A Microseismic / Acoustic Emission Source Location Method with Unknown Wave Velocity Based on Heavy-Tail Proximity

Abstract

The present invention provides a method for locating unknown wave velocity microseismic / acoustic emission sources based on heavy-tailed proximity, comprising the following steps: constructing a velocity-free hyperbolic equation based on time difference of arrival; introducing a proximity function representing the distance between a guessed point and a hyperboloid, and weighting the proximity function using a heavy-tailed distribution function; converting and superimposing the proximity function in the local coordinate system into the total proximity in the global coordinate system by using coordinate transformation technology; and using a particle swarm optimization algorithm to search for the total proximity to obtain an optimal solution and accurately determine the robust position of the seismic source. The method for locating unknown wave velocity microseismic / acoustic emission sources based on heavy-tailed proximity provided by the present invention has high positioning accuracy, positioning results with high outlier tolerance, does not require prior measurement of the medium wave velocity during the positioning process, and has more robust positioning accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of microseismic / sound source positioning, and specifically relates to a method for positioning microseismic / acoustic emission sources with unknown wave speed based on heavy-tailed proximity. Background Art

[0002] As an indispensable non-destructive testing method, microseismic monitoring technology is crucial for the health and safety of fields such as mine exploitation and tunnel engineering. The accuracy of source location is the basis of an advanced monitoring system, and its purpose is to early identify structural vulnerabilities and prevent the occurrence of catastrophic events such as potential structural collapses, water inrushes, and rock bursts. To achieve positioning accuracy, scholars have proposed many methods. Traditional positioning techniques often rely to a large extent on predefined wave speeds and the quality of arrival time picking. However, in practical engineering applications, the problem of abnormal arrival time picking is widespread. For example, due to the continuous change of rock stress and rock mass structure with construction activities, the predefined speed is prone to errors. Due to the error transmission and amplification effects of the control equations, small differences in wave speeds can also lead to large deviations in positioning accuracy. In addition, the influence of outliers is equally profound. In practical engineering monitoring, outliers may be caused by various factors, including signal interference, sensor mispositioning, multipath propagation, sensor failures, etc. If not effectively identified or mitigated, these outliers may lead to serious deviations in the localization results. In fact, there is an obvious interaction between wave speed measurement errors and the identification of outliers. If the wave speed measurement errors cannot be effectively reduced, then effectively eliminating outliers becomes extremely challenging; similarly, if outliers are not properly managed, it is also difficult to reduce the impact of wave speed measurement errors. Therefore, there is an urgent need to develop a positioning method that can solve both wave speed measurement errors and outlier-related problems. Summary of the Invention

[0003] Aiming at the technical problem that the positioning accuracy in the existing microseismic monitoring technology is seriously affected by wave speed measurement errors and abnormal arrival time picking, the present invention provides a method for positioning microseismic / acoustic emission sources with unknown wave speed based on heavy-tailed proximity.

[0004] To solve the above technical problems, the present invention adopts the following technical solutions:

[0005] A method for positioning microseismic / acoustic emission sources with unknown wave speed based on heavy-tailed proximity, comprising the following steps:

[0006] S1. Construct a velocity-free hyperbolic equation based on the time difference of arrival;

[0007] S2. Introduce a proximity function representing the distance between a guessed point and a hyperboloid, and weight the proximity function using a heavy-tailed distribution function;

[0008] S3. Use coordinate transformation technology to convert and superimpose the proximity function in the local coordinate system into the total proximity in the global coordinate system;

[0009] S4. Adopt the particle swarm optimization algorithm to search for the total proximity to obtain the optimal solution and accurately determine the robust position of the seismic source.

[0010] Furthermore, in the step S1, the hyperbolic equation is:

[0011]

[0012] where, taking sensor 1 as the reference sensor, r i1 is the difference in distances between the acoustic emission source and sensors i and 1, v is the wave speed of the propagation medium, t i represents the arrival time received by sensor i, t1 represents the arrival time received by the reference sensor 1, (x0, y0, z0) represents the coordinates of the seismic source to be determined, (x i , y i , z i ) represents the coordinates of sensor i, and (x1, y1, z1) represents the coordinates of the reference sensor 1.

[0013] Furthermore, in the step S2, the weighted proximity function after weighting the proximity function using the heavy-tailed distribution function is:

[0014]

[0015] where, p i1 is the proximity function representing the distance between the guessed point (X, Y, Z) and the hyperboloid, and the expression is:

[0016]

[0017] where, b i1 2 = c i1 2 - a i1 2 ,

[0018] Furthermore, in the step S3, the coordinate transformation of the proximity function in the local coordinate system to the global coordinate system is:

[0019]

[0020] where, R i1 represents a 3×3 rotation matrix, and the elements of R i1 are determined by the positions of the sensor pairs:

[0021]

[0022] where λ is the rotation angle and n is the rotation axis vector, and their expressions are respectively:

[0023]

[0024]

[0025] where u1 = (x i , y i , z i ) - (x1, y1, z1), and u2 = (0, 0, c i1 ) - (0, 0, -c i1 ).

[0026] Furthermore, in the step S3, the total proximity in the global coordinate system is:

[0027]

[0028] where m is the number of selected sensors.

[0029] Compared with the prior art, the method for locating unknown wave speed microseismic / acoustic emission sources based on heavy-tailed proximity provided by the present invention has high positioning accuracy, positioning results with high outlier tolerance, does not require prior determination of the medium wave speed during the positioning process, and has more robust positioning accuracy, specifically reflected in: (1) avoiding the necessity of prior wave speed measurement, thus reducing the potential impact of inaccurate wave speed measurement on the positioning results; (2) the construction of the weighted proximity function significantly reduces the adverse effects of a large number of picking errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic flow chart of the method for locating unknown wave speed microseismic / acoustic emission sources based on heavy-tailed proximity provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] In order to make the technical means, creative features, achieved purposes and functions of the present invention easy to understand, the present invention will be further described below with reference to specific drawings.

[0032] Please refer to Figure 1 as shown, the present invention provides a method for locating unknown wave speed microseismic / acoustic emission sources based on heavy-tailed proximity, including the following steps:

[0033] S1. Construct a velocity-free hyperbolic equation based on the time difference of arrival;

[0034] S2. Introduce a proximity function representing the distance between the guessed point and the hyperboloid, and weight the proximity function using a heavy-tailed distribution function;

[0035] S3. Use coordinate transformation technology to transform and superimpose the proximity function in the local coordinate system into the total proximity in the global coordinate system;

[0036] S4. Use the existing particle swarm optimization algorithm to search for the total proximity to obtain the optimal solution and accurately determine the robust position of the seismic source.

[0037] As a specific embodiment, in step S1, the hyperbolic equation is:

[0038]

[0039] where, taking sensor 1 as the reference sensor, r i1 is the difference in distance between the acoustic emission source and sensors i and 1, v is the wave speed of the propagation medium, t i represents the arrival time received by sensor i, t1 represents the arrival time received by the reference sensor 1, (x0, y0, z0) represents the coordinates of the seismic source to be determined, (x i , y i , z i ) represents the coordinates of sensor i, and (x1, y1, z1) represents the coordinates of the reference sensor 1. By using the hyperbolic equation in this embodiment and positioning by searching for the position where the maximum number of hyperboloids in this embodiment pass through, the robustness of the positioning result when abnormal arrivals occur is enhanced.

[0040] As a specific embodiment, in step S2, the weighted proximity function after weighting the proximity function with the heavy-tailed distribution function is:

[0041]

[0042] where, p i1 is the proximity function representing the distance between the guessed point (X, Y, Z) and the hyperboloid, and the expression is:

[0043]

[0044] where, By using the weighted proximity function in this embodiment, the heavy-tailed distribution function used is good at dealing with large errors with low sensitivity, can flexibly recalibrate the influence of data points in the calculation process, and effectively reduces the influence of outliers. Therefore, the influence of outliers on the overall result can be significantly reduced.

[0045] As a specific embodiment, in step S3, the coordinate transformation of the proximity function in the local coordinate system to the global coordinate system is:

[0046]

[0047] where, R i1Represents a 3×3 rotation matrix, R i1 The elements are determined by the positions of the sensor pairs:

[0048]

[0049] where λ is the rotation angle and n is the rotation axis vector, and their expressions are respectively:

[0050]

[0051]

[0052] where u1 = (x i , y i , z i ) - (x1, y1, z1), u2 = (0, 0, c i1 ) - (0, 0, -c i1 ).

[0053] By adopting the coordinate transformation in this embodiment, seamless integration of proximity metrics in different local coordinate systems can be achieved thereby.

[0054] As a specific embodiment, in step S3, the total proximity in the global coordinate system is:

[0055]

[0056] where m is the number of sensors selected. By adopting the total proximity in this embodiment, a solution with high anomaly tolerance can be obtained by minimizing the total proximity metric.

[0057] To better illustrate the technical effects of the present invention, experimental verification will be carried out below:

[0058] Assume a cube positioning system with a side length of 100 mm. Fifteen sensors are scattered and evenly surround the positioning system, and their coordinates are respectively (0, 0, 0), (0, 0, 100), (0, 50, 50), (0, 100, 0), (0, 100, 100), (50, 0, 50), (50, 50, 0), (50, 50, 50), (50, 50, 100), (50, 100, 50), (100, 0, 0), (100, 0, 100), (100, 50, 50), (100, 100, 0), (100, 100, 100), in units of mm. And a sound emission source with coordinates S(88, 53, 82) is randomly preset in the system to verify the positioning accuracy. Assume the wave speed is unknown, and a set of arrival time data is generated by simulation, and a standard deviation of 0.2×10 -6Random errors of s are used to simulate small random noise errors, and large errors of 12×10 -6 s are added to the arrival-time data to simulate outliers. After the above processing, a set of TDOA data is obtained as follows: 26.4, 21.0, 18.7, 25.9, 20.3, 14.8, 18.3, -2.6, 8.2, 13.5, 19.4, 11.5, 7.0, 31.1, 10.3, with the unit of 10 -6 s.

[0059] The acoustic emission source coordinates obtained by searching according to the steps described in the above embodiment are (86.77, 53.48, 81.77), with the unit of mm. This estimated value is in good agreement with the true sound source coordinates. Therefore, the technical solution provided by the present invention can well tolerate outliers and has a high acoustic emission source coordinate estimation accuracy.

[0060] Compared with the prior art, the microseismic / acoustic emission source location method based on heavy-tailed proximity provided by the present invention has high location accuracy, a location result with high outlier tolerance, does not require prior determination of the medium wave speed during the location process, and has a more robust location accuracy, specifically reflected in: (1) avoiding the necessity of prior wave speed measurement, thereby reducing the potential impact of inaccurate wave speed measurement on the location result; (2) the construction of the weighted proximity function significantly reduces the adverse effects of a large number of picking errors.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for locating unknown wave velocity microseismic / acoustic emission sources based on heavy-tailed proximity, characterized in that, Including the following steps: S1. Construct a hyperboloid equation based on time difference of arrival without velocity measurement; S2. Introduce a proximity function representing the distance between the guessed point and the hyperboloid, and embed the heavy-tailed distribution function into the proximity function for weighting; S3. Use the coordinate transformation technology to transform and superimpose the proximity function in the local coordinate system into the total proximity in the global coordinate system; S4. Adopt the particle swarm optimization algorithm to search for the total proximity to obtain the optimal solution and accurately determine the robust position of the seismic source.

2. The microseismic / acoustic emission source location method with unknown wave velocity based on heavy-tailed proximity according to claim 1, wherein In step S1, the hyperboloid equation is: Among them, using sensor 1 as the reference sensor, r i1 is the distance difference between the acoustic emission source and sensors i and 1, v is the wave speed of the propagation medium, t i represents the arrival time received by sensor i, t1 represents the arrival time received by the reference sensor 1, (x0, y0, z0) represents the source coordinates to be determined, (x i , y i , z i ) represents the coordinates of sensor i, and (x1, y1, z1) represents the coordinates of the reference sensor 1.

3. The method for locating unknown wave velocity microseismic / acoustic emission sources based on heavy-tailed proximity according to claim 2, characterized in that In step S2, the weighted proximity function after weighting the proximity function with the heavy-tailed distribution function is: where p i1 is a proximity function representing the distance between the guessed point (X, Y, Z) and the hyperboloid, and the expression is: where b i1 2 = c i1 2 - a i1 2 , 4. The method for locating microseismic / acoustic emission sources with unknown wave velocity based on heavy-tailed proximity according to claim 3, characterized in that, In step S3, the coordinate transformation of the proximity function in the local coordinate system to the global coordinate system is: wherein, R i1 represents a 3×3 rotation matrix, and the R i1 elements are determined by the positions of the sensor pairs: where λ is the rotation angle and n is the rotation axis vector, and their expressions are respectively: where u1 = (x i , y i , z i ) - (x1, y1, z1), u2 = (0, 0, c i1 ) - (0, 0, -c i1 ).

5. The method for locating unknown wave velocity microseismic / acoustic emission sources based on heavy-tailed proximity according to claim 4, wherein In step S3, the total proximity in the global coordinate system is: where m is the number of selected sensors.

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