Generalized regression neural network ore grade estimation method considering anisotropy

Abstract

The application discloses a generalized regression neural network ore grade estimation method considering anisotropy, and comprises the following steps: acquiring ore grade sample data and performing pretreatment; constructing an experimental variation function, calculating a standardized experimental difference value based on the experimental variation function and the pretreated data, fitting the experimental variation function by using a standard Gaussian variation function model, and obtaining a main variation direction and a corresponding theoretical variation function model; obtaining a unified variation function model according to the theoretical variation function model; obtaining a covariance function by using the unified variation function model to fit and calculate a GRNN mode layer transfer function, replacing the mode layer transfer function, obtaining an improved model, optimizing the model according to the error between a predicted value and an actual value, and using the model to perform ore grade estimation. The application can better maintain the structure correlation of data and improve the prediction accuracy by fitting the variability structure in each direction and integrating the variability structure into the GRNN model.

Description

Technical Field

[0001] This invention belongs to the fields of machine learning and geostatistics, and in particular relates to a generalized regression neural network method for estimating ore grade that takes into account anisotropy. Background Technology

[0002] Generalized Regressive Neural Networks (GRNNs) are an improved form of Radial Basis Function Networks (RBF). Let the input data be x, and the corresponding output be y, with f(x, y) being the joint probability density function. When x takes the value x0, the GRNN takes the expected value of y as its regression value. The calculation formula is as follows:

[0003]

[0004] Where, x i ,y i Let x be the i-th observation of random variables x and y, n be the sample size, and σ be the smoothing factor. In typical spatial interpolation problems, random variable x represents the three coordinate components (X, Y, Z) of the measured point or the point to be estimated, with a dimension of 3. Applying this method to ore grade estimation in geostatistics, random variable x represents the three-dimensional coordinates of the point to be estimated. Ore grade data has the characteristic of unique sampling, making it difficult to achieve repeated sampling, resulting in insufficient final sample data. For grade values ​​at unsampled locations, spatial interpolation algorithms are usually required for calculation. The structure of the generalized regression neural network three-dimensional spatial interpolation model is as follows: Figure 1 As shown.

[0005] Anisotropy refers to the characteristic that data exhibits varying degrees of continuity or variability across different associated attributes. This characteristic is common in both natural and social sciences. For example, when dealing with environmental pollution issues, it is easy to observe that the continuity of pollutants along the river channel is significantly greater than that perpendicular to the channel. Therefore, anisotropy is of great importance for estimation and prediction accuracy.

[0006] As the above analysis shows, although the GRNN model is simple and efficient, it does not fully consider the anisotropy of the data during the estimation and prediction process. Therefore, the predictive performance of GRNN has significant room for improvement. Summary of the Invention

[0007] The purpose of this invention is to provide a generalized regression neural network method for ore grade estimation that takes into account anisotropy, so as to solve the problems existing in the prior art.

[0008] To achieve the above objectives, this invention provides a generalized regression neural network method for ore grade estimation that takes into account anisotropy, comprising:

[0009] Obtain ore grade sample data and preprocess the ore grade data;

[0010] An experimental variation function is constructed, and standardized experimental differences are calculated on the preprocessed ore grade sample data using the experimental variation function. Based on the standardized experimental differences, a standard Gaussian variation function model is used to fit the experimental variation function in several directions to obtain the main variation directions and the corresponding theoretical variation function models.

[0011] A unified variogram model is obtained based on the geometric anisotropic structure of the theoretical variogram model; the covariance function is obtained by overlaying the GRNN mode layer transfer function with the unified variogram model.

[0012] The mode layer transfer function of the GRNN model is replaced with the covariance function to obtain an improved GRNN model. The improved GRNN model is used for prediction, and the error between the predicted value and the true value is judged. The above steps are repeated until the error value is within the preset range. Then, the improved GRNN model is used to estimate the ore grade.

[0013] Optionally, the preprocessing process includes: processing missing values, outliers, and erroneous values ​​in the ore grade sample data; and normalizing the processed data.

[0014] Optionally, the experimental variation function is expressed as:

[0015]

[0016] In the formula, h represents the distance between any two sample points. For example, sample point X i With sample point X j The distance between them, h = (X i -X j (X) i -X j ) T ;Y(x i +h) and Y(x i ) respectively represent positions (x i +h) and (x i The attribute values ​​of two sampling points (i.e., two sample points that are h apart) are given by Y. N(h) represents the number of sample point data pairs with a distance of h; Var(Y) is the variance of Y.

[0017] Optionally, the fitting process includes: plotting scatter plots of the experimental variation function of the sampled data in different directions based on the standardized experimental difference, minimizing the difference between the theoretical curve corresponding to the standard Gaussian variation function model and the experimental variation values ​​in several directions, thus completing the fitting.

[0018] Optionally, the process of obtaining the direction of variation and the corresponding theoretical variogram model includes:

[0019] Obtain the theoretical variogram model with the largest range value among several directions, and take the calculation direction corresponding to this model as the first principal variogram direction;

[0020] Find the theoretical variogram model corresponding to all directions perpendicular to the first principal variation direction, and select the calculation direction corresponding to the variogram model with the largest range value as the second principal variation direction;

[0021] Select theoretical variogram models corresponding to all directions perpendicular to the plane formed by the first principal variation direction and the second principal variation direction, compare the range values, and take the calculation direction with the largest range value as the third principal variation direction.

[0022] Optionally, the process of obtaining a unified variogram model includes: obtaining the difference values ​​of range values ​​and sill values ​​between various theoretical variogram models; if the difference value does not exceed the limit, then the variogram model in any direction is selected as the unified variogram model; if the difference value exceeds the limit, then a linear transformation is performed on the theoretical variogram model to obtain the unified variogram model.

[0023] Optionally, if the difference value exceeds the limit value, and the direction of the main variation is inconsistent with the direction of the variation value of the corresponding theoretical variation function model, then after the linear transformation is completed, a coordinate transformation is performed to obtain a unified variation function model.

[0024] The technical effects of this invention are as follows:

[0025] This invention optimizes the representation of the transfer function of the GRNN model's modal layer, enabling it to fully consider the anisotropic characteristics of the data and improving the efficiency of parameter search. It avoids the extensive iterative calculations of existing methods, saving time and costs, and exhibits greater adaptability. Even when sampling data is insufficient for cross-validation and variogram calculation, a Gaussian variogram model of the study area can be established based on expert experience, ensuring the smooth implementation of this method. Applied to ore grade estimation in geostatistics, which involves spatial interpolation of spatial data, the improved GRNN model yields more accurate interpolation results. The simulation data is selected, with the first three columns representing three-dimensional coordinates and the last column representing the grade value. The data is preprocessed, and normalization is used to eliminate the influence of dimensions between data points. Attached Figure Description

[0026] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0027] Figure 1This is a structural diagram of the GRNN three-dimensional spatial interpolation model in an embodiment of the present invention;

[0028] Figure 2 This is a scatter plot of the variation function in this embodiment of the invention;

[0029] Figure 3 This is a diagram of the geometric anisotropy variation function structure in an embodiment of the present invention;

[0030] Figure 4 This is a direction-range diagram in an embodiment of the present invention;

[0031] Figure 5 This is an overall flowchart of the method in an embodiment of the present invention;

[0032] Figure 6 This is an example diagram of the original data in an embodiment of the present invention;

[0033] Figure 7 This is a schematic diagram of the interpolation prediction results in an embodiment of the present invention. Detailed Implementation

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0036] Example 1

[0037] like Figure 1-7 As shown, this embodiment provides a generalized regression neural network method for estimating ore grade that takes into account anisotropy, including:

[0038] Data preprocessing

[0039] In constructing a generalized regression neural network using ore grade data, the ore grade data typically needs to be preprocessed, including:

[0040] Process missing values, abnormal values ​​such as extremely high or low ore grade, and erroneous values ​​contained in the ore grade data;

[0041] The ore grade data are generally normalized, that is, transformed to the [0, 1] interval to eliminate the influence of dimensions;

[0042] The experimental variation function was fitted using a Gaussian model.

[0043] The variogram is a fundamental tool in geostatistics for studying the variability and continuity of variables. Anisotropy refers to the varying variability or continuity of a regionalized variable in different directions. The standardized experimental variogram γ(h) of the sampled data is calculated using the following formula:

[0044]

[0045] Where h represents the distance between any two sample points. For example, sample point X i With sample point X j The distance between them, h = (X i -X j (X) i -X j ) T ;Y(x i +h) and Y(x i ) respectively represent positions (x i +h) and (x i The attribute values ​​of two sampling points (i.e., two sample points that are h apart) are given by Y. N(h) represents the number of sample point data pairs with a distance of h; Var(Y) is the variance of Y.

[0046] The experimental variation function effect is calculated using equation (1) as follows: Figure 2 The scatter plot is shown in the image.

[0047] Scatter plots of the experimental variogram of the sampled data in different directions were plotted. A standard Gaussian variogram model was used to fit the experimental variogram in each direction, minimizing the difference between the theoretical curve and the experimental variogram value. The theoretical variogram model with the largest range value in each direction was identified, and its calculation direction was designated as the first principal direction of variation. Then, theoretical variogram models corresponding to all directions perpendicular to this first principal direction were identified, and their calculation directions were selected as the second principal direction of variation. Finally, theoretical variogram models corresponding to all directions perpendicular to the plane formed by these two directions were selected, and their range values ​​were compared. The calculation direction corresponding to the model with the largest range value among these models was designated as the third principal direction of variation. This process was repeated for selecting theoretical variogram models for the three directions. The calculation formula for the standard Gaussian variogram model is as follows:

[0048]

[0049] Here, 'a' represents an unknown parameter to be determined. Parameter 'a' can be adjusted manually or automatically to obtain Gaussian models of different forms, allowing them to achieve the optimal match with the experimental variogram scatter plot.

[0050] Variation function structure fitting and GRNN model improvement

[0051] The analysis of the variogram structure model primarily focuses on geometric anisotropy, meaning that the variograms in all directions have the same sill value but different range values. This can be transformed into an isotropic structure through a simple geometric transformation (linear transformation). The geometrically anisotropic variogram structure is shown below. Figure 3 As shown.

[0052] A direction-range graph can be constructed using direction and range, such as Figure 4 As shown in the figure. Here, u, w, and v are the relative angles of the three selected directions, and the length is the range value corresponding to each of the three directions. The variogram structures of the three directions are overlaid, and the range values ​​and sill values ​​are observed. If the differences between the range values ​​and sill values ​​corresponding to the three directions are very small, then the data in each direction are considered to lack anisotropic characteristics. The direction-range plot results are shown in the figure. Figure 4 As shown in (a), which approximates a circle, the variogram model in any direction can be chosen as the unified variogram model. In this case, the range of the unified variogram model is the radius of the circle.

[0053] If the sill values ​​are the same but the range values ​​are different, then the variogram has a geometrically anisotropic structure, as shown in the following figure. Figure 4 As shown in (b), it approximates an ellipse. Let u, v, and w be the three directions generated in the above steps, and let the variograms be γ. u (h u ), γ v (h v ) and γ w (h w The sill value for all three models is c, and the ranges are a, a, and a, respectively. u a v and a w If the semi-major axis and semi-minor axis u′ and w′ of the generated ellipse coincide with the directions u and w, let a u >a v >a W Then this geometric anisotropy ratio This actually means that the range of influence of Y(x) in the u direction is equal to k times the range of influence in the w direction. Clearly, u′ and w′ are perpendicular to each other; in this case, if a linear transformation matrix is ​​chosen...

[0054]

[0055] The transformed coordinate vector is

[0056]

[0057] In other words, geometric anisotropy was transformed into isotropy in the new coordinate system h′. u h′ wThe following can be represented by a unified variogram model, which uses the semi-major axis u′ as the range value.

[0058] However, under normal circumstances, the directions u and w do not coincide with the semi-major and semi-minor axes u′ and w′ of the ellipse; there is often an angle between u and u′. In this case, performing the above linear transformation requires an additional coordinate rotation transformation to ensure that the directions u and w coincide with the principal axes of the ellipse. Let...

[0059]

[0060] Then h′ u h′ w and h u h w The transformation relationship between them is

[0061]

[0062] Then, the ellipse is transformed into a circle with a radius equal to the semi-major axis of the ellipse. This is done by left-multiplying the new coordinate system by the linear transformation matrix A, resulting in:

[0063]

[0064] After linear transformation, the original coordinates Become After that, the range of variation is equal in all directions, so it can be regarded as isotropic and can be represented by a unified variation function model.

[0065] The above steps allow for the analysis of geometric anisotropy and the generation of a unified variogram model. This variogram model leads to the corresponding covariance function model. The covariance function, obtained by overlaying the GRNN mode layer transfer function with the variogram structure, effectively reflects the anisotropic characteristics of the data.

[0066]

[0067] Training GRNN models

[0068] Train the GRNN model using cross-validation or K-fold cross-validation. Replace the model layer transfer function with the covariance function generated in the above steps, and calculate the error between the predicted and true values. If the error is large, return to steps 2 and 3, recalculate and fit the experimental variability function, and perform structural fitting on the fitted theoretical variability function to obtain a new covariance function model. Test again until the prediction results achieve sufficient accuracy.

[0069] Applying GRNN model

[0070] Construct a GRNN model based on the steps outlined above. This model can then be used to estimate ore grade.

[0071] This example solution is applied to ore grade estimation in the field of geostatistics, involving spatial interpolation of spatial data. An improved GRNN model is used to obtain more accurate interpolation results. Simulated data is selected as follows: Figure 6 As shown, the first three columns are three-dimensional coordinates, and the last column represents the grade value. The data is preprocessed and normalized to eliminate the influence of dimensions between data.

[0072] The covariance function is represented by the transfer function of the GRNN model layer after calculation using a variation function structure. The improved GRNN model is then applied to predict attribute values ​​at unknown points, i.e., grade prediction. The prediction results are as follows: Figure 7 As shown.

[0073] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A generalized regression neural network method for estimating ore grade that takes anisotropy into account, characterized in that, Includes the following steps: Obtain ore grade sample data and preprocess the ore grade data; An experimental variation function is constructed, and standardized experimental differences are calculated on the preprocessed ore grade sample data using the experimental variation function. Based on the standardized experimental differences, a standard Gaussian variation function model is used to fit the experimental variation function in several directions to obtain the main variation directions and the corresponding theoretical variation function models. The process of obtaining the direction of variation and the corresponding theoretical variogram model includes: Obtain the theoretical variogram model with the largest range value among several directions, and take the calculation direction corresponding to this model as the first principal variogram direction; Find the theoretical variogram model corresponding to all directions perpendicular to the first principal variation direction, and select the calculation direction corresponding to the variogram model with the largest range value as the second principal variation direction; Select all theoretical variogram models corresponding to the plane formed by the first principal variation direction and the second principal variation direction, compare the range values, and take the calculation direction with the largest range value as the third principal variation direction. A unified variogram model is obtained based on the geometric anisotropic structure of the theoretical variogram model; the covariance function is obtained by overlaying the GRNN mode layer transfer function with the unified variogram model. The process of obtaining a unified variogram model includes: obtaining the differences in range values ​​and sill values ​​between various theoretical variogram models; if the differences do not exceed the limit, then the variogram model in any direction is selected as the unified variogram model; if the differences exceed the limit, then a linear transformation is performed on the theoretical variogram model to obtain the unified variogram model. The mode layer transfer function of the GRNN model is replaced with the covariance function to obtain an improved GRNN model. The improved GRNN model is used for prediction, and the error between the predicted value and the true value is judged. The above steps are repeated until the error value is within the preset range. Then, the improved GRNN model is used to estimate the ore grade.

2. The anisotropy-insensitive generalized regression neural network ore grade estimation method according to claim 1, characterized in that, The preprocessing process includes: processing missing values, outliers, and erroneous values ​​in the ore grade sample data; and normalizing the processed data.

3. The anisotropy-considering generalized regression neural network ore grade estimation method according to claim 1, characterized in that, The experimental variation function is expressed as: ， In the formula, This represents the distance between any two sample points. and They represent the positions respectively. and The attribute values ​​of the two sampling points, The representative distance is The number of sample point data pairs; for The variance.

4. The anisotropy-insensitive generalized regression neural network ore grade estimation method according to claim 1, characterized in that, The fitting process includes: plotting scatter plots of the experimental variation function of the sampled data in different directions based on the standardized experimental difference, minimizing the difference between the theoretical curve corresponding to the standard Gaussian variation function model and the experimental variation values ​​in several directions, thus completing the fitting.

5. The anisotropy-considering generalized regression neural network ore grade estimation method according to claim 1, characterized in that, If the difference value exceeds the limit, and the direction of the main variation is inconsistent with the direction of the variation value of the corresponding theoretical variation function model, then after the linear transformation is completed, a coordinate transformation is performed to obtain a unified variation function model.

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