CN115081335B - Soil heavy metal spatial distribution prediction method for improved deep extreme learning machine - Google Patents

Abstract

A method for predicting the spatial distribution of heavy metals in soil by improving a deep extreme learning machine includes the following steps: step 1: determining the survey grid in the study area; step 2: collecting soil samples in the study area; step 3: measuring the heavy metal concentration of the collected soil samples; step 4: determining the required multi-source auxiliary variables; step 5: screening the multi-source auxiliary variables; step 6: constructing a deep extreme learning machine based on the soil heavy metal concentration data and the auxiliary variable data; step 7: optimizing the constructed deep extreme learning machine with a tuna school optimization algorithm; step 8: obtaining a spatial distribution map of heavy metals in soil. The purpose of the present invention is to provide a method for predicting the spatial concentration of heavy metals in soil by using a deep extreme learning machine DELM, so as to improve the accuracy of spatial prediction of the concentration of heavy metals in soil, and thus prepare for better prevention and control of soil heavy metal pollution.

Description

A method for predicting spatial distribution of soil heavy metals based on improved deep extreme learning machine

Technical Field

The invention belongs to the technical field of soil heavy metal prediction, and in particular relates to a method for predicting the spatial distribution of soil heavy metals.

Background technique

In the study of heavy metals in soil, for a long time, the information on heavy metal pollution in soil obtained by relying on only a small number of sampling points was very limited, which could not meet the spatial distribution characteristics, pollution degree and pollution risk of heavy metal pollution in soil at the regional scale. With the rapid development of geographic information system technology and high-precision remote sensing images, GIS technology provides technical support for the spatial visualization of soil heavy metal concentrations, so that the description of soil heavy metal pollution status no longer relies solely on simple statistical numerical indicators, and digital mapping can more intuitively reflect the pollution status in regional space. Related studies have shown that the source and diffusion of heavy metals in farmland soil are affected by a combination of multiple environmental factors. The prediction accuracy of the prediction model can be improved by using a certain relationship between certain environmental variables and soil heavy metals.

At present, the main research uses the linear relationship between environmental variables and target soil heavy metals. However, there are more complex nonlinear relationships between soil heavy metals and environmental variables. How to measure this nonlinear relationship and use this nonlinear relationship to improve the prediction accuracy of soil heavy metals is a current problem. Heavy metal elements are important attributes of soil. In order to obtain accurate soil heavy metal concentration data, it is usually necessary to randomly layout and sample the study area. Then, according to the soil heavy metal data of known sample points and the complex relationship between the data, select an appropriate spatial prediction model to predict the spatial distribution of soil heavy metals at unknown sample points. The main prediction algorithms currently include geostatistical interpolation, linear regression, and neural networks. Among them, geostatistical interpolation only considers spatial autocorrelation and ignores other influencing factors, while linear regression assumes that the relationship between soil heavy metal concentration and auxiliary variables is linear. In practical applications, the relationship between soil heavy metal concentration and auxiliary variables is nonlinear. Therefore, it is necessary to establish a nonlinear machine learning model to predict the spatial distribution of soil heavy metals.

Summary of the invention

The purpose of the present invention is to provide a method for spatially predicting soil heavy metal concentrations using a deep extreme learning machine (DELM) to improve the accuracy of spatial prediction of soil heavy metal concentrations, thereby preparing for better prevention and control of soil heavy metal pollution.

A method for predicting the spatial distribution of heavy metals in soil using an improved deep extreme learning machine comprises the following steps:

Step 1: Determine the survey grid within the study area;

Step 2: Collect soil samples in the study area;

Step 3: Determine the heavy metal concentration of the collected soil samples;

Step 4: Determine the required multi-source auxiliary variables;

Step 5: Screening of multi-source auxiliary variables;

Step 6: Construct a deep extreme learning machine DELM based on the soil heavy metal concentration data and auxiliary variable data, use the auxiliary variable data in the training set as the input of the deep extreme learning machine DELM, and use the soil heavy metal concentration data in the training set as the output of the deep extreme learning machine DELM;

Step 7: Optimize the constructed deep extreme learning machine DELM using the tuna swarm optimization algorithm;

Step 8: Obtain the spatial distribution map of soil heavy metals.

In step 3, the heavy metals include one or more of Pb, Cd, As, Cr, and Hg.

In step 4, the multi-source auxiliary variables include terrain factor auxiliary variables, remote sensing data auxiliary variables, spatial position auxiliary variables, and soil property auxiliary variables;

In step 5, multi-source auxiliary variable factors are screened to detect the explanatory power of each influencing factor on soil heavy metal elements.

In step 6, the expression of the deep extreme learning machine DELM is:

x _l =β·g(w, b, x _l-1 )

The hidden layer output weights are:

Among them, _xl-1 is the output of the l-1th hidden layer soil heavy metal concentration data, _xl is the output of the lth hidden layer soil heavy metal concentration data, β is the output weight, w is the input weight, b is the hidden layer bias value, g(·) is the activation function, H is the hidden layer output feature, C is the regularization coefficient, I is the unit matrix, and X is the input auxiliary variable data.

In step 7, the input weight w and hidden layer bias value b of the deep extreme learning machine DELM are selected by the tuna school optimization algorithm to obtain an improved deep extreme learning machine DELM soil heavy metal spatial prediction model; specifically, the following steps are included:

(1) Randomly initialize the positions of the tuna population _Xi,j , (i = 1, 2, ..., D, j = 1, 2, ..., M) as the initial population NP, where M represents the number of tunas and D represents the dimension of the input auxiliary variable;

(2) Constructing the reverse population OP of the initial population NP according to the reverse learning strategy method; then merging the population NP and the population OP;

(3) Calculate the root mean square error of the DELM network training by formula (1), and use it as the fitness function to select M individuals with high fitness values as the initial population;

Among them, _{yi is} the predicted value of soil heavy metal concentration trained by deep extreme learning machine DELM, _ti is the actual value of soil heavy metal concentration, and N is the number of training samples.

(4) Randomly initialize relevant parameters in the search space: the population initialized by the reverse learning strategy, the maximum number of iterations t _max , the current number of iterations, the upper bound ub and the lower bound lb of the search space;

in, is the initial position of the ith individual, ub and lb are the upper and lower bounds of the search space, NP is the number of tuna populations, and rand is a uniformly distributed random vector in [0,1];

(5) Assign free parameters a and z;

(6) According to step 6, a deep extreme learning machine DELM is constructed based on the soil heavy metal concentration data and the auxiliary variable data, the auxiliary variable data in the training set is used as the input of the deep extreme learning machine DELM, and the soil heavy metal concentration data in the training set is used as the output of the deep extreme learning machine DELM;

(7) Calculate the root mean square error between the predicted value of soil heavy metal concentration trained by the deep extreme learning machine DELM and the actual value of soil heavy metal concentration of the training sample by formula (1), and use it as the fitness value of the tuna group;

(8) Determine whether the current number of iterations t reaches the maximum number of iterations; if so, execute step (10); otherwise, execute step (9);

(9) Calculate the current best individual position update: If rand < z, return to step (1) to reinitialize, otherwise use the two foraging strategies of the tuna school to cooperatively hunt. If rand < 0.5, use the tuna spiral foraging strategy to update the current best individual position.

in, is the i-th individual in the t+1-th iteration, Is the best individual at the moment, is a randomly generated reference point in the search space, _α1 is the weight coefficient that controls the tendency of the individual to move toward the best individual, _α2 is the weight coefficient that controls the tendency of the individual to move toward the previous individual, a is a constant that determines the degree to which the tuna follows the best individual and the previous individual in the initial stage, β is the degree to which the tuna follows the best individual and the previous individual in the initial stage, t represents the current number of iterations, _tmax represents the maximum number of iterations, and b is a random number uniformly distributed between 0 and 1.

Otherwise, select the tuna parabolic foraging strategy to update the current best individual position, the current iteration number t = t + 1, and then update the fitness value of the tuna group according to formula (1), and compare it with the current best individual. If it is better than the current best individual, update it, otherwise execute step (8);

Among them, TF is a random number with a value of 1 or -1, and p is the parabola control coefficient.

(10) The best individual X _best and the best fitness value F(X _best ) are returned, from which the input layer weights w and hidden layer biases b required by the DELM network are extracted.

(11) In the process of selecting the input layer weight w and the hidden layer bias b by the improved tuna school algorithm, the model will also complete the training, build the improved tuna school optimized deep extreme learning machine DELM prediction model, and then input the test data into the improved tuna school optimized deep extreme learning machine DELM prediction model to finally complete the prediction and output the predicted soil heavy metal concentration value.

In step 8, the estimated predicted values of soil heavy metal concentrations were saved in a notepad format, imported into ArcGIS 10.8, and then converted into raster data to draw a spatial prediction map of soil heavy metal concentrations.

Compared with the prior art, the present invention has the following beneficial effects:

1) The present invention mainly uses multi-source auxiliary variables and a machine learning method, deep extreme learning machine DELM, to construct a soil heavy metal spatial distribution prediction model. Traditional soil heavy metal spatial prediction methods only consider the linear relationship between multi-source auxiliary variables and soil heavy metals, ignoring the nonlinear relationship between them. Therefore, we use a nonlinear machine learning method, deep extreme learning machine DELM, to automatically capture the nonlinear relationship between multi-source auxiliary variables and soil heavy metals through learning to improve the accuracy of model prediction;

2) The input weights and hidden layer bias values in the traditional deep extreme learning machine DELM are randomly generated, which will lead to unstable algorithm effects. The tuna school algorithm is used to optimize the input weights and hidden layer bias values of the deep extreme learning machine DELM to enhance the algorithm reliability and model prediction accuracy;

3) The tuna swarm algorithm adopts a pure random strategy in its population initialization stage, which will affect the population convergence speed to a certain extent and cause the tuna swarm algorithm to be unstable. The reverse learning strategy is used to improve the initial population individuals of the tuna swarm algorithm and improve the stability of the tuna swarm algorithm. An improved tuna swarm algorithm is used to optimize the accuracy of the soil heavy metal spatial prediction model of the deep extreme learning machine DELM to improve the accuracy of the soil heavy metal spatial prediction, which has practical significance and guiding value in the prediction, prevention and control of soil heavy metal pollution.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

Fig. 1 is a flow chart of the present invention;

Figure 2 shows the optimization process of the improved tuna school algorithm.

Detailed ways

As shown in FIG1 , a spatial prediction method for soil heavy metal concentration using an improved deep extreme learning machine includes the following steps:

Step 1: Determine the survey grid within the study area according to relevant regulations;

Step 2: Collect soil samples in the study area, including the following steps:

1) Select typical farmland soil environment for regional division, randomly distribute points, and determine sampling points;

2) During the collection process, the surface soil within a depth of 20 cm was taken as the soil sample;

3) After removing impurities from the collected soil samples, the samples were air-dried, ground and screened through a 100-mesh nylon sieve.

In order to accurately obtain auxiliary variable information of soil, we can choose to collect samples in a relatively dry season, because the sampled soil is exposed at this time, which can make the auxiliary variable hyperspectral remote sensing information more accurate.

Step 3: Determine the heavy metal concentration of the collected soil samples by digesting them with HNO3-HCl-H2O2 and using an atomic absorption spectrometer to determine the concentrations of heavy metals Pb, Cd, As, Cr and Hg in the digestion solution.

Step 4: Determine the required multi-source auxiliary variables, which include the following aspects:

1) Terrain factor auxiliary variables include _n1 auxiliary variables, where _n1 represents the number of terrain factor auxiliary variables; 2) Remote sensing data auxiliary variables include _n2 auxiliary variables, where _n2 represents the number of remote sensing data auxiliary variables; 3) Spatial position auxiliary variables include _n3 auxiliary variables, where _n3 represents the number of spatial position auxiliary variables; 4) Soil property auxiliary variables include _n4 auxiliary variables, where _n4 represents the number of soil property auxiliary variables.

Step 5: Use geographic detectors to screen multi-source auxiliary variable factors, and use factor detectors to detect the explanatory power of each influencing factor on soil heavy metal elements. A total of _np auxiliary variables are screened out, where _np represents the number of auxiliary variables after screening.

Step 6: Construct a deep extreme learning machine DELM based on the soil heavy metal concentration data and auxiliary variable data, use the auxiliary variable data in the training set as the input of the deep extreme learning machine DELM, and use the soil heavy metal concentration data in the training set as the output of the deep extreme learning machine DELM, which specifically includes the following steps:

6-1: Establish a deep extreme learning machine DELM model, and set the number of input layer nodes of the deep extreme learning machine DELM model to the number of auxiliary variables _np after screening;

6-2: Set the number of hidden layers in the deep extreme learning machine DELM to 2, set the number of nodes in the first hidden layer to 15, and the number of nodes in the second hidden layer to 10; each hidden layer is an extreme learning machine-autoencoder (ELM-AE), where the output of the first hidden layer is the input of the second hidden layer, and the ELM-AE model formula in the DELM network is as follows:

x _l =β·g(w, b, x _l-1 )

The hidden layer output weights are:

Among them, x _l-1 is the output of the l-1th hidden layer soil heavy metal concentration data, x _l is the output of the lth hidden layer soil heavy metal concentration data, β is the output weight, w is the input weight, b is the hidden layer bias value, g(·) is the activation function, H is the hidden layer output feature, C is the regularization coefficient, I is the unit matrix, and X is the input auxiliary variable data.

6-3: Set the number of output layer nodes of the DELM neural network model to 1;

Step 7: Since the input weights w and hidden layer bias values b in the deep extreme learning machine DELM are randomly generated, they are easy to affect the prediction accuracy of the model. An improved tuna school algorithm is proposed to optimize the deep extreme learning machine DELM soil heavy metal spatial prediction model. The input weights w and hidden layer bias values b of the deep extreme learning machine DELM model are selected by the improved tuna school optimization algorithm to obtain a deep extreme learning machine neural network soil heavy metal spatial prediction model based on the improved tuna school algorithm optimization. The improved tuna school algorithm introduces the reverse learning strategy into the population initialization process of the tuna school algorithm. An improved tuna school algorithm optimizes the deep extreme learning machine DELM soil heavy metal spatial prediction model specifically includes the following steps:

(1) Randomly initialize the positions of the tuna population x _i,j , (i=1, 2, ..., D, j=1, 2, ..., M) as the initial population NP, where M represents the number of tunas and D represents the dimension of the input auxiliary variables;

(2) Constructing the reverse population OP of the initial population NP according to the reverse learning strategy method; then merging the population NP and the population OP;

(3) Calculate the root mean square error of the deep extreme learning machine DELM training by formula (1), and select M individuals with high fitness values as the initial population as the fitness function;

Among them, _{yi is} the predicted value of soil heavy metal concentration trained by deep extreme learning machine DELM, _ti is the actual value of soil heavy metal concentration, and N is the number of training samples.

(4) Randomly initialize relevant parameters in the search space: the population initialized by the reverse learning strategy, the maximum number of iterations t _max = 50, the current number of iterations t = 1, the upper bound ub and the lower bound lb of the search space;

in, is the initial position of the ith individual, ub and lb are the upper and lower bounds of the search space, NP is the number of tuna populations, and rand is a uniformly distributed random vector in [0,1];

(5) Assign free parameters a and z, a = 0.7, z = 0.05;

(6) According to step 6, a deep extreme learning machine DELM is constructed based on the soil heavy metal concentration data and the auxiliary variable data, the auxiliary variable data in the training set is used as the input of the deep extreme learning machine DELM, and the soil heavy metal concentration data in the training set is used as the output of the deep extreme learning machine DELM;

(7) Calculate the root mean square error between the predicted value of soil heavy metal concentration trained by the deep extreme learning machine DELM and the actual value of soil heavy metal concentration of the training sample by formula (1), and use it as the fitness value of the tuna group;

(8) Determine whether the current number of iterations t reaches the maximum number of iterations; if so, execute step (10); otherwise, execute step (9);

(9) Calculate the current best individual position update: If rand < z, return to step (1) to reinitialize, otherwise use the two foraging strategies of the tuna school to cooperatively hunt. If rand < 0.5, use the tuna spiral foraging strategy to update the current best individual position.

in, is the i-th individual in the t+1-th iteration, Is the best individual at the moment, is a randomly generated reference point in the search space, _α1 is the weight coefficient that controls the tendency of the individual to move toward the best individual, _α2 is the weight coefficient that controls the tendency of the individual to move toward the previous individual, a is a constant that determines the degree to which the tuna follows the best individual and the previous individual in the initial stage, β is the degree to which the tuna follows the best individual and the previous individual in the initial stage, t represents the current number of iterations, _tmax represents the maximum number of iterations, and b is a random number uniformly distributed between 0 and 1.

Otherwise, select the tuna parabolic foraging strategy to update the current best individual position, the current iteration number t = t + 1, and then update the fitness value of the tuna group according to formula (1), and compare it with the current best individual. If it is better than the current best individual, update it, otherwise execute step (8);

Among them, TF is a random number with a value of 1 or -1, and p is the parabola control coefficient.

(10) The best individual X _best and the best fitness value F(X _best ) are returned, from which the input layer weights w and hidden layer biases b required by the DELM network are extracted.

(11) In the process of selecting the input layer weight w and the hidden layer bias b by the improved tuna school algorithm, the model will also complete the training, build the improved tuna school optimized deep extreme learning machine DELM prediction model, and then input the test data into the improved tuna school optimized deep extreme learning machine DELM prediction model to finally complete the prediction and output the predicted soil heavy metal concentration value.

Step 8: Draw a prediction map of the spatial distribution of soil heavy metals, save the estimated predicted values of soil heavy metal concentrations in Notepad format, import them into ArcGIS 10.8, and then convert them into raster data to draw a prediction map of soil heavy metal concentrations.

An improved tuna school algorithm, characterized in that it comprises the following steps:

(1) Randomly initialize the positions of the tuna population _Xi,j , (i = 1, 2, ..., D, j = 1, 2, ..., M) as the initial population P, where M represents the number of tunas and D represents the dimension of the input auxiliary variables;

(2) Constructing the reverse population OP of the initial population NP according to the reverse learning strategy method; then merging the population NP and the population OP;

(3) The root mean square error between the predicted value of soil heavy metal concentration trained by the deep extreme learning machine DELM and the actual value of soil heavy metal concentration of the training sample is calculated by formula (1) as the fitness value of the tuna group, and M individuals with high fitness values are selected as the initial population as the fitness function;

Compared with the existing tuna school algorithm, the present invention adopts a reverse learning strategy to improve the initial population individuals of the tuna school algorithm; after the improvement, the population convergence speed of the tuna school algorithm is improved to a certain extent, the stability of the tuna school algorithm is ensured, and the performance is better.

The purpose of the present invention is to address the problem that the input weights and hidden layer bias values in the deep extreme learning machine DELM are randomly generated, which affects the accuracy of the spatial prediction model of soil heavy metal concentration. In order to use a more accurate model to obtain the spatial prediction distribution of soil heavy metals, an improved tuna school optimization algorithm is proposed to optimize the two parameters of input weights and hidden layer bias values in the deep extreme learning machine DELM, so that the parameters have universal applicability. The method mainly improves the initial value of the tuna school population through a reverse learning strategy method, and then uses the improved tuna school method to optimize the input weights and hidden layer bias values in the deep extreme learning machine DELM. Through this improvement, the accuracy of the spatial prediction model of soil heavy metal concentration is improved, which helps us accurately grasp the problem of soil heavy metal pollution prevention and control.

Claims (3)

1. The soil heavy metal spatial distribution prediction method for the improved deep extreme learning machine is characterized by comprising the following steps of:

step 1: determining a survey grid within the study area;

Step 2: collecting a soil sample in a research area;

step 3: measuring the concentration of heavy metals in the collected soil sample;

step 4: determining a required multisource auxiliary variable;

Step 5: screening the multisource auxiliary variables;

Step 6: constructing a deep extreme learning machine DELM based on the soil heavy metal concentration data and the auxiliary variable data, taking the auxiliary variable data in the training set as input of the deep extreme learning machine DELM, and taking the soil heavy metal concentration data in the training set as output of the deep extreme learning machine DELM;

step 7: optimizing the constructed deep extreme learning machine DELM by using a tuna group optimization algorithm;

Step 8: obtaining a soil heavy metal space distribution map;

in step 4, the multisource auxiliary variables comprise a topography factor auxiliary variable, a remote sensing data auxiliary variable, a space position auxiliary variable and a soil attribute auxiliary variable;

In step 5, screening multisource auxiliary variable factors, and detecting the interpretation power of each influence factor on soil heavy metal elements;

in step 6, the expression of the deep extreme learning machine DELM is:

x_l＝β·g(ω,b,x_l-1)

the hidden layer output weight is:

Wherein X _l-1 is the output of the heavy metal concentration data of the first-1 hidden layer soil, X _l is the output of the heavy metal concentration data of the first hidden layer soil, beta is the output weight, w is the input weight, b is the bias value of the hidden layer, g (-) is the activation function, H is the output characteristic of the hidden layer, C is the regularization coefficient, I is the identity matrix, and X is the input auxiliary variable data;

In step 7, selecting an input weight w and a hidden layer bias value b of a depth extreme learning machine DELM through a tuna group optimization algorithm to obtain an improved soil heavy metal spatial prediction model; the method specifically comprises the following steps:

(1) Randomly initializing relevant parameters in a search space: the population initialized by the reverse learning strategy, the maximum iteration number t _max, the current iteration number t, the upper bound ub and the lower bound lb of the search space;

Wherein, Is the initial position of the ith individual, ub and lb are the upper and lower bounds of the search space, NP is the number of tuna populations, and rand is a random vector within 0,1 distributed uniformly;

(2) Assigning free parameters a and z;

(3) According to step 6, a deep extreme learning machine DELM is constructed based on the soil heavy metal concentration data and the auxiliary variable data, the auxiliary variable data in the training set is input as the deep extreme learning machine DELM, and the soil heavy metal concentration data in the training set is output as the deep extreme learning machine DELM;

(4) Calculating root mean square error of a soil heavy metal concentration predicted value trained by the deep extreme learning machine DELM and a training sample soil heavy metal concentration actual value through a formula (1), and taking the root mean square error as a tuna group fitness value fitness;

Wherein y _i is a predicted value of the concentration of the heavy metal in the soil trained by the deep extreme learning machine DELM, t _i is an actual value of the concentration of the heavy metal in the soil, and N is the number of training samples;

(5) Judging whether the current iteration number t reaches the maximum iteration number or not; if yes, executing the step (7), otherwise executing the step (6);

(6) Calculating a current best individual location update: if rand < z, returning to the step (1) for reinitialization, otherwise, carrying out cooperative hunting through two foraging strategies of the tuna group; if rand <0.5, the current optimal individual position is updated by using the tuna spiral foraging strategy,

β＝e^bl·cos2πb

Wherein,Is the ith individual of the t +1 th iteration,Is the best individual to be used at present,Is a randomly generated reference point in the search space, alpha ₁ is a weight coefficient for controlling the movement trend of an individual to an optimal individual, alpha ₂ is a weight coefficient for controlling the movement trend of an individual to a previous individual, a is a constant for determining the degree to which tuna follows the optimal individual and the previous individual in the initial stage, t represents the current iteration number, t _max represents the maximum iteration number, and b is a random number uniformly distributed between 0 and 1;

Otherwise, selecting a tuna parabolic foraging strategy to update the current optimal individual position, updating the fitness value of the tuna group according to a formula (1) according to the current iteration times t=t+1, comparing with the current optimal individual, if the fitness value is superior to the current optimal individual, updating, otherwise, executing the step (5);

Wherein T F is a random number with a value of 1 or-1;

(7) Returning the optimal individual X _best and the optimal adaptation value F (X _best), and extracting the input layer weight w and the hidden layer bias b required by the DELM network from the optimal individual X _best and the optimal adaptation value F;

(8) Training is completed by the model in the process of selecting the input layer weight w and the hidden layer bias b by the improved tuna group algorithm, an improved tuna group optimization deep extreme learning machine DELM prediction model is constructed, then test data are input into the improved tuna group optimization deep extreme learning machine DELM prediction model to finally complete prediction, and a predicted soil heavy metal concentration value is output.

2. The method of claim 1, wherein in step 3, the heavy metal comprises one or more of Pb, cd, as, cr, hg.

3. The method according to claim 1, wherein in step 8, the estimated soil heavy metal concentration predicted value is stored as a notepad format and imported into arcgis10.8 and then converted into raster data to draw a soil heavy metal concentration spatial prediction map.