A method for automatic partitioning of search ellipsoid based on coefficient of variation

Abstract

The present invention discloses a method for automatically partitioning a search ellipsoid based on a coefficient of variation, comprising: step 1, obtaining a spatial variability model of sample data; step 2, setting the orientation, size and partitioning mode to be optimized of the search ellipsoid; step 3, obtaining sample data inside the search ellipsoid in a study area; step 4, partitioning the sample data according to the partitioning mode to be optimized, and obtaining the partitioning mode; step 5, calculating the anisotropic distance between the sample data according to the partitioning mode; step 6, obtaining the coefficient of variation of the anisotropic distance based on the anisotropic distance between the sample data; step 7, selecting the partition corresponding to the minimum coefficient of variation; step 8, iterating step 3 to step 7 until all points to be estimated are processed, and the determination of the partitioning mode of the search ellipsoid for all unknown points in the study area is completed. The present invention can automatically set the partitioning mode for each local valuation point efficiently and quickly.

Description

Technical Field

[0001] The invention belongs to the technical field of geological statistics mineral resource reserve estimation, and in particular relates to an automatic partitioning method for a search ellipsoid based on a coefficient of variation. Background Art

[0002] Mineral resource reserve estimation is an important way for mining companies and natural resource management departments to grasp the quantity and quality of exploitable mineral resources. The geostatistical mineral resource reserve estimation method is an important method to achieve this goal; the calculation results of this method are highly recognized in the international mineral product market. However, compared with traditional mineral resource reserve estimation methods, the geostatistical method has the disadvantages of complex method principles, cumbersome operation steps, and a large number of parameter types and quantities. This has led to a certain extent that the promotion and application of this method in my country is still very limited. Therefore, it is particularly important to automatically optimize the geostatistical mineral resource reserve estimation method. The search ellipsoid is an important model in the application process of the geostatistical mineral resource reserve estimation method. Usually, in order to reduce the negative impact of uneven distribution of data on valuation, the search ellipsoid model needs to be spatially partitioned. Figure 4 Describes a typical estimation pattern. Observing the spatial distribution of sample data, it can be seen that the sample data is often dense in the upper right corner of the search ellipsoid. In this way, when using the sample data inside the search ellipsoid for estimation, whether it is the Kriging method or the inverse distance power method, the calculation results will easily skew toward the sample data values ​​in the upper right corner of the ellipsoid. This "skewness" generally has a negative impact on the estimated value, so it needs to be avoided. Spatially partition the search ellipsoid used so that the number of sample data falling within each interval is equal (such as Figure 8 and Fig. 9 The more common partitioning methods include two partitions, four partitions, eight partitions, and sixteen partitions along different axes. Figure 1As shown. For example, for four partitions, you can choose to divide along the axis of the ellipsoid and along the 45-degree diagonal. Therefore, there are many forms for the specific implementation of the search ellipsoid partition method. Different partition methods usually generate different sample data search results and ore estimates of different precision. However, there is currently no effective solution for how to set and select a specific partition method. The mainstream method is to adopt a globally consistent partitioning mode, and the specific form of this globally consistent partitioning mode needs to be manually judged and selected. This processing method has at least two shortcomings: (1) The globally consistent model is difficult to meet the specific conditions of all estimation points. The sparsity of data distribution at different locations is different, and different partitioning methods often need to be set; (2) Manual selection is time-consuming and prone to errors. Therefore, the conventional search ellipsoid partition model has the problem that the specific partitioning method is difficult to determine, and it is urgent to propose an automatic partitioning method for the search ellipsoid. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a method for automatically partitioning a search ellipsoid based on a coefficient of variation, which can automatically set a partitioning mode for each local valuation point efficiently and quickly.

[0004] To achieve the above object, the present invention provides a method for automatically partitioning a search ellipsoid based on a coefficient of variation, comprising the following steps:

[0005] Step 1: obtaining a spatial variability model of sample data, wherein the sample data includes drilling data, adit and trench data;

[0006] Step 2: setting the orientation, size and partitioning method of the search ellipsoid;

[0007] Step 3, obtaining sample data inside the search ellipsoid in the study area;

[0008] Step 4: partition the sample data according to the partitioning method to be optimized to obtain a partitioning method;

[0009] Step 5: calculating the anisotropic distance between the sample data according to the partitioning method;

[0010] Step 6: obtaining the coefficient of variation of the anisotropic distance based on the anisotropic distance between the sample data;

[0011] Step 7: Select the partition corresponding to the minimum coefficient of variation;

[0012] Step 8. Iterate steps 3 to 7 until all points to be estimated are processed, and the search ellipsoid partitioning method for all unknown points in the study area is determined.

[0013] Optionally, a method for obtaining a spatial variability model of sample data includes:

[0014] Preprocessing the sample data to obtain the spatial distribution and statistical characteristics of the sample data;

[0015] According to the spatial distribution and statistical characteristics of the sample data, the experimental variogram is calculated to obtain experimental variograms in multiple different directions;

[0016] According to the experimental variogram values ​​in the multiple different directions, a theoretical model is selected for fitting to obtain a theoretical variogram model;

[0017] The experimental variograms in the multiple different directions are structurally fitted with the theoretical variogram model to obtain a spatial variability model of the sample data.

[0018] Optionally, the method of setting the orientation, size and partitioning method to be optimized of the search ellipsoid includes:

[0019] The orientation of the search ellipsoid is set according to the occurrence of the ore body and the spatial continuity direction of the ore grade;

[0020] Set the size of the search ellipsoid according to the spacing of the exploration projects and the continuity range of the ore grade;

[0021] The inner space of the search ellipsoid is divided into a plurality of subspaces with equal angles, and a partitioning method to be optimized for the search ellipsoid is set according to the plurality of subspaces and different partitioning methods.

[0022] Optionally, the method for obtaining sample data inside the search ellipsoid is:

[0023]

[0024] Among them, a, b, c are the lengths of the major axis, median axis, and minor axis of the ellipsoid.

[0025] Optionally, the sample data is partitioned according to the partitioning method to be optimized, and the method for obtaining the partitioning method includes: based on the sample data inside the search ellipsoid that has been obtained, classifying according to the spatial orientation of the sample data relative to the center point of the ellipsoid;

[0026] Partitioning is performed according to the classification of the sample data to obtain a partitioning method.

[0027] Optionally, anisotropic distances between the sample data are calculated according to the partitioning method;

[0028]

[0029] in,

[0030]

[0031] d i =∑ i≠j d(i, j)

[0032] Among them, α represents the angle of clockwise rotation along the Z axis, is the angle of clockwise rotation along the Y axis, a x , a y , a z are the continuity ranges on the X, Y, and Z axes, respectively; n is the total number of samples in the search ellipsoid; i and j are the numbers of any two sample points in the search ellipsoid, respectively; (x i ,y i , z i ) and (x j ,y j , z j ) are the coordinates of the two points, d i is the cumulative distance between the i-th sample point and other sample points in the search ellipsoid.

[0033] Optionally, obtaining a coefficient of variation of the anisotropic distance based on the anisotropic distance between the sample data;

[0034]

[0035] Where cv is the coefficient of variation, d i is the cumulative distance between the i-th sample point and other sample points in the search ellipsoid, n is the total number of samples in the search ellipsoid, and i is the number of any sample point in the search ellipsoid.

[0036] Technical effect of the invention: The invention discloses an automatic partitioning method for searching an ellipsoid based on a coefficient of variation, which automatically evaluates a variety of partitioning methods, searches the spatial distribution of sample data within the ellipsoid at each position, and selects a suitable partitioning method; the automation level of the algorithm is improved, and the problems of large errors and instability in the calculation results caused by the uncertainty of the partitioning method are avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0038] Figure 1 This is a common search ellipsoid partitioning method in the embodiment of the present invention, where (a) and (b) are both two partitions, (c) and (d) are both four partitions, (e) is eight partitions, and (f) is sixteen partitions;

[0039] Figure 2 A schematic diagram of a flow chart of a method for automatically partitioning a search ellipsoid based on a coefficient of variation according to an embodiment of the present invention;

[0040] Figure 3 The sample data, the points to be estimated and the set search ellipsoid spatial distribution of the embodiment of the present invention;

[0041] Figure 4 Extracting sample data for searching inside the ellipsoid for the embodiment of the present invention;

[0042] Figure 5 Searching for the distance between the center point of the ellipsoid and the sample data inside the ellipsoid in the embodiment of the present invention;

[0043] Figure 6 It is a four-partition method with axial parallelism in an embodiment of the present invention;

[0044] Figure 7 The four-zone method of the embodiment of the present invention is four zones along a 45-degree angle;

[0045] Figure 8 The partition result corresponding to the axially parallel four-partition method of the embodiment of the present invention;

[0046] Fig. 9 This is a partition result corresponding to the four-partition method of four partitions along a 45-degree angle in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0049] like Figure 2 As shown, this embodiment provides a method for automatically partitioning a search ellipsoid based on a coefficient of variation, comprising the following steps:

[0050] Step 1: Obtain the spatial variability model of sample data.

[0051] Specifically, obtaining the spatial variability model of sample data is a routine operation of the geostatistical reserve estimation method, which mainly includes the following steps: data preprocessing, experimental variogram calculation, theoretical variogram model fitting and structure fitting.

[0052] (1) Data preprocessing. This mainly includes: processing abnormal values ​​and error values ​​contained in the data, performing spatial transformation and statistical transformation on the data, etc.

[0053] (2) Experimental variogram calculation. This mainly includes: calculating the experimental variogram values ​​in multiple different directions based on the spatial distribution and statistical characteristics of the sample data.

[0054] (3) Theoretical variogram model fitting. This mainly includes: according to the experimental variogram results, select an appropriate theoretical model (for example, a spherical model, an exponential model, etc.) to fit it, and obtain a theoretical variogram model that matches the experimental variogram calculation results.

[0055] (4) Structural fitting. This mainly includes fitting theoretical variograms in multiple directions together to form a complete model.

[0056] The results of spatial variability modeling generally include the continuity direction and range of ore grade in space, which are expressed as angle and range values, respectively, and recorded as parameter vectors: Among them, α represents the angle of clockwise rotation along the Z axis; is the angle of clockwise rotation along the Y axis. x , a y , a z They are the continuity range on the X, Y, and Z axes, that is, the range value.

[0057] The data set has the same continuity in different directions, that is, isotropy. Therefore, for equation (2), we have: x =a y =a z , At this time, the anisotropic distance is equivalent to the Euclidean distance, that is:

[0058]

[0059] Step 2: Set the orientation, size and partitioning method of the search ellipsoid.

[0060] Specifically, set the orientation, size and preferred partitioning method of the search ellipsoid. In general, the orientation setting of the search ellipsoid can refer to the occurrence of the ore body and the spatial continuity direction of the ore grade. The size setting of the search ellipsoid can refer to the spacing of the exploration project and the continuity range (range value) of the ore grade. The spatial partitioning of the search ellipsoid refers to dividing the internal space of the ellipsoid into multiple subspaces of equal angles with the center point of the ellipsoid as a reference. Common partitioning methods include: two partitions, four partitions, eight partitions, etc. ( Figure 3 ). In this method, these commonly used models can be set as partitioning modes to be evaluated or optimized.

[0061] The orientation and size of the search ellipsoid are set as Figure 3 For ease of illustration, only two partitioning methods are selected for evaluation: (1) four partitions parallel to the axis; (2) four partitions along a 45-degree angle.

[0062] Step 3: Calculate and obtain samples inside the search ellipsoid.

[0063] Specifically, according to the size and orientation of the search ellipsoid, sample data that meets the conditions is extracted, such as Figure 4 As shown in the figure, there are more data points on the upper right side of the ellipsoid, which shows that these data are obviously clustered, so a partitioning mechanism is needed.

[0064] Taking any point to be estimated (x0, y0, z0) as the center of the ellipsoid, the mathematical equation of the ellipsoid can be used to determine whether the sample data (assuming the coordinates are (x, y, z)) is located inside it. Assuming that the axis of the ellipsoid is parallel to the coordinate axis, the following formula is used for judgment:

[0065]

[0066] Among them, a, b, and c are the lengths of the major axis, median axis, and minor axis of the ellipsoid.

[0067] For any sample point with coordinates (x, y, z), if f(x, y, z) ≤ 1, the sample point is considered to be inside the ellipsoid. Otherwise, the point is outside the ellipsoid.

[0068] Figure 5 Displayed are the sample data within these search ellipsoids and the distance between them and the center of the ellipsoid.

[0069] Figure 6 and Figure 7 Four partitions parallel to the axis and four partitions along a 45-degree angle are shown, as well as sample data points within each partition.

[0070] Step 4: Partition the sample data using the partitioning method to be optimized.

[0071] Specifically, the main content of spatial partitioning is to classify the sample data inside the search ellipsoid based on its spatial orientation relative to the center point of the ellipsoid based on the sample data that has been obtained. For example, for a two-partition ellipsoid, the data inside it is divided into two categories; for a four-partition ellipsoid, the data inside it is divided into four categories; for an eight-partition ellipsoid, the data inside it is divided into eight categories. For the data inside the search ellipsoid that has been obtained, it is only necessary to determine which partition it belongs to based on its position relative to the center point. For example, for the four-partition model divided along the axis ( Figure 1c), the sample coordinates in the four partitions are: (x>=0, y>0), (x>=0, y<0), (x<0, y>=0), (x<0, y=<0). In order to ensure the relative balance of the data, the number of sample data in each partition needs to be consistent. Therefore, after determining which partition the sample data belongs to, it is necessary to further determine which data in the partition needs to be retained. The basic principle adopted by this method is to only retain data close to the center of the ellipsoid, and data farther away will not be considered.

[0072] According to the relative position of the sample data in the search ellipsoid, the number of sample points in each partition is set. In order to facilitate observation and analysis, one sample is retained in each partition in this case. Based on the principle of retaining sample data close to the point to be estimated, sample data under two partitioning methods are obtained, such as Figure 8 and Fig. 9 As shown. It is not difficult to observe that among the two partitioning methods, the four-partitioning method along the 45-degree angle ( Fig. 9 ) corresponds to a relatively uniform distribution of sample points in space; while the axially parallel four-partition method ( Figure 8 ) The corresponding sample points are relatively unevenly distributed in space (showing different degrees of sparse distribution).

[0073] The main purpose of searching for ellipsoid partitions is to obtain relatively uniform sample data. Therefore, intuitively, the four-partition method along the 45-degree angle should be selected ( Fig. 9 ).

[0074] Step 5: Calculate the anisotropic distance between sample data under each partitioning method.

[0075] Specifically, assume that the spatial variability model parameter vector obtained in the previous steps is The total number of samples in the search ellipsoid is n, and the coordinates of any two sample points in the search ellipsoid are (x i ,y i , z i ) and (x j ,y j , z j ), (where i, j = 1, 2, ..., n), then the anisotropic distance between sample points i and j can be calculated by the following formula:

[0076]

[0077] in,

[0078]

[0079] Based on formula (2), the mean of the anisotropic distance between each sample point and other sample points in the search ellipsoid is further calculated.

[0080] Assume that the coordinates of any sample point are (x i ,y i , z i ), then the mean anisotropic distance between it and other points in the search ellipsoid is d i The calculation formula is:

[0081] d i =∑ i≠j d(i,j) (3)

[0082] According to formula (2), we can calculate Figure 8 and Fig. 9 The anisotropic distance of each sample point relative to other sample points in the . The calculation results corresponding to the two partitioning methods are shown in Table 1 and Table 2 respectively.

[0083] Table 1

[0084] Sample point number 16 17 25 34 16 0 3.605551 3.605551 6 17 3.605551 0 5.09902 8.544004 25 3.605551 5.09902 0 3.605551 34 6 8.544004 3.605551 0

[0085] Table 2

[0086] Sample point number 16 22 25 31 16 0 2.236068 3.605551 5.09902 22 2.236068 0 4.472136 5 25 3.605551 4.472136 0 2.236068 31 5.09902 5 2.236068 0

[0087] Step 6: Calculate the coefficient of variation of the anisotropic distance.

[0088] Specifically, based on the average anisotropic distances between the sample point and other points obtained in the above steps, the coefficients of variation corresponding to these average distances are further calculated. The calculation formula is as follows:

[0089]

[0090] According to Table 1, Table 2 and formula (3), the mean of the anisotropic distance between each sample point and other points is further calculated. For the axially parallel four-partition method, the four distance means are: 3.940153077, 5.599097401, 3.472815224, 5.421272232. Their corresponding coefficient of variation is 0.199424397; for the four-partition method along the 45-degree angle, the four distance means are: 3.372537131, 3.65591997, 2.97372351, 3.721149312. Their corresponding coefficient of variation is 0.085885507.

[0091] Step 7: Select the partition corresponding to the minimum coefficient of variation as the partition result.

[0092] Specifically, for each search ellipsoid partitioning method to be evaluated, the coefficient of variation of the anisotropic distance of the sample point is calculated using formulas (1)-(4), and the partition with the smallest coefficient of variation is selected as the preferred result. Compared with the axial parallel partitioning method, the coefficient of variation of the anisotropic distance corresponding to the four-partitioning method along the 45-degree angle is smaller. Therefore, it should be selected as the partitioning result of the current point to be evaluated. This result is consistent with the direct observation. Figure 8 and Fig. 9 , the understanding obtained is consistent.

[0093] Repeat steps 3 to 7 above to complete the determination of the partitioning method of the search ellipsoid for all positions to be estimated.

[0094] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for automatic partitioning of a search ellipsoid based on coefficient of variation, characterized in that: include: Step 1: obtaining a spatial variability model of sample data, wherein the sample data includes drilling data, adit and trench data; Step 2: setting the orientation, size and partitioning method of the search ellipsoid; Step 3, obtaining sample data inside the search ellipsoid in the study area; Step 4: partition the sample data according to the partitioning method to be optimized to obtain a partitioning method; Step 5: calculating the anisotropic distance between the sample data according to the partitioning method; Calculate the anisotropic distance between the sample data according to the partitioning method: in, d i =∑ i≠j d(i,j) Among them, α represents the angle of clockwise rotation along the Z axis, is the angle of clockwise rotation along the Y axis, a x , a y , a z are the continuity ranges on the X, Y, and Z axes respectively, i and j are the numbers of any two sample points in the search ellipsoid, (x i ,y i , z i ) and (x j ,y j , z j ) are the coordinates of the two points, d i is the cumulative distance between the i-th sample point and other sample points in the search ellipsoid; Step 6: obtaining the coefficient of variation of the anisotropic distance based on the anisotropic distance between the sample data; Step 7: Select the partition corresponding to the minimum coefficient of variation; Step 8. Iterate steps 3 to 7 until all points to be estimated are processed, and the search ellipsoid partitioning method for all unknown points in the study area is determined.

2. The automatic partitioning method for a search ellipsoid based on a coefficient of variation as claimed in claim 1, characterized in that: Methods for obtaining a model of the spatial variability of sample data include: Preprocessing the sample data to obtain the spatial distribution and statistical characteristics of the sample data; According to the spatial distribution and statistical characteristics of the sample data, the experimental variogram is calculated to obtain experimental variograms in multiple different directions; According to the experimental variogram values ​​in the multiple different directions, a theoretical model is selected for fitting to obtain a theoretical variogram model; The experimental variograms in the multiple different directions are structurally fitted with the theoretical variogram model to obtain a spatial variability model of the sample data.

3. The automatic partitioning method for searching ellipsoid based on coefficient of variation as claimed in claim 1, characterized in that: The method for setting the orientation, size and preferred partitioning method of the search ellipsoid includes: The orientation of the search ellipsoid is set according to the occurrence of the ore body and the spatial continuity direction of the ore grade; Set the size of the search ellipsoid according to the spacing of the exploration projects and the continuity range of the ore grade; The inner space of the search ellipsoid is divided into a plurality of subspaces with equal angles, and a partitioning method to be optimized for the search ellipsoid is set according to the plurality of subspaces and different partitioning methods.

4. The automatic partitioning method for a search ellipsoid based on a coefficient of variation as claimed in claim 1, characterized in that: The method to obtain sample data inside the search ellipsoid is: Take any point to be estimated (x0, y0, z0) as the center of the ellipsoid, and use the mathematical equation of the ellipsoid to determine whether the sample data with assumed coordinates (x, y, z) is located inside it; assuming that the axis of the ellipsoid is parallel to the coordinate axis, use the following formula to determine: Among them, a, b, c are the lengths of the major axis, median axis, and minor axis of the ellipsoid; For any sample point with coordinates (x, y, z), if f(x, y, z) ≤ 1, the sample point is inside the ellipsoid; otherwise, the point is outside the ellipsoid.

5. The automatic partitioning method for searching ellipsoid based on coefficient of variation as claimed in claim 1, characterized in that: Partitioning the sample data according to the partitioning method to be optimized, the method for obtaining the partitioning method comprises: classifying the sample data according to the spatial orientation of the sample data relative to the center point of the ellipsoid based on the sample data inside the search ellipsoid that has been obtained; Partitioning is performed according to the classification of the sample data to obtain a partitioning method.

6. The automatic partitioning method for searching ellipsoid based on coefficient of variation as claimed in claim 1, characterized in that: Obtain the coefficient of variation of the anisotropic distance based on the anisotropic distance between the sample data: Where cv is the coefficient of variation, d i is the cumulative distance between the i-th sample point and other sample points in the search ellipsoid, n is the total number of samples in the search ellipsoid, and i is the number of any sample point in the search ellipsoid.

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