A remote sensing inversion method for soil organic matter based on stacking model

Abstract

The invention discloses a soil organic matter remote sensing inversion method based on a stacking model, comprising the following steps: step 1: data acquisition and preprocessing; step 2: spectral feature variable optimization; step 3: soil organic matter inversion model construction; step 4: model combination optimization based on a genetic algorithm; step 5: soil organic matter remote sensing inversion based on the stacking model of the optimal model combination. The invention introduces spectral features and terrain features as covariates for soil organic matter remote sensing inversion, integrates multiple machine learning models through stacking, adopts a genetic algorithm to optimize the basic learner combination of the stacking integrated learning model, and constructs a soil organic matter remote sensing inversion model based on the stacking model of the optimal model combination, so as to solve the problems that a single machine learning model is prone to overfitting and has weak generalization ability, and not only enhances the generalization ability of the model, but also improves the inversion accuracy of soil organic matter.

Description

Technical Field

[0001] The invention relates to a soil organic matter remote sensing inversion method based on a stacking model, and belongs to the technical field of big data and quantitative remote sensing. Background Art

[0002] Soil organic matter (SOM) is an important component of soil, an important indicator for evaluating soil quality, and the basis for maintaining stable and increasing crop yields. The composition of soil organic matter is complex, and its spectral characteristics vary greatly, but overall, it shows a trend of increasing soil organic matter content and gradually decreasing reflectance spectrum, which also provides a theoretical basis for using remote sensing technology to invert soil organic matter content. Satellite remote sensing has become the main means of remote sensing inversion of soil organic matter.

[0003] Scholars at home and abroad have developed a variety of soil organic matter remote sensing inversion models, mainly including linear regression models and nonlinear regression models. Linear regression models mainly include multivariate linear regression, partial least squares regression, quadratic polynomial stepwise regression, principal component regression, etc. The advantages of linear regression models are simple and easy to understand, high computational efficiency, and strong interpretability. However, linear regression models are not good at fitting nonlinear relationships, and are sensitive to outliers and feature correlations, resulting in poor model stability. Nonlinear regression models mainly include machine learning models such as support vector machines, random forests, extreme gradient boosting trees, and neural networks. Machine learning models have the advantages of high efficiency, accuracy, and strong adaptability, and can effectively characterize the complex relationship between soil characteristics and environmental variables. However, the performance of machine learning models depends largely on the amount and quality of available data, and their prediction results are easily affected by training data. Each machine learning model has its own advantages, but a single model has the problem of easy overfitting and weak generalization ability.

[0004] Therefore, the existing technology has limitations and needs to be improved. Summary of the invention

[0005] The purpose of the present invention is to provide a soil organic matter remote sensing inversion method based on a stacking model to improve the accuracy of soil organic matter remote sensing inversion in view of the deficiencies in the prior art.

[0006] The technical solution of the present invention is as follows:

[0007] A soil organic matter remote sensing inversion method based on a stacking model comprises the following steps:

[0008] Step 1: Data acquisition and preprocessing

[0009] Acquire Sentinel-2 Level-1C (L1C) satellite remote sensing data; use Sentinel data processing software SNAP and Sen2Cor to process Sentinel-2 L1C data;

[0010] Step 2: Optimization of spectral feature variables

[0011] Four index forms, namely normalized difference index NDI, ratio index RI, generalized difference index GDVI and product index PI, were selected to construct the spectral index;

[0012] Using the data of 11 bands of Sentinel-2A, 220 spectral indices were constructed, and a spectral feature set containing 236 characteristic variables was constructed;

[0013] The maximum information coefficient (MIC) method was used to measure the correlation between each characteristic variable and soil organic matter, and to evaluate the impact of different characteristic variables on soil organic matter inversion.

[0014] The recursive feature elimination (RFE) algorithm is used to further select spectral feature variables; the spectral feature variables that are sensitive to soil organic matter are identified by iteratively training the model and gradually eliminating the feature variables that have the least impact on model performance; the spectral feature variables that are sensitive to soil organic matter are determined by the RFE algorithm;

[0015] Step 3: Construction of soil organic matter inversion model

[0016] The stacking model is used to integrate multiple machine learning models to construct a soil organic matter inversion model; the stacking model structure is divided into two layers, one layer is called the basic learner, and the other layer is called the meta-learner; nine models, including partial least squares regression model (PLSR), random forest model (RF), support vector machine model (SVM), multi-layer perceptron model (MLP), extreme random tree model (Extra-Trees), gradient boosting tree model (GBR), adaptive boosting model (Adaboost), bagging model (Bagging) and extreme gradient boosting model (XGBoost), are selected as the basic learners of the stacking model;

[0017] The selected spectral characteristic variables are used as input data for soil organic matter inversion modeling;

[0018] Step 4: Model combination optimization based on genetic algorithm

[0019] Using genetic algorithm to optimize the combination of base learners in the stacking model;

[0020] Step 5: Remote sensing inversion of soil organic matter based on the stacking model of the optimal model combination

[0021] Taking 30 characteristic variables including spectral characteristics and terrain characteristics as covariates, the stacking model of the optimal model combination was applied to Sentinel-2 image inversion of soil organic matter, and the spatial distribution map of Sentinel-2 soil organic matter was obtained.

[0022] The method, the specific method of step 1 is: obtain Sentinel-2Level-1C satellite remote sensing data from the European Space Agency Copernicus Open Access Center; the multispectral imager MSI carried by the Sentinel-2 satellite includes 13 spectral bands, and the spatial resolutions are 10m, 20m and 60m respectively;

[0023] Sentinel-2L1C data were processed using Sentinel data processing software SNAP and Sen2Cor, including sub-pixel precision geometric and radiometric corrections and atmospheric corrections to obtain more accurate Level 2A (L2A) data; the band data with a spatial resolution of 20m and 60m were resampled to 10m to ensure the consistency of spatial resolution of all band data; the quality_scene_classification quality flag was used to mask clouds and shadows; the Sentinel-2 remote sensing images were mosaicked and cropped to obtain clear, high-quality images of the study area;

[0024] In the Sentinel-2L1C data set, bands B1 and B10 were excluded from subsequent analysis; subsequent analysis focused on the 11 bands included in the L2A data, which cover the spectral range from 490 nm to 2190 nm.

[0025] The method described, the specific method of step 2 is: select four index forms of normalized index NDI, ratio index RI, generalized index GDVI and product index PI to construct the spectral index:

[0026]

[0027] PI=R i ×R j (4)

[0028] In the formula, R i and R j represent any two bands in the Sentinel-2A data, and R i Not equal to R j ;

[0029] 220 spectral indices were constructed using the data of 11 bands of Sentinel-2A. On this basis, a spectral feature set containing 236 characteristic variables was constructed by combining the data of 11 spectral bands of Sentinel-2A and five terrain characteristic parameters: elevation, slope, aspect, slope change rate and aspect change rate.

[0030] The maximum information coefficient (MIC) method was used to measure the correlation between each characteristic variable and soil organic matter, which was used to evaluate the impact of different characteristic variables on soil organic matter inversion; each characteristic variable and soil organic matter were ranked and transformed, and the Spearman rank correlation coefficient of the transformed data was calculated; for each characteristic, all possible permutations were generated; for each permutation, the Spearman rank correlation coefficient was recalculated; MIC was the maximum value of the coefficient in all permutations; the MIC value ranged from 0 to 1; the above steps were repeated for all characteristics to evaluate the correlation between each characteristic variable and soil organic matter;

[0031] The recursive feature elimination (RFE) algorithm is used to further select spectral feature variables. The spectral feature variables that are sensitive to soil organic matter are identified by iteratively training the model and gradually eliminating the feature variables that have the least impact on model performance. The spectral feature variables that are sensitive to soil organic matter are determined through the RFE algorithm.

[0032] The method described, step 2 finally selects 30 characteristic variables: 2 bands B2 and B4, 6 generalized indexes GDI, 4 product indexes PI, 6 normalized indexes NDI, 8 ratio indexes RI, and 4 terrain related parameters: elevation, slope, slope change rate and slope aspect change rate.

[0033] The method described, the method of step 3 is:

[0034] The 30 selected spectral feature variables are used as input data for soil organic matter inversion modeling; first, the original training data set is divided into 5 subsets to ensure that each data subset does not overlap; during the operation, one data subset is selected as the prediction set for each basic learner, and the remaining data subsets are used as the training set; the optimal basic learner combination (n basic learners) is selected, and the prediction results of the first layer are obtained through accuracy verification index analysis; a new data set is constructed according to the prediction results of the basic learners as the training set of the second-layer meta-learner; linear regression is selected as the meta-learner of the stacking model to buffer and prevent overfitting caused by small sample size; finally, the prediction results of the model are obtained through the meta-learner.

[0035] The method described, the method of step 4 is:

[0036] The combination of base learners is regarded as a combination of nine candidate machine learning models, using nine-bit binary coding, each position corresponds to an alternative machine learning model, where 1 indicates that the selected model is enabled and 0 indicates that the model is not enabled. The chromosome is set to a 9-bit binary coding, representing the solution of the combination configuration of the base learners in the stacking model;

[0037] Initialize a population of 40 chromosomes as the starting point of the genetic algorithm iteration; select excellent chromosomes for reproduction according to the fitness of each individual through the roulette wheel selection method; in the crossover operation, use single-point crossover with a probability of 0.5 to promote the transmission of excellent genes; in the mutation operation, set a mutation probability of 0.005 to introduce new gene mutations, thereby exploring a wider solution space; select linear regression as the meta-learner, and integrate the basic learner combination optimized by the genetic algorithm to form a comprehensive stacked ensemble learning model;

[0038] In order to evaluate the fitness of each model combination, the coefficient of determination (R 2 ) is used as the fitness function, which is an indicator to measure the goodness of fit of the model; R 2 The closer the value is to 1, the better the model fit is, and the corresponding model combination is considered to be better. Finally, the optimal model combination is a stacked model of five models: random forest model (RF), gradient boosted tree model (GBR), adaptive boosting model (Adaboost), extreme random tree model (Extra-Trees), and support vector machine model (SVM).

[0039] The beneficial effects of the present invention are as follows: spectral features and terrain features are introduced as covariates for remote sensing inversion of soil organic matter, multiple machine learning models are stacked and integrated, a basic learner combination of the stacked integrated learning model is optimized using a genetic algorithm, and a soil organic matter remote sensing inversion model of the stacked model based on the optimal model combination is constructed, so as to solve the problems of easy overfitting and weak generalization ability of a single machine learning model, thereby not only enhancing the generalization ability of the model, but also improving the inversion accuracy of soil organic matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flowchart of soil organic matter remote sensing inversion method based on stacking model;

[0041] Figure 2 The soil organic matter inversion accuracy of the stacking model based on the optimal model combination was evaluated using ground-truth soil organic matter measurements.

[0042] Figure 3 Spatial distribution map of soil organic matter inverted by the stacking model based on the optimal model combination;

[0043] Figure 4Accuracy comparison of nine single machine learning models and stacked models based on the best model combination. ETR: Extreme Random Trees Model, RF: Random Forest Model, GBR: Gradient Boosted Trees Model, XGB: Extreme Gradient Boosted Model, ADB: Adaptive Boosting Model, Bag: Bagging Model, SVR: Support Vector Machine Model, PLSR: Partial Least Squares Regression Model, MLP: Multilayer Perceptron Model, GA_stack: Stacked Model Based on the Best Model Combination; DETAILED DESCRIPTION

[0044] The present invention is described in detail below in conjunction with specific embodiments.

[0045] refer to Figure 1 , a soil organic matter remote sensing inversion method based on stacking model, comprising the following steps:

[0046] Step 1: Data acquisition and preprocessing

[0047] Get the Sentinel-2 Level-1C (L1C) satellite remote sensing data from the European Space Agency Copernicus Open Access Hub (https: / / scihub.copernicus.eu / ). The multispectral imager MSI on the Sentinel-2 satellite includes 13 spectral bands with spatial resolutions of 10m, 20m and 60m respectively.

[0048] Sentinel-2L1C data were processed using Sentinel data processing software SNAP and Sen2Cor, including sub-pixel precision geometric and radiometric corrections and atmospheric corrections to obtain more accurate Level 2A (L2A) data. Band data with spatial resolutions of 20m and 60m were resampled to 10m to ensure the consistency of spatial resolution of all band data. Clouds and shadows were masked using the quality_scene_classification quality flag. Sentinel-2 remote sensing images were mosaicked and cropped to obtain clear, high-quality images of the study area.

[0049] In the Sentinel-2L1C data set, the B1 (443nm) and B10 (1375nm) bands are specifically used for atmospheric condition monitoring, corresponding to aerosol and cirrus detection, respectively. These two bands are not included in the atmospheric correction process of the L2A data and are therefore excluded in subsequent analysis. Subsequent analysis focuses on the 11 bands included in the L2A data, which cover the spectral range from 490nm to 2190nm.

[0050] Step 2: Optimization of spectral feature variables

[0051] Four index forms, namely normalized index NDI, ratio index RI, generalized index GDVI and product index PI, are selected to construct the spectral index:

[0052]

[0053] PI=R i ×R j (4)

[0054] In the formula, R i and R j represent any two bands in the Sentinel-2A data, and R i Not equal to R j .

[0055] 220 spectral indices were constructed using the data of 11 bands of Sentinel-2A. On this basis, a spectral feature set containing 236 characteristic variables was constructed by combining the data of 11 spectral bands of Sentinel-2A and 5 terrain characteristic parameters (elevation, slope, aspect, slope change rate and aspect change rate).

[0056] The maximum information coefficient (MIC) method was used to measure the correlation between each characteristic variable and soil organic matter to evaluate the impact of different characteristic variables on soil organic matter inversion. Each characteristic variable and soil organic matter were ranked and transformed, and the Spearman rank correlation coefficient of the transformed data was calculated. For each characteristic, all possible permutations were generated. For each permutation, the Spearman rank correlation coefficient was recalculated. MIC is the maximum value of the coefficient among all permutations. The MIC value ranges from 0 (no correlation) to 1 (perfect correlation). Repeat the above steps for all characteristics to evaluate the correlation between each characteristic variable and soil organic matter.

[0057] The recursive feature elimination (RFE) algorithm was used to further select spectral feature variables. By iteratively training the model and gradually eliminating the feature variables with the least impact on the model performance, the spectral feature variables sensitive to soil organic matter were identified. The spectral feature variables sensitive to soil organic matter were determined by the RFE algorithm. Finally, 30 feature variables were selected: 2 bands B2 (490nm) and B4 (665nm), 6 generalized indices (GDI), 4 product indices (PI), 6 normalized difference indices (NDI), 8 ratio indices (RI), and 4 terrain-related parameters (elevation, slope, slope change rate, and aspect change rate).

[0058] Step 3: Construction of soil organic matter inversion model

[0059] The stacking model is used to integrate multiple machine learning models to construct a soil organic matter inversion model. The stacking model structure is divided into two layers, one layer is called the basic learner, and the other layer is called the meta-learner. Nine models, including partial least squares regression model (PLSR), random forest model (RF), support vector machine model (SVM), multi-layer perceptron model (MLP), extreme random tree model (Extra-Trees), gradient boosting tree model (GBR), adaptive boosting model (Adaboost), bagging model (Bagging) and extreme gradient boosting model (XGBoost), are selected as the basic learners of the stacking model.

[0060] The 30 selected spectral feature variables were used as input data for soil organic matter inversion modeling. First, the original training data set was divided into 5 subsets to ensure that each data subset did not overlap. During the operation, a data subset was selected as the prediction set for each base learner, and the remaining data subsets were used as training sets. The optimal base learner combination (n base learners) was selected, and the prediction results of the first layer were obtained through accuracy verification index analysis. A new data set was constructed based on the prediction results of the base learner as the training set for the second-layer meta-learner. Linear regression was selected as the meta-learner of the stacked model to buffer and prevent overfitting caused by small sample size. Finally, the prediction results of the model were obtained through the meta-learner.

[0061] Step 4: Model combination optimization based on genetic algorithm

[0062] Genetic algorithm is used to optimize the combination of base learners in the stacking model. The combination of base learners is regarded as a combination of nine candidate machine learning models, using nine-bit binary coding, each position corresponds to an alternative machine learning model, where 1 indicates that the selected model is enabled and 0 indicates that the model is not enabled. The chromosome is set to a 9-bit binary coding, representing the solution of the combination configuration of the base learners in the stacking model.

[0063] Initialize a population of 40 chromosomes as the starting point for the iteration of the genetic algorithm. Through the roulette wheel selection method, select excellent chromosomes for reproduction according to the fitness of each individual. In the crossover operation, single-point crossover is used with a probability of 0.5 to promote the transmission of excellent genes. In the mutation operation, a mutation probability of 0.005 is set to introduce new gene mutations to explore a wider solution space. Linear regression is selected as the meta-learner, and the basic learner combination optimized by the genetic algorithm is integrated to form a comprehensive stacked ensemble learning model.

[0064] In order to evaluate the fitness of each model combination, the coefficient of determination (R 2 ) is used as the fitness function, which is an indicator to measure the goodness of fit of the model. 2The closer the value is to 1, the better the model fit is, and the corresponding model combination is considered to be better. Finally, the optimal model combination is a stacked model of five models: random forest model (RF), gradient boosted tree model (GBR), adaptive boosting model (Adaboost), extreme random tree model (Extra-Trees), and support vector machine model (SVM).

[0065] Step 5: Remote sensing inversion of soil organic matter based on the stacking model of the optimal model combination

[0066] Taking 30 characteristic variables including spectral characteristics and terrain characteristics as covariates, the stacking model of the optimal model combination was applied to Sentinel-2 image inversion of soil organic matter, and the spatial distribution map of Sentinel-2 soil organic matter was obtained.

[0067] Figure 2 To evaluate the soil organic matter inversion accuracy of the stacking model based on the optimal model combination using ground-truth soil organic matter. Figure 2 It can be seen that the R between the measured soil organic matter on the ground and the soil organic matter inverted by the stacking model based on the optimal model combination is 2 The value is 0.748 and the RMSE is 0.252%, which indicates the high consistency between the inverted value and the measured value and the reliability of the method. Figure 3 The spatial distribution map of soil organic matter inverted by the stacking model based on the optimal model combination. Figure 3 It can be seen that the inverted soil organic matter effectively reflects the spatial distribution of soil organic matter. Figure 4 The accuracy of nine single machine learning models was compared with a stacked model based on the best model combination. Figure 4 It can be seen that compared with a single machine learning model, the accuracy of the stacked model based on the optimal model combination is the best.

[0068] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A soil organic matter remote sensing inversion method based on a stacking model, characterized in that: The following steps are involved: Step 1: Data acquisition and preprocessing Acquire Sentinel-2 Level-1C (L1C) satellite remote sensing data; use Sentinel data processing software SNAP and Sen2Cor to process Sentinel-2 L1C data; Step 2: Optimization of spectral feature variables Four index forms, namely normalized difference index NDI, ratio index RI, generalized difference index GDVI and product index PI, were selected to construct the spectral index; Using the data of 11 bands of Sentinel-2A, 220 spectral indices were constructed, and a spectral feature set containing 236 characteristic variables was constructed; The maximum information coefficient (MIC) method was used to measure the correlation between each characteristic variable and soil organic matter, and to evaluate the impact of different characteristic variables on soil organic matter inversion. The recursive feature elimination (RFE) algorithm is used to further select spectral feature variables; the spectral feature variables that are sensitive to soil organic matter are identified by iteratively training the model and gradually eliminating the feature variables that have the least impact on model performance; the spectral feature variables that are sensitive to soil organic matter are determined by the RFE algorithm; Step 3: Construction of soil organic matter inversion model The stacking model is used to integrate multiple machine learning models to construct a soil organic matter inversion model; the stacking model structure is divided into two layers, one layer is called the basic learner, and the other layer is called the meta-learner; nine models, including partial least squares regression model (PLSR), random forest model (RF), support vector machine model (SVM), multi-layer perceptron model (MLP), extreme random tree model (Extra-Trees), gradient boosting tree model (GBR), adaptive boosting model (Adaboost), bagging model (Bagging) and extreme gradient boosting model (XGBoost), are selected as the basic learners of the stacking model; The selected spectral characteristic variables are used as input data for soil organic matter inversion modeling; Step 4: Model combination optimization based on genetic algorithm Using genetic algorithm to optimize the combination of base learners in the stacking model; Step 5: Remote sensing inversion of soil organic matter based on the stacking model of the optimal model combination Taking 30 characteristic variables including spectral characteristics and terrain characteristics as covariates, the stacking model of the optimal model combination was applied to Sentinel-2 image inversion of soil organic matter, and the spatial distribution map of Sentinel-2 soil organic matter was obtained.

2. The method according to claim 1, characterized in that The specific method of step 1 is: obtain Sentinel-2 Level-1C satellite remote sensing data from the European Space Agency Copernicus Open Access Center; the multispectral imager MSI carried by the Sentinel-2 satellite includes 13 spectral bands with spatial resolutions of 10m, 20m and 60m respectively; The Sentinel-2L1C data were processed using the Sentinel data processing software SNAP and Sen2Cor, including sub-pixel precision geometric and radiometric corrections and atmospheric corrections, to obtain more accurate Level 2A (L2A) data; the band data with a spatial resolution of 20m and 60m were resampled to 10m to ensure the consistency of spatial resolution of all band data; Use the quality_scene_classification quality flag to mask clouds and shadows; mosaic and crop the Sentinel-2 remote sensing images to obtain clear, high-quality images of the study area; In the Sentinel-2L1C data set, bands B1 and B10 were excluded from subsequent analysis; subsequent analysis focused on the 11 bands included in the L2A data, which cover the spectral range from 490 nm to 2190 nm.

3. The method according to claim 1, characterized in that: The specific method of step 2 is: select four index forms, namely, normalized index NDI, ratio index RI, generalized index GDVI and product index PI, to construct a spectral index: PI=R i ×R j (4) In the formula, R i and R j represent any two bands in the Sentinel-2A data, and R i Not equal to R j ; 220 spectral indices were constructed using the data of 11 bands of Sentinel-2A. On this basis, a spectral feature set containing 236 characteristic variables was constructed by combining the data of 11 spectral bands of Sentinel-2A and five terrain characteristic parameters: elevation, slope, aspect, slope change rate and aspect change rate. The maximum information coefficient (MIC) method was used to measure the correlation between each characteristic variable and soil organic matter, which was used to evaluate the impact of different characteristic variables on soil organic matter inversion; each characteristic variable and soil organic matter were ranked and transformed, and the Spearman rank correlation coefficient of the transformed data was calculated; for each characteristic, all possible permutations were generated; for each permutation, the Spearman rank correlation coefficient was recalculated; MIC is the maximum value of the coefficients in all permutations; MIC values ​​range from 0 to 1; repeat the above steps for all features to evaluate the correlation between each feature variable and soil organic matter; The recursive feature elimination (RFE) algorithm is used to further select spectral feature variables. The spectral feature variables that are sensitive to soil organic matter are identified by iteratively training the model and gradually eliminating the feature variables that have the least impact on model performance. The spectral feature variables that are sensitive to soil organic matter are determined through the RFE algorithm.

4. The method according to claim 3, characterized in that The step 2 finally selects 30 characteristic variables: 2 bands B2 and B4, 6 generalized indexes GDI, 4 product indexes PI, 6 normalized indexes NDI, 8 ratio indexes RI, and 4 terrain related parameters: elevation, slope, slope change rate and aspect change rate.

5. The method according to claim 1, characterized in that: The method of step 3 is: The 30 selected spectral characteristic variables were used as input data for soil organic matter inversion modeling. First, the original training data set was divided into 5 sub-data sets to ensure that each data subset did not overlap. During the operation, a data subset is selected as the prediction set for each base learner, and the remaining data subsets are used as training sets; Select the optimal combination of basic learners and obtain the prediction results of the first layer through accuracy verification indicator analysis; A new dataset is constructed based on the prediction results of the basic learner as the training set for the second-layer meta-learner. Linear regression is selected as the meta-learner of the stacked model to buffer and prevent overfitting caused by small sample size. Finally, the prediction results of the model are obtained through the meta-learner.

6. The method according to claim 1, characterized in that The method of step 4 is: The combination of base learners is regarded as a combination of nine candidate machine learning models, using nine-bit binary coding, each position corresponds to an alternative machine learning model, where 1 indicates that the selected model is enabled and 0 indicates that the model is not enabled. The chromosome is set to a 9-bit binary coding, representing the solution of the combination configuration of the base learners in the stacking model; Initialize a population of 40 chromosomes as the starting point for the genetic algorithm iteration; Through the roulette wheel selection method, excellent chromosomes are selected for reproduction according to the fitness of each individual; in the crossover operation, single-point crossover is used with a probability set to 0.5 to promote the transmission of excellent genes; in the mutation operation, a mutation probability of 0.005 is set to introduce new gene mutations to explore a wider solution space; linear regression is selected as the meta-learner, and the basic learner combination optimized by the genetic algorithm is integrated to form a comprehensive stacked ensemble learning model; In order to evaluate the fitness of each model combination, the coefficient of determination (R 2 ) is used as the fitness function, which is an indicator to measure the goodness of fit of the model; R 2 The closer the value is to 1, the better the model fit is, and the corresponding model combination is considered to be better. Finally, the optimal model combination is a stacked model of five models: random forest model (RF), gradient boosted tree model (GBR), adaptive boosting model (Adaboost), extreme random tree model (Extra-Trees), and support vector machine model (SVM).

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