Downward filling mining method filling body lateral cantilever body safety monitoring method based on dynamic response
By arranging triaxial vibration acceleration sensors on the surface of the cantilever structure and monitoring the natural frequency of the cantilever using dynamic response, the waste of resources and safety hazards in cantilever support treatment are solved, and the accurate identification and quantitative assessment of early damage are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INNER MONGOLIA UNIV OF SCI & TECH
- Filing Date
- 2026-02-03
- Publication Date
- 2026-05-12
AI Technical Summary
In the downfill mining method, the support treatment of cantilever structures is wasteful of resources and poses safety hazards. Existing monitoring methods cannot accurately identify the critical point of damage evolution, leading to over- or under-support problems.
A triaxial vibration acceleration sensor is used to monitor the dynamic response of the cantilever. By using the eigenvalue decomposition of the covariance matrix and the minimum projection criterion, vibration data in the principal vibration direction of the cantilever are extracted, the natural frequency is calculated, and a safety factor mapping model is established to achieve non-invasive online monitoring.
Accurately identify early damage to cantilever structures, reduce monitoring costs, avoid resource waste and safety hazards, and improve the economic efficiency of engineering projects.
Smart Images
Figure CN122016278A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mine safety engineering and structural health monitoring technology, and more specifically to a method for monitoring the safety of lateral cantilever bodies in downfill mining based on dynamic response. Background Technology
[0002] Downward-entry backfilling mining method, with its significant advantages in controlling ground pressure manifestation, improving pillar recovery rate and adapting to complex ore body conditions, has become one of the core technologies for safe and efficient mining of deep fractured ore bodies.
[0003] During the mining process, the backfill material on both sides, which serves as the surrounding rock, detaches from the underlying ore body, and irregular convex portions of the backfill material form cantilever structures. One end of this structure is constrained by the surrounding rock of the lateral backfill material, while the other end is free. Affected by blasting vibrations, micro-cracks easily develop at the connection between the cantilever section of the backfill material and the matrix. As the dominant cracks continue to expand, the cantilever structure will separate along the crack surface, eventually leading to tensile-fall instability under its own weight. Since treating the protruding cantilever structure may interrupt the mining process, conflict with the blasting plan of adjacent routes, and forcibly cutting the protrusion may cause new cracks to form inside the backfill material, support treatment should be prioritized for protruding cantilever structures. However, excessive support inevitably leads to a waste of resources. How to accurately decide the timing and intensity of support while ensuring safety becomes a key challenge in optimizing the on-site engineering.
[0004] Therefore, it is urgent to establish a quantitative dynamic risk perception mechanism to identify the critical point of damage evolution through easily implemented monitoring methods, thereby avoiding resource redundancy caused by empirical over-support and avoiding blind spots in safety early warning caused by monitoring lag. Summary of the Invention
[0005] In view of this, the present invention provides a method for safety monitoring of the lateral cantilever of the backfill body in the downfill mining method based on dynamic response, in order to solve the problems existing in the background art.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for monitoring the safety of lateral cantilever sections of backfill in downfill mining based on dynamic response includes: S1, a triaxial vibration acceleration sensor is arranged on the surface of the cantilever structure of the lateral filling body of the roadway to collect triaxial vibration acceleration time series data, the triaxial vibration acceleration time series data is divided into multiple time periods, and a data matrix of triaxial vibration acceleration time series data for each time period is constructed. S2, standardize the data matrix to obtain the covariance matrix, perform matrix eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors, and construct an eigenvalue matrix based on the eigenvectors; S3, the column vectors in the eigenvalue matrix of each time period are filtered according to the minimum projection criterion to determine the steady-state vibration time period index; the triaxial vibration acceleration time series data are reconstructed based on the steady-state vibration time period index; S4. Based on the reconstructed triaxial vibration acceleration time series data, repeat step S2 to extract the feature vector corresponding to the largest feature value as the first principal direction feature vector; extract the feature vector corresponding to the smallest feature value as the second principal direction feature vector. S5, the reconstructed triaxial vibration acceleration data are projected onto the first principal direction feature vector and the second principal direction feature vector respectively to obtain the cantilever body principal vibration direction vibration time series data and the surrounding rock reference vibration time series data; S6, calculate the spectrum of the vibration time series data of the cantilever body in the main vibration direction and the reference vibration time series data of the surrounding rock respectively, and calculate the amplitude-frequency response function based on the spectrum of the two. S7. Identify the frequency corresponding to the peak value of the amplitude-frequency response function as the current natural frequency of the cantilever. Based on the pre-calibrated mapping relationship function between the natural frequency of the cantilever and the safety factor, calculate the corresponding safety factor in combination with the current natural frequency. Use the safety factor to evaluate the stability of the cantilever and assist in support decision-making.
[0007] Preferably, in step S1, a triaxial vibration acceleration sensor is deployed on the surface of the cantilever structure formed by the lateral filling body of the roadway. The constant micro-vibration present in the mine roadway environment is used as the excitation source to collect the triaxial vibration acceleration time series data of the cantilever structure in real time. The triaxial vibration acceleration time series data is divided into multiple time periods to construct a data matrix of triaxial vibration acceleration time series data for each time period.
[0008] Preferably, constructing the eigenvalue matrix based on the feature vector specifically includes: dividing the triaxial vibration acceleration time series data into equal parts. Section, for the first Repeat step S2 on the segmented data to obtain the feature vector. Construct the eigenvalue matrix ;in, For the first i The eigenvalue vectors of the triaxial vibration sequence are respectively , and .
[0009] Preferably, S3 specifically includes: S3.1, Calculation The sum of the absolute values of the correlation coefficients between each column vector and the other column vectors: ; In the formula, Calculate operators for cross-correlation coefficients; For matrix The Column vector; The Kronecker function; S3.2, Initialize the orthogonal complement space operator, let... For the corresponding Let be a column vector, denoted as . Zhang Cheng's column space is denoted as Initialized orthogonal complement space operator: ;in, For orthogonal complement space projection operator; It is the identity matrix; S3.3, for Calculate the projection norm of the remaining candidate column vectors ; S3.4, Select ,renew : ; S3.5, repeat S3.3-S3.4, until... The CCP Column vectors, and construct an index set. ; S3.6, based on index set Select the triaxial vibration acceleration sequence into segments, and reconstruct it by connecting the beginning and end to obtain the reconstructed triaxial vibration acceleration time series data.
[0010] Preferably, S4 specifically includes: a time-series data reconstruction matrix based on the reconstruction. The principal vibration orientation vector of the cantilever body is extracted via S2. Reference vibration vector of the lateral filling surrounding rock ;in, The eigenvector corresponding to the largest eigenvalue, The eigenvector corresponding to the smallest eigenvalue.
[0011] Preferably, step S5 specifically includes: calculating the data sequence of vibration time-series data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock .
[0012] Preferably, step S6 specifically includes: a data sequence of vibration time-series data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock Calculate the spectrum separately, and then calculate the amplitude-frequency response function based on the spectrum data. ;in, and These are the main vibration azimuth spectrum of the cantilever body and the reference spectrum of the surrounding rock, respectively.
[0013] Preferably, the mapping function based on the pre-calibrated natural frequency of the cantilever and the safety factor specifically includes: ; in, The natural frequency of the cantilever body is pre-calibrated. For safety reasons, This is a mapping function.
[0014] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for safety monitoring of the lateral cantilever body of the backfill in the downfill mining method based on dynamic response. It uses the naturally occurring constant micro-vibration in the tunnel environment as the excitation source, without the need for additional artificial excitation, thus avoiding the interference of artificial excitation on mining operations in traditional monitoring methods, and reducing the deployment and operation costs of monitoring equipment. Moreover, the triaxial vibration sensor is easy to deploy and operate, does not damage the structural integrity of the backfill, and realizes non-invasive continuous online monitoring of the lateral cantilever body, which is perfectly adapted to the complex underground environment of the downfill mining method.
[0015] By using eigenvalue decomposition of the covariance matrix and the minimum projection criterion, the vibration sequence of the cantilever body's main vibration orientation is accurately separated, effectively eliminating unsteady-state interference and surrounding rock vibration noise. The extracted natural frequencies are highly sensitive to the depth of hidden cracks at the root of the cantilever body and damage to the bonding layer. Through physical model tests and numerical simulations, the natural frequencies' response sensitivity to bonding layer damage is nearly three orders of magnitude higher than that of traditional displacement monitoring, accurately capturing early damage precursors at the millimeter level. This solves the pain point of existing technologies being slow or unable to identify hidden and early damage. A quantitative mapping model between natural frequencies and safety factors is established, transforming the cantilever body stability assessment from traditional experience-based judgment to quantitative data support. This clarifies the timing and strength threshold of support, avoiding resource waste caused by over-support and eliminating safety hazards caused by insufficient support. This significantly reduces mine support costs and resource redundancy, improving the economic efficiency of the project. Attached Figure Description
[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0017] Figure 1 A flowchart of the method steps provided by the present invention; Figure 2The physical experimental model diagram provided by this invention; Figure 3 The following is a time-series data diagram of the three-dimensional vibration acceleration of the cantilever body provided by the present invention; Figure 4 The amplitude-frequency response function curve of the cantilever body provided by the present invention; Figure 5 The amplitude-frequency response function curve provided for this invention; Figure 6 A correlation diagram between the inherent frequency and the safety factor provided by this invention; Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 skilled in the art without creative effort are within the scope of protection of the present invention.
[0019] This invention discloses a method for monitoring the safety of lateral cantilever bodies in downfill mining based on dynamic response, such as... Figure 1 As shown, it includes: S1. Arrange triaxial vibration acceleration sensors on the surface of the cantilever structure of the lateral filling body of the roadway to collect triaxial vibration acceleration time series data, divide the triaxial vibration acceleration time series data into multiple time periods, and construct a data matrix of triaxial vibration acceleration time series data for each time period. S2, standardize the data matrix to obtain the covariance matrix, perform matrix eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors, and construct the eigenvalue matrix based on the eigenvectors; S3, based on the minimum projection criterion, the column vectors in the eigenvalue matrix of each time period are selected to determine the steady-state vibration time period index; the triaxial vibration acceleration time series data are reconstructed based on the steady-state vibration time period index; S4. Based on the reconstructed triaxial vibration acceleration time series data, repeat step S2 to extract the feature vector corresponding to the largest feature value as the first principal direction feature vector; extract the feature vector corresponding to the smallest feature value as the second principal direction feature vector. S5, the reconstructed triaxial vibration acceleration data are projected onto the first principal direction feature vector and the second principal direction feature vector respectively to obtain the vibration time series data of the cantilever body in the principal vibration direction and the reference vibration time series data of the surrounding rock. S6, calculate the spectrum of the vibration time series data of the cantilever body in the main vibration direction and the reference vibration time series data of the surrounding rock respectively, and calculate the amplitude-frequency response function based on the spectrum of the two. S7. Identify the frequency corresponding to the peak value of the amplitude-frequency response function as the current natural frequency of the cantilever. Based on the pre-calibrated mapping relationship function between the natural frequency of the cantilever and the safety factor, calculate the corresponding safety factor in combination with the current natural frequency. Use the safety factor to evaluate the stability of the cantilever and assist in support decision-making.
[0020] In one specific embodiment, in step S1, a triaxial vibration acceleration sensor is arranged on the surface of the cantilever structure of the lateral filling body in the roadway to collect triaxial vibration acceleration time-series data and construct a data matrix. ,in for The three-dimensional acceleration vector at any given time.
[0021] right Standardization process:
[0022] in, It is a three-way mean vector. It is a diagonal matrix of standard deviation.
[0023] calculate The covariance matrix is obtained and its eigenvalues are decomposed.
[0024] in, Eigenvalue matrix , This is the eigenvector matrix corresponding to the eigenvalues.
[0025] The triaxial vibration acceleration time series data is divided into equal parts. Section, for the first Repeat steps S2-S3 on the segmented data to obtain the feature vector. Construct the eigenvalue matrix: ;in, For the first i The eigenvalue vectors of the triaxial vibration sequence are respectively , and .
[0026] In one specific embodiment, S3 specifically includes: S3.1, Calculation The sum of the absolute values of the correlation coefficients between each column vector and the other column vectors: ; In the formula, Calculate operators for cross-correlation coefficients; For matrix The Column vector; The Kronecker function; S3.2, Initialize the orthogonal complement space operator, let... For the corresponding Let be a column vector, denoted as . Zhang Cheng's column space is denoted as Initialized orthogonal complement space operator: ;in, For orthogonal complement space projection operator; It is the identity matrix; S3.3, for Calculate the projection norm of the remaining candidate column vectors ; S3.4, Select ,renew : ; S3.5, repeat S3.3-S3.4, until... The CCP Column vectors, and construct an index set. ; S3.6, based on index set Select the triaxial vibration acceleration sequence into segments, and reconstruct it by connecting the beginning and end to obtain the reconstructed triaxial vibration acceleration time series data.
[0027] In one specific embodiment, S4 specifically includes: a time-series data reconstruction matrix based on the reconstruction. The principal vibration orientation vector of the cantilever body is extracted via S2. Reference vibration vector of the lateral filling surrounding rock ;in, The eigenvector corresponding to the largest eigenvalue, The eigenvector corresponding to the smallest eigenvalue.
[0028] In one specific embodiment, S5 specifically includes: calculating the data sequence of vibration time-series data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock .
[0029] In one specific embodiment, S6 specifically includes: a data sequence of vibration time-series data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock Calculate the spectrum separately, and then calculate the amplitude-frequency response function based on the spectrum data. ;in, and These are the main vibration azimuth spectrum of the cantilever body and the reference spectrum of the surrounding rock, respectively.
[0030] In one specific embodiment, the mapping function based on the pre-calibrated natural frequency of the cantilever and the safety factor specifically includes: ; in, The natural frequency of the cantilever body is pre-calibrated. For safety reasons, The mapping relationship function needs to be obtained through theoretical calculations, model experiments, or numerical simulation calibration.
[0031] In specific embodiment 1
[0032] Model building such as Figure 2 As shown, the main body of the indoor casting physical test model is 30cm × 30cm × 30cm, and the cantilever section is 12cm long, 11.5cm wide, and 9.5cm high. The physical model was cast using a single mold to ensure close contact between the cantilever section and the surrounding rock (the main body of the model). The model material ratio is quartz sand: barite powder: gypsum: retarder: purified water: glycerin = 50:30:8:0.02:10:1.5. The physical and mechanical parameters are shown in Table 1. Table 1 Physical and Mechanical Parameters
[0033] A triaxial vibration acceleration sensor was installed at the end of the simulated cantilever structure. The sensor was connected to a signal acquisition device and then to a PC. No artificial vibration excitation was applied; the constant micro-motions in the mine tunnel were simulated solely by relying on the background noise of the indoor environment. Damage was simulated by cutting cracks at the trailing edge of the cantilever, with different crack depths representing different degrees of damage. The main model was fixed to simulate the surrounding rock constraints, and time-series data of the triaxial vibration acceleration of the cantilever were collected. Figure 3 As shown, the sampling settings ensure coverage of the main frequency bands.
[0034] The collected triaxial acceleration time series data were standardized: Calculate the average values of the time series accelerations in the X, Y, and Z directions respectively. and standard deviation .
[0035] Acceleration values at each time point along each axis The standard value is calculated using the following formula: ; Obtain the standardized triaxial acceleration data matrix Based on standardized data matrix Calculate its covariance matrix : ; in This represents the total number of time points.
[0036] For covariance matrix Perform eigenvalue decomposition: ; Obtain the eigenvalue diagonal matrix , and its corresponding eigenvector matrix .
[0037] Total time series data with a duration of 1 minute Divided into For each time period, Data: Repeatedly perform data standardization and feature decomposition to obtain feature vectors. Combine the feature vectors from all time periods to construct the eigenvalue matrix: ; calculate Each column of feature vectors With all other column vectors The sum of the absolute values of the correlation coefficients: ; Calculate the operator for the Pearson correlation coefficient; For matrix The Column vector; The Kronecker function is used; the highest score is selected as the initial baseline vector. This vector can represent the time period in which data consistency is at its best.
[0038] Initialize the reference space and projection operator: (1) The initial reference column vector spans the space .
[0039] (2) Computational space Orthogonal complement space projection operator: ; Iterative filtering of column vectors: (1) To China was not selected Perform the following operation on all remaining candidate column vectors: 1) Calculate the projection norm: ; This norm characterization Spanning a space with the selected vectors The degree of deviation.
[0040] 2) Select similar segments: Select the candidate vector with the smallest projection norm.
[0041] 3) Update the baseline space: And based on new space Recalculate the orthogonal complement space projection operator .
[0042] 4) Repeat the above process until the number of filtered vector columns reaches the predetermined value. .
[0043] Retrieve steady-state segment index: Record the final selected segments. The original time period indices corresponding to all column vectors form the steady-state segment index set. .
[0044] Data Restructuring: Based on Index Set The sequence segments corresponding to the time period are extracted from the standardized data of the original triaxial acceleration data and connected in chronological order to form the reconstructed triaxial vibration acceleration matrix. The data matrix has eliminated interference from unsteady vibrations.
[0045] Extracting the feature vector of the principal vibration direction
[0046] 1. For the reconstructed matrix Calculate the covariance matrix Perform eigenvalue decomposition: ; 2. Extraction Maximum eigenvalue corresponding feature vector , used to characterize the principal vibration direction of the cantilever body; extract Minimum eigenvalue corresponding feature vector , is an eigenvector used to characterize the reference vibration of the surrounding rock (the main body of the model).
[0047] The principal vibration azimuth vibration signal and the surrounding rock reference vibration signal are obtained by projection. The reconstructed triaxial vibration acceleration data (unnormalized) are then projected onto the feature vectors. and In terms of location: 1. Vibration signal sequence of the cantilever body's main vibration orientation: .
[0048] 2. Reference vibration signal sequence of surrounding rock: .
[0049] Amplitude-frequency response calculation, calculate the signal respectively. and Spectrum Calculate the amplitude-frequency response function based on the spectrum: ; And thus obtain Figure 4 Amplitude-frequency response function curve of a cantilever body.
[0050] In the amplitude-frequency response function curve The highest peak value is identified above, such as Figure 5 As shown, the frequency corresponding to this peak point is the natural frequency of the cantilever body in the current state.
[0051] The mapping function needs to be theoretically analyzed or numerically simulated based on the specific geometric characteristics, material properties, and constraints of the target cantilever structure to calibrate and establish the natural frequency-safety factor relationship. The natural frequency corresponds one-to-one with the crack depth, and the natural frequency value monotonically decreases with increasing crack depth. The relationship between the natural frequency and the safety factor is as follows: Figure 6 As shown, there is a clear negative correlation between the natural frequency of the cantilever and the safety factor, that is, the safety factor decreases as the natural frequency decreases. The two have a one-to-one mapping relationship, so the safety factor can be quantitatively characterized by real-time monitoring of the natural frequency change.
[0052] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The methods disclosed in the embodiments are described simply because they correspond to the methods disclosed in the embodiments; relevant parts can be found in the method section.
[0053] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for safety monitoring of lateral cantilever bodies in downfill mining based on dynamic response, characterized in that, include: S1, a triaxial vibration acceleration sensor is arranged on the surface of the cantilever structure of the lateral filling body of the roadway to collect triaxial vibration acceleration time series data, the triaxial vibration acceleration time series data is divided into multiple time periods, and a data matrix of triaxial vibration acceleration time series data for each time period is constructed. S2, standardize the data matrix to obtain the covariance matrix, perform matrix eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors, and construct an eigenvalue matrix based on the eigenvectors; S3, the column vectors in the eigenvalue matrix of each time period are filtered according to the minimum projection criterion to determine the steady-state vibration time period index; the triaxial vibration acceleration time series data are reconstructed based on the steady-state vibration time period index; S4. Based on the reconstructed triaxial vibration acceleration time series data, repeat step S2 to extract the feature vector corresponding to the largest feature value as the first principal direction feature vector; extract the feature vector corresponding to the smallest feature value as the second principal direction feature vector. S5, the reconstructed triaxial vibration acceleration data are projected onto the first principal direction feature vector and the second principal direction feature vector respectively to obtain the cantilever body principal vibration direction vibration time series data and the surrounding rock reference vibration time series data; S6, calculate the spectrum of the vibration time series data of the cantilever body in the main vibration direction and the reference vibration time series data of the surrounding rock respectively, and calculate the amplitude-frequency response function based on the spectrum of the two. S7. Identify the frequency corresponding to the peak value of the amplitude-frequency response function as the current natural frequency of the cantilever. Based on the pre-calibrated mapping relationship function between the natural frequency of the cantilever and the safety factor, calculate the corresponding safety factor in combination with the current natural frequency. Use the safety factor to evaluate the stability of the cantilever and assist in support decision-making.
2. The method for safety monitoring of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 1, is characterized in that... In step S1, a triaxial vibration acceleration sensor is deployed on the surface of the cantilever structure formed by the lateral filling body of the roadway. The constant micro-vibration present in the mine roadway environment is used as the excitation source to collect the triaxial vibration acceleration time series data of the cantilever structure in real time. The triaxial vibration acceleration time series data is divided into multiple time periods to construct a data matrix of triaxial vibration acceleration time series data for each time period.
3. The method for safety monitoring of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 1, is characterized in that... The specific steps of constructing the eigenvalue matrix based on the feature vector include: dividing the triaxial vibration acceleration time series data into equal parts. Section, for the first Repeat step S2 on the segmented data to obtain the feature vector. Construct the eigenvalue matrix ;in, For the first i The eigenvalue vectors of the triaxial vibration sequence are respectively , and .
4. The method for safety monitoring of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 3, is characterized in that... S3 specifically includes: S3.1, Calculation The sum of the absolute values of the correlation coefficients between each column vector and the other column vectors: ； In the formula, Calculate operators for cross-correlation coefficients; For matrix The Column vector; The Kronecker function; S3.2, Initialize the orthogonal complement space operator, let... For the corresponding Let be a column vector, denoted as . Zhang Cheng's column space is denoted as Initialized orthogonal complement space operator: ;in, For orthogonal complement space projection operator; It is the identity matrix; S3.3, for Calculate the projection norm of the remaining candidate column vectors ; S3.4, Select ,renew : ; S3.5, repeat S3.3-S3.4, until... The CCP Column vectors, and construct an index set. ; S3.6, based on index set Select the triaxial vibration acceleration sequence into segments, and reconstruct it by connecting the beginning and end to obtain the reconstructed triaxial vibration acceleration time series data.
5. A method for monitoring the safety of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 4, characterized in that, S4 specifically includes: a time-series data reconstruction matrix based on the reconstruction. The principal vibration orientation vector of the cantilever body is extracted via S2. Reference vibration vector of the lateral filling surrounding rock ;in, The eigenvector corresponding to the largest eigenvalue, The eigenvector corresponding to the smallest eigenvalue.
6. The method for safety monitoring of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 5, is characterized in that... S5 specifically includes: calculating the data sequence of vibration time-series data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock .
7. A method for monitoring the safety of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 5, is characterized in that... S6 specifically includes: a data sequence of vibration time data in the principal vibration direction of the cantilever body. and the data sequence of reference vibration time series data of surrounding rock Calculate the spectrum separately, and then calculate the amplitude-frequency response function based on the spectrum data. ;in, and These are the main vibration azimuth spectrum of the cantilever body and the reference spectrum of the surrounding rock, respectively.
8. A method for monitoring the safety of lateral cantilever bodies in downfill mining based on dynamic response, as described in claim 1, characterized in that, The mapping function based on the pre-calibrated natural frequency of the cantilever and the safety factor specifically includes: ； in, The natural frequency of the cantilever body is pre-calibrated. For safety reasons, This is a mapping function.