A method and system for predicting the spatial distribution of heavy metal arsenic in soil

Abstract

A soil heavy metal arsenic spatial distribution prediction method and system, the method comprises the following steps: 1, collecting spatial heavy metal arsenic content data and environmental auxiliary variable data; 2, screening the environmental auxiliary variable data affecting the heavy metal arsenic content data one by one through the Pearson correlation coefficient method; 3, inputting the environmental auxiliary variable data into the double network extreme learning machine loaded with two models, and obtaining two soil heavy metal arsenic prediction content values; 4, assigning different weights to the soil heavy metal arsenic content values predicted by the two models respectively, and combining to obtain the final soil heavy metal arsenic content value prediction result; 5, according to the predicted soil heavy metal arsenic content data, spatial mapping is carried out. The present application solves the overfitting problem of the extreme learning machine network on the basis of improving the prediction accuracy of the extreme learning machine, provides more accurate information for soil investigation and environmental protection, and controls and governs the soil heavy metal arsenic.

Description

Technical Field

[0001] This invention belongs to the field of soil heavy metal prediction technology, specifically, it relates to a method and system for predicting the spatial distribution of arsenic in soil. Background Technology

[0002] The stability and safety of China's agricultural soils are being undermined by the increasing accumulation of heavy metals caused by human activities such as mining, fertilization, and pesticide application. Their migration and accumulation seriously threaten ecological security and human health. Furthermore, heavy metals in soil are characterized by long residual times, high concealment, low mobility, and difficulty in degradation. Arsenic, in particular, is a toxic and carcinogenic substance; excessive arsenic can enter the body through agricultural products, leading to a range of health problems. Excessive arsenic can also cause abnormal plant growth and disrupt the ecological balance. Therefore, investigating the spatial distribution of arsenic pollution in agricultural soils is crucial.

[0003] Current predictions of the spatial distribution of arsenic in soil mainly rely on multi-source auxiliary variables and machine learning methods to establish predictive models. The aim is to better identify the nonlinear relationship between auxiliary variables and arsenic content in soil, improve model prediction accuracy, and accurately generate spatial distribution maps of arsenic in soil, thus providing guidance for soil environmental quality assessment and arsenic pollution prevention and control. In existing literature, Shi Guang et al. used soil arsenic pollution in farmland surrounding an arsenic mine smelter as a case study. By integrating multi-source environmental data, including environmental elements, remote sensing data, and topographical elements, they used the RF model (Research-Focused Radiation Facility) machine learning method to simulate the spatial distribution of arsenic in the study area, effectively improving the accuracy of spatial distribution predictions for soil pollutants. Chinese invention patent CN202210778405.2 discloses an improved deep extreme learning machine method for predicting the spatial distribution of heavy metals in soil. By combining multi-source auxiliary variables such as topographic factors, remote sensing data, spatial location, and soil properties with an improved deep extreme learning machine prediction model, the spatial distribution of heavy metal concentration in soil is predicted. This method solves the problem of difficulty in predicting numerical values ​​due to the nonlinear relationship between heavy metal concentration and auxiliary variables, and improves the accuracy of the prediction model to a certain extent.

[0004] While the aforementioned existing technologies have improved the model's prediction accuracy to some extent, excessive environmental auxiliary variable data in machine learning models can easily lead to increased computational load and overfitting of the algorithm. Summary of the Invention

[0005] To address the technical problem that excessive environmental auxiliary variable data in extreme learning machine models can easily lead to increased system computation and overfitting, this invention proposes a method and system for predicting the spatial distribution of heavy metal arsenic in soil.

[0006] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for predicting the spatial distribution of the heavy metal arsenic in soil includes the following steps:

[0008] S1. Collect data on the content of heavy metal arsenic and environmental auxiliary variables in the space;

[0009] S2. Environmental auxiliary variable data affecting the arsenic content data were screened one by one using the Pearson correlation coefficient method.

[0010] S3. Input the environmental auxiliary variable data into a dual-network extreme learning machine equipped with two models to obtain two predicted values ​​of soil heavy metal arsenic content.

[0011] S4. Then, assign different weights to the soil heavy metal arsenic content values ​​predicted by the two models respectively, and combine them to obtain the final soil heavy metal arsenic content prediction result.

[0012] S5. Create spatial maps based on the predicted soil heavy metal arsenic content data.

[0013] Furthermore, the two models in step S3 include Model 1 and Model 2. Model 1 is introduced into a dual-network extreme learning machine using the minimum error entropy method to predict the arsenic content of heavy metals in the soil, thereby improving the prediction accuracy.

[0014] Model 2 introduces the node hiding method into a dual-network extreme learning machine to predict the arsenic content of heavy metals in soil, thus preventing overfitting.

[0015] Furthermore, the detailed steps of the Model 1 minimum error entropy method include:

[0016] S3-1-1, Given a training set k is the number of the k-th sample point, x k Let y represent the auxiliary variable value at the k-th sample point. k The objective function for the k-th sample point, representing the arsenic content of the soil heavy metal, is obtained using formula (1):

[0017]

[0018]

[0019] In the formula, N k Let c be the set of neighboring sample points of sample point k. lk Let H(·) be the weights of node k and its neighboring sample points l, and let q be the entropy function. α (x kThe density function of the auxiliary variable data at the k-th sample point is the Renyi entropy, which approximates the Shannon entropy when α→1; when α=2, we can calculate the quadratic Renyi entropy.

[0020] S3-1-2, Then, introduce a quadratic information potential using the quadratic Renyi entropy: that is, introduce a quadratic information potential through formulas (3) and (4):

[0021]

[0022]

[0023] In the formula, V2(·) is the second-order information potential, and H2(·) is the total error. The second-order Renyi entropy has a monotonically increasing log function, so minimizing the second-order Renyi entropy is equivalent to maximizing the second-order information potential, where q(·) is the density function.

[0024] S3-1-3. Combining steps S3-1-1 and S3-1-2, the objective function can be transformed into maximization using formula (5):

[0025]

[0026] S3-1-4. Determine the current iteration number n. If n reaches the maximum iteration number L and k∈K, then proceed to step S3-1-7; otherwise, proceed to step S3-1-5.

[0027] S3-1-5, When inputting a new number of sample points x k (n), the output of Model 1 is obtained through formula (6):

[0028]

[0029] Where k represents the number of the k-th sample point, c lk Let ξk be the weights of node k and its neighboring sample points l, μ be the learning step size, γ be the regularization coefficient, ξ0 be a K×1 vector, and K be the number of samples. The total error of adjacent sample point l, For environmental auxiliary variable data, Data on the content of the heavy metal arsenic in the soil;

[0030] S3-1-6. When n = n + 1 and k ∈ K, return to step S3-1-4.

[0031] S3-1-7, Output the best predicted value for soil heavy metal arsenic content.

[0032] Furthermore, the steps of the Model 2 node hiding method include:

[0033] S3-2-1 Given a training set D={(x i y i )|x i ∈R d y i ∈R k ,1≤i≤n},,x i As an auxiliary variable, y i Let represent the arsenic content of the soil heavy metal, and n be the number of samples in the dataset. The SLFN single-hidden-layer feedforward neural network with the structure (d, m, k) can be represented by formula (7):

[0034]

[0035] In the formula, f(x) i ) represents the target soil arsenic content value, β j Here, g(.) represents the output weights of a single hidden layer feedforward neural network (SLFN), g(.) is the activation function, and w... j b represents the input weights of a single hidden layer feedforward neural network (SLFN). j The hidden layer threshold is the threshold value for a single hidden layer feedforward neural network (SLFN).

[0036] S3-2-2, Input auxiliary variable data: Training set D = {(x i y i )|x i ∈R d y i ∈R k ,1≤i≤n}, Number of training iterations P; Test data x;

[0037] S3-2-3, Output soil heavy metal arsenic content data: the class label y(x) of the test data x;

[0038] S3-2-4. Initialize a relatively large SLFN single hidden layer feedforward neural network, assuming it contains m hidden layer nodes;

[0039] S3-2-5. Generate a 0-1 dimension vector with a uniform distribution, and discard the hidden layer nodes with corresponding components of 0 to obtain an SLFN. i Single-hidden-layer feedforward neural network;

[0040] S3-2-6, Then use the Extreme Learning Machine algorithm to train the SLFN obtained in step S3-2-4. i Designing a single-hidden-layer feedforward neural network, SLFN i The output of a single hidden-layer feedforward neural network is a k-dimensional 0-1 tuple (y i1 (x), y i2 (x), ..., y ik (x))T ∈{0,1} k ;

[0041] Among them, y ij (x) = 1, if SLFN i If the sample data x in a single hidden-layer feedforward neural network belongs to the j-th class, then y belongs to the j-th class. ij(x) =0.1≤j≤k

[0042] S3-2-7. Using the SLFN trained in step S3-2-5 i A single-hidden-layer feedforward neural network calculates the output of the test data x, i.e., the class label vector (y) of x. i1 (x), y i2 (x), ..., y ik (x)) T ∈{0,1} k ;

[0043] S3-2-8. Then, use formula (8) to determine the category of the test data x by majority voting:

[0044]

[0045] S3-2-9. Output the class label y(x) of the test data x, where x represents an auxiliary variable and y represents the content of arsenic in the soil.

[0046] Furthermore, the detailed steps in step S2 include:

[0047] S2-1. Import the arsenic content data into an array;

[0048] S2-2, Import the auxiliary variable data into another array;

[0049] S2-3. Substitute any selected array of heavy metal arsenic content data and environmental ancillary variable data into the Pearson correlation coefficient calculation formula, as follows:

[0050]

[0051] In the formula, X represents the arsenic content data and Y represents the environmental auxiliary variable data;

[0052] S2-4. Based on the output results, remove environmental auxiliary variable data with low relevance. Removing unnecessary environmental auxiliary variable data reduces the computational difficulty of the entire algorithm, improves the efficiency of subsequent dual-network extreme learning machines by reducing the types and amount of data required for learning.

[0053] Furthermore, the environmental ancillary variable data include:

[0054] Environmental auxiliary variables: elevation, slope, aspect, slope variability, aspect variability, topographic relief, atmospheric dustfall, and annual average precipitation data corresponding to each sampling point;

[0055] Auxiliary variables for soil properties: other heavy metal data (Hg, Cr, Cd, Pb) and ditch sediment data corresponding to each sampling point;

[0056] Artificial auxiliary variables: Arsenic content in the type of fertilizer corresponding to each sampling point, including arsenic content in commercial organic fertilizer, arsenic content in bio-organic fertilizer, arsenic content in organic-inorganic compound fertilizer, arsenic content in superphosphate, and arsenic content in compound fertilizer.

[0057] A soil heavy metal arsenic spatial distribution prediction system includes a heavy metal arsenic content data acquisition unit, an environmental auxiliary variable data acquisition unit, an environmental auxiliary variable data screening unit, a dual-network extreme learning machine, a weight allocation unit, a soil heavy metal arsenic content value prediction unit, and a soil heavy metal arsenic content data mapping unit.

[0058] The heavy metal arsenic content data acquisition unit is used to collect data on the heavy metal arsenic content in the space.

[0059] The environmental auxiliary variable data acquisition unit is used to collect environmental auxiliary variable data within the space.

[0060] The environmental auxiliary variable data screening unit uses the Pearson correlation coefficient method to screen environmental auxiliary variable data that affect the heavy metal arsenic content data one by one, and deletes excessive environmental auxiliary variable data that are not related to the heavy metal arsenic content data.

[0061] The dual-network extreme learning machine is equipped with two models, namely Model 1 and Model 2. Model 1 is introduced into the dual-network extreme learning machine through the minimum error entropy method to predict the arsenic content of soil heavy metals. Model 2 is introduced into the dual-network extreme learning machine through the node hiding method to predict the arsenic content of soil heavy metals.

[0062] The weight allocation unit reassigns different weights to the predicted values ​​of soil heavy metal arsenic content calculated by Model 1 and Model 2.

[0063] The soil heavy metal arsenic content prediction unit, based on the different weights redistributed according to the predicted soil heavy metal arsenic content values, yields the final predicted soil heavy metal arsenic content value.

[0064] The soil heavy metal arsenic content data mapping unit is used to draw a spatial distribution map of soil heavy metal arsenic content based on the predicted soil heavy metal arsenic content values.

[0065] Compared with the prior art, the present invention has the following advantages:

[0066] 1) In Model 1, the minimum error entropy method is used to replace the traditional mean square error (MSE) in the extreme learning machine, which solves the problems of unstable prediction results and difficulty in improving accuracy of the traditional prediction method based on mean square error (MSE). This improves the prediction accuracy of Model 1 to a certain extent.

[0067] 2) In Model 2, the node drop-off method is introduced into the Extreme Learning Machine, which solves the problem that too much environmental auxiliary variable data in the Extreme Learning Machine model can easily lead to an increase in the computational load of the model and overfitting of the algorithm, thus ensuring the stability and generalization ability of the model.

[0068] 3) The method proposed in this invention not only improves the accuracy of the spatial distribution prediction method of heavy metal arsenic in soil to a certain extent, but also solves the overfitting problem of extreme learning machine network, ensuring the reliability of the prediction model, providing more accurate information for soil survey and environmental protection, and having important guiding significance for the prevention and control of heavy metal arsenic in soil and agricultural planning. Attached Figure Description

[0069] Figure 1 This is a flowchart of a method for predicting the spatial distribution of arsenic, a heavy metal in soil, according to the present invention.

[0070] Figure 2 This is a structural block diagram of a soil heavy metal arsenic spatial distribution prediction system according to the present invention;

[0071] Figure 3 This is a graph showing the test set prediction results of the dual-network model in this invention;

[0072] Figure 4 This is a spatial distribution map of the heavy metal arsenic in soil in this invention. Detailed Implementation

[0073] like Figure 1 As shown, this invention provides a method for predicting the spatial distribution of heavy metal arsenic in soil, comprising the following steps: S1, collecting spatial data on heavy metal arsenic content and environmental auxiliary variables; S2, filtering environmental auxiliary variables that affect heavy metal arsenic content data one by one using the Pearson correlation coefficient method; S3, inputting the environmental auxiliary variable data into a dual-network extreme learning machine equipped with two models to obtain two predicted values ​​of heavy metal arsenic content in soil; S4, assigning different weights to the soil heavy metal arsenic content values ​​predicted by the two models respectively, and combining them to obtain the final predicted value of heavy metal arsenic content in soil; S5, performing spatial mapping based on the predicted soil heavy metal arsenic content data.

[0074] The two models in step S3 include Model 1 and Model 2. Model 1 is introduced into a dual-network extreme learning machine using the minimum error entropy method to predict the arsenic content of heavy metals in soil, thereby improving the prediction accuracy.

[0075] Model 2 introduces a node hiding method into a dual-network extreme learning machine to predict the arsenic content of heavy metals in soil, thus preventing overfitting.

[0076] The detailed steps of the Model 1 minimum error entropy method include:

[0077] S3-1-1, Given a training set k is the number of the k-th sample point, x k Let y represent the auxiliary variable value at the k-th sample point. k The objective function for the k-th sample point, representing the arsenic content of the soil heavy metal, is obtained using formula (1):

[0078]

[0079]

[0080] In the formula, N k Let c be the set of neighboring sample points of sample point k. lk Let H(·) be the weights of node k and its neighboring sample points l, and let q be the entropy function. α (x k The density function of the auxiliary variable data at the k-th sample point is the Renyi entropy, which approximates the Shannon entropy when α→1; when α=2, we can calculate the quadratic Renyi entropy.

[0081] S3-1-2, Then, introduce a quadratic information potential using the quadratic Renyi entropy: that is, introduce a quadratic information potential through formulas (3) and (4):

[0082]

[0083]

[0084] In the formula, V2(·) is the second-order information potential, and H2(·) is the total error. The second-order Renyi entropy has a monotonically increasing log function, so minimizing the second-order Renyi entropy is equivalent to maximizing the second-order information potential, where q(·) is the density function.

[0085] S3-1-3. Combining steps S3-1-1 and S3-1-2, the objective function can be transformed into maximization using formula (5):

[0086]

[0087] S3-1-4. Determine the current iteration number n. If n reaches the maximum iteration number L and k∈K, then proceed to step S3-1-7; otherwise, proceed to step S3-1-5.

[0088] S3-1-5, When inputting a new number of sample points x k (n), the output of Model 1 is obtained through formula (6):

[0089]

[0090] Where k represents the number of the k-th sample point, c lk Let ξk be the weights of node k and its neighboring sample points l, μ be the learning step size, γ be the regularization coefficient, ξ0 be a K×1 vector, and K be the number of samples. The total error of adjacent sample point l, For environmental auxiliary variable data, Data on the content of the heavy metal arsenic in the soil;

[0091] S3-1-6. When n = n + 1 and k ∈ K, return to step S3-1-4.

[0092] S3-1-7, Output the best predicted value for soil heavy metal arsenic content.

[0093] The detailed steps of the Model 2 method for predicting soil arsenic content include:

[0094] S3-2-1, Input auxiliary variable data: Training set D = {(x i y i )|x i ∈R d y i ∈R k ,1≤i≤n}, Number of training iterations P; Test data x;

[0095] S3-2-2, Output soil heavy metal arsenic data: the class label y(x) of the test data x;

[0096] S3-2-3. Initialize a relatively large SLFN single hidden layer feedforward neural network, assuming it contains m hidden layer nodes;

[0097] S3-2-4. Generate a 0-1 dimension vector with a uniform distribution, and discard the hidden layer nodes with corresponding components of 0 to obtain an SLFN. i Single-hidden-layer feedforward neural network;

[0098] S3-2-5. Then use the Extreme Learning Machine algorithm to train the SLFN obtained in step S3-2-4. i Designing a single-hidden-layer feedforward neural network, SLFNi The output of a single hidden-layer feedforward neural network is a k-dimensional 0-1 tuple (y i1 (x), y i2 (x), ..., y ik (x)) T ∈{0,1} k ;

[0099] Among them, y ij (x) = 1, if SLFN i If the sample data x in a single hidden-layer feedforward neural network belongs to the j-th class, then y belongs to the j-th class. ij(x) =0.1≤j≤k

[0100] S3-2-6. Using the SLFN trained in step S3-2-5 i A single-hidden-layer feedforward neural network calculates the output of the test data x, i.e., the class label vector (y) of x. i1 (x), y i2 (x), ..., y ik (x)) T ∈{0,1} k ;

[0101] S3-2-7 Then, using formula (8) and the majority voting method, determine the category of the test data x:

[0102]

[0103] S3-2-8. Output the class label y(x) of the test data x, where x represents an auxiliary variable and y represents the content of arsenic in the soil.

[0104] The detailed steps in step S2 include: S2-1, importing the heavy metal arsenic content data into one array; S2-2, importing the auxiliary variable data into another array; S2-3, substituting the heavy metal arsenic content data and environmental auxiliary variable data from either array into the Pearson correlation coefficient calculation formula, as follows:

[0105]

[0106] In the formula, X represents the arsenic content data and Y represents the environmental auxiliary variable data;

[0107] The results of the correlation analysis are shown in the table below (insignificant variables have been removed):

[0108]

[0109] ** indicates a significant correlation at the 0.01 level (two-tailed); * indicates a significant correlation at the 0.05 level.

[0110] S2-4. Based on the output results, remove environmental auxiliary variable data with low relevance. Removing unnecessary environmental auxiliary variable data reduces the computational difficulty of the entire algorithm, improves the efficiency of subsequent dual-network extreme learning machines by reducing the types and amount of data required for learning.

[0111] Environmental ancillary variable data include environmental factor ancillary variables, soil property ancillary variables, and anthropogenic factor ancillary variables.

[0112] In step S1, after the auxiliary variable is selected, the existing soil heavy metal arsenic data (684 data points) and the selected auxiliary variable data are combined to form a sample dataset, which is divided into a training set and a test set in a 7:3 ratio. The dataset is then input into Model 1 and Model 2 in step 3 respectively to calculate the predicted value of soil heavy metal arsenic content.

[0113] like Figure 2 As shown, a soil heavy metal arsenic spatial distribution prediction system includes a heavy metal arsenic content data acquisition unit, an environmental auxiliary variable data acquisition unit, an environmental auxiliary variable data filtering unit, a dual-network extreme learning machine, a weight allocation unit, a soil heavy metal arsenic content prediction unit, and a soil heavy metal arsenic content data mapping unit. The heavy metal arsenic content data acquisition unit is used to collect heavy metal arsenic content data within a specific space. The environmental auxiliary variable data acquisition unit is used to collect environmental auxiliary variable data within a specific space. The environmental auxiliary variable data filtering unit uses the Pearson correlation coefficient method to filter environmental auxiliary variable data that affect heavy metal arsenic content data one by one, deleting excessive data related to heavy metal arsenic content. Unrelated environmental ancillary variable data; a dual-network extreme learning machine (DLM) with two models, Model 1 and Model 2. Model 1 uses the minimum error entropy method to predict soil arsenic content, while Model 2 uses a node hiding method. A weight allocation unit reassigns different weights to the predicted soil arsenic content values ​​calculated by Model 1 and Model 2. A soil arsenic content prediction unit derives the final predicted soil arsenic content value based on the reassigned weights. The dual-network model prediction results are as follows: Figure 3 As shown in the figure. The soil heavy metal arsenic content data mapping unit is used to draw a spatial distribution map of soil heavy metal arsenic content based on the predicted soil heavy metal arsenic content values. The spatial distribution of soil heavy metal arsenic is shown in the figure. Figure 4 As shown.

[0114] The method proposed in this invention can not only improve the accuracy of soil heavy metal arsenic spatial distribution prediction methods to a certain extent, but also solve the overfitting problem of extreme learning machine networks, ensuring the reliability of the prediction model. It provides more accurate information for soil surveys and environmental protection, and has important guiding significance for the prevention and control of soil heavy metal arsenic and agricultural planning.

Claims

1. A method for predicting the spatial distribution of the heavy metal arsenic in soil, characterized in that, Including the following steps: S1. Collect data on the content of heavy metal arsenic and environmental auxiliary variables in the space; S2. Environmental auxiliary variable data affecting the arsenic content data were screened one by one using the Pearson correlation coefficient method. S3. Input the environmental auxiliary variable data into a dual-network extreme learning machine equipped with two models to obtain two predicted values ​​of soil heavy metal arsenic content. S4. Then, assign different weights to the soil heavy metal arsenic content values ​​predicted by the two models respectively, and combine them to obtain the final soil heavy metal arsenic content prediction result. S5. Spatial mapping is performed based on the predicted soil arsenic content data. The two models in step S3 include Model 1 and Model 2. Model 1 is introduced into a dual-network extreme learning machine using the minimum error entropy method to predict the arsenic content of heavy metals in the soil. Model 2 introduces the node hiding method into a dual-network extreme learning machine to predict the arsenic content of heavy metals in soil. The detailed steps of the Model 1 minimum error entropy method include: S3-1-1, Given a training set {( , ) |} , The number of the k-th sample point. This represents the value of the auxiliary variable at the k-th sample point. Let represent the arsenic content of the soil at the k-th sample point. The objective function at the k-th sample point is obtained using formula (1): In the formula, For sample points k, Let node k and its neighboring sample points be... The weights, where n is the number of iterations. neighboring sample points of k The overall error, It is the entropy function. This represents the value of the auxiliary variable at the k-th sample point. For the parameters of the entropy function, Let be the density function of the auxiliary variable data at the k-th sample point, when When α = 2, the Renyi entropy approximates the Shannon entropy; when α = 2, the quadratic Renyi entropy is calculated. S3-1-2, Then, introduce a quadratic information potential using the quadratic Renyi entropy: that is, introduce a quadratic information potential through formulas (3) and (4): In the formula, n is the number of iterations. E Indicates error. neighboring sample points of k The overall error, Total error Secondary information potential, Total error The quadratic Renyi entropy has a monotonically increasing log function, so minimizing the quadratic Renyi entropy is equivalent to maximizing the quadratic information potential. Total error Density function; S3-1-3. Combining steps S3-1-1 and S3-1-2, the objective function can be transformed into maximization using formula (5): In the formula, n is the number of iterations. Let node k and its neighboring sample points be... The weight, neighboring sample points of k The overall error, Total error Secondary information potential; S3-1-4. Determine the current iteration number n. If n reaches the maximum iteration number L and If yes, proceed to step S3-1-7; otherwise, proceed to step S3-1-5. S3-1-5, When inputting a new number of sample points x k (n), the output of Model 1 is obtained through formula (6): In the formula, k represents the number of the k-th sample point. Let node k and its neighboring sample points be... The weights are μ, the learning step size is μ, and γ is the regularization coefficient. for The vector, where K is the number of samples. For adjacent sample points The total error, where n is the number of iterations. Total error The relative gradient of the second-order information potential. For environmental auxiliary variable data, neighboring sample points of k Environmental auxiliary variable data, This represents the arsenic content data for the (n-1)th iteration of heavy metals in the soil. This represents the arsenic content data for soil heavy metals at the nth iteration. S3-1-6, When n=n+1 and Then return to step S3-1-4; S3-1-7, Output the best predicted value for soil heavy metal arsenic content. ; The detailed steps of the Model 2 node hiding method include: S3-2-1, Given a training set D = {( , ) | ∈ , ∈ ,1≤i≤n}, As an auxiliary variable, Let represent the arsenic content of the soil heavy metal, and n be the number of samples in the dataset. The SLFN single-hidden-layer feedforward neural network with the structure (d, m, k) can be represented by formula (7): In the formula, The target soil heavy metal arsenic content value, These are the output weights of a single hidden layer feedforward neural network (SLFN). For activation function, These are the input weights for a single hidden layer feedforward neural network (SLFN). The hidden layer threshold is the threshold value for a single-hidden-layer feedforward neural network (SLFN). S3-2-2, Input auxiliary variable data: Training set D = {( , ) | ∈ , ∈ , 1≤i≤n}, For the auxiliary variable data at the i-th sample point, Let x be the soil arsenic content data at the i-th sample point, and let P be the number of training iterations; x be the test data. S3-2-3, Output soil heavy metal arsenic content data: the class label y(x) of the test data x; S3-2-4. Initialize a single hidden layer feedforward neural network (SLFN), assuming it contains m hidden layer nodes; S3-2-5. Generate a 0-1 dimension vector with a uniform distribution, and discard the hidden layer nodes with corresponding components of 0 to obtain an SLFN. i Single-hidden-layer feedforward neural network; S3-2-6, Then use the Extreme Learning Machine algorithm to train the SLFN obtained in step S3-2-4. i Designing a single-hidden-layer feedforward neural network, SLFN i The output of a single hidden-layer feedforward neural network is a k-dimensional 0-1 tuple ( , , ..., ) T ∈{0,1} k ; in, If SLFN i If the sample data x in a single hidden-layer feedforward neural network belongs to class j, then... ; S3-2-7. Using the SLFN trained in step S3-2-5 i A single-hidden-layer feedforward neural network calculates the output of the test data x, i.e., the class label vector of x. , , ..., ) T ∈{0,1} k ; S3-2-8, Then use formula (8) majority voting method to determine the output of test data x: In the formula, x is the auxiliary variable data. Let represent the output soil heavy metal arsenic data, where i represents the i-th sample point, k represents the number of soil heavy metal arsenic samples, and P represents the number of training iterations. The output data for soil heavy metal arsenic for data x in the j-th class; S3-2-9. Output the class label y(x) of the test data x, where x represents an auxiliary variable and y represents the content of arsenic in the soil.

2. The method according to claim 1, characterized in that, The detailed steps in step S2 include: S2-1. Import the arsenic content data into an array; S2-2, Import the auxiliary variable data into another array; S2-3. Substitute any selected array of heavy metal arsenic content data and environmental ancillary variable data into the Pearson correlation coefficient calculation formula, as follows: In the formula, N is the sample size, X represents auxiliary variable data, and Y represents soil heavy metal arsenic content data. For the covariance of auxiliary variable data, The covariance of soil heavy metal arsenic content data. The standard deviation of the auxiliary variable data. The standard deviation of soil arsenic content data. The average value of the auxiliary variable data. Let represent the average value of the soil heavy metal arsenic content data, and let i be the i-th sample point. For the auxiliary variable data at the i-th sample point, This represents the soil arsenic content data at the i-th sample point; S2-4. Based on the output results, delete environmental auxiliary variable data with low relevance.

3. The method according to claim 1 or 2, characterized in that, Environmental ancillary variable data include environmental factor ancillary variables, soil property ancillary variables, and anthropogenic factor ancillary variables.

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