1, after decomposition, contains 10 intrinsic mode functions (IMF1 to IMF10) and one residual. Regarding vibration intensity, IMF1, IMF2, IMF3, and IMF4 have higher vibration velocities. IMF components, which retain a high proportion of vibration energy and have a frequency distribution consistent with the original signal, are considered the main components of the signal. IMF5 to IMF10 represent the low-frequency components of the original vibration signal. The residual term, the remaining part after decomposition of the original signal, is a monotonic function. It represents the average trend of the original vibration signal, showing that the vibration intensity gradually decays over time.

[0082] Geological interference terms such as residual terms (IMF10) and low-frequency components (IMF5-9) that characterize geological influences unrelated to blasting impact, such as uneven site conditions and fissures, are removed; the true dominant frequency and the signal with high-frequency IMF components accounting for more than 85% of the energy are retained.

[0083] Step S3: In Matlab software, perform HHT transform on the denoised IMF components to generate a time-frequency spectrum (e.g., ...). Figure 2 (as shown) and marginal spectrum (as shown) Figure 3 As shown, the generated spectrum and marginal spectrum are used to analyze the change of the main frequency over time, determine the distribution range of the main frequency, statistically analyze the distribution characteristics of the main frequency, observe the distribution of signal energy on the time-frequency plane, and understand the change of the main frequency over time.

[0084] When performing HHT processing, this monotonic trend can be considered a secondary factor because it does not significantly affect the analysis results. The generated marginal spectrum visually displays the time-energy-frequency relationship of the signal at the measurement point. From Figure 3 As can be seen, the vibration activity is mainly concentrated in the frequency range of 0 to 200 Hz, and the main oscillation frequency is concentrated in 10 to 60 Hz, i.e., f∈[10,60].

[0085] The advantage of the HHT method lies in its ability to convert vibration time-domain signals into frequency-domain signals, such as... Figure 2 As shown, this reveals the pattern of frequency migration over time.

[0086] The main frequency of a single HHT is affected by random fluctuations, which may be due to geological factors such as site factors. For example, the blasting site is complex and variable, and the vertical vibration signal is affected by the changes in ground undulations. Outliers need to be eliminated through statistical methods.

[0087] Step S4: Determine an appropriate confidence level according to the requirements of actual applications and accuracy requirements. Generally, 95% is used. In this embodiment, 95% confidence level is taken as an example to calculate the confidence interval width and relative width. Taking the radial main frequencies as an example, 58.94Hz, 24.24Hz, 15.69Hz, 51.28Hz, 19.8Hz, 18.82Hz, the sample size is 6, and the degree of freedom df = n - 1 = 5. The main frequency is 33.13, the standard deviation s is 16.74, α = 1 - 0.95 = 0.05, and the confidence level Looking up Table 2, we can get 2.571,

[0088] Table 2 Partial Confidence Levels and Degrees of Freedom

[0089]

[0090] Substituting the data into Equation (1), the sample standard deviation of the main frequency can be obtained:

[0091]

[0092] In the formula: S is the sample standard deviation; n is the sample size; x i is the i-th value in the sample; μ is the sample mean.

[0093] Step S5: Use formulas (2) and (3) to obtain the confidence interval width and relative width. The relative width is used to evaluate the statistical reliability of the main frequency estimation;

[0094]

[0095] In the formula: W is the confidence interval width; S is the sample standard deviation; is the critical value of the t-distribution; n is the sample size. RW is the relative width, dimensionless; is the main frequency mean.

[0096] If RW ≤ 30%, take the median value of the interval as the reliable main frequency; if 30% < RW ≤ 50%, take the value with the same and highest occurrence frequency of the main frequency sample frequency. If the sample frequency distribution is too dispersed, take the frequency corresponding to the energy peak in the marginal spectrum as the reliable main frequency; if RW > 50%, it is considered that there is no reliable main frequency for the sample frequency, and a reliable main frequency needs to be obtained through calculation and comparison.

[0097] From formula (2), we can get W = 35.14. Substituting W = 35.14 into formula (3), we get the relative width RW = 106.1% > 50%. Then it is considered a low confidence level scenario. It is necessary to determine the main frequency based on the frequency band where the HHT spectrum energy ratio > 80%. The specific method is as follows:

[0098] (1). Calculate the total energy, as shown in Table 1.

[0099] The denoised IMF components are subjected to HHT transform to generate the Hilbert spectrum H(ω,t), and then the marginal spectrum M(ω) is calculated:

[0100]

[0101] Where T is the signal duration, and M(ω) represents the energy accumulation of frequency ω over the entire time axis.

[0102] Divide the marginal spectrum into frequency bands (e.g., 0-10Hz, 10-20Hz, etc.), and integrate the marginal spectrum for each frequency band ωi to obtain the energy Ei of that frequency band:

[0103]

[0104] The total energy Etotal is the sum of the energy across all frequency bands:

[0105]

[0106] Energy percentage per frequency band:

[0107]

[0108] (2). Determine the >80% frequency band by starting the expansion from the highest energy region of 20-30Hz (35%). The cumulative energy of 10-40Hz = 25% + 35% + 30% = 90% > 80%. Target frequency band: 10-40Hz

[0109] (3) Find the main frequency within 10-40Hz: the energy peak is in the 20-30Hz range, take the median value of 25Hz.

[0110] Table 1. Segmented Energy Distribution of Marginal Spectrum

[0111] Frequency (Hz) Energy value Cumulative Energy Cumulative percentage 0-10 5％ 5％ 5％ 10-20 25％ 30％ 30％ 20-30 35％ 65％ 65％ 30-40 30％ 95％ 95％ 40-60 5％ 100％ 100％

[0112] The "Safety Regulations for Blasting" (GB 6722-2014) stipulate that for blasting in mine roadways, the safe permissible vibration frequency of the structure is 10-50Hz and the safe particle vibration velocity is 18-25cm / s.

[0113] The predicted main frequency is 25Hz, calculated in S5. If the vibration velocity exceeds the safe allowable value based on the test vibration data, the blasting parameters such as the initiation delay time, charge structure, hole spacing, and row spacing can be adjusted.

[0114] The predicted reliable dominant frequency is used to assess whether the blasting vibration effect meets safety standards, and provides feedback to guide the optimization and adjustment of blasting parameters (such as maximum single-stage charge, borehole parameters, and initiation sequence) to reduce the vibration impact of subsequent blasts. By comparing the predicted dominant frequency with the actual monitored dominant frequency, the model parameters can be further calibrated.

[0115] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. The above descriptions are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for obtaining a reliable dominant frequency of blasting vibration, characterized in that, It includes the following steps: Step S1: Conduct a vibration test experiment, collect vibration data and save it; Step S2: Use Matlab software to open the.txt format file, call the EMD toolbox to perform empirical mode decomposition on the vibration signal, eliminate the low-frequency noise component and the residual term, and retain the IMF component corresponding to the high-frequency vibration signal that is closest to the frequency components of the original signal; Step S3: Perform Hilbert-Huang transform (HHT) on the effective IMF components retained in Step S2 to generate a time-frequency spectrum diagram; Step S4: Collect all the main frequency observation values within the main frequency distribution interval determined in Step S3, organize them into a data set; calculate the sample standard deviation; Step S5: Obtain the confidence interval width and relative width through the following method, and obtain the credible blasting vibration main frequency according to the size of the relative width; In the formula, W is the confidence interval width; S is the sample standard deviation; is the critical value of the t-distribution; n is the sample size. RW is the relative width, dimensionless. It is the mean of the main frequency.

2. The method for obtaining a reliable blasting vibration dominant frequency according to claim 1, characterized in that, In Step S5, if RW ≤ 30%, take the median of the interval as the reliable main frequency; If 30% < RW ≤ 50%, take the value with the same and highest occurrence frequency of the main frequency sample frequency. If the sample frequency distribution is too dispersed, take the frequency corresponding to the energy peak in the marginal spectrum as the reliable main frequency; If RW > 50%, then the reliable main frequency needs to be obtained through calculation and comparison; 3. The method for obtaining a reliable blasting vibration dominant frequency according to claim 2, characterized in that, The method for obtaining the reliable main frequency through calculation and comparison is as follows: (1) Calculate the total energy Perform HHT transform on the noise-reduced IMF components to generate the Hilbert spectrum H(ω,t), and then calculate the marginal spectrum M(ω): where T is the signal duration, and M(ω) represents the energy accumulation of frequency ω on the entire time axis; Segment the marginal spectrum by frequency band, integrate the marginal spectrum for each frequency band ωi to obtain the energy Ei of that frequency band; The total energy Etotal is the sum of the energies of all frequency bands: The proportion of energy in each frequency band: (2) Starting from the highest energy area, expand towards both ends to determine the target frequency band with cumulative energy > 80%; (3) Take the median of the target frequency band as the main frequency.

4. The method for obtaining a reliable blasting vibration dominant frequency according to claim 1, characterized in that, In Step S1, when conducting the vibration test experiment, arrange 3 - 5 monitoring points, and the monitoring points cover different geological conditions and vibration propagation paths; use a blasting vibration instrument to collect blasting vibration data at a sampling frequency not lower than 1000Hz.

5. The method for obtaining a reliable blasting vibration dominant frequency according to claim 4, characterized in that, In Step S1, the collected blasting vibration data is saved in the.txt format.

6. The method for obtaining a reliable blasting vibration dominant frequency according to claim 1, characterized in that, In Step S2, after calling the EMD toolbox to perform empirical mode decomposition on the vibration signal, 10 mode functions (IMF components) and 1 residual are obtained.

7. The method for obtaining a reliable blasting vibration dominant frequency according to claim 1, characterized in that, In Step S4, the selected confidence level is 95%.

8. The method for obtaining the credible blasting vibration main frequency according to claim 1, wherein In Step S4, the method for calculating the sample standard deviation is: In the formula: S is the sample standard deviation; n is the sample size; x i is the i-th value in the sample; μ is the sample mean.

9. The use of the reliable blasting vibration dominant frequency obtained by the method according to any one of claims 1-8, characterized in that, It is used to evaluate whether the blasting vibration effect meets the safety standard, used to feedback and guide the optimization and adjustment of blasting parameters to reduce the vibration impact of subsequent blasting; used to compare with the actual monitored main frequency, and can further calibrate the model parameters.

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