High-precision positioning method for micro-seismic event of deep mine

Abstract

The invention provides a high-precision positioning method for a micro-seismic event of a deep mine, and belongs to the technical field of geophysical exploration and mine safety monitoring. According to the method, an iterative least square method is adopted to perform preliminary positioning on a micro-seismic event, and a physical initial solution including three-dimensional coordinates of a seismic source, seismic time and wave velocity assumption is obtained; constructing a five-dimensional feature vector based on the physical initial solution, and mining the internal correlation between the positioning error and the seismic source parameter; inputting the feature vector into a pre-trained gradient boosting tree model, and accurately predicting a three-dimensional space positioning residual error; and finally, through fusion calculation of the residual error and the physical initial solution, outputting a corrected accurate seismic source position. The problem of positioning deviation of a traditional physical inversion method in a non-uniform velocity field is effectively solved, the positioning precision and the effective coverage density of a sensor network are remarkably improved, excellent positioning performance and engineering applicability are shown in a complex geological environment of a deep mine, and reliable technical support is provided for mine micro-seismic monitoring and disaster early warning.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration and mine safety monitoring technology, and in particular to a high-precision method for locating microseismic events in deep mines. Background Technology

[0002] Microseismic monitoring, as a passive and non-destructive detection technology, has become a core means of safety monitoring in deep mines by capturing high-frequency elastic waves radiated when underground rock masses fracture. Its core requirement is to achieve high-precision location of microseismic events to track the spatiotemporal evolution of rock mass fracture propagation, providing crucial evidence for early warning of disasters such as rockbursts and roof instability. Field statistics show that the spatial distribution of microseismic events is highly correlated with the stress state of the surrounding rock; high-precision location results can quantify the extent of fracture zones, directly determining the reliability of hazard zone delineation.

[0003] The current mainstream microseismic location method is the physical inversion method based on iterative least squares (ILS). This method solves for source parameters by inverting the arrival times of P-waves and S-waves, and can achieve good location results under conditions of uniform velocity fields and regular sensor arrays. However, there are two major technical bottlenecks in practical applications in deep mines: First, the underground rock mass is affected by fault cutting and lithological differences, resulting in a strong non-uniformity of the velocity field. Related experiments show that even small velocity deviations can lead to horizontal or vertical location errors on the order of tens of meters. Second, the narrow tunnel space restricts the geometric deployment of sensors, creating observation coverage defects, which further amplifies the location deviation caused by velocity model errors. Ultimately, the location error of the traditional ILS method often reaches the order of hundreds of meters, which is far from meeting the engineering requirements for the accuracy of disaster early warning.

[0004] Existing improvement solutions have significant limitations: Patent CN112904414B (Method for Localization of Ground Sound Events and Early Warning of Instability Disasters, Sensor, and Monitoring System) improves positioning accuracy by integrating multi-dimensional waveform features such as time-domain parameters and spectral information, but it still relies on a physical inversion model, resulting in significant errors under the conditions of strong non-uniform velocity fields in deep mines; Patent CN113567927B (A Ground Sound Positioning System Based on a Controllable Seismic Source) uses an artificially controllable seismic source and simulated annealing algorithm to optimize positioning, but the system is complex to deploy, costly, and difficult to apply to real-time monitoring of natural microseismic events; Patent CN118465848A (An Intelligent Monitoring System Based on Mine Ground Sound Signals and Its Deployment Method) focuses on hardware deployment and adaptive noise reduction, and classifies signal types using CNN, but its positioning module still relies on traditional physical methods and does not solve the positioning deviation problem caused by velocity model errors. Summary of the Invention

[0005] This invention provides a high-precision location method for microseismic events in deep mines, which solves the problems of large errors in traditional physical inversion methods and the reliance on samples in pure machine learning methods.

[0006] To address the aforementioned technical problems, this invention provides a high-precision location method for microseismic events in deep mines, the method comprising at least:

[0007] Step 1: Obtaining the initial physical solution:

[0008] The iterative least squares method was used to initially locate the microseismic event and obtain the initial physical solution including the three-dimensional coordinates of the source, the time of occurrence, and the wave velocity assumption.

[0009] Step 2: Construct a five-dimensional feature vector based on the initial physical solution:

[0010] Based on the initial physical solution in step one, key information related to system error is extracted, and a five-dimensional feature vector is constructed, which includes the initial value of the three-dimensional coordinates of the earthquake source, the earthquake time, and the assumption of uniform wave velocity.

[0011] Step 3: Training and Inference of the Machine Learning Residual Correction Model:

[0012] Using known seismic events available at the mine site as supervised samples, the model is trained to learn the nonlinear mapping relationship between "initial physical solution and location residual". The feature vector is then input into a pre-trained gradient boosting tree model to accurately predict the three-dimensional spatial location residual.

[0013] Step 4: Correct the output of the seismic source location:

[0014] By combining the residual and the initial physical solution, the corrected and accurate source location is output, thus achieving high-precision positioning.

[0015] Step one above specifically includes: defining the source parameter vector; calculating the theoretical arrival time of the station; constructing the residual vector and using the least squares method to iterate the source parameters to preliminarily locate the microseismic event and obtain the initial physical solution.

[0016] In step one above, the source parameter vector includes the three-dimensional coordinates of the source, the time of origin, and the assumption of uniform wave velocity. The assumption of uniform wave velocity is used to simplify the velocity field model and reduce the dependence on prior information.

[0017] In step one above, calculating the theoretical arrival time of the station specifically includes: for each station, based on the Euclidean distance between its location and the source location, combined with the assumption of uniform wave velocity, calculating the theoretical arrival time of the microseismic event received by the station, that is, the time of occurrence plus the ratio of the Euclidean distance to the uniform wave velocity.

[0018] In step one above, the construction of the residual vector and iterative optimization specifically includes: comparing the observed arrival time with the theoretical arrival time for each station to form a residual vector; using the Levenberg-Marquardt damped least squares method to minimize the weighted residual norm 2; and iteratively updating the source parameters until both the model increment and the residual norm are less than 10. -8 We obtain the initial physical solution, which includes the initial three-dimensional coordinates of the earthquake source, the earthquake occurrence time, and the uniform wave velocity.

[0019] Step one above also includes quality control: calculating the root mean square residual, which is the square root of the sum of the squares of the differences between the observed time and the theoretical arrival time of all stations divided by the number of valid stations. If the root mean square residual is greater than m milliseconds or the number of valid stations is less than n, where m and n are set according to actual needs, the preliminary location result of the event is determined to be invalid and will not participate in subsequent steps.

[0020] Step three above specifically includes:

[0021] a) Sample preparation: Mine blasting events at real earthquake source locations were used and divided into training and validation sets according to proportions;

[0022] b) Model selection and parameter setting: Select multiple models with strong nonlinear fitting capabilities, covering ensemble learning and statistical learning types, to ensure method adaptability;

[0023] c) Model training: Independent regressors are established for the residuals in the three-dimensional directions. The residuals in the three-dimensional directions refer to the differences between the physical initial solution and the actual source location in the X, Y, and Z directions. Ten-fold cross-validation is used in the training process to control the risk of overfitting.

[0024] d) Residual inference: For a new microseismic event, the five-dimensional feature vector constructed in step two is input into the trained model, and the three-dimensional spatial residual prediction value is output, that is, the prediction deviation between the physical initial solution and the actual source location in the X, Y and Z directions.

[0025] The aforementioned models with strong nonlinear fitting capabilities specifically include:

[0026] Random Forest: Multiple decision trees are generated through Bootstrap sampling. When each tree node splits, some features are randomly selected. Weak learners and maximum depth are set, and the residuals are output by arithmetic mean of multiple trees.

[0027] Gradient boosting tree: serial iterative training, each tree fits the residual of the previous model, sets weak learners, maximum depth, and learning rate to balance fitting accuracy and overfitting risk;

[0028] Extreme gradient boosting: Introducing second-order optimization and leaf node regularization, setting weak learners, maximum depth, and learning rate, and enabling a mechanism to randomly select some features to participate in modeling to enhance generalization;

[0029] Lightweight Gradient Boosting Machine: It uses gradient one-sided sampling to retain high gradient samples, packs mutually exclusive features to reduce dimensionality, and sets weak learners, maximum leaf number, and learning rate to improve training efficiency;

[0030] Support Vector Regression: A regression hyperplane is constructed by mapping the radial basis function kernel function to a high-dimensional space. Hyperparameters such as kernel width, penalty factor, and insensitive interval are tuned through grid search and the Optuna automation framework.

[0031] The fusion calculation in step four above is as follows: the predicted value of the three-dimensional spatial residual obtained in step three is added to the initial value of the three-dimensional coordinates of the source in the physical initial solution in step one to obtain the final corrected source position.

[0032] This invention innovatively proposes a hybrid positioning framework of "physical initial solution + machine learning residual correction". By learning the nonlinear residual mapping between the physical initial solution and the actual location through models such as Gradient Boosting Tree (GBDT), the invention has been verified in practice. Using only 62 known blasting events as supervision samples, the median error of 3D positioning has been reduced by approximately 57.11%, and an effective sensor network coverage density of over 92% has been achieved. This effectively overcomes the problem of insufficient accuracy (i.e., positioning deviation) of traditional physical methods in non-uniform media, as well as the dependence of pure machine learning methods on massive samples and interpretability. It significantly improves positioning accuracy and effective sensor network coverage density, demonstrating superior positioning performance and engineering applicability in the complex geological environment of deep mines, and providing reliable technical support for mine microseismic monitoring and disaster early warning. Attached Figure Description

[0033] Figure 1 Complete technical flowchart for high-precision positioning of microseismic events;

[0034] Figure 2 Flowchart for high-precision positioning and effect analysis of microseismic events. Detailed Implementation

[0035] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0036] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments in order to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the art will recognize that embodiments may be practiced without one or more of these specific details. In other instances, well-known apparatuses, structures, and techniques associated with this application may not have been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0037] Throughout this specification, references to "an embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Therefore, the appearance of "in an embodiment" or "an embodiment" in various places throughout the specification does not necessarily refer to the same embodiment. Furthermore, a particular feature, structure, or characteristic may be combined in any manner in one or more embodiments.

[0038] In the following description, in order to clearly demonstrate the structure and working method of the present invention, a number of directional terms will be used. However, terms such as "front", "back", "left", "right", "outer", "inner", "outward", "inward", "up", and "down" should be understood as convenient terms and not as limiting terms.

[0039] This embodiment provides a high-precision microseismic event location method suitable for complex geological conditions in deep mines. The specific steps are as follows:

[0040] Step 1: Obtaining the initial physical solution:

[0041] Define the source parameter vector: it includes the three-dimensional coordinates of the source, the time of origin, and the assumption of uniform wave velocity. The assumption of uniform wave velocity is used to simplify the velocity field model and reduce the dependence on prior information.

[0042] Calculate the theoretical arrival time of the station: For each station, based on the Euclidean distance between its location and the source location, and combined with the assumption of uniform wave velocity, calculate the theoretical arrival time of the microseismic event received by the station, which is the time of occurrence plus the ratio of the Euclidean distance to the uniform wave velocity.

[0043] Construction of residual vectors and iterative optimization: The observed arrival time and theoretical arrival time of each station are compared to form a residual vector. The Levenberg-Marquardt damped least squares method is used to minimize the weighted residual norm 2 (the weighting matrix is ​​used to adjust the reliability of data from different stations). Source parameters are iteratively updated (the parameters after each iteration equal the previous parameters plus the parameter increment) until both the model increment and the residual norm are less than 10. -8 We obtain the initial physical solution, which includes the initial three-dimensional coordinates of the earthquake source, the earthquake occurrence time, and the uniform wave velocity.

[0044] Quality control: Calculate the root mean square residual, which is the square root of the sum of the squares of the differences between the observed time and the theoretical arrival time of all stations divided by the number of valid stations. If the root mean square residual is greater than 2 milliseconds (the arrival time fitting error is too large) or the number of valid stations is less than 4 (insufficient observation information), the preliminary positioning result of the event is deemed invalid and will not be included in subsequent steps.

[0045] Step 2: Construction of five-dimensional feature vectors:

[0046] Based on the initial physical solution in step one, key information related to system error is extracted, and a five-dimensional feature vector is constructed. The feature vector includes the initial three-dimensional coordinates of the earthquake source, the earthquake time, and the assumption of uniform wave velocity.

[0047] Among them, the initial three-dimensional coordinates of the earthquake source reflect the spatial location of the initial solution and are directly related to the spatial offset caused by the non-uniformity of the velocity field; the earthquake occurrence time is related to the cumulative error of the time of earthquake wave propagation; the uniform wave velocity assumption reflects the error caused by the simplification of the velocity model;

[0048] This feature vector can effectively characterize the error dependency between the initial physical solution and the actual source location, providing input for subsequent residual correction.

[0049] Step 3: Training and Inference of the Machine Learning Residual Correction Model:

[0050] Using known seismic events (blasting calibration events) available at the mine site as supervised samples, the model is trained to learn the nonlinear mapping relationship between "initial physical solution → location residual":

[0051] 1) Sample preparation: Mine blasting events with real seismic source locations (controlled blasting on site, accurate seismic source location) were used and divided into training and validation sets in an 8:2 ratio;

[0052] 2) Model selection and parameter setting: Five models with strong nonlinear fitting capabilities were selected, covering ensemble learning and statistical learning types, to ensure method adaptability. Parameters can be adjusted as needed.

[0053] a) Random Forest (RF): Multiple decision trees are generated through Bootstrap sampling. When each tree node splits, some features are randomly selected. 100 weak learners are set, with a maximum depth of 5. The residual is output by arithmetic mean of multiple trees.

[0054] b) Gradient Boosting Tree (GBDT): Serial iterative training, each tree fits the residual of the previous model, 100 weak learners are set, maximum depth is 3, learning rate is 0.1, balancing fitting accuracy and overfitting risk.

[0055] c) Extreme Gradient Boosting (XGBoost): Introduces second-order optimization and leaf node regularization, sets 100 weak learners, a maximum depth of 5, a learning rate of 0.1, and enables a mechanism to randomly select some features to participate in modeling to enhance generalization;

[0056] d) Lightweight Gradient Boosting Machine (LightGBM): Employs gradient one-sided sampling to retain high gradient samples, packs mutually exclusive features to reduce dimensionality, sets 100 weak learners, a maximum of 31 leaves, and a learning rate of 0.1 to improve training efficiency;

[0057] e) Support Vector Regression (SVR): A regression hyperplane is constructed by mapping the radial basis function kernel function to a high-dimensional space. Hyperparameters such as kernel width, penalty factor and insensitive interval are tuned through grid search and the Optuna automation framework.

[0058] 3) Model training: Independent regressors are built for the residuals in the three dimensions (i.e., the differences between the initial physical solution and the actual source location in the X, Y, and Z directions). Each dimension has different error characteristics, and separate modeling improves accuracy. The training process uses ten-fold cross-validation (the training set is divided into 10 subsets, and 9 are used for training and 1 for validation in turn) to control the risk of overfitting.

[0059] 4) Residual inference: For a new microseismic event, the five-dimensional feature vector constructed in step two is input into the trained model, and the three-dimensional spatial residual prediction value is output (i.e. the prediction deviation between the initial physical solution and the actual source location in the X, Y, and Z directions).

[0060] Step 4: Correct the output of the seismic source location:

[0061] The predicted three-dimensional spatial residual value obtained in step three is added to the initial three-dimensional coordinates of the seismic source in the physical initial solution in step one to obtain the final corrected seismic source position, thus completing the high-precision positioning.

[0062] Based on measured data from a deep lead-zinc mine, the following provides a detailed explanation of the specific implementation process and effects of the above method. Figure 1 and Figure 2 As shown, it includes:

[0063] 1. Microseismic signal collection in mines:

[0064] A microseismic monitoring network consisting of 26 single-axis accelerometers was deployed in the complex geological structure area of ​​the mine, and monitoring data containing 12,105 microseismic events were collected.

[0065] 2. Initial Physical Solution Calculation (ILS):

[0066] Perform ILS preliminary localization and quality control on all microseismic events:

[0067] Iteration parameters: The iteration stop threshold is set to 10. -8 The damping factor is adaptively adjusted by the algorithm (balancing convergence rate and numerical stability).

[0068] Quality control results: All 62 blasting events met the criteria of "root mean square residual ≤ 2 milliseconds and number of valid stations ≥ 4", and were all valid; among the 12,105 unknown events, after removing invalid events, 11,982 events remained for subsequent localization.

[0069] Preliminary accuracy: The traditional ILS method has a 3D Euclidean median error of 91.53 meters for 62 blasting events, a 90% confidence radius of 156.87 meters, and an effective sensor network coverage density of 57.9% (a large number of positioning points are outside the sensor monitoring range, resulting in poor physical rationality).

[0070] 3. Model Training and Validation:

[0071] Using 62 explosion events as samples, five machine learning models—Random Forest (RF), Gradient Boosting Tree (GBDT), XGBoost, LightGBM, and Support Vector Regression (SVR)—were trained to correct the residuals of the initial localization results from the traditional Iterative Least Squares (ILS) method. On the validation set (13 events), the "3D Euclidean Median Error" and "90% Confidence Radius" were used as the core evaluation metrics. The results are shown in Table 1.

[0072] Table 1. Error indices of each model in the verification of known blasting events.

[0073]

[0074] As shown in Table 1, the 3D Euclidean median error of all five machine learning models on the validation set is significantly lower than that of the traditional ILS method. Among them, the GBDT model performs best, with a 3D Euclidean median error of 13.4 meters, which is about 57.11% lower than that of the ILS method (24.5 meters), and the 90% confidence radius is reduced to 62.30 meters, demonstrating the most significant error control effect. In addition, GBDT has a more balanced error distribution in the X, Y, and Z directions, showing good comprehensive correction capabilities.

[0075] 4. Application in Unknown Event Scenes

[0076] For 11,982 valid unknown microseismic events, the "effective coverage density of the sensor network" was used to evaluate the rationality of the location results (effective coverage is defined as: the distance from the event to the nearest sensor is less than the average nearest neighbor distance of the sensors, or it is located within the envelope formed by all sensors). The application effects of each model are shown in Table 2 below:

[0077] Table 2. Application metrics of each model in unknown events.

[0078]

[0079] As shown in Table 2:

[0080] Both GBDT and Random Forest have an effective coverage density of over 92%, which is significantly better than SVR, LightGBM and traditional ILS methods, indicating that the location results are more physically plausible.

[0081] In terms of spatial distribution, random forest exhibits strip-shaped clusters that do not conform to the geological environment (caused by model overfitting), while GBDT location points are naturally distributed in the core area of ​​the tunnel, perfectly matching the range where rock mass fractures may occur, resulting in the best overall performance.

[0082] 5. Verification of three-dimensional orientation error:

[0083] To further verify the robustness of the models, the median errors of each model in the three-dimensional directions of X (horizontal), Y (horizontal), and Z (vertical) (based on 62 blasting events) were compared. The results are shown in Table 3 below:

[0084] Table 3. Median error of each model in three dimensions (unit: meters)

[0085]

[0086] As shown in Table 3, GBDT has the best error control in the Z direction (vertical direction) (3.93 meters), and the errors in the X and Y directions are also kept at a low level. The three-dimensional errors are balanced. Vertical rock mass stability in deep mines is crucial for early warning of roof instability. GBDT's high-precision vertical positioning capability can significantly improve the reliability of disaster early warning.

[0087] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A high-precision positioning method for microseismic events in deep mines, characterized in that, The method includes at least: Step 1: Obtaining the initial physical solution: The iterative least squares method was used to initially locate the microseismic event and obtain the initial physical solution including the three-dimensional coordinates of the source, the time of occurrence, and the wave velocity assumption. Step 2: Construct a five-dimensional feature vector based on the initial physical solution: Based on the initial physical solution in step one, key information related to system error is extracted, and a five-dimensional feature vector is constructed, which includes the initial value of the three-dimensional coordinates of the earthquake source, the earthquake time, and the assumption of uniform wave velocity. Step 3: Training and Inference of the Machine Learning Residual Correction Model: Using known seismic events available at the mine site as supervised samples, the model is trained to learn the nonlinear mapping relationship between "initial physical solution and location residual". The feature vector is then input into a pre-trained gradient boosting tree model to accurately predict the three-dimensional spatial location residual. Step 4: Correct the output of the seismic source location: By combining the residual and the initial physical solution, the corrected and accurate source location is output, thus achieving high-precision positioning.

2. The positioning method according to claim 1, characterized in that, Step one specifically includes: defining the source parameter vector; calculating the theoretical arrival time of the station; constructing the residual vector and using the least squares method to iterate the source parameters to preliminarily locate the microseismic event and obtain the initial physical solution.

3. The positioning method according to claim 2, characterized in that, The source parameter vector includes the three-dimensional coordinates of the source, the time of origin, and the assumption of uniform wave velocity. The assumption of uniform wave velocity is used to simplify the velocity field model and reduce the dependence on prior information.

4. The positioning method according to claim 2, characterized in that, The calculation of the theoretical arrival time of a station specifically includes: for each station, based on the Euclidean distance between its location and the earthquake source location, and combined with the assumption of uniform wave velocity, calculating the theoretical arrival time of the microseismic event received by the station, which is the time of occurrence plus the ratio of the Euclidean distance to the uniform wave velocity.

5. The positioning method according to claim 2, characterized in that, The construction of the residual vector and iterative optimization specifically includes: comparing the observed arrival time with the theoretical arrival time for each station to form a residual vector; using the Levenberg-Marquardt damped least squares method to minimize the weighted residual norm 2; and iteratively updating the source parameters until both the model increment and the residual norm are less than 10. -8 We obtain the initial physical solution, which includes the initial three-dimensional coordinates of the earthquake source, the earthquake occurrence time, and the uniform wave velocity.

6. The positioning method according to claim 2, characterized in that, Step one also includes quality control: calculate the root mean square residual, which is the square root of the sum of the squares of the differences between the observed time and the theoretical arrival time of all stations divided by the number of valid stations. If the root mean square residual is greater than m milliseconds or the number of valid stations is less than n, m and n are set according to actual needs, then the preliminary location result of the event is determined to be invalid and will not participate in subsequent steps.

7. The positioning method according to claim 1, characterized in that, Step three specifically includes: a) Sample preparation: Mine blasting events at real earthquake source locations were used and divided into training and validation sets according to proportions; b) Model selection and parameter setting: Select multiple models with strong nonlinear fitting capabilities, covering ensemble learning and statistical learning types, to ensure method adaptability; c) Model training: Independent regressors are established for the residuals in the three-dimensional directions. The residuals in the three-dimensional directions refer to the differences between the physical initial solution and the actual source location in the X, Y, and Z directions. Ten-fold cross-validation is used in the training process to control the risk of overfitting. d) Residual inference: For a new microseismic event, the five-dimensional feature vector constructed in step two is input into the trained model, and the three-dimensional spatial residual prediction value is output, that is, the prediction deviation between the physical initial solution and the actual source location in the X, Y and Z directions.

8. The positioning method according to claim 7, characterized in that, The various models with strong nonlinear fitting capabilities mentioned in b) specifically include: Random Forest: Multiple decision trees are generated through Bootstrap sampling. When each tree node splits, some features are randomly selected. Weak learners and maximum depth are set, and the residuals are output by arithmetic mean of multiple trees. Gradient boosting tree: serial iterative training, each tree fits the residual of the previous model, sets weak learners, maximum depth, and learning rate to balance fitting accuracy and overfitting risk; Extreme gradient boosting: Introducing second-order optimization and leaf node regularization, setting weak learners, maximum depth, and learning rate, and enabling a mechanism to randomly select some features to participate in modeling to enhance generalization; Lightweight Gradient Boosting Machine: It uses gradient one-sided sampling to retain high gradient samples, packs mutually exclusive features to reduce dimensionality, and sets weak learners, maximum leaf number, and learning rate to improve training efficiency; Support Vector Regression: A regression hyperplane is constructed by mapping the radial basis function kernel function to a high-dimensional space. Hyperparameters such as kernel width, penalty factor, and insensitive interval are tuned through grid search and the Optuna automation framework.

9. The positioning method according to claim 1, characterized in that, The fusion calculation in step four is as follows: the predicted value of the three-dimensional spatial residual obtained in step three is added to the initial value of the three-dimensional coordinates of the source in the physical initial solution in step one to obtain the final corrected source position.

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