GRNN smoothing factor setting method and system based on variogram model
Through the GRNN smoothing factor setting method based on the variogram model, the problems of large calculation amount and insufficient basis for GRNN smoothing factor setting are solved, and an efficient and adaptable ore grade valuation prediction is achieved.
Patent Information
- Application Number
- CN202211012960.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-23
- Publication Date
- 2025-09-16
- Estimated Expiration
- 2042-08-23
AI Technical Summary
The existing GRNN smoothing factor setting method is computationally intensive, lacks a basis, and is prone to missing the optimal solution. In particular, repeated sampling is difficult to achieve in ore grade estimation in the field of geostatistics, making it difficult to effectively optimize the smoothing factor when the sampling data is too small.
The GRNN smoothing factor setting method based on the variogram model is adopted. By preprocessing the sample data, fitting the omnidirectional experimental variogram and obtaining the range value as the smoothing factor, a GRNN model is constructed for prediction, and cross-validation is used to adjust the prediction error until the preset accuracy is achieved.
It is easier to obtain the optimal smoothing factor, improves the efficiency of parameter search, reduces the amount of calculation and time cost, has stronger adaptability, and is suitable for situations where sampling data is insufficient.
Smart Images
Figure CN115345282B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the fields of machine learning and geostatistics, and in particular relates to a GRNN smoothing factor setting method and system based on a variogram model. Background Art
[0002] Generalized Regression Neural Network (GRNN) is a variant of Radial Basis Neural Network (RBF). The network training process uses sample data as the posterior condition and calculates the network output based on the maximum probability criterion. Let the input data of the GRNN network be x, and the corresponding network output be y. Its learning process is: let the joint probability density of x and y be f(x,y). When x is x0, take the mathematical expectation of y as its regression value. Right now:
[0003]
[0004] Using nonparametric estimation, the probability density function f(x0,y) is estimated as follows:
[0005]
[0006] Where x i ,y i is the i-th observation value of random variables x and y, n is the sample size, p is the dimension of random variable x, and σ is the smoothing factor (smoothing parameter). After integral transformation, the expected output of the network can be obtained:
[0007]
[0008] The network structure of GRNN is as follows Figure 1 As shown, the entire network consists of four layers of neurons, namely input layer, pattern layer, summation layer and output layer. The corresponding network input is X = [x1, x2, x3…x n ] T , its output is [y1,y2,y3…y k ] T .
[0009] Input layer: The number of neurons in the input layer is equal to the dimension of the input vector in the learning sample. Each neuron is a simple distribution unit that directly passes the input variable to the pattern layer.
[0010] Pattern layer: The number of neurons in the pattern layer is equal to the capacity of the learning sample. Each neuron corresponds to a different sample point. The transfer function of the neurons in the pattern layer is:
[0011]
[0012] Among them, X is the network input vector, X iis the learning sample point corresponding to the i-th neuron, n is the sample capacity, and σ is the smoothing factor.
[0013] Summation layer: Two types of neurons are used in the summation layer for summation.
[0014] The first type of summation process performs arithmetic summation on the outputs of all pattern layer neurons. The connection weight between the pattern layer and each neuron is 1, and the transfer function is:
[0015]
[0016] The second type of summation process performs weighted summation on the neurons of all pattern layers. The connection weight between the i-th neuron in the pattern layer and the j-th neuron in the summation layer is Y i The jth element (i.e. Y ij ), the transfer function is:
[0017]
[0018] Output layer: The number of neurons in the output layer is equal to the dimension k of the output vector in the learning sample. Each neuron divides the output of the summation layer, that is, the output result y of neuron j j for:
[0019]
[0020] The primary purpose of GRNN network training is to find a suitable smoothing factor. Existing solutions primarily rely on traversal search and cross-validation methods, whereby possible smoothing factors are sequentially compared and screened, retaining the one with the highest cross-validation accuracy. This approach suffers from high computational complexity, a lack of rationale for the calculation process, and a tendency to miss optimal solutions. In geostatistics, when using GRNN for ore grade estimation, repeated sampling is difficult due to the unique sampling nature of geological data. Consequently, insufficient sampling data may be required, making it difficult to optimize the GRNN smoothing factor. Therefore, a method for setting the GRNN smoothing factor based on the Gaussian variogram model is urgently needed. Summary of the Invention
[0021] To solve the above technical problems, the present invention proposes a GRNN smoothing factor setting method and system based on a variogram model, which can more easily obtain the optimal smoothing factor, improve the efficiency of parameter search, and have stronger adaptability.
[0022] On the one hand, to achieve the above-mentioned object, the present invention provides a GRNN smoothing factor setting method based on a variogram model, comprising:
[0023] Preprocess the sampled data;
[0024] Obtaining the omnidirectional experimental variogram of the preprocessed sampling data, and fitting the omnidirectional experimental variogram to obtain a range value;
[0025] The range value is used as a smoothing factor to perform GRNN prediction;
[0026] Based on the smoothing factor that satisfies the prediction result and the pre-processed sampling data, a GRNN model is constructed, and the grade value of the unknown position is predicted by the GRNN model.
[0027] Optionally, preprocessing the sampled data includes:
[0028] Identifying and processing error values, abnormal values, and missing values in the sampled data;
[0029] Normalizing the processed sampling data;
[0030] Performing data dimension reduction processing on the normalized sampling data.
[0031] Optionally, the omnidirectional experimental variation function is:
[0032]
[0033] Among them, γ(h) is the variation value of the omnidirectional experimental variation function, h is the distance between any two sample points, Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ), N(h) is the number of sample point data pairs with a distance of h, and Var(Y) is the variance of Y.
[0034] Optionally, the method of fitting the omnidirectional experimental variogram is: using a fitting method of a standard Gaussian variogram model;
[0035] The standard Gaussian variogram model is:
[0036]
[0037] Among them, a is the unknown parameter to be determined, and e is the natural logarithm;
[0038] The range value is:
[0039] Optionally, performing GRNN prediction includes:
[0040] Within the framework of a preset verification method, the GRNN prediction is performed based on the smoothing factor, and the gap between the predicted value and the true value is calculated. If the prediction error is greater than a preset threshold, the omnidirectional experimental variation function is reacquired and fitted to obtain a new range value and the GRNN prediction is performed again until the prediction result reaches the preset accuracy.
[0041] On the other hand, to achieve the above-mentioned purpose, the present invention also provides a GRNN smoothing factor setting system based on a variogram model, comprising: a preprocessing module, a fitting module, a prediction module and an output module;
[0042] The preprocessing module is used to preprocess the sampled data;
[0043] The fitting module is used to obtain the omnidirectional experimental variation function of the pre-processed sampling data, and fit the omnidirectional experimental variation function to obtain the range value;
[0044] The prediction module is used to perform GRNN prediction using the range value as a smoothing factor;
[0045] The output module is used to construct a GRNN model based on the smoothing factor that meets the prediction result and the preprocessed sampling data, and predict the grade value of the unknown position through the GRNN model.
[0046] Optionally, the preprocessing module includes: a cleaning unit, a normalization unit and a dimensionality reduction unit;
[0047] The cleaning unit is used to identify and process error values, abnormal values and missing values in the sampled data;
[0048] The normalization unit is used to normalize the cleaned sampling data;
[0049] The dimension reduction unit is used to perform data dimension reduction processing on the normalized sampling data.
[0050] Optionally, the omnidirectional experimental variation function is:
[0051]
[0052] Among them, γ(h) is the variation value of the omnidirectional experimental variation function, h is the distance between any two sample points, Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ), N(h) is the number of sample point data pairs with a distance of h, and Var(Y) is the variance of Y.
[0053] Optionally, the method of fitting the omnidirectional experimental variogram is: using a fitting method of a standard Gaussian variogram model;
[0054] The standard Gaussian variogram model is:
[0055]
[0056] Among them, a is the unknown parameter to be determined, and e is the natural logarithm;
[0057] The range value is:
[0058] Optionally, performing GRNN prediction in the prediction module includes:
[0059] Within the framework of a preset verification method, the GRNN prediction is performed based on the smoothing factor, and the gap between the predicted value and the true value is calculated. If the prediction error is greater than a preset threshold, the omnidirectional experimental variation function is reacquired and fitted to obtain a new range value and the GRNN prediction is performed again until the prediction result reaches the preset accuracy.
[0060] Compared with the prior art, the present invention has the following advantages and technical effects:
[0061] It is easier to obtain the optimal smoothing factor. Based on the variogram model, the present invention provides a clear reference and basis for setting the GRNN smoothing factor, which can avoid blind searching and reduce the possibility of missing the optimal solution.
[0062] Improved the efficiency of parameter search. Avoided the large number of iterative calculation processes of existing methods, saving time and cost;
[0063] It has stronger adaptability. When the sampling data is too small to be used for cross-validation and variogram calculation, a Gaussian variogram model of the study area can be established based on expert experience, so that this method can be implemented smoothly. BRIEF DESCRIPTION OF THE DRAWINGS
[0064] 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:
[0065] Figure 1 Schematic diagram of the flow of the GRNN smoothing factor setting method based on the variogram model according to Example 1 of the present invention;
[0066] Figure 2 Schematic diagram of the omnidirectional experimental variation function of Example 1 of the present invention;
[0067] Figure 3This is a schematic diagram of the original data of Example 1 of the present invention;
[0068] Figure 4 This is a schematic diagram of normalized data according to Example 1 of the present invention;
[0069] Figure 5 This is a schematic diagram of Gaussian model fitting in Example 1 of the present invention;
[0070] Figure 6 Schematic diagram of the root mean square error of Example 1 of the present invention;
[0071] Figure 7 This is a schematic diagram of the system structure for setting the GRNN smoothing factor based on the variogram model according to Example 2 of the present invention. DETAILED DESCRIPTION
[0072] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this 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.
[0073] 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.
[0074] Example 1
[0075] like Figure 1 As shown, this embodiment provides a GRNN smoothing factor setting method based on a variogram model, including:
[0076] Preprocess the sampled data;
[0077] Obtaining the omnidirectional experimental variogram of the preprocessed sampling data, and fitting the omnidirectional experimental variogram to obtain a range value;
[0078] The range value is used as a smoothing factor to perform GRNN prediction;
[0079] Based on the smoothing factor that satisfies the prediction result and the pre-processed sampling data, a GRNN model is constructed, and the grade value of the unknown position is predicted by the GRNN model.
[0080] Furthermore, preprocessing the sampled data includes:
[0081] Identifying and processing error values, abnormal values, and missing values in the sampled data;
[0082] Normalizing the processed sampling data;
[0083] Performing data dimension reduction processing on the normalized sampling data.
[0084] Furthermore, the method of fitting the omnidirectional experimental variogram is: adopting the fitting method of the standard Gaussian variogram model.
[0085] Furthermore, performing GRNN prediction includes:
[0086] Within the framework of a preset verification method, the GRNN prediction is performed based on the smoothing factor, and the gap between the predicted value and the true value is calculated. If the prediction error is greater than a preset threshold, the omnidirectional experimental variation function is reacquired and fitted to obtain a new range value and the GRNN prediction is performed again until the prediction result reaches the preset accuracy.
[0087] The specific steps of the GRNN smoothing factor setting method based on the variogram model are as follows:
[0088] 1. Perform data preprocessing
[0089] Data preprocessing is an important step that cannot be ignored in the process of building a generalized regression neural network model, including:
[0090] 1) Identify and process erroneous values, abnormal values, and missing values in sampling data (such as drilling data, which mainly includes three-dimensional coordinate information and attribute information related to ore grade);
[0091] 2) Normalize the sample data, i.e. transform it to the interval [0,1] to eliminate the influence of dimension;
[0092] 3). When the capacity of the input sample is large, data dimensionality reduction can be performed.
[0093] 2. Calculate the variogram of the omnidirectional experiment
[0094] The variogram is a fundamental tool in geostatistics for studying the spatial variability and continuity of variables. To determine the smoothing factor for a GRNN using a variogram, the first step is to plot the experimental variogram scatter plot of the sampled data. Then, a theoretical variogram model is selected to fit the experimental variogram scatter plot. The parameters of the variogram model corresponding to the optimal fit are obtained, and the range of variation is used as the smoothing factor for the GRNN.
[0095] The standardized omnidirectional experimental variation γ(h) of the sampling data is calculated using the following formula:
[0096]
[0097] Where: h represents the distance between any two sample points. For example, sample point X i With sample point X jThe distance between h=(X i -X j )(X i -X j ) T ; Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ) (i.e., two sample points with a distance h between them). N(h) is the number of sample point data pairs with a distance h; Var(Y) is the variance of Y.
[0098] The experimental variation function is calculated using formula (8) as follows: Figure 2 As shown in the scattered points.
[0099] 3. Fitting experimental variogram
[0100] The standard Gaussian variogram model is used to fit the experimental variation value calculated in step 2, that is, to minimize the gap between the theoretical curve corresponding to the model and the experimental variation value. The calculation formula of the standard Gaussian variogram model is as follows:
[0101]
[0102] Where a is an unknown parameter to be determined. The parameter a can be adjusted manually or automatically to obtain Gaussian models of different shapes, so that it can show the best matching effect with the experimental variogram scatter plot. The parameter corresponding to this effect is It can be regarded as the smoothing factor σ of formula (3) or (4). In the standard Gaussian variogram model, e is the natural logarithm, and the square root is the range value. In order to match the transfer function of the neuron in the pattern layer of GRNN, a is selected as the undetermined parameter.
[0103] The distance (i.e., the x-axis coordinate) at which the variogram model first becomes horizontal is called the range. Sample locations separated by distances closer than the range are spatially autocorrelated, while sample locations separated by distances greater than the range are not. By fitting the experimental variogram to obtain the variogram model, the range can be calculated from the x-axis coordinate corresponding to the model's horizontal state.
[0104] 4. Training the GRNN model
[0105] Within the framework of cross-validation or K-fold cross-validation, GRNN predictions are performed based on the smoothing factors obtained in the above steps, and the difference between the predicted value and the true value is calculated. If the prediction error is large, return to steps 2 and 3, recalculate and refit the experimental variogram, obtain a new smoothing factor, and test again until the prediction results achieve sufficient accuracy. When using the smoothing factor for GRNN predictions, the calculated range value can be used as the smoothing factor, without the need to first build a GRNN model. The process of building a GRNN model is the process of optimizing the smoothing factor.
[0106] 5. Applying the GRNN model
[0107] Keep the smoothing factor generated in the previous step. Use this parameter and all sample data to build a GRNN model. Based on this model, you can predict the attribute values of unknown points. In the field of geostatistics, the GRNN model is used to predict the grade value of unknown locations.
[0108] This embodiment, starting from the analysis of the spatial variability of the research data itself, provides a method for setting the GRNN smoothing factor with moderate computational effort and sufficient theoretical basis. This method combines the Gaussian variogram model with the GRNN smoothing factor setting, i.e., determining the GRNN smoothing factor by analyzing the spatial variability of the sampled data. The key corresponding contents are steps 2 to 4 in the embodiment, namely, the calculation of the omnidirectional experimental variogram, the fitting of the experimental variogram, and the training of the GRNN model.
[0109] The present invention proposes to use the geostatistical method to determine the GRNN smoothing factor. The determined GRNN model can be used for the prediction of various data, but is not limited to the field of geostatistics. The above technical solution is applied to the following specific examples:
[0110] 1. Select 460 data points such as Figure 3 As shown, the data is normalized and the results are as follows Figure 4 .
[0111] 2. Calculate the omnidirectional experimental variation function of the processed data, select the Gaussian model to fit the experimental variation function, and obtain the range value. The variation function diagram is as follows: Figure 5 shown.
[0112] 3. Record the obtained Gaussian model range value and use it to build the GRNN model. For the sake of comparison, select the GRNN smoothing factor from 0.1 to 1 and increase it by 0.1 each time to build the GRNN model. Compare the prediction error values of these ten times with the GRNN prediction error value with the range as the smoothing factor. The results are as follows Figure 6The red dot in the figure is the GRNN prediction error with the range as the smoothing factor. It can be seen that the root mean square error is lower than that of other smoothing factors used, indicating better results.
[0113] Example 2
[0114] like Figure 7 As shown, this embodiment provides a GRNN smoothing factor setting system based on a variogram model, characterized by comprising: a preprocessing module, a fitting module, a prediction module and an output module;
[0115] The preprocessing module is used to preprocess the sampled data;
[0116] The fitting module is used to obtain the omnidirectional experimental variation function of the pre-processed sampling data, and fit the omnidirectional experimental variation function to obtain the range value;
[0117] The prediction module is used to perform GRNN prediction using the range value as a smoothing factor;
[0118] The output module is used to construct a GRNN model based on the smoothing factor that meets the prediction result and the preprocessed sampling data, and predict the grade value of the unknown position through the GRNN model.
[0119] Furthermore, the pre-processing module includes: a cleaning unit, a normalization unit and a dimensionality reduction unit;
[0120] The cleaning unit is used to identify and process error values, abnormal values and missing values in the sampling data (such as drilling data, mainly including three-dimensional coordinate information and attribute information associated with ore grade);
[0121] The normalization unit is used to perform normalization processing on the cleaned sample data, that is, to transform it into the interval [0, 1] to eliminate the influence of dimension;
[0122] The dimension reduction unit is used to perform data dimension reduction processing on the normalized sampled data. When the capacity of the input sample is large, data dimension reduction processing can be performed.
[0123] Furthermore, the omnidirectional experimental variation function is calculated as:
[0124] The variogram is a fundamental tool in geostatistics for studying the spatial variability and continuity of variables. To determine the smoothing factor for a GRNN using a variogram, the first step is to plot the experimental variogram scatter plot of the sampled data. Then, a theoretical variogram model is selected to fit the experimental variogram scatter plot. The parameters of the variogram model corresponding to the optimal fit are obtained, and the range of variation is used as the smoothing factor for the GRNN.
[0125] The standardized omnidirectional experimental variation γ(h) of the sampling data is calculated using the following formula:
[0126]
[0127] Among them, γ(h) is the variation value of the omnidirectional experimental variation function, h is the distance between any two sample points, Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ), N(h) is the number of sample point data pairs with a distance of h, and Var(Y) is the variance of Y.
[0128] The experimental variation function is calculated using the above formula as follows: Figure 2 As shown in the scattered points.
[0129] Furthermore, the method for fitting the omnidirectional experimental variogram is to use a standard Gaussian variogram model to fit the experimental variogram values calculated above, that is, to minimize the gap between the theoretical curve corresponding to the model and the experimental variogram values. The calculation formula of the standard Gaussian variogram model is as follows:
[0130]
[0131] Where a is an unknown parameter to be determined, and e is the natural logarithm. The parameter a can be adjusted manually or automatically to obtain Gaussian models of different shapes, so that it can show the best matching effect with the experimental variogram scatter plot. The parameter a corresponding to this effect can be regarded as the smoothing factor σ of formula (3) or (4). is the range value.
[0132] Furthermore, performing GRNN prediction in the prediction module includes:
[0133] Under the framework of cross-validation or K-fold cross-validation, GRNN prediction is performed based on the smoothing factor obtained in the above steps, and the difference between the predicted value and the true value is calculated. If the prediction error is large, the experiment variogram is recalculated and fitted to obtain a new smoothing factor and tested again until the prediction result reaches sufficient accuracy.
[0134] Keep the smoothing factor generated in the previous step. Use this parameter and all sample data to build a GRNN model. Based on this model, you can predict the attribute values of unknown points. In the field of geostatistics, the GRNN model is used to predict the grade value of unknown locations.
[0135] The above are merely preferred embodiments 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 this 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. The GRNN smoothing factor setting method based on the variogram model is characterized by: include: Preprocessing the sampled data, wherein the sampled data includes three-dimensional coordinate information and attribute information associated with the ore grade; Obtain the omnidirectional experimental variation function of the preprocessed sampling data, and fit the omnidirectional experimental variation function to obtain the range value; the omnidirectional experimental variation function is: Among them, γ(h) is the variation value of the omnidirectional experimental variation function, h is the distance between any two sample points, Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ), N(h) is the number of sample point data pairs with a distance of h, and Var(Y) is the variance of Y; The range value is used as a smoothing factor to perform GRNN prediction; Based on the smoothing factor that satisfies the prediction result and the pre-processed sampling data, a GRNN model is constructed. In the field of geostatistical ore grade estimation, the grade value of an unknown location is predicted by the GRNN model.
2. The GRNN smoothing factor setting method based on the variogram model according to claim 1 is characterized in that: The preprocessing of the sampled data includes: Identifying and processing error values, abnormal values, and missing values in the sampled data; Normalizing the processed sampling data; Performing data dimension reduction processing on the normalized sampling data.
3. The GRNN smoothing factor setting method based on the variogram model according to claim 1, characterized in that: The method of fitting the omnidirectional experimental variogram is: using a fitting method of a standard Gaussian variogram model; The standard Gaussian variogram model is: Among them, a is the unknown parameter to be determined, and e is the natural logarithm; The range value is:
4. The GRNN smoothing factor setting method based on the variogram model according to claim 1, characterized in that: Performing GRNN predictions involves: Within the framework of a preset verification method, the GRNN prediction is performed based on the smoothing factor, and the gap between the predicted value and the true value is calculated. If the prediction error is greater than a preset threshold, the omnidirectional experimental variation function is reacquired and fitted to obtain a new range value and the GRNN prediction is performed again until the prediction result reaches the preset accuracy.
5. The GRNN smoothing factor setting system based on the variogram model is characterized by: include: Preprocessing module, fitting module, prediction module and output module; The preprocessing module is used to preprocess the sampling data, wherein the sampling data includes three-dimensional coordinate information and attribute information associated with the ore grade; The fitting module is used to obtain the omnidirectional experimental variogram of the pre-processed sampling data, and fit the omnidirectional experimental variogram to obtain the range value. The omnidirectional experimental variogram is used in geostatistical methods to study the variability and continuity of ore grade in space; the omnidirectional experimental variogram is: Among them, γ(h) is the variation value of the omnidirectional experimental variation function, h is the distance between any two sample points, Y(x i +h) and Y(x i ) respectively represent the position (x i +h) and (x i ), N(h) is the number of sample point data pairs with a distance of h, and Var(Y) is the variance of Y; The prediction module is used to perform GRNN prediction using the range value as a smoothing factor; The output module is used to construct a GRNN model based on the smoothing factor that meets the prediction result and the preprocessed sampling data, and in the field of geostatistical ore grade estimation, the grade value of an unknown location is predicted by the GRNN model.
6. The GRNN smoothing factor setting system based on the variogram model according to claim 5, characterized in that: The pre-processing module includes: a cleaning unit, a normalization unit and a dimension reduction unit; The cleaning unit is used to identify and process error values, abnormal values and missing values in the sampled data; The normalization unit is used to normalize the cleaned sampling data; The dimension reduction unit is used to perform data dimension reduction processing on the normalized sampling data.
7. The GRNN smoothing factor setting system based on the variogram model according to claim 5, characterized in that: The method of fitting the omnidirectional experimental variogram is: using a fitting method of a standard Gaussian variogram model; The standard Gaussian variogram model is: Among them, a is the unknown parameter to be determined, and e is the natural logarithm; The range value is:
8. The GRNN smoothing factor setting system based on the variogram model according to claim 5, characterized in that: The GRNN prediction in the prediction module includes: Within the framework of a preset verification method, the GRNN prediction is performed based on the smoothing factor, and the gap between the predicted value and the true value is calculated. If the prediction error is greater than a preset threshold, the omnidirectional experimental variation function is reacquired and fitted to obtain a new range value and the GRNN prediction is performed again until the prediction result reaches the preset accuracy.