Reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and stacking model

Abstract

The invention discloses a reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and a stacking model, and relates to the technical field of agricultural water resource management, and the method comprises the following steps: obtaining and preprocessing the historical data of a meteorological station; calculating the evapotranspiration standard value of the reference crop by adopting an FAO-56 Penman-Monte's formula; screening dominant meteorological factors through a heterogeneous integrated feature selection method in combination with a fuzzy Borda method; an HIFS-Stacking model is constructed, RF, XGBoost and MLP are taken as base models, LR is taken as a meta model, and K-fold cross validation is adopted to generate meta features; real-time data are subjected to same preprocessing and then input into the model to output a prediction result. According to the method, the meteorological factors having significant influence on prediction of the evapotranspiration of the reference crop can be effectively determined, the complex nonlinear relationship between the key meteorological factors and ET0 is accurately fitted in combination with the optimized model architecture, and high-precision prediction is realized under limited meteorological data.

Description

Technical Field

[0001] The present invention belongs to the technical field of agricultural water resources management, and in particular relates to a reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and stacking model. Background Art

[0002] Precision irrigation is a key measure for improving crop yield and quality, and a core approach for optimizing water resource utilization. Traditional irrigation management relies on experience, often leading to excessive water use, which wastes water resources and harms crop growth. Evapotranspiration is a key indicator for assessing crop water requirements, involving soil evaporation and crop transpiration. Therefore, accurately obtaining reference crop evapotranspiration is crucial for calculating crop water requirements, scheduling crop irrigation, and maintaining soil and water conservation.

[0003] Although measuring crop water requirements using gravimetric lysimeters or eddy covariance systems is a direct and effective method, these methods suffer from the high cost of instrument manufacturing and maintenance. To address this issue, the FAO-56 Penman-Monteith (PM) equation is recognized by the Food and Agriculture Organization of the United Nations as the standard method for estimating cropland evapotranspiration by calculating reference crop evapotranspiration (ET0). However, the traditional Penman-Monteith equation requires complete meteorological data, which limits its application in data-scarce regions. Therefore, it is necessary to develop an ET0 model that can achieve high prediction accuracy while using as few meteorological inputs as possible.

[0004] With the development of big data technology and high-performance computing, machine learning (ML) methods, with their powerful ability to process and analyze big data, have been widely applied in agriculture, offering new approaches for improving the accuracy of ET0 estimation under complex conditions. While machine learning models can achieve ET0 estimation using limited data, the feature selection of a single model is not stable, and ensemble methods such as bagging and boosting struggle to fully integrate the strengths of multiple models. Stably and accurately determining model input factors, integrating the strengths of each basic model, and achieving accurate ET0 prediction under limited conditions have become pressing technical challenges. Summary of the Invention

[0005] In view of this, in order to address the deficiencies of the above-mentioned prior art, the object of the present invention is to provide a reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and stacking model. The proposed feature selection method can effectively determine the meteorological factors that have a significant impact on the predicted reference crop evapotranspiration, and use the HIFS-Stacking (Heterogeneous Integrated Feature Selection-Stacking) model to accurately fit the complex nonlinear relationship between key meteorological influencing factors and ET0, thereby achieving efficient and accurate prediction of ET0 under limited meteorological conditions.

[0006] To achieve the above object, the technical solution adopted by the present invention is: A reference crop evapotranspiration estimation method based on heterogeneous ensemble feature selection and stacking model includes the following steps: S1. Obtain historical meteorological data from the weather station and perform preprocessing; S2, using the FAO-56 Penman-Montes formula to calculate the reference crop evapotranspiration standard value as the label for model training; S3. Use heterogeneous integrated feature selection method to select features from the historical meteorological data preprocessed in S1. Use fuzzy Borda method to comprehensively evaluate the importance of each meteorological factor to the estimated ET0 and calculate its fuzzy Borda score. Select the dominant meteorological factor based on the fuzzy Borda score. S4. Build a stacked ensemble prediction model HIFS-Stacking: Using random forest, extreme gradient boosting, and multilayer perceptron as base models, linear regression as a meta-model, and using K-fold cross validation to generate base model prediction results as meta-features; S5, collect meteorological data in real time, and process the real-time meteorological data using the same data preprocessing method as S1; S6. Input the meteorological data preprocessed by S5 corresponding to the dominant meteorological factors selected by S3 into the HIFS-Stacking prediction model trained by S4 to obtain the reference crop evapotranspiration prediction result.

[0007] As a preferred solution, in S2, the FAO-56 Penman-Monteis formula is used to calculate the reference crop evapotranspiration standard value, which is as follows: Where ET0 is the reference crop evapotranspiration, in mm / d; Δ is the slope of the saturated water vapor pressure-temperature curve, in kPa / °C; γ is the hygrometer constant, in kPa / °C; Rn is the net radiation, in MJ / (m²·d); e s is the saturated water vapor pressure, in kPa; e ais the actual water vapor pressure, in kPa; T mean is the average temperature in °C; G is the soil heat flux in MJ / (m²·d); U2 is the wind speed at 2 meters above the ground in m / s.

[0008] As a preferred solution, the feature selection in S3 is performed based on the heterogeneous integrated feature selection method, which specifically includes the following sub-steps: S31. Assume that the meteorological factors collected by the weather station are used as the feature vector U = (s1, s2,…, s n ) T , where n represents the number of features, s i is the i-th feature; S32. The heterogeneous integrated feature selection method uses at least three different embedded machine learning feature selection methods to calculate the feature importance score of each meteorological factor respectively. The feature selection result of the mth method is J m , J m = (u1,u2,…, u n ) T , n is the number of features, the results of all the above feature selection methods are combined to construct the feature selection matrix T; S33, using the fuzzy Borda method to comprehensively evaluate the importance scores of each meteorological factor in the feature selection matrix T, and calculating the fuzzy Borda score of each meteorological factor. The importance score matrix of each meteorological factor is B n = (f1,f2,…, f n ) T ; Compare the n values ​​of the feature importance score matrix and construct important input combinations based on the scores.

[0009] As a preferred solution, the feature selection matrix T is: Among them, J m It is a column matrix; the j column of the matrix T represents the feature selection results of the m feature selection method obtained for all meteorological factors at a certain meteorological station.

[0010] As a preferred solution, the fuzzy Borda method includes the following sub-steps: S331, calculating the membership degree for the original importance scores in the feature selection matrix; S332, calculating the fuzzy frequency and fuzzy frequency of each feature at different ranking positions; S333. Convert the ranking into a score using the following formula: in Represents the score of feature i ranked at the hth position.

[0011] S334. Calculate the fuzzy Borda score of each meteorological factor according to the formula: in, is the score of feature i ranked hth in feature selection method j.

[0012] As a preferred solution, the feature selection method in S32 includes random forest, extreme gradient boosting and gradient boosting decision tree.

[0013] As a preferred solution, the S4 includes the following sub-steps: S41, taking the dominant meteorological factors output by S3 as input, configures random forest, extreme gradient boosting and multi-layer perceptron as base models, linear regression as meta-model, and uses particle swarm optimization algorithm to determine the hyperparameters of each base model; S42, training each base model through K-fold cross validation and generating prediction results as meta-features; S43. Use meta-features to train the meta-model and build the HIFS-Stacking prediction model.

[0014] The beneficial effects of the present invention are: This paper proposes a reference crop evapotranspiration estimation method based on heterogeneous ensemble feature selection and stacking models. By introducing a stacking model, combining random forest (RF), extreme gradient boosting (XGBoost), and multilayer perceptron (MLP) as base models, and linear regression (LR) as a meta-model, this method effectively integrates the advantages of multiple models and accurately fits the complex nonlinear relationship between key meteorological factors and ET0. This method utilizes a Particle Swarm Optimization (PSO) optimization algorithm to determine the hyperparameters of each model, addressing the difficulty of hyperparameter adjustment and significantly improving prediction accuracy. This method achieves efficient and accurate ET0 prediction under limited meteorological conditions.

[0015] Furthermore, this method utilizes a heterogeneous ensemble feature selection method, combining multiple embedded feature selection techniques such as random forest (RF), extreme gradient boosting (XGBoost), and gradient boosted decision tree (GBDT). Using the fuzzy Borda method to comprehensively evaluate feature importance, it can reliably screen out meteorological factors that significantly influence ET0 predictions, such as daily maximum temperature, sunshine hours, relative humidity, and wind speed. This method avoids the subjectivity of manual feature selection, overcomes the dependency on a single algorithm, effectively eliminates redundant features, and improves the model's interpretability and reliability. Experimental results demonstrate that the model maintains high prediction accuracy (R² > 0.963) even with limited meteorological data input, outperforming single models or other ensemble methods, providing more efficient and accurate technical support for agricultural water resources management. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0017] Figure 1 It is a framework diagram of the reference crop evapotranspiration prediction method under limited meteorological conditions of the present invention; Figure 2 It is a pseudo code diagram of the present invention based on the Stacking model; Figure 3 It is a pseudo code diagram based on heterogeneous integrated feature selection of the present invention; Figure 4 This is a map of the area where the weather station is located in Example 2 of the present invention; Figure 5 is a feature importance score graph based on the integrated embedded feature selection method in Example 2 of the present invention; Figure 6 Schematic diagram of fuzzy Borda score calculation of feature selection matrix T in Example 2. DETAILED DESCRIPTION

[0018] The following specific embodiments are provided to further clearly, completely, and in detail illustrate the technical solutions of the present invention. Obviously, the embodiments described are only a portion of the embodiments of this application, rather than all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of this application.

[0019] Example 1 like Figures 1 to 3As shown in FIG, a reference crop evapotranspiration estimation method based on heterogeneous ensemble feature selection and stacking model includes the following steps: S1. Obtain historical meteorological data from meteorological stations in the Central Plains urban agglomeration and perform preprocessing, including detecting and processing missing values ​​and outliers, and normalizing the data. The specific steps include: S11. Historical daily data collected by meteorological stations in the Central Plains urban agglomeration, including daily maximum temperature, daily minimum temperature, average temperature, sunshine hours, relative humidity, and wind speed; S12. The method for detecting outliers is the quartile criterion: L1=Q L -1.5×I QR L2=Q U +1.5×I QR Among them, Q L It is called the lower quartile, which means that one quarter of all the data have values ​​smaller than it; Q U It is called the upper quartile, which means that one quarter of all the data have values ​​greater than it; QR It is called the interquartile range, which is the upper quartile Q U and the lower quartile Q L The difference between the two values; L1 is the lower limit of the abnormal threshold, L2 is the upper limit of the abnormal threshold, and the abnormal value judgment standard is that the sample value is less than the lower limit L1 or greater than the upper limit L2; S13. The missing values ​​and outliers are processed using the K-nearest neighbor interpolation method. This method identifies k samples in the dataset that are spatially close to the missing values ​​and uses the Euclidean distance to measure the distance between these samples and the missing values. The missing values ​​and outliers of each sample are interpolated using the average of the k samples found in the dataset. S14, normalize the data after processing missing values ​​and outliers in step S13, the formula is: Among them, X norm is the normalized value; X i is the input value; X max and X min The input values ​​X i The corresponding maximum and minimum values ​​in the data series.

[0020] S2. Use the FAO-56 Penman-Monteith formula to calculate the reference crop evapotranspiration standard value as the label for model training; the specific formula is as follows: Where ET0 is the reference crop evapotranspiration, in mm / d; Δ is the slope of the saturated water vapor pressure-temperature curve, in kPa / °C; γ is the hygrometer constant, in kPa / °C; Rn is the net radiation, in MJ / (m²·d); e s is the saturated water vapor pressure, in kPa; e a is the actual water vapor pressure, in kPa; T mean is the average temperature in °C; G is the soil heat flux in MJ / (m²·d); U2 is the wind speed at 2 meters above the ground in m / s.

[0021] S3. Use a heterogeneous integrated feature selection method to perform feature selection on the pre-processed historical meteorological data. The heterogeneous integrated feature selection method combines multiple embedded feature selection methods. When performing feature selection, an integrated strategy is used to combine the feature selection results of multiple embedded feature selection methods. Specifically, it includes the following contents: S31. Assume that the meteorological factors collected by the weather station are used as the feature vector U = (s1, s2,…,s n ) T , where n represents the number of features, s i represents the i-th feature; S32. If there are m feature selection methods, the feature selection result of the mth method is J m , J m = (u1, u2,…,u n ) T If feature s i In the mth feature selection method, the importance score is 2, that is, u1 = 2; similarly, other features s i Also assign values ​​in this way; construct the feature selection matrix T by combining the results of all feature selection methods; Where Jm is a column matrix; the j column of the matrix T represents the feature selection results of the m feature selection method obtained for all meteorological factors at a certain meteorological station; S33, using the fuzzy Borda method to comprehensively evaluate the importance scores of each meteorological factor in the feature selection matrix T, and calculating the fuzzy Borda score of each meteorological factor. The importance score matrix of each meteorological factor is B n = (f1,f2,…, f n ) T ; Compare the n values ​​of the feature importance score matrix and construct important input combinations based on the scores.

[0022] S331. Given that different methods assign different ranges of importance scores, in order to unify the measurement standard, the membership degree of the importance scores is calculated; the formula is: in, is the normalized value; is the input value; and Input values The corresponding maximum and minimum values ​​in the data series.

[0023] S332. Calculate the fuzzy frequency and fuzzy frequency of the characteristic importance score of the meteorological factor according to the fuzzy Borda method for the data after the membership degree is calculated in step S331. The formula is as follows: Fuzzy frequency: Among them, is the fuzzy frequency of the i-th feature to be evaluated ranked in the h-th position; If the i-th feature ranks h-th in the j-feature selection method, then: The fuzzy frequency is: S333. To widen the score difference, convert the ranking of the features to be evaluated into scores: in Represents the score of feature i ranked at the hth position.

[0024] S334, calculate the fuzzy Borda score of each meteorological factor according to the results of steps S33 and S34; then the importance score matrix B of each meteorological factor is B n = (f1, f2,…, f n ) T Finally, n values ​​are obtained, and the n values ​​of the feature importance score matrix B are compared. The higher the score, the more significant the impact of the meteorological factor on the predicted ET0. Then, the important input combination is constructed based on the score. The formula is: in, is the score of feature i ranked hth in feature selection method j.

[0025] In this embodiment, the multiple embedded feature selection methods include random forest (RF), extreme gradient boosting (XGBoost) and gradient boosted decision tree (GBDT). The principles of these three methods are as follows: RF uses the out-of-bag (OOB) error to calculate the importance of each feature during model training. GBDT is a boosting-based ensemble algorithm, and XGBoost is an improved framework based on GBDT. It measures feature importance by calculating how often a feature is used to partition data across all trees and the average gain it brings as a partitioning attribute.

[0026] S4: Use the data after feature selection in S3 to train the Stacking model, and use the Stacking model to train the data after feature selection to build a HIFS-Stacking prediction model, which specifically includes the following steps: S41, using the data after feature selection as input to determine the base model and meta-model of the Stacking model; S42, train each base model and use K-fold cross validation to generate a new feature dataset; S43. Use the new feature dataset to train the meta-model and build the HIFS-Stacking prediction model.

[0027] In this embodiment, the base models include random forest (RF), extreme gradient boosting (XGBoost) and multi-layer perceptron (MLP), and the meta-model is a linear regression model.

[0028] S5: collect meteorological data in real time and process the meteorological data collected in real time using the same data preprocessing method as S1.

[0029] S6. Input the processed real-time meteorological data into the HIFS-Stacking prediction model according to the important meteorological factors selected in S3 to obtain a reference crop evapotranspiration prediction result.

[0030] Example 2 Based on a reference crop evapotranspiration stacking estimation model for the Central Plains urban agglomeration based on heterogeneous integrated feature selection provided in Example 1, daily meteorological observation data from 32 meteorological stations in the Central Plains urban agglomeration from January 1969 to December 2019 were selected. The locations of the meteorological stations are as follows: Figure 4 As shown, efficient and accurate prediction of ET0 is achieved under limited meteorological conditions.

[0031] All meteorological data are from the National Meteorological Information Center (NMIC) of the China Meteorological Administration and have been strictly quality controlled, including the minimum temperature (Tmin), maximum temperature (Tmax), wind speed at 10m (U 10 ), sunshine duration (SSD) and relative humidity (RH), etc., among which the wind speed is calculated according to the PM calculation guide, and the wind speed U 10According to the wind profile relationship, it is converted into the wind speed U2 at 2m above the ground.

[0032] The specific prediction method is as follows: S1. Obtain historical meteorological data from meteorological stations in the Central Plains Urban Agglomeration and perform preprocessing, including detecting and processing missing values ​​and outliers, and normalizing the data. After detecting and processing missing values ​​and outliers, the meteorological data for each station is divided into two parts in a 4:1 ratio. The first part (1969-2009) is used to train / calibrate the machine learning model, and the second part (2010-2019) is used to test model performance. In this embodiment, the training set is used as historical meteorological data, and the test set is used as measured meteorological data.

[0033] S2. Based on the meteorological data obtained in S1, the FAO-56 Penman-Monteith formula is used to calculate the reference crop evapotranspiration standard value as the label of the dataset. The formula is as follows: Where ET0 is the reference crop evapotranspiration, in mm / d; Δ is the slope of the saturated water vapor pressure-temperature curve, in kPa / °C; γ is the hygrometer constant, in kPa / °C; Rn is the net radiation, in MJ / (m²·d); e s is the saturated water vapor pressure, in kPa; e a is the actual water vapor pressure, in kPa; T mean is the average temperature in °C; G is the soil heat flux in MJ / (m²·d); U2 is the wind speed at 2 meters above the ground in m / s.

[0034] S3. Use heterogeneous integrated feature selection method to perform feature selection on pre-processed historical meteorological data. This embodiment uses the data of each meteorological station after data pre-processing to perform feature selection, and obtains the importance scores of 6 meteorological factors for predicting ET0 of 32 meteorological stations in the Central Plains urban agglomeration under 3 feature selection methods, as shown in the following example: Figure 5 The fuzzy Borda method is used to select integrated features of meteorological factors selected by the three embedded methods, as shown in Figure 5 As shown in the figure, the feature selection matrix T is obtained. The first, second, and third columns in the matrix are the results of feature selection by GBDT, RF, and XGBoost methods respectively, and the elements in each column are the important scores of each feature.

[0035] like Figure 6As shown in Figure 1, each row of data in matrix T corresponds to a meteorological factor, and the nth column of the fuzzy matrix represents the nth ranking of the meteorological factor. Based on the fuzzy Borda score derived from the heterogeneous integrated feature selection method, the most important meteorological factors for predicting ET0 are Tmax, SSD, RH, U2, Tmean, and Tmin, in order.

[0036] As an option, this embodiment selects the top four factors and all the factors to form two important meteorological factor combinations as input items for constructing the ET0 model, specifically M1 (Tmax, SSD, RH, U2) and M2 (Tmax, SSD, RH, U2, Tmean and Tmin).

[0037] S4. Use the data after feature selection in S3 to train the Stacking model. The base models are RF, XGBoost and MLP. The meta-model is the linear regression model. The Stacking model is used to train the data after feature selection to build the HIFS-Stacking prediction model.

[0038] The PSO optimization algorithm is used to optimize the hyperparameters of the three base models. The PSO settings include a population size of 30, a maximum number of iterations of 30, a learning factor of c1 = c2 = 2, an inertia weight ranging from 0.4 to 0.9, and a maximum velocity of 1200.

[0039] S5. Use the same data preprocessing method as S1 to process the meteorological data collected in real time.

[0040] S6. Input the processed real-time meteorological data into the HIFS-Stacking prediction model according to the important meteorological data selected in S3 to obtain the reference crop evapotranspiration prediction result. The details are as follows: Based on the preprocessing method for the training set in S1, the test set is preprocessed using the same rules. Subsequently, this embodiment transmits the preprocessed test set data to the HIFS-Stacking reference crop evapotranspiration prediction model based on the important meteorological factors selected in S3, and outputs the prediction results.

[0041] This example uses the root mean square error (RMSE), mean absolute error (MAE), Nash efficiency (NSE), and coefficient of determination (R²) to evaluate the error and consistency between the prediction results of the model constructed in this example and the standard values ​​calculated by the FAO-56 Penman-Monteith method. The closer the NSE and R² are to 1, and the closer the MAE and RMSE are to 0, the better the model performance.

[0042] R² assesses the relationship between the true value and the estimated value. The R² calculation formula is as follows: NSE is used to evaluate the prediction accuracy and fit of the model. The NSE calculation formula is as follows: RMSE is a commonly used indicator for measuring model performance, which represents the root mean square difference between the predicted value and the actual value. The RMSE calculation formula is as follows: MAE represents the actual situation of the predicted value deviation. The MAE calculation formula is as follows: Among them, A i represents ET0 calculated by the FAO-56 Penman-Monteith equation, P i represents the ET0 predicted by the machine learning model, and Respectively represent the corresponding average values.

[0043] Result Analysis As shown in Table 1 below, the statistical accuracy index results of the HIFS-Stacking, RF, XGBoost, and MLP models for predicting daily ET0 at 32 meteorological stations in the Central Plains urban agglomeration under two important combination inputs are shown.

[0044] The results show that compared with the three original models (RF, XGBoost and MLP models), the HIFS-Stacking model has the highest prediction accuracy.

[0045] Table 1 Statistical accuracy index results of the ET0 prediction model at 32 meteorological stations in the Central Plains urban agglomeration In summary, under two key combinations, HIFS-Stacking accurately reflects the complex nonlinear relationship between meteorological factors and ET0, achieving satisfactory prediction accuracy (R² > 0.963) with relatively few meteorological inputs. Compared with the RF, XGBoost, and MLP models, the HIFS-Stacking model achieved the best ET0 prediction performance under all input combinations.

[0046] The above shows and describes the main features, basic principles, and advantages of the present invention. The present invention is not limited to the above model, and analysis and calculation can be performed for different numbers of segments and different types of cages. Those skilled in the art should understand that the present invention is not limited to the above embodiment. The above embodiment and description are merely illustrative of the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements based on actual circumstances. Such changes and improvements fall within the scope of the invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A reference crop evapotranspiration estimation method based on heterogeneous ensemble feature selection and stacking model, characterized in that: The following steps are involved: S1. Obtain historical meteorological data from the weather station and perform preprocessing; S2, using the FAO-56 Penman-Montes formula to calculate the reference crop evapotranspiration standard value as the label for model training; S3. Use heterogeneous integrated feature selection method to select features from the historical meteorological data preprocessed in S1. Use fuzzy Borda method to comprehensively evaluate the importance of each meteorological factor to the estimated ET0 and calculate its fuzzy Borda score. Select the dominant meteorological factor based on the fuzzy Borda score. S4. Build a stacked ensemble prediction model HIFS-Stacking: Using random forest, extreme gradient boosting, and multilayer perceptron as base models, linear regression as a meta-model, and using K-fold cross validation to generate base model prediction results as meta-features; S5, collect meteorological data in real time, and process the real-time meteorological data using the same data preprocessing method as S1; S6. Input the meteorological data preprocessed by S5 corresponding to the dominant meteorological factors selected by S3 into the HIFS-Stacking prediction model trained by S4 to obtain the reference crop evapotranspiration prediction result.

2. The reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and stacking model according to claim 1, characterized in that: In S2, the FAO-56 Penman-Montes formula is used to calculate the reference crop evapotranspiration standard value, which is as follows: Where ET0 is the reference crop evapotranspiration, in mm / d; Δ is the slope of the saturated water vapor pressure-temperature curve, in kPa / °C; γ is the hygrometer constant, in kPa / °C; Rn is the net radiation, in MJ / (m²·d); e s is the saturated water vapor pressure, in kPa; e a is the actual water vapor pressure, in kPa; T mean is the average temperature in °C; G is the soil heat flux in MJ / (m²·d); U2 is the wind speed at 2 meters above the ground in m / s.

3. The reference crop evapotranspiration estimation method based on heterogeneous integrated feature selection and stacking model according to claim 1, characterized in that: In S3, feature selection is performed based on a heterogeneous integrated feature selection method, specifically including the following sub-steps: S31. Assume that the meteorological factors collected by the weather station are used as the feature vector U = (s1, s2,…, s n ) T , where n represents the number of features, s i is the i-th feature; S32. The heterogeneous integrated feature selection method uses at least three different embedded machine learning feature selection methods to calculate the feature importance score of each meteorological factor respectively. The feature selection result of the mth method is J m , J m = (u1,u2,…, u n ) T , n is the number of features, the results of all the above feature selection methods are combined to construct the feature selection matrix T; S33, using the fuzzy Borda method to comprehensively evaluate the importance scores of each meteorological factor in the feature selection matrix T, and calculating the fuzzy Borda score of each meteorological factor. The importance score matrix of each meteorological factor is B n = (f1,f2,…, f n ) T ; Compare n values ​​of the feature importance score matrix and construct important input combinations based on the scores.

4. The method for estimating reference crop evapotranspiration based on heterogeneous integrated feature selection and stacking model according to claim 3, characterized in that: The feature selection matrix T is: Among them, J m It is a column matrix; the j column of the matrix T represents the feature selection results of the m feature selection method obtained for all meteorological factors at a certain meteorological station.

5. The method for estimating reference crop evapotranspiration based on heterogeneous integrated feature selection and stacking model according to claim 3, characterized in that: The fuzzy Borda method includes the following sub-steps: S331, calculating the membership degree for the original importance scores in the feature selection matrix; S332, calculating the fuzzy frequency and fuzzy frequency of each feature at different ranking positions; S333. Convert the ranking into a score using the following formula: in Represents the score of feature i ranked at the hth position.

6. S334. Calculate the fuzzy Borda score for each meteorological factor using the following formula: in, is the score of feature i ranked hth in feature selection method j.

7. The method for estimating reference crop evapotranspiration based on heterogeneous integrated feature selection and stacking model according to claim 3, characterized in that: The feature selection methods in S32 include random forest, extreme gradient boosting and gradient boosting decision tree.

8. The method for estimating reference crop evapotranspiration based on heterogeneous integrated feature selection and stacking model according to claim 1, characterized in that: The S4 includes the following sub-steps: S41, taking the dominant meteorological factors output by S3 as input, configures random forest, extreme gradient boosting and multi-layer perceptron as base models, linear regression as meta-model, and uses particle swarm optimization algorithm to determine the hyperparameters of each base model; S42, training each base model through K-fold cross validation and generating prediction results as meta-features; S43. Use meta-features to train the meta-model and build the HIFS-Stacking prediction model.

Images