A Method for Automatically Constructing Theoretical Variogram Model

Abstract

The present invention discloses a method for automatically constructing a theoretical variogram model, which relates to the field of geostatistics and specifically includes the following steps: preprocessing spatial data; obtaining variogram point cloud data from the preprocessed spatial data; and fitting a theoretical variogram model based on the variogram point cloud data. Compared with conventional experimental variogram fitting methods, the present invention uses point cloud data to fit the theoretical variogram model, which reduces the process of selecting various parameters when constructing the experimental variogram, and can more simply obtain a relatively reasonable theoretical variogram model. The present invention uses a particle swarm optimization algorithm to automatically optimize the key parameters of the theoretical variogram model, effectively solving the subjective problem of parameter setting in the theoretical variogram model and improving the accuracy and stability of the theoretical variogram model construction.

Description

Technical Field

[0001] The present invention belongs to the field of geostatistics, and in particular relates to a method for automatically constructing a theoretical variogram model. Background Art

[0002] In geostatistics, the variogram is a tool used to measure the differences or variations between data values ​​at different locations in geospatial space. It describes the spatial relationships and variability between data points and can be used to understand spatial patterns of data change. It is often used to reveal spatial correlations, trends, and structures in data, facilitating analyses such as spatial interpolation, spatial prediction, and geological resource assessment.

[0003] Fitting experimental variograms is generally done in two ways: automatic fitting and manual fitting. While manual fitting yields the highest degree of fit between the experimental variogram scatter plot and the theoretical variogram model, it lacks a unified, objective standard, and subjective factors significantly impact the fitting quality and efficiency. Automatic fitting methods also suffer from a high reliance on the experimental variogram. The calculation of the experimental variogram is subject to uncertainty and complexity, depending on the data acquisition method and density. Different data acquisition methods and densities can lead to significant discrepancies in the calculated experimental variogram, thus impacting the accuracy and reliability of the theoretical variogram model. Calculating the experimental variogram is relatively straightforward when the spatial distribution of the data is strictly regular. However, data distributions are often not strictly regular. For irregular data distributions, considering only the basic lag distances can result in many sample points being excluded from the calculation, resulting in an experimental variogram that fails to represent the spatial structure of the data. In such cases, setting multiple calculation parameters is challenging and requires a certain level of expertise. Setting appropriate parameters based on industry context is crucial. Improper parameter settings can result in an inappropriate experimental variogram, ultimately impacting the overall variogram modeling performance.

[0004] Therefore, conventional variogram automatic modeling methods still have limitations such as difficulty in parameter setting. It is crucial to solve problems such as the dependence of the theoretical variogram model on the experimental variogram and the uncertainty of the experimental variogram itself. Summary of the Invention

[0005] The purpose of the present invention is to propose a method for automatically constructing a theoretical variogram model to solve the problems in the field of geostatistics such as the complexity of variogram modeling, high dependence on experimental variogram data, and strong subjectivity.

[0006] To achieve the above object, the present invention provides a method for automatically constructing a theoretical variogram model, which specifically includes the following steps:

[0007] Preprocess spatial data;

[0008] Obtain degraded point cloud data through preprocessed spatial data;

[0009] A theoretical variogram model is fitted based on the variogram point cloud data.

[0010] According to a method for automatically constructing a theoretical variogram model provided by the present invention, preprocessing the spatial data includes:

[0011] The spatial data is cleaned, detrended, and spatially transformed to obtain the pre-processed spatial data.

[0012] According to a method for automatically constructing a theoretical variogram model provided by the present invention, data cleaning, detrending, and spatial transformation are performed on the spatial data to obtain the pre-processed spatial data, including:

[0013] Performing missing value processing, outlier processing, and error value processing on the spatial data to obtain spatial data after data cleaning;

[0014] Eliminating mixed distribution, drift and scale effects in the spatial data after data cleaning to obtain detrended spatial data;

[0015] Logarithmic transformation and standardization are performed on the detrended spatial data to obtain the preprocessed spatial data.

[0016] According to a method for automatically constructing a theoretical variogram model provided by the present invention, obtaining the variation point cloud data through the preprocessed spatial data includes:

[0017] Obtaining data pairs in a target spatial domain through the preprocessed spatial data, and calculating a dissimilarity measure of the data pairs;

[0018] Based on the dissimilarity measure, the degraded point cloud data is obtained.

[0019] According to a method for automatically constructing a theoretical variogram model provided by the present invention, the dissimilarity measure of the data pair is:

[0020]

[0021] Among them, γ * Represents Z α and Z β Dissimilarity measure, α, β are the positions of any two data points in space, Z α 、Z β is a data pair in the spatial domain.

[0022] According to a method for automatically constructing a theoretical variogram model provided by the present invention, fitting the theoretical variogram model based on the variation point cloud data includes:

[0023] Step 1: Determine the parameter values ​​of the particle swarm algorithm, initialize the speed and position of each particle according to the value range of the parameter to be solved, and obtain the initial speed and initial position of each particle;

[0024] Step 2: Calculate the fitness value of each particle;

[0025] Step 3: Compare the fitness value of each particle with the best position fitness value of each particle to obtain the optimal solution for each particle;

[0026] Step 4: Compare the fitness value of each particle with the fitness value of the best position of the group to obtain the global optimal solution of the population;

[0027] Step 5: Update the speed and position of each particle based on the individual optimal solution of the particle and the global optimal solution of the population.

[0028] Step 6: Check if the global optimal position of the iterative optimization process meets the minimum limit or has reached the maximum number of iterations, then stop searching and output the global optimal solution; otherwise, return to step 2.

[0029] According to a method for automatically constructing a theoretical variogram model provided by the present invention, the fitness value of each particle is:

[0030]

[0031] Among them, F(i) is the fitness value of the i-th particle, n represents the number of data pairs; y i Represents the true value of the i-th data pair, that is, the experimental variation value of the i-th point cloud sample pair; Represents the theoretical variation function value of the i-th point cloud sample pair.

[0032] The present invention has the following beneficial effects:

[0033] Compared with conventional experimental variogram fitting methods, the present invention uses point cloud data to fit the theoretical variogram model, which reduces the selection process of various parameters when constructing the experimental variogram, and can relatively simply obtain a relatively reasonable theoretical variogram model; the present invention uses a particle swarm optimization algorithm to automatically optimize the key parameters of the theoretical variogram model, effectively solving the subjective problem of parameter setting in the theoretical variogram model, and improving the accuracy and stability of the theoretical variogram model construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0035] Figure 1 This is a flow chart of a method for automatically constructing a theoretical variogram model according to an embodiment of the present invention;

[0036] Figure 2 This is a diagram showing the actual distribution of case data proposed in an embodiment of the present invention;

[0037] Figure 3 This is a diagram of the fitting model results in a specific direction according to an embodiment of the present invention;

[0038] Figure 4 A Kriging estimation graph obtained based on the theoretical variogram model provided by the method according to an embodiment of the present invention;

[0039] Figure 5 This is an estimated graph obtained by the inverse distance power (IDW) method proposed in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention 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.

[0041] 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.

[0042] The mainstream approach to modeling spatial variability is to calculate the variogram of regionalized variables. However, theoretical variogram models have multiple parameters, each of which is typically obtained by fitting the experimental variogram. There are generally two approaches to fitting the experimental variogram: automatic fitting and manual fitting. Manual fitting involves plotting the experimental variogram scatterplot to estimate the approximate range, sill, and nugget values. Based on these estimates, a theoretical variogram model is derived. The theoretical variogram model is then compared with the experimental variogram scatterplot, and the range, sill, and nugget values ​​are continuously modified to achieve the best fit between the experimental variogram scatterplot and the theoretical variogram model. However, manual fitting methods lack unified, objective standards, and subjective factors significantly impact fitting quality and efficiency. Therefore, current variogram fitting methods are typically automated, typically using methods such as least squares, weighted polynomial regression, linear programming, and genetic algorithms to determine the parameters of the theoretical variogram model. Automatic fitting methods also suffer from a high reliance on experimental variograms. The calculation of experimental variograms is subject to uncertainty and complexity, depending on the data acquisition method and density. When the data acquisition method and density differ, the calculated experimental variogram results can vary significantly, thus affecting the accuracy and reliability of the theoretical variogram model. When the spatial distribution of the data is strictly regular, calculating the experimental variogram is relatively simple and does not require consideration of parameters such as tolerance; only the basic lag distance, search direction, and maximum search distance are required. However, data distribution is often less strictly regular. In cases of irregular data distribution, considering only the basic lag distance will result in many sample points being excluded from the calculation, and the resulting experimental variogram will not represent the spatial structure of the data. In such cases, parameters that need to be set include azimuth, bandwidth, search radius, tolerance angle, lag distance, lag distance tolerance, and number of lag distances. These parameters are difficult to calculate and require a certain level of expertise. Setting appropriate parameters based on industry context is crucial. Inappropriate parameter settings can result in an unreasonable experimental variogram, ultimately impacting the overall variogram modeling performance. In response to such technical problems, the present invention proposes a method for automatically constructing a theoretical variogram model.

[0043] like Figure 1 As shown, this embodiment provides a method for automatically constructing a theoretical variogram model, which specifically includes the following steps:

[0044] Preprocess spatial data;

[0045] Specifically, before modeling the variogram, the spatial data in the spatial database needs to be preprocessed by data cleaning, detrending, spatial transformation, etc., where the spatial data contains missing values, abnormal values ​​such as extremely high and low values, and error values.

[0046] Obtain degraded point cloud data through preprocessed spatial data;

[0047] Specifically, the variogram is a basic model for characterizing spatial variability. Compared to the experimental variogram, the variogram is less commonly used due to its large data volume and lack of clear spatial visualization. Currently, only a very small number of software programs use this model in manual modeling functions for geostatistical analysis. The variogram evaluates paired sample values ​​by calculating the squared difference between the data values. The distance and squared difference between the paired sample values ​​are used as coordinate axes to form a point cloud.

[0048] Fitting the theoretical variogram model based on the variogram point cloud data;

[0049] Specifically, by calculating the variation point cloud data of experimental data and using the particle swarm algorithm to automatically fit the theoretical variation function model, the efficiency of automatic variation function modeling can be improved and human subjectivity can be reduced.

[0050] Based on this, an embodiment of the present invention provides a method for automatically constructing a theoretical variogram model. By calculating the variation point cloud data of experimental data and using a particle swarm optimization algorithm to fit the theoretical variogram model, the process of selecting various parameters when constructing the experimental variogram is reduced, and a relatively reasonable theoretical variogram model can be obtained more simply. It also effectively solves the subjective problem of parameter setting in the theoretical variogram model and improves the accuracy and stability of the theoretical variogram model construction.

[0051] Optionally, preprocessing the spatial data includes: performing data cleaning, detrending and spatial transformation on the spatial data to obtain preprocessed spatial data;

[0052] Specifically, data cleaning includes missing value processing, outlier processing and error value processing, detrending processing includes eliminating mixed distribution, drift and proportional effects, and spatial transformation includes logarithmic transformation and standardization.

[0053] Optionally, perform data cleaning, detrending, and spatial transformation on the spatial data. The pre-processed spatial data includes:

[0054] Process missing values, outliers, and errors in spatial data to obtain cleaned spatial data;

[0055] Eliminate mixed distribution, drift and scale effects in the spatial data after data cleaning to obtain detrended spatial data;

[0056] The detrended spatial data are logarithmically transformed and standardized to obtain preprocessed spatial data.

[0057] Specifically, the preprocessing of spatial data includes:

[0058] (1) Processing of missing values, abnormal values ​​such as extremely high and extremely low values, and erroneous values ​​contained in the data;

[0059] (2) Eliminate possible mixed distribution, drift, and proportional effects in the data. Reduce the impact of trends;

[0060] (3) Perform spatial transformation on the data, including logarithmic transformation and standardization, so that the data conforms to the assumptions of the variogram.

[0061] Optionally, obtaining degraded point cloud data through preprocessed spatial data includes:

[0062] Obtain data pairs in the target spatial domain through the preprocessed spatial data and calculate the dissimilarity measure of the data pairs;

[0063] Based on the dissimilarity measure, the degraded point cloud data is obtained.

[0064] Specifically, by calculating the data pair Z in the spatial domain α and Z β The dissimilarity between them is used to measure the variability of the regionalized variable Z(x) at different scales and obtain the dissimilarity measure of the two values;

[0065] The point cloud data corresponding to the experimental data is calculated using the dissimilarity measure of the two values. The calculated results can be directly used as input data for the automatic variogram modeling process. When the point cloud computing result is large and significantly affects the calculation speed, it is also possible to extract at least 30% of the data for use in the modeling process.

[0066] Optionally, the dissimilarity measure for the data pair is:

[0067]

[0068] Among them, γ * Represents Z α and Z β Dissimilarity measure, α, β are the positions of any two data points in space, Z α 、Z β is a data pair in the spatial domain.

[0069] Specifically, use γ * Represents Z α and Z β The dissimilarity measure of , as shown in formula (1), is the variance of the two values. * This dissimilarity measure γ depends on the distance and direction of the point pair described by the vector h. * (h) is expressed as:

[0070]

[0071] Among them, h is a space vector formed by two coordinate points in space.

[0072] Optionally, based on the variogram data, fitting a theoretical variogram model includes:

[0073] Step 1: Determine the parameter values ​​of the particle swarm algorithm, initialize the speed and position of each particle according to the value range of the parameters to be solved, and obtain the initial speed and initial position of each particle;

[0074] Step 2: Calculate the fitness value of each particle;

[0075] Step 3: Compare the fitness value of each particle with the fitness value of the best position of each particle to obtain the optimal solution for each particle;

[0076] Step 4: Compare the fitness value of each particle with the fitness value of the best position of the group to obtain the global optimal solution of the population;

[0077] Step 5: Update the speed and position of each particle through the individual optimal solution of the particle and the global optimal solution of the population

[0078] Step 6: Check if the global optimal position of the iterative optimization process meets the minimum limit or has reached the maximum number of iterations, then stop searching and output the global optimal solution; otherwise, return to step 2.

[0079] Specifically, a particle swarm optimization (PSO) algorithm is used to encode the nugget value, sill value, and other parameters of the theoretical variogram model into the position vector of each particle in the PSO algorithm. Different theoretical variogram models are obtained by adjusting the value of each particle dimension. The fitting steps are as follows:

[0080] (1) Determine the values ​​of various parameters of the particle swarm algorithm, such as the number of particles, number of iterations, inertia weight, etc. Determine the value range of the parameters to be solved, use the parameters to be solved as the position vector of the particle, and initialize the particle swarm. Set the initial velocity of each particle;

[0081] (2) Calculate the fitness value of each particle;

[0082] (3) Compare the current fitness value of each particle with the fitness value of its best position. If the current fitness value is better, update the particle's best position and fitness value.

[0083] (4) Compare the fitness value of each particle with the fitness value of the best position of the group. If the particle fitness value is better, update the best position and fitness value of the group.

[0084] (5) Update the particle's velocity and position;

[0085] (6) Check if the global optimal position of the iterative optimization process meets the minimum limit or has reached the maximum number of iterations, then stop searching and output the global optimal solution. Otherwise, return to step (2).

[0086] Optionally, the fitness value of each particle is:

[0087]

[0088] Among them, F(i) is the fitness value of the i-th particle, n represents the number of data pairs; y i Represents the true value of the i-th data pair, that is, the experimental variation value of the i-th point cloud sample pair; Represents the theoretical variation function value of the i-th point cloud sample pair.

[0089] Specifically, in order to complete the fitting of the theoretical variogram model, a corresponding objective function is designed, such as formula (3), which converts the variogram fitting problem into the problem of finding the minimum value. Among them, the parameters such as the main direction angle, nugget value, range value, and sill value in the theoretical variogram model are used as undetermined parameters.

[0090] An embodiment of the present invention provides a method for automatically constructing a theoretical variogram model. The method first preprocesses spatial data; then, variogram point cloud data is obtained through the preprocessed spatial data; finally, the variogram point cloud data of the calculated experimental data is used to fit the theoretical variogram model using a particle swarm optimization algorithm. This improves the efficiency of automatic variogram modeling, reduces human subjectivity, and realizes a simpler automatic variogram modeling method.

[0091] The theoretical variogram model constructed using this invention analyzes spatial data characteristics, primarily for use in kriging interpolation, estimating values ​​at unknown locations based on the spatial correlation between sample points at known locations. It can be widely used in geological resource assessment, pollutant dispersion prediction, and surface water or atmospheric data modeling.

[0092] Example

[0093] This solution is applied to automatic modeling of variograms, and automatic modeling of variograms is performed through point cloud data. Figure 2 As shown, 290 sample data were randomly extracted from the real data for analysis. Table 1 shows a portion of the sample data, with the first three columns representing 3D coordinates and the last column representing attribute values. The generated sample data was preprocessed using error checking, completion, and normalization.

[0094] Table 1

[0095] X Y Z Value 11 8 0.5 0 8 30 0.5 0 9 48 0.5 224.4 8 69 0.5 434.4 9 90 0.5 412.1 10 110 0.5 587.2 9 129 0.5 192.3 11 150 0.5 31.3 10 170 0.5 388.5 8 188 0.5 174.6 9 209 0.5 187.8 10 231 0.5 82.1 11 250 0.5 81.1 10 269 0.5 124.3 8 288 0.5 188 31 11 0.5 28.7 29 29 0.5 78.1 28 51 0.5 292.1 31 68 0.5 895.2 28 88 0.5 702.6 30 110 0.5 490.3 28 130 0.5 136.1 28 150 0.5 335 30 171 0.5 277 28 190 0.5 206.1 31 209 0.5 24.5 28 229 0.5 198.1 30 250 0.5 60.3 31 269 0.5 312.6

[0096] The theoretical variogram model of spatial data is obtained by automatically fitting the theoretical variogram model using the variation point cloud and particle swarm optimization. Figure 3 As shown, the fitting of the experimental variogram model and the theoretical simulation at an azimuth angle of 30 degrees and an inclination angle of 0 degrees is shown. It can be seen that the results obtained in this embodiment also have a good fitting effect on the experimental variogram.

[0097] The variogram model obtained in this embodiment is used to perform ordinary kriging (OK) estimation, and the results obtained are as follows: Figure 4 As shown in Figure 2, the calculation results can generally reflect the distribution of actual data. In order to further confirm its effect, the inverse distance power (IDW) method was also used for valuation, and the corresponding results are shown in Figure 2. Figure 5 As shown. Figure 2 、 Figure 4 and Figure 5 It can be seen that the variogram model generated by this embodiment can obtain effective interpolation results. Table 2 quantitatively describes the error comparison between the kriging estimation results based on this method and the IDW, proving the effectiveness of the model provided by this embodiment.

[0098] Table 2

[0099]

[0100] The above description is merely a preferred embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for automatically constructing a theoretical variogram model, characterized in that: The specific steps include: Preprocessing spatial data, wherein the spatial data includes three-dimensional coordinates and attribute values; Preprocessing the spatial data includes: Performing data cleaning, detrending and spatial transformation on the spatial data to obtain pre-processed spatial data; Obtain degraded point cloud data through preprocessed spatial data; Fitting a theoretical variogram model based on the variogram point cloud data, wherein the main direction angle, nugget value, range value, and sill value parameters in the theoretical variogram model are used as undetermined parameters; Use the constructed theoretical variogram model to analyze spatial data characteristics and apply it to Kriging interpolation to estimate the value of unknown locations based on the spatial correlation between sample points at known locations. This method is used in geological resource assessment, pollutant dispersion prediction, and surface water or atmospheric data modeling. Fitting the theoretical variogram model based on the variogram point cloud data includes: Step 1: Determine the parameter values ​​of the particle swarm algorithm, initialize the speed and position of each particle according to the value range of the parameter to be solved, and obtain the initial speed and initial position of each particle; Step 2: Calculate the fitness value of each particle; Step 3: Compare the fitness value of each particle with the best position fitness value of each particle to obtain the optimal solution for each particle; Step 4: Compare the fitness value of each particle with the fitness value of the best position of the group to obtain the global optimal solution of the population; Step 5: Update the speed and position of each particle using the individual optimal solution of the particle and the global optimal solution of the population; Step 6: Check if the global optimal position of the iterative optimization process meets the minimum limit or has reached the maximum number of iterations, then stop searching and output the global optimal solution; otherwise, return to step 2; The fitness value of each particle is: in, For the The fitness value of a particle, Represents the number of data pairs; Representative The true value of the data pair, that is, The experimental variation value of the point cloud sample pair; Representative The theoretical variogram value of a point cloud sample pair.

2. The method for automatically constructing a theoretical variogram model according to claim 1, wherein: Performing data cleaning, detrending, and spatial transformation on the spatial data to obtain the pre-processed spatial data includes: Performing missing value processing, outlier processing, and error value processing on the spatial data to obtain spatial data after data cleaning; Eliminating mixed distribution, drift and scale effects in the spatial data after data cleaning to obtain detrended spatial data; Logarithmic transformation and standardization are performed on the detrended spatial data to obtain the preprocessed spatial data.

3. The method for automatically constructing a theoretical variogram model according to claim 1, wherein: Obtaining the degraded point cloud data through the preprocessed spatial data includes: Obtaining data pairs in a target spatial domain through the preprocessed spatial data, and calculating a dissimilarity measure of the data pairs; Based on the dissimilarity measure, the degraded point cloud data is obtained.

4. The method for automatically constructing a theoretical variogram model according to claim 3, wherein: The dissimilarity measure of the data pair is: in, express and The dissimilarity measure, 、 are the positions of any two data points in space, 、 is a data pair in the spatial domain.

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