A spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning

Abstract

The present application relates to a kind of spatial interpolation method based on fuzzy theory and integrated learning to geological exploration, belong to geological spatial data interpolation field.The spatial interpolation method based on fuzzy theory and integrated learning to geological exploration provided by the present application, by utilizing fuzzy theory, two kinds of spatial interpolation methods are effectively integrated, by selecting multiple central observation points as interpolation reference, effectively block the influence of the data with strong spatial variability on interpolation method, and by constructing the functional relationship between observation distance and attribute, the correlation between attribute information and topography in space is better reflected.The present application is based on fuzzy theory, by establishing integrated learning spatial interpolation prediction model, provide a kind of higher precision, lower time cost solution for spatial three-dimensional data expansion, the present application can solve the problem that spatial three-dimensional data points obtained due to topographic factor, instrument failure and human factor are sparse and unevenly distributed.

Description

Technical Field

[0001] This invention relates to a spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning, belonging to the field of geological spatial data interpolation. Background Technology

[0002] Currently, when conducting spatial data analysis in actual geological exploration scenarios, the desired outcome is often to obtain attribute data encompassing all geological exploration study areas. However, considering factors such as manpower, time costs, and actual topography, most spatial data originates from methods like field surveys, engineering drilling, and site monitoring. The resulting data are often spatially discrete, sparse, and unevenly distributed three-dimensional data points. To obtain data beyond the sampling points, spatial data interpolation is often used for data extrapolation.

[0003] Traditional data interpolation typically employs methods such as polynomial interpolation, spline interpolation, and least squares interpolation to extrapolate attribute information beyond the sampled points. However, these methods often suffer from poor performance, low accuracy, limited data representation, and an inability to characterize significant data fluctuations. Furthermore, because they do not consider actual spatial terrain, they fail to capture substantial spatial variability. In contrast, commonly used spatial data methods such as inverse distance weighted interpolation, natural neighborhood interpolation, and Kriging interpolation each have their own advantages and disadvantages. Inverse distance weighted interpolation assigns weights based on distance from sample points; closer sample points are given greater weights, indicating a greater influence from that sample point. While it can limit the number and range of interpolation points, using power values ​​to determine the influence of sample points on interpolation points, it offers high flexibility and accuracy. However, it is not suitable for regularly arranged interpolation points and suffers from low accuracy. Natural neighborhood interpolation works by constructing Thiessen polygons. All spatial points are represented as Thiessen polygons, and the point to be analyzed is also represented as a Thiessen polygon. This creates numerous intersections with the polygons. Weights are then assigned proportionally based on the area of ​​each intersection, allowing the determination of the value of the desired point. However, this method does not perform interpolation through a data model, requiring no additional parameters. While simple, it lacks flexibility and is unsuitable for interpolating overly discrete points due to the formation of irregular interpolation boundaries. The interpolation results are relatively accurate and closely approximate actual values, making it suitable for interpolating regularly arranged, densely packed points. Kriging interpolation, while considering the spatial correlation properties of the described object during data gridding, making the interpolation results more scientific and closer to reality, and providing the interpolation error (Kriging variance) to clearly demonstrate the reliability of the results, suffers from a smooth estimation of random fields. This means that Kriging is sensitive to outliers in skewed samples. Therefore, how to integrate and utilize various spatial data interpolation methods to fully leverage their respective advantages and obtain the best interpolation results is a pressing issue in spatial data interpolation and a key step in obtaining high-quality, high-precision, and complete spatial data. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning. Based on fuzzy theory, this invention establishes an ensemble learning spatial interpolation prediction model, offering a more accurate and less time-consuming solution for spatial 3D data augmentation. This invention solves the problem of sparse and unevenly distributed spatial 3D data points obtained due to terrain factors, instrument malfunctions, and human error. It not only contributes to the improvement of spatial data interpolation methods but also facilitates the application of fuzzy theory and artificial neural network algorithms in the fields of geography and geology.

[0005] To achieve the above objectives, the technical solution provided by this invention is: a spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning, comprising the following steps:

[0006] (1) Sample data preprocessing: Sample data with missing attributes and abnormal attributes in geological exploration data are preprocessed and the relevant parameters required for calculation are input. The required input parameters include sample dataset S, dataset SP to be interpolated, strong influence distance of the central observation point R0, number of observation points n and average absolute percentage error rate threshold ε.

[0007] (2) Establish a central observation point: Define the central observation point as a vector that includes the location of the central observation point and the strong action distance R0 of the central observation point in space, and add it to the sample dataset S;

[0008] (3) Improve the sample dataset: Using the central observation point as a reference, iteratively select other observation points and add them to the sample dataset; the other observation points are determined by defining the composite distance in the sample space, selecting the initial position of a certain observation point, and then adjusting the position of the observation point according to the local features of the sample dataset near the initial position to determine the final position of the observation point;

[0009] (4) Training the observation model: Train the observation model of each observation point relative to the sample dataset. First, pre-train the interpolation model of each observation point, then evaluate whether the current model selection is reasonable through the pre-training results, and finally determine the interpolation model selected for all n observation points.

[0010] (5) Calculate the interpolation results: Transfer each observation point and observation model to the interpolation space, construct the fuzzy system of the interpolation points, and calculate the interpolation results of each interpolation point.

[0011] The specific requirements for data preprocessing in step (1) are as follows:

[0012] 1) Sample data with missing attribute values: Use a hierarchical clustering-based missing value imputation method to fill in the missing attribute values;

[0013] 2) Sample data with abnormal attribute values: Use the interquartile range of the box plot to detect and remove sample data with abnormal attribute values.

[0014] In step (2), the central observation point is added to the sample dataset by calculation and assignment, and the definition of the central observation point is shown in Equation 1:

[0015] [X0 Y0 Z0 R0] Equation 1

[0016] In the formula: R0 is the strong action distance of the central observation point, which means that no other observation points are selected within the spherical region with the central observation point as the center and R0 as the radius; X0, Y0, and Z0 represent the position information of the central observation point in different dimensions of space, and their positions are consistent with the density center position of the sample dataset S.

[0017] When the target attribute is T, the position vectors X0, Y0, and Z0 of the central observation point are calculated according to Equation 2:

[0018]

[0019] Where: ∑T i ∑T represents the sum of attribute T values ​​for all sample points in the current sample dataset S; i X i ,∑T i Y i and ∑T i Z i The distribution represents the sum of the products of the X, Y, and Z coordinate values ​​of all sample points in the current sample dataset S and their corresponding attribute T values;

[0020] In step (3), the Jth observation point is selected according to the following steps:

[0021] 1) Calculation of the initial position of the observation point: When selecting the initial position of the Jth observation point, the probability P of a point i in the sample dataset S being selected as the initial position of the Jth observation point is... i (J) satisfies equation 3:

[0022]

[0023] Where Σdist(i,j) represents the sum of the composite distances from point i to all nJ selected observation points. This composite distance is determined by the distance between the two points in the location space and the distance in the attribute space. For two points i and j in the space, the composite distance between them is calculated by Equation 4:

[0024] dist(i,j)=dist(z i ,z j )+dist(ti ,t j Equation 4

[0025] In the formula: dist(z) i ,z j The position information of two points in space is determined by the position information of the two points, and the calculation method is shown in Equation 5; dist(t i ,t j The value is determined by the spatial attribute information of the two points, and the calculation method is shown in Equation 6:

[0026]

[0027]

[0028] In the formula: Nx, Ny, and Nz represent the ranges of the sample space S in their respective dimensions; N t This represents the range of attribute values ​​in the sample space S.

[0029] 2) Final location determination of the observation point: After determining the initial location of the observation point J, the location of the observation point is corrected by extracting data features near the initial location, and the final location of the observation point is finally determined. The specific steps are as follows:

[0030] a. Calculate the strong influence radius of observation point J: Based on the strong influence distance R0 of the central observation point, calculate the radius by dividing R0 by a random number rand within the interval [0.25, 1.25). J Multiply to calculate the strong action distance R at observation point J. J R J The calculation method is as shown in Equation 7:

[0031] R J =R0·rand J Formula 7

[0032] b. Nearby location data feature perception: The search is centered on the initial position of point J, and the strong influence radius R of observation point J is... J Let S be the set of all sample data points within a spherical region with radius . J ;

[0033] c. Determining the final location of the observation point: Set S J The density centroid is set as the observation point location of this observation J, and the calculation method of the density centroid coordinates is consistent with Equation 2;

[0034] d. Verification of the rationality of the observation point location: Calculate the Euclidean distance between the selected observation point J and all the previously selected J-1 observation points. If there exists an observation point I such that the distance between I and J is less than R... I or less than R JIf the selected location is deemed unreasonable, the process is reversed to step a, and the process is repeated until a reasonable observation point J is selected.

[0035] In step (4), the model is selected for the Jth observation point according to the following steps:

[0036] 1) Model pre-training: Calculate the set of Euclidean distances between the J-th observation point and all points in the sample dataset, with E as the independent variable and the attribute value T of the sample point corresponding to each distance as the dependent variable, train the RBF model, i.e., the radial basis artificial neural network model, and use grid search to perform hyperparameter tuning of the model.

[0037] 2) Pre-training effect evaluation: The mean absolute percentage error (MAPE) of observation point J when using this model for spatial attribute value prediction was calculated using ten-fold cross-validation. J The calculation method for this value is shown in Equation 8:

[0038]

[0039] in yi represents the estimated value of an attribute at a point in the sample space when spatial interpolation is performed at observation point J; yi represents the true value of the attribute at that point.

[0040] 3) Model selection: If the mean absolute percentage error (MAPE) of the interpolation using the RBF model is used for observation point J... J If the value is less than the threshold ε, then the observation point J selects the RBF model for prediction and uses the RBF model for interpolation calculation; otherwise, the observation point J selects the EBK model for interpolation calculation.

[0041] In step (5), firstly, the Euclidean distance between each interpolation point and all n observation points is calculated. Then, this distance and the mean absolute percentage error (MAPE) of the observation points are used together as the decision basis to calculate the weight of the influence of all n observation points on a given interpolation point. Finally, the final interpolation result of the interpolation point is determined by weighted averaging. Taking a given interpolation point I as an example, the specific calculation method of its interpolation result is as follows:

[0042] 1) Constructing a fuzzy interpolation point system: For a certain observation point J, the weighting of its effect on the predicted attributes of the interpolation point I is calculated as shown in Equation 9:

[0043]

[0044] In the formula: E IJ σ represents the Euclidean distance between an observation point J and the interpolation point I; σ represents the distance between the observation point J and the interpolation space S. P The standard deviation of the set of all Euclidean distances between points;

[0045] 2) Calculate the interpolation result: For the point I to be interpolated, its target attribute T I Calculation is performed using Equation 10.

[0046]

[0047] In the formula This represents the estimated value of the attribute of point I when interpolating using the interpolation model of observation point j; the spatial interpolation method in this invention ends after calculating the estimated value of all points in the interpolation space.

[0048] As can be seen from the above technical solution, the spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning provided by this invention effectively integrates two spatial interpolation methods by utilizing fuzzy theory. By selecting multiple central observation points as interpolation benchmarks, it effectively blocks the influence of spatially variable data on the interpolation method. Furthermore, by constructing a functional relationship between observation distance and attributes, it better reflects the correlation between attribute information and topography in space. This invention has a wide range of applications and strong predictive capabilities. Compared with existing technologies, this invention has the following advantages:

[0049] (1) Because the technical solution adopted in this invention uses an ensemble learning interpolation model based on fuzzy theory to utilize the information of all important sample points in space to assist in interpolation, and uses an ensemble learning interpolation model of artificial radial basis function and Bayesian skrygian interpolation method, this invention can have lower time complexity and higher model prediction accuracy.

[0050] (2) Because the technical solution adopted in this invention proposes to select and optimize the prediction interpolation model using grid search + k-fold cross-validation and Train-Validation-Split methods. Among them, grid search is used for hyperparameter tuning of artificial radial basis model; Train-Validation-Split is used for selection and evaluation of interpolation model. Therefore, this invention can integrate and learn spatial interpolation prediction models, providing a more accurate and less time-consuming solution for spatial 3D data augmentation, and solving the problem of sparse and unevenly distributed spatial 3D data points obtained due to terrain factors, instrument failures and human factors. Attached Figure Description

[0051] Figure 1 This is a flowchart of the observation point selection part of the present invention;

[0052] Figure 2 This is the overall flowchart of the present invention;

[0053] Figure 3 This is a schematic diagram of the composite distance in this invention;

[0054] Figure 4 This is a schematic diagram of the RBF artificial neural network structure used in this invention;

[0055] Figure 5 This is a map showing the grade distribution of solid mineral drilling samples in a certain area;

[0056] Figure 6 This is a schematic diagram of the central observation point calculated by the present invention in this experimental dataset;

[0057] Figure 7 This is a schematic diagram of all observation points calculated by the present invention in this experimental dataset. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0059] The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning provided in this invention effectively offers a solution for spatial data interpolation. This method operates according to the following steps:

[0060] (1) Sample data preprocessing: Sample data with missing attributes and abnormal attributes in geological exploration data are preprocessed and the relevant parameters required for calculation are input. The required input parameters include sample dataset S, dataset SP to be interpolated, strong influence distance of the central observation point R0, number of observation points n and average absolute percentage error rate threshold ε.

[0061] In this embodiment of the method, the test data comes from 3328 sample data obtained during solid mineral drilling in a certain area. The distribution of these sampling points is as follows: Figure 5 As shown. The data includes the coordinates and grade values ​​of the sampling points. The coordinates represent the spatial location information of the sampling points, and the grade values ​​represent their attribute information. The data to be interpolated consists of 1241 points separated after the test data is divided into equal intervals. System parameters are set as follows: the number of observation points n is set to 11, the strong influence distance R0 of the central observation point is set to 750 units, and the mean absolute percentage error ε is set to 20%.

[0062] like Figure 2 In the data preprocessing shown, in this embodiment, hierarchical clustering algorithm and box plot are used to implement data preprocessing. The specific requirements for data preprocessing in step (1) are as follows:

[0063] 1) Sample data with missing attribute values: Missing attribute values ​​were filled using a hierarchical clustering-based missing value imputation method; missing value queries were performed on the test data, and 341 missing values ​​were imputed using hierarchical clustering.

[0064] 2) Sample data with outlier attribute values: Box plots were used to detect and remove sample data with outlier attribute values. Preliminary screening and analysis of the test data was performed, and 11 outliers were removed using the box plot's interquartile range. Ultimately, 2076 valid test data points were obtained for model training.

[0065] (2) Establish a central observation point: Define the central observation point as a vector that includes the location of the central observation point and the strong action distance R0 of the central observation point in space, and add it to the sample dataset S;

[0066] In step (2), the central observation point is added to the sample dataset by calculation and assignment, and the definition of the central observation point is shown in Equation 1:

[0067] [X0 Y0 Z0 R0] Equation 1

[0068] In the formula: R0 is the strong action distance of the central observation point, which means that no other observation points are selected within the spherical region with the central observation point as the center and R0 as the radius; X0, Y0, and Z0 represent the position information of the central observation point in different dimensions of space, and their positions are consistent with the density center position of the sample dataset S.

[0069] When the target attribute is T, the position vectors X0, Y0, and Z0 of the central observation point are calculated according to Equation 2:

[0070]

[0071] Where: ∑T i ∑T represents the sum of attribute T values ​​for all sample points in the current sample dataset S; i X i ,∑T i Y i and ∑T i Z i The distribution represents the sum of the products of the X, Y, and Z coordinates of all sample points in the current sample dataset S and their corresponding attribute T values.

[0072] (3) Improve the sample dataset: Using the central observation point as a reference, iteratively select other observation points and add them to the sample dataset; the other observation points are determined by defining the composite distance in the sample space, selecting the initial position of a certain observation point, and then adjusting the position of the observation point according to the local features of the sample dataset near the initial position to determine the final position of the observation point;

[0073] In step (3), the Jth observation point is selected according to the following steps:

[0074] 1) Calculation of the initial position of the observation point: When selecting the initial position of the observation point J, the probability P of a point i in the sample dataset S being selected as the initial position of the observation point J is... i (J) satisfies equation 3:

[0075]

[0076] Where Σdist(i,j) represents the sum of the composite distances from point i to all nJ selected observation points. This composite distance is determined by the distance between the two points in the location space and the distance in the attribute space. For two points i and j in the space, the composite distance between them is calculated by Equation 4:

[0077] dist(i,j)=dist(z i ,z j )+dist(t i ,t j Equation 4

[0078] In the formula: dist(z) i ,z j The position information of two points in space is determined by the position information of the two points, and the calculation method is shown in Equation 5; dist(t i ,t j The value is determined by the spatial attribute information of the two points, and the calculation method is shown in Equation 6:

[0079]

[0080]

[0081] In the formula: Nx, Ny, and Nz represent the ranges of the sample space S in their respective dimensions; N t This represents the range of attribute values ​​in the sample space S.

[0082] 2) Final location determination of the observation point: After determining the initial location of the observation point J, the location of the observation point is corrected by extracting data features near the initial location, and the final location of the observation point is finally determined. The specific steps are as follows:

[0083] a. Calculate the strong influence radius of observation point J: Based on the strong influence distance R0 of the central observation point, calculate the radius by dividing R0 by a random number rand within the interval [0.25, 1.25). J Multiply to calculate the strong action distance R at observation point J. J R J The calculation method is as shown in Equation 7:

[0084] R J =R0·rand J Formula 7

[0085] b. Nearby location data feature perception: The search is centered on the initial position of point J, and the strong influence radius R of observation point J is... J Let S be the set of all sample data points within a spherical region with radius . J ;

[0086] c. Determining the final location of the observation point: Set S J The density centroid is set as the observation point location of this observation J, and the calculation method of the density centroid coordinates is consistent with Equation 2;

[0087] d. Verification of the rationality of the observation point location: Calculate the Euclidean distance between the selected observation point J and all the previously selected J-1 observation points. If there exists an observation point I such that the distance between I and J is less than R... I or less than R J If the selected location is deemed unreasonable, the process is reversed to step a, and the process is repeated until a reasonable observation point J is selected.

[0088] (4) Training the observation model: Train the observation model of each observation point relative to the sample dataset. First, pre-train the interpolation model of each observation point, then evaluate whether the current model selection is reasonable through the pre-training results, and finally determine the interpolation model selected for all n observation points.

[0089] In this embodiment: after selecting n observation points; according to Figure 1 The steps shown are for selecting observation points, specifically including the following steps:

[0090] Step S301: Calculate the density center C of the sample dataset S according to Equation 2, and set C as the central observation point of this interpolation process;

[0091] Step S302: According to Equation 5, calculate the composite distance (dist) from all points in S to all known observation points. Please refer to the diagram of the composite distance. Figure 3 ;

[0092] Step S303: Select the point with the largest dist value in S as the starting position J of the next observation point;

[0093] Step S304: According to Equation 7, calculate the strong action range R of J based on the initial strong action distance R0. J ;

[0094] Step S305: Calculate the sphere with J as the center and R... J The intersection S of a sphere with radius S and the sample dataset J ;

[0095] Step S306: Move J to S JFind the density centroid and calculate its Euclidean distance d from any observation point i. i ;

[0096] Step S307: Compare d i and R i The size of d i <R i If yes, return to step S304; otherwise, continue to step S308.

[0097] Step S308: Compare the number of existing observation points with n. If the number of existing observation points is less than n, return to step S302 and continue to select the next observation point; otherwise, the selection of 11 observation points is completed.

[0098] In step (4), the model is selected for the Jth observation point according to the following steps:

[0099] 1) Model pre-training: Calculate the set of Euclidean distances between the J-th observation point and all points in the sample dataset, with E as the independent variable and the attribute value T of the sample point corresponding to each distance as the dependent variable, train the RBF model, i.e., the radial basis artificial neural network model, and use grid search to perform hyperparameter tuning of the model.

[0100] 2) Pre-training effect evaluation: The mean absolute percentage error (MAPE) of observation point J when using this model for spatial attribute value prediction was calculated using ten-fold cross-validation. J The calculation method for this value is shown in Equation 8:

[0101]

[0102] in yi represents the estimated value of an attribute at a point in the sample space when spatial interpolation is performed at observation point J; yi represents the true value of the attribute at that point.

[0103] 3) Model selection: If the mean absolute percentage error (MAPE) of the interpolation using the RBF model is used for observation point J... J If the value is less than the threshold ε, then the observation point J selects the RBF model for prediction and uses the RBF model for interpolation calculation; otherwise, the observation point J selects the EBK model for interpolation calculation.

[0104] In this embodiment, the observation point model is established according to the following steps:

[0105] Step S401: For each observation point, using the Euclidean distance E between all sample points in the sample data and the grade as the dependent variable, train a radial basis function artificial neural network model. The network structure is as follows: Figure 4 As shown, the model parameters are dynamically adjusted using the grid search method to obtain stable hyperparameters;

[0106] Step S402: For each observation point, calculate the MAPE of its trained RBF model according to Equation 8 and compare it with ε. If MAPE < ε, select the RBF model at the observation point; otherwise, select the EBK model at the observation point.

[0107] Ultimately, 8 out of the 11 observation points had MAPE less than ε, so the RBF model was selected; 3 observation points had MAPE greater than ε, so the EBK model was selected.

[0108] (5) Calculate the interpolation results: Transfer each observation point and observation model to the interpolation space, construct the fuzzy system of the interpolation points, and calculate the interpolation results of each interpolation point.

[0109] In step (5), firstly, the Euclidean distance between each interpolation point and all n observation points is calculated. Then, this distance and the mean absolute percentage error (MAPE) of the observation points are used together as the decision basis to calculate the weight of the influence of all n observation points on a given interpolation point. Finally, the final interpolation result of the interpolation point is determined by weighted averaging. Taking a given interpolation point I as an example, the specific calculation method of its interpolation result is as follows:

[0110] 1) Constructing a fuzzy interpolation point system: For a certain observation point J, the weighting of its effect on the predicted attributes of the interpolation point I is calculated as shown in Equation 9:

[0111]

[0112] In the formula: EIJ represents the Euclidean distance between an observation point J and the interpolation point I; σ represents the distance between the observation point J and the interpolation space S. P The standard deviation of the set of Euclidean distances between all points.

[0113] 2) Calculate the interpolation result: For the point I to be interpolated, its target attribute T I Calculation is performed using Equation 10.

[0114]

[0115] In the formula This represents the estimated value of the attribute of point I when interpolating using the interpolation model of observation point j; the spatial interpolation method in this invention ends after calculating the estimated value of all points in the interpolation space.

[0116] In this embodiment, a fuzzy interpolation system is established; the weight of each observation point in the interpolation process for a certain interpolation point in the interpolation space is calculated according to Equation 9. Spatial interpolation is performed; the target attribute of each interpolation point is calculated according to Equation 10. Finally, the root mean square error between the interpolation result and the true value is calculated, and the interpolation results are compared with those of the Inverse Distance Weighted Method (IDW) and the Ordinary Kriging Method (OK) on the same dataset. Experimental results show that the accuracy of the interpolation method in this invention is significantly improved compared with the IDW and OK methods.

[0117] The core idea of ​​this invention is: firstly, through hierarchical clustering algorithm and box-shaped... Figure 4 Quantile detection is used for data preprocessing; then, n observation points are selected from all sample points; for each observation point, a radial basis function (RBF) artificial neural network model is established for pre-interpolation; then, the mean absolute percentage error rate of each model is calculated through ten-fold cross-validation, and the choice between RBF and empirical Bayesian skrygian methods is made based on the error rate; finally, a fuzzy interpolation system is constructed by calculating the weight of each observation point on the interpolation point; ultimately, the purpose of spatial interpolation is achieved using this fuzzy system. This invention utilizes the information of all important sample points in space to assist interpolation through fuzzy theory, and uses an ensemble learning model for interpolation, resulting in lower time complexity and higher model prediction accuracy. A grid search + k-fold cross-validation and Train-Validation-Split method is proposed to select and optimize the prediction interpolation model, which has higher stability and prediction accuracy.

Claims

1. A spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning, characterized in that... Includes the following steps: (1) Sample data preprocessing: Sample data with missing attributes and abnormal attributes in geological exploration data are preprocessed and the relevant parameters required for calculation are input. The required input parameters include sample dataset S, dataset SP to be interpolated, strong influence distance of the central observation point R0, number of observation points n and average absolute percentage error rate threshold ε. R0 is the strong action distance of the central observation point, which means that no other observation points are selected within the spherical region with the central observation point as the center and R0 as the radius. (2) Establish a central observation point: Define the central observation point as a vector that includes the location of the central observation point and the strong action distance R0 of the central observation point in space, and add it to the sample dataset S; (3) Improve the sample dataset: Using the central observation point as a reference, iteratively select other observation points and add them to the sample dataset; the other observation points are determined by defining the composite distance in the sample space, selecting the initial position of a certain observation point, and then adjusting the position of the observation point according to the local features of the sample dataset near the initial position to determine the final position of the observation point; The composite distance is determined by the distance between two points in the location space and the distance in the attribute space. For two points i and j in the space, the composite distance between them is calculated by Equation 4: Formula 4 In the formula: It is determined by the position information of the two points in space, and the calculation method is shown in Equation 5; The calculation method is determined by the spatial attribute information of the two points, as shown in Equation 6: Formula 5 Formula 6 In the formula: Nx, Ny, and Nz represent the ranges of the sample space S in their respective dimensions; N t x represents the range of attribute values ​​in the sample space S; i x j y i y j , z i , z j Let t represent the X, Y, and Z coordinates of two points i and j in space, respectively; i , t j Let T be the attribute values ​​corresponding to two points i and j in space; (4) Training the observation model: Train the observation model of each observation point relative to the sample dataset. First, pre-train the interpolation model of each observation point, then evaluate whether the current model selection is reasonable through the pre-training results, and finally determine the interpolation model selected for all n observation points. (5) Calculate the interpolation results: transfer each observation point and observation model to the interpolation space, construct the fuzzy system of the interpolation points, and calculate the interpolation results of each interpolation point.

2. The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning according to claim 1, characterized in that: The specific requirements for data preprocessing in step (1) are as follows: 1) Sample data with missing attribute values: Use a hierarchical clustering-based missing value imputation method to fill in the missing attribute values; 2) Sample data with abnormal attribute values: Use the interquartile range of the box plot to detect and remove sample data with abnormal attribute values.

3. The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning according to claim 1, characterized in that: In step (2), the central observation point is added to the sample dataset by calculation and assignment, and the definition of the central observation point is shown in Equation 1: Formula 1 In the formula: R0 is the strong action distance of the central observation point, which means that no other observation points are selected within the spherical region with the central observation point as the center and R0 as the radius; X0, Y0, and Z0 represent the position information of the central observation point in different dimensions of space, and their positions are consistent with the density center position of the sample dataset S. When the target attribute is T, the position vectors X0, Y0, and Z0 of the central observation point are calculated according to Equation 2: Formula 2 In the formula: This represents the sum of attribute T values ​​for all sample points in the current sample dataset S; , and The distribution represents the sum of the products of the X, Y, and Z coordinate values ​​of all sample points in the current sample dataset S and their corresponding attribute T values; N represents the total number of sample points in the current sample dataset S.

4. The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning as described in claim 1, characterized in that: In step (3), the Jth observation point is selected according to the following steps: 1) Calculation of the initial position of the observation point: When selecting the initial position of the Jth observation point, the probability P of a point i in the sample dataset S being selected as the initial position of the Jth observation point is... i (J) satisfies equation 3: Formula 3 Where Σ This represents the sum of the composite distances from point i to all nJ selected observation points. This composite distance is determined by the distance between the two points in the location space and the distance in the attribute space. For two points i and j in the space, the composite distance between them is calculated by Equation 4: Formula 4 In the formula: It is determined by the position information of the two points in space, and the calculation method is shown in Equation 5; The calculation method is determined by the spatial attribute information of the two points, as shown in Equation 6: Formula 5 Formula 6 In the formula: Nx, Ny, and Nz represent the ranges of the sample space S in their respective dimensions; N t x represents the range of attribute values ​​in the sample space S; i x j y i y j , z i , z j Let t represent the X, Y, and Z coordinates of two points i and j in space, respectively; i , t j Let T be the attribute values ​​corresponding to two points i and j in space; 2) Final location determination of the observation point: After determining the initial location of the observation point J, the location of the observation point is corrected by extracting data features near the initial location, and the final location of the observation point is finally determined. The specific steps are as follows: a. Calculate the strong influence radius of observation point J: Based on the strong influence distance R0 of the central observation point, calculate the radius by dividing R0 by a random number rand within the interval [0.25, 1.25). J Multiply to calculate the strong action distance R at observation point J. J R J The calculation method is as shown in Equation 7: Formula 7 b. Nearby location data feature perception: The search is centered on the initial position of point J, and the strong influence radius R of observation point J is... J Let S be the set of all sample data points within a spherical region with radius . J ; c. Determining the final location of the observation point: Set S J The density centroid is set as the observation point location of this observation J, and the calculation method of the density centroid coordinates is consistent with Equation 2; d. Verification of the rationality of the observation point location: Calculate the Euclidean distance between the selected observation point J and all the previously selected J-1 observation points. If there exists an observation point I such that the distance between I and J is less than R... I or less than R J If the selected location is deemed unreasonable, the process is reversed to step a, and step ad is repeated until a reasonable observation point J is selected.

5. The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning as described in claim 1, characterized in that: In step (4), the model is selected for the Jth observation point according to the following steps: 1) Model pre-training: Calculate the set of Euclidean distances between the J-th observation point and all points in the sample dataset, with E as the independent variable and the attribute value T of the sample point corresponding to each distance as the dependent variable, train the RBF model, i.e., the radial basis artificial neural network model, and use grid search to perform hyperparameter tuning of the model. 2) Pre-training effect evaluation: The mean absolute percentage error (MAPE) of observation point J when using this model for spatial attribute value prediction was calculated using ten-fold cross-validation. J The calculation method for this value is shown in Equation 8: Formula 8 in This represents the estimated value of an attribute at a certain point in the sample space when spatial interpolation is performed at observation point J. This represents the true value of the attribute at that point; N represents the total number of sample points in the current sample dataset S. 3) Model selection: If the mean absolute percentage error (MAPE) of the interpolation using the RBF model is used for observation point J... J If the value is less than the threshold ε, then the observation point J selects the RBF model for prediction and uses the RBF model for interpolation calculation; otherwise, the observation point J selects the EBK model for interpolation calculation.

6. The spatial interpolation method for geological exploration based on fuzzy theory and ensemble learning as described in claim 1, characterized in that: In step (5), firstly, the Euclidean distance between each interpolation point and all n observation points is calculated. Then, this distance and the mean absolute percentage error (MAPE) of the observation points are used together as the decision basis to calculate the weight of the influence of all n observation points on a certain interpolation point. Finally, the final interpolation result of the interpolation point is determined by weighted averaging. Taking a certain interpolation point I as an example, the specific calculation method of its interpolation result is as follows: 1) Constructing a fuzzy interpolation point system: For a certain observation point J, the weighting of its effect on the predicted attributes of the interpolation point I is calculated as shown in Equation 9: Formula 9 In the formula: This represents the Euclidean distance between a given observation point J and the point I to be interpolated; This represents the relationship between observation point J and the interpolation space S. P Standard deviation of the set of Euclidean distances between all points; MAPE J This represents the average absolute percentage error of observation point J when selecting this model for spatial attribute value prediction; 2) Calculate the interpolation result: For the point I to be interpolated, its target attribute T I Calculation is performed using Equation 10. Formula 10 In the formula This represents the estimated value of attribute I when interpolating using the interpolation model of observation point j; N represents the total number of sample points in the current sample dataset S; the spatial interpolation method ends after calculating the estimated value of all points in the interpolation space.

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