High-precision source positioning method suitable for cross-scale complex rock mass medium

Abstract

The invention provides a high-precision source positioning method suitable for a cross-scale complex rock mass medium. The high-precision source positioning method comprises the following steps of construction of a homogenized reference frame, generation of a linear equation set, dynamic weight estimation, matrix truncation decomposition for enhancing stability, and output of sound source coordinates, wave velocity and trigger time. According to the method, error transmission of a single sensor is eliminated through a homogenized reference frame, noise interference is suppressed through dynamic weight estimation, the problem of ill-conditioned matrix inversion is solved in combination with matrix truncation decomposition, geometric limitation of a sensor array is broken through, and finally high-precision and high-stability cross-scale acoustic emission source positioning is achieved. Reliable technical support is provided for complex engineering environments such as a dynamic velocity field, random sensor layout and multi-scale monitoring requirements.

Description

Technical Field

[0001] The present invention relates to the technical fields of acoustic emission / microseismic source positioning, structural health, and engineering safety monitoring, and in particular to a high-precision source positioning method applicable to cross-scale complex rock media. Background Art

[0002] Acoustic emission (AE) and microseismic (MS) source positioning technology is the core technology for structural health monitoring, geological disaster warning and industrial facility safety assessment. It is widely used in key areas such as deep mine rock burst warning, nuclear power plant structural integrity detection, dam leakage monitoring, and aerospace composite material damage diagnosis. For example, in deep mining, the precise positioning of microseismic events (error <10m) can warn of rock bursts several hours in advance and avoid casualties; in nuclear power plants, the millimeter-level positioning accuracy of acoustic emission sources (error <15mm) is the key to detecting early crack propagation. However, the non-uniformity and time-varying nature of wave velocity in complex media (such as mine dynamic velocity fields and anisotropic composite materials), as well as the noise interference of sensor networks, have severely limited the accuracy and robustness of traditional positioning methods. The specific existing methods still have the following major problems:

[0003] 1) Speed dependence and reference error: Traditional methods rely on the arrival time of a single reference sensor and are susceptible to the cumulative propagation effect of measurement errors, resulting in positioning deviations.

[0004] 2) Ill-conditioned equations and numerical instability: Traditional positioning methods improve positioning accuracy by minimizing the arrival time difference residual. However, their coefficient matrices are often ill-conditioned due to redundant dependent variables, making matrix inversion difficult and sensitive to small disturbances, reducing computational stability.

[0005] 3) Insufficient weight allocation: Existing methods only use the minimum number of sensors to construct equations and fail to dynamically weight and integrate multi-sensor information. In particular, they cannot suppress outliers in high-noise environments, affecting positioning robustness.

[0006] 4) Geometric limitations: Analytical methods based on specific geometries (such as cylindrical arrays) cannot adapt to randomly distributed sensor networks in complex engineering projects, limiting the scope of practical applications.

[0007] 5) Cross-scale positioning and size effect: Existing algorithms perform well in small-scale laboratory environments (such as pencil lead fracture experiments). However, in large-scale engineering scenarios (such as mine microseismic monitoring), the positioning accuracy drops sharply due to the long signal propagation distance and enhanced spatiotemporal heterogeneity of wave velocity (the wave velocity fluctuation in mine rock mass reaches 30%). This limitation hinders the unified application of technology in multi-scale engineering projects, and there is an urgent need to develop a positioning framework with scale invariance.

[0008] These issues lead to significant positioning errors in existing methods in complex media (such as the dynamic velocity field of mines), making it difficult to meet the requirements of high-precision engineering. Therefore, a robust positioning method that is cross-scale, interference-resistant, and adaptable to random arrays is urgently needed. Summary of the Invention

[0009] In response to the technical problems of existing acoustic emission / microseismic source positioning technology, such as single reference sensor error propagation, numerical instability caused by equation ill-conditioning, insufficient multi-sensor data fusion, geometric constraint-limited universality, and insufficient cross-scale positioning accuracy, the present invention provides a high-precision source positioning method suitable for cross-scale complex rock media. This method eliminates single-sensor error propagation through a homogenized reference frame, suppresses noise interference using dynamic weight estimation, and solves the problem of inverting ill-conditioned matrices in combination with matrix truncation decomposition. It also breaks through the geometric limitations of sensor arrays, ultimately achieving high-precision and high-stability cross-scale acoustic emission source positioning, providing reliable technical support for complex engineering environments such as dynamic velocity fields, random sensor layouts, and multi-scale monitoring needs.

[0010] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0011] A high-precision source positioning method applicable to complex rock media across scales includes the following steps:

[0012] S1. Construction of a uniform reference frame: The arrival times of N sensors are squared and averaged to generate the following uniform reference equation:

[0013]

[0014] Among them, (x, y, z) is the coordinate of the sound source to be solved; t0 is the trigger time; v is the wave velocity, which is considered as an unknown number in the positioning process; (x i ,y i ,z i ) is the coordinate of the i-th sensor; t i is the arrival time of the i-th sensor;

[0015] S2. Linear equation group generation: By combining the homogenized reference equation with the original equations of each sensor and eliminating the trigger time t0, the following linear equation group L is obtained: i :

[0016] L i =a i x+b i y+c i z+d i K+e i V

[0017] Among them, a i 、bi 、c i d i 、e i are the coefficients of the equations, and are calculated from the sensor coordinates and arrival time. K=Vt0,V=v 2 ; The original equation of each sensor is (x i -x) 2 +(y i -y) 2 +(z i -z) 2 =v 2 (t i -t0) 2 , i=1,2,…,N;

[0018] Since the arrival time measurement contains errors, the two sides of the linear equation system are not equal. The deviation between the left and right sides is recorded as the equation residual ε, which is expressed in matrix form as:

[0019] ε=L-Aθ

[0020] in,

[0021] S3. Dynamic weight estimation: Calculate the weight matrix W = ψ based on the covariance matrix ψ of the arrival time error -1 , where ψ=E(ε T ε)≈4V 2 RQR, E represents expectation, ε T is the transposed matrix of ε, R is the propagation time diagonal matrix, and Q is the Gaussian white noise covariance matrix;

[0022] S4. Matrix truncation decomposition to enhance stability: Perform matrix truncation decomposition on the coefficient matrix A, expressed as A=UHY T ; Where H is a diagonal matrix, and the elements on the main diagonal are the singular values arranged in descending order, namely σ1, σ2, L, σ N-1 ,σ N ; U is the left singular vector, Y is the right singular vector;

[0023] The singular values less than the threshold tol are truncated as follows:

[0024]

[0025] At this time, the coefficient matrix A changes to:

[0026]

[0027] Construct pseudo-inverse matrix And solve the linear equations in a weighted manner to obtain the vector θ containing two unknown parameters: the source coordinates and the wave velocity:

[0028]

[0029] S5, output the sound source coordinates (x, y, z) and wave speed according to the solved θ And the trigger time t0 = K / V.

[0030] Furthermore, in step S1, the sensor array adopts any asymmetric and non-planar geometric distribution, and the number N of sensors is dynamically expanded to N≥5.

[0031] Furthermore, the calculation of the covariance matrix ψ in step S3 includes:

[0032] Through the existing error transfer model, the equation residual ε caused by measurement uncertainty is obtained j :

[0033]

[0034] in, is the noise-free propagation time, n i is the arrival time error, and is approximately calculated based on the (x, y, z) and V calculated in step S5 as follows:

[0035]

[0036] Furthermore, the threshold value tol in step S4 is in the range of 10 -10 ≤tol≤10 -6 .

[0037] Furthermore, the threshold tol is set to 10 -8 .

[0038] Furthermore, the calculation of the wave velocity v in step S5 does not require the foreknowledge of the medium wave velocity, and the coupling error between the medium wave velocity and the trigger time is eliminated through dynamic inversion.

[0039] Compared with the existing technology, the high-precision source positioning method provided by the present invention, which is applicable to cross-scale complex rock media, has the following advantages:

[0040] 1. Breakthrough in high-precision positioning and noise immunity:

[0041] By eliminating the error transmission of a single sensor through a homogenized reference frame and combining it with dynamic weight estimation to suppress noise interference, the average positioning error in laboratory pencil lead fracture experiments was only 10.6 mm (an improvement of 32% to 62% compared to existing methods), and the error in field blasting experiments was 10.4 m (an improvement of 55% to 68% in accuracy).

[0042] 2. Improved stability of ill-conditioned equations:

[0043] Matrix truncation decomposition is used to truncate small singular values, greatly reducing the coefficient matrix condition number and solving the matrix inversion divergence problem. The solution success rate of large sensor networks reaches 100%, significantly improving the robustness in complex media such as dynamic velocity fields in mines.

[0044] 3. Geometric universality and speed independence:

[0045] It supports any randomly distributed sensor array, such as the irregular layout of a mine, breaking through the geometric limitations of traditional methods such as cylindrical / rectangular arrays. It directly eliminates the synchronization time by homogenizing the reference equation, avoids the coupling error of wave velocity parameters, and maintains precise positioning in scenarios with large wave velocity fluctuations.

[0046] 4. Enhanced cross-scale adaptability:

[0047] Dynamic wave velocity inversion and adaptive weighting mechanism correct signal measurement errors and the size effect of wave velocity anisotropy. The positioning performance is consistent in both small-scale laboratory (positioning range <1m) and large-scale engineering (positioning range >100m) scenarios, and is suitable for multi-scale positioning needs from millimeter-scale composite material cracks to kilometer-scale geological faults.

[0048] 5. Real-time and computing efficiency optimization:

[0049] Based on closed-form analytical solution (non-iterative), it avoids initial value sensitivity and divergence risk, and its computational efficiency is about 20 times higher than that of the iterative method, meeting the real-time monitoring needs of the project.

[0050] 6. Engineering applicability expansion:

[0051] By weighted fusion of multi-sensor data (N≥5), outlier interference is effectively suppressed, and dynamic expansion of the sensor network is supported (such as adding or removing sensors in long-term bridge monitoring). The sensor network module supports irregular deployment in mine tunnels, dams, or aviation composite materials, and there is no need to remodel when sensors are dynamically added or removed.

[0052] In summary, the present invention is significantly superior to existing technologies in terms of positioning accuracy, noise resistance, stability, and cross-scale adaptability, providing a highly reliable solution for complex engineering scenarios such as dynamic velocity fields, random array layouts, and multi-scale monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the high-precision source positioning method applicable to cross-scale complex rock media provided by the present invention.

[0054] Figure 2 This is a schematic diagram of the average positioning errors of six sources obtained by the five methods provided by the present invention.

[0055] Figure 3 This is a schematic diagram of the average positioning error of 16 sources under different error conditions provided by the present invention.

[0056] Figure 4 This is a schematic diagram of average positioning errors determined by five methods provided by the present invention. DETAILED DESCRIPTION

[0057] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below with reference to specific illustrations.

[0058] Please refer to Figure 1 As shown, the present invention provides a high-precision source positioning method applicable to cross-scale complex rock media, comprising the following steps:

[0059] S1. Construction of a uniform reference frame: The arrival times of N sensors are squared and averaged to generate the following uniform reference equation:

[0060]

[0061] Among them, (x, y, z) is the coordinate of the sound source to be solved; t0 is the trigger time; v is the wave velocity, which is considered as an unknown number in the positioning process; (x i ,y i ,z i ) is the coordinate of the i-th sensor; t i is the arrival time of the i-th sensor;

[0062] S2. Linear equation group generation: By combining the homogenized reference equation with the original equations of each sensor and eliminating the trigger time t0, the following linear equation group L is obtained: i :

[0063] L i =a i x+b i y+c i z+d i K+e i V

[0064] Among them, a i 、b i 、c i d i 、e i are the coefficients of the equations, and are calculated from the sensor coordinates and arrival time. K=Vt0,V=v 2 ; The original equation of each sensor is (x i -x) 2+(y i -y) 2 +(z i -z) 2 =v 2 (t i -t0) 2 , i=1,2,…,N;

[0065] Since the arrival time measurement contains errors, the two sides of the linear equation system are not equal. The deviation between the left and right sides is recorded as the equation residual ε, which is equivalent to the existence of the equation residual ε in the linear equation system. It can be expressed in matrix form as:

[0066] ε=L-Aθ

[0067] in,

[0068] S3. Dynamic weight estimation: Calculate the weight matrix W = ψ based on the covariance matrix ψ of the arrival time error -1 , where ψ=E(ε T ε)≈4V 2 RQR, E represents expectation, ε T is the transposed matrix of ε, R is the propagation time diagonal matrix, and Q is the Gaussian white noise covariance matrix;

[0069] S4. Matrix truncation decomposition to enhance stability: Perform matrix truncation decomposition on the coefficient matrix A, expressed as A=UHY T ; Where H is a diagonal matrix, and the elements on the main diagonal are the singular values arranged in descending order, namely σ1, σ2, L, σ N-1 ,σ N ; U is the left singular vector, Y is the right singular vector;

[0070] The singular values less than the threshold tol are truncated as follows:

[0071]

[0072] At this time, the coefficient matrix A changes to:

[0073]

[0074] Construct pseudo-inverse matrix And solve the linear equations in a weighted manner to obtain the vector θ containing two unknown parameters: the source coordinates and the wave velocity:

[0075]

[0076] S5, output the sound source coordinates (x, y, z) and wave speed according to the solved θ And the trigger time t0 = K / V.

[0077] As a specific implementation, in step S1, the sensor array adopts an arbitrary asymmetric and non-planar geometric distribution, and the number of sensors N is dynamically expanded to N≥5, thereby fusing multi-sensor data and effectively suppressing outlier interference.

[0078] As a specific implementation, the calculation of the covariance matrix ψ in step S3 includes:

[0079] Through the existing error transfer model, the equation residual ε caused by measurement uncertainty is obtained j :

[0080]

[0081] in, is the noise-free propagation time, n i is the arrival time error, and is approximately calculated based on the (x, y, z) and V calculated in step S5 as follows:

[0082]

[0083] As a specific implementation, the value range of the threshold tol in step S4 is 10 -10 ≤tol≤10 -6 Preferably, the threshold tol is set to 10 -8 .

[0084] As a specific implementation, the calculation of the wave velocity v in step S5 does not require the foreknowledge of the medium wave velocity. The coupling error between the medium wave velocity and the trigger time is eliminated by dynamic inversion, thereby reducing the influence of the medium wave velocity measurement error on the positioning accuracy.

[0085] In order to better understand the high-precision source positioning method applicable to cross-scale complex rock media provided by the present invention, it will be described below with reference to specific embodiments.

[0086] Example 1: Laboratory pencil lead fracture test

[0087] (1) Structural composition and implementation steps

[0088] Experimental setup: 16 acoustic emission sensors were randomly arranged on the surface of a granite specimen with dimensions of 200 mm × 179 mm × 84 mm. The sensors were connected to a DS5-16C signal analyzer via a signal amplifier (gain 40 dB) with a sampling frequency of 3 MHz.

[0089] Acoustic source generation: Six acoustic emission sources (AF) were generated by breaking a 0.5 mm diameter HB pencil lead at a 30° angle on the specimen surface.

[0090] Signal acquisition and processing: The acoustic emission waveform received by the sensor is collected and the P-wave arrival time is automatically extracted using a threshold method. The sound source coordinates (x, y, z) are then determined using the method of the present invention.

[0091] (2) Positioning effect

[0092] like Figure 2 As shown in the figure, the average localization error of the proposed method for six sound sources is 10.6mm, which is 32% to 62% higher than that of traditional methods (such as CAS and ASUV). For example, the true coordinates of sound source D are (0mm, 60mm, 42mm), and the positioning result of the proposed method is (-0.5mm, 74.1mm, 44.3mm), with an error of 14.3mm, while the error of the ASUV method is as high as 17.6mm.

[0093] Example 2: Source localization test in simulation

[0094] (1) Structural composition and implementation steps

[0095] Simulation setup: 16 sensors are placed on the surface of a cube with a side length of 300 mm in a spiral arrangement to verify the 3D positioning capability.

[0096] Simulate 16 sound sources with coordinates distributed inside and outside the cube (e.g. source 1: 250mm, 150mm, 25mm; source 16: 250mm, 150mm, 275mm).

[0097] Gaussian noise with standard deviations of 0.3μs, 0.6μs, 0.9μs, 1.2μs, and 1.5μs and outliers (simulating sensor failure) were added to the arrival times. Then, the method of the present invention was applied to solve the sound source coordinates (x, y, z).

[0098] (2) Positioning effect

[0099] like Figure 3 As shown, the present invention maintains the highest accuracy at different noise levels. For example, when the noise level is 0.3μs, the average positioning error of the new method is only 1.2mm, which is 24% to 86% lower than that of the traditional method.

[0100] Example 3: Microseismic Source Location in Mine Field Blasting Experiments

[0101] (1) Structural composition and implementation steps

[0102] On-site setup: Microseismic sensors were deployed in the mine tunnels and four blasting experiments were conducted. Their true coordinates were calibrated by drilling positioning (e.g., source 1: 365.18m, 876.91m, 145.15m). Then, the proposed method was applied to solve the source coordinates (x, y, z).

[0103] (2) Working principle and effect

[0104] Engineering applicability: Figure 4 As shown in the figure, the average positioning error of the proposed method is 10.4m, which is 55% to 68% higher than that of traditional methods (such as ASUV and TD). For example, the true coordinates of source 1 are (365.18m, 876.91m, 145.15m), and the positioning result of the proposed method is (362.74m, 876.05m, 149.87m), with an error of 5.39m, while the error of the ASUV method is 20.67m.

[0105] Compared with the existing technology, the high-precision source positioning method provided by the present invention, which is applicable to cross-scale complex rock media, has the following advantages:

[0106] 1. Breakthrough in high-precision positioning and noise immunity:

[0107] By eliminating the error transmission of a single sensor through a homogenized reference frame and combining it with dynamic weight estimation to suppress noise interference, the average positioning error in laboratory pencil lead fracture experiments was only 10.6 mm (an improvement of 32% to 62% compared to existing methods), and the error in field blasting experiments was 10.4 m (an improvement of 55% to 68% in accuracy).

[0108] 2. Improved stability of ill-conditioned equations:

[0109] Matrix truncation decomposition is used to truncate small singular values, greatly reducing the coefficient matrix condition number and solving the matrix inversion divergence problem. The solution success rate of large sensor networks reaches 100%, significantly improving the robustness in complex media such as dynamic velocity fields in mines.

[0110] 3. Geometric universality and speed independence:

[0111] It supports any randomly distributed sensor array, such as the irregular layout of a mine, breaking through the geometric limitations of traditional methods such as cylindrical / rectangular arrays. It directly eliminates the synchronization time by homogenizing the reference equation, avoids the coupling error of wave velocity parameters, and maintains precise positioning in scenarios with large wave velocity fluctuations.

[0112] 4. Enhanced cross-scale adaptability:

[0113] Dynamic wave velocity inversion and adaptive weighting mechanism correct signal measurement errors and the size effect of wave velocity anisotropy. The positioning performance is consistent in both small-scale laboratory (positioning range <1m) and large-scale engineering (positioning range >100m) scenarios, and is suitable for multi-scale positioning needs from millimeter-scale composite material cracks to kilometer-scale geological faults.

[0114] 5. Real-time and computing efficiency optimization:

[0115] Based on closed-form analytical solution (non-iterative), it avoids initial value sensitivity and divergence risk, and its computational efficiency is about 20 times higher than that of the iterative method, meeting the real-time monitoring needs of the project.

[0116] 6. Engineering applicability expansion:

[0117] By weighted fusion of multi-sensor data (N≥5), outlier interference is effectively suppressed, and dynamic expansion of the sensor network is supported (such as adding or removing sensors in long-term bridge monitoring). The sensor network module supports irregular deployment in mine tunnels, dams, or aviation composite materials, and there is no need to remodel when sensors are dynamically added or removed.

[0118] In summary, the present invention is significantly superior to existing technologies in terms of positioning accuracy, noise resistance, stability, and cross-scale adaptability, providing a highly reliable solution for complex engineering scenarios such as dynamic velocity fields, random array layouts, and multi-scale monitoring.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A high-precision source positioning method suitable for complex rock media across scales, characterized by: The following steps are involved: S1. Construction of a uniform reference frame: The arrival times of N sensors are squared and averaged to generate the following uniform reference equation: Among them, (x, y, z) is the coordinate of the sound source to be solved; t0 is the trigger time; v is the wave velocity, which is considered as an unknown number in the positioning process; (x i ,y i ,z i ) is the coordinate of the i-th sensor; t i is the arrival time of the i-th sensor; S2. Linear equation group generation: By combining the homogenized reference equation with the original equations of each sensor and eliminating the trigger time t0, the following linear equation group L is obtained: i : L i =a i x+b i y+c i z+d i K+e i V Among them, a i 、b i 、c i d i 、e i are the coefficients of the equations, and are calculated from the sensor coordinates and arrival time. K=Vt0,V=v 2 ; The original equation of each sensor is (x i -x) 2 +(y i -y) 2 +(z i -z) 2 =v 2 (t i -t0) 2 , i=1,2,…,N; Since the arrival time measurement contains errors, the two sides of the linear equation system are not equal. The deviation between the left and right sides is recorded as the equation residual ε, which is expressed in matrix form as: ε=L-Aθ in, S3. Dynamic weight estimation: Calculate the weight matrix W = ψ based on the covariance matrix ψ of the arrival time error -1 , where ψ=E(ε T ε)≈4V 2 RQR, E represents expectation, ε T is the transposed matrix of ε, R is the propagation time diagonal matrix, and Q is the Gaussian white noise covariance matrix; S4. Matrix truncation decomposition to enhance stability: Perform matrix truncation decomposition on the coefficient matrix A, expressed as A=UHY T ; Where H is a diagonal matrix, and the elements on the main diagonal are the singular values arranged in descending order, namely σ1, σ2, L, σ N-1 ,σ N ; U is the left singular vector, Y is the right singular vector; The singular values less than the threshold tol are truncated as follows: At this time, the coefficient matrix A changes to: Construct pseudo-inverse matrix And solve the linear equations in a weighted manner to obtain the vector θ containing two unknown parameters: the source coordinates and the wave velocity: S5, output the sound source coordinates (x, y, z) and wave speed according to the solved θ And the trigger time t0 = K / V.

2. The high-precision source positioning method applicable to cross-scale complex rock media according to claim 1, characterized in that: In step S1, the sensor array adopts an arbitrary asymmetric and non-planar geometric distribution, and the number N of sensors is dynamically expanded to N≥5.

3. The high-precision source positioning method applicable to cross-scale complex rock media according to claim 1, characterized in that: The calculation of the covariance matrix ψ in step S3 includes: Through the existing error transfer model, the equation residual ε caused by measurement uncertainty is obtained j : in, is the noise-free propagation time, n i is the arrival time error, and is approximately calculated based on the (x, y, z) and V calculated in step S5 as follows:

4. The high-precision source positioning method applicable to cross-scale complex rock media according to claim 1, characterized in that: The value range of the threshold tol in step S4 is 10 -10 ≤tol≤10 -6 .

5. The high-precision source positioning method applicable to cross-scale complex rock media according to claim 4, characterized in that: The threshold tol is set to 10 -8 .

6. The high-precision source positioning method applicable to cross-scale complex rock media according to claim 1, characterized in that: The calculation of the wave velocity v in step S5 does not require the foreknowledge of the medium wave velocity, and the coupling error between the medium wave velocity and the trigger time is eliminated through dynamic inversion.

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