CN116681158A - Reference crop evapotranspiration prediction method based on integrated extreme learning machine - Google Patents
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Abstract
The invention discloses a reference crop evapotranspiration prediction method based on an integrated extreme learning machine, which comprises the following steps: acquiring meteorological data of a research area and preprocessing the meteorological data; calculating standard reference crop evapotranspiration ET by adopting P-M formula according to meteorological data 0 label The method comprises the steps of carrying out a first treatment on the surface of the Based on ET 0 label Disturbance is applied to each meteorological factor in the P-M formula, the sensitivity degree of the reference crop evapotranspiration to different meteorological factors is obtained, and sensitive meteorological factors are selected; construction based on sensitive meteorological factorsIntegrating an ELM model, and optimizing to obtain a predicted value of the evapotranspiration of the reference cropThe invention establishes an extreme learning machine model based on the space-time variation characteristics of meteorological factors, designs different activation functions and integrates the activation functions, establishes a model, and realizes ET under the condition of meteorological data deficiency 0 Is provided.
Description
Technical Field
The invention belongs to the technical field of reference crop transpiration prediction methods, and particularly relates to a reference crop transpiration prediction method based on an integrated extreme learning machine.
Background
Crop evapotranspiration is a key parameter of agricultural irrigation and is also an important part of agricultural water circulation and water balance, and the calculation accuracy of the crop evapotranspiration mainly depends on reference crop evapotranspiration (ET 0 ). Thus, ET is accurately estimated and predicted 0 Has important significance for accurate irrigation decision and water resource management of irrigation areas.
The reference crop evapotranspiration can be obtained directly through experiments or indirectly through mathematical calculation. The field test method needs large-scale instruments, has high cost investment, large process difficulty and long time consumption, and lacks relevant test conditions in many areas at present. In many ET' s 0 In the calculation model, penman (Penman-Monteth) formula is recommended by the United nations grain and agricultural organization (FAO) as the calculation ET 0 Is a standard model of (c). Pengman formula calculation ET 0 A large amount of weather data such as a large amount of air temperature, sunshine hours, humidity, wind speed and the like need to be input, and most areas are difficult to acquire due to the limitation of the scale of a weather station, complicated and various topography and landforms and high costs, so that the complete required data cannot be obtained, and therefore, the Pengman formula has a certain limitation in application.
In summary, how to accurately estimate and predict ET in the absence of meteorological data 0 Has a certain research significance for high-efficiency irrigation management and decision.
Disclosure of Invention
The invention aims to provide a reference crop evapotranspiration prediction method based on an integrated extreme learning machine, which can be used for ET under the condition of lack of complete meteorological data 0 And carrying out high-precision prediction.
The technical scheme adopted by the invention is as follows: the reference crop evapotranspiration prediction method based on the integrated extreme learning machine comprises the following steps of:
step 1, acquiring meteorological data of a research area and preprocessing the meteorological data;
step 2, calculating the standard reference crop evapotranspiration ET by adopting a P-M formula according to the meteorological data obtained in the step 1 0 label ；
Step 3, based on the ET obtained in step 2 0 label Disturbance is applied to each meteorological factor in the P-M formula, so that the sensitivity degree of the reference crop evapotranspiration to different meteorological factors is obtained, and meteorological factors are selected;
step 4, constructing an integrated ELM model based on the sensitive meteorological factors obtained in the step 3, and optimizing to obtain a reference crop evapotranspiration predicted value
The present invention is also characterized in that,
the step 1 specifically comprises the following steps:
step 1.1, collecting daily meteorological data collected by each meteorological station in a research area, wherein the daily meteorological data comprise a daily maximum temperature T max Minimum temperature T min Average temperature T of day mean The sunshine duration n, the relative humidity RH and the wind speed u;
when missing data exists in the time sequence of the meteorological data collected in the step 1.2 and the step 1.1, the space analysis module is utilized to carry out space analysis, and the inverse distance weight method is adopted to carry out space interpolation, and the method specifically comprises the following steps:
assume that the point to be interpolated in the analog range is P (x p ,y p ,z p ) P point adjacent in-range point Q i (x i ,y i ,z i ) I=1, 2,..n, interpolating the correlation value Zp of the P point by using a distance weighting method, wherein the calculation formula is as follows:
in the formula (1), d i Is the distance between the interpolation point and the ith point in the adjacent range.
The formula of P-M used in step 2 is as follows:
in formula (2), ET 0 label The unit is mm/d for the standard reference crop evapotranspiration; g is soil heat flux, and the unit is MJ/(m) 2 ·d)；R n The unit of the net radiation quantity of the crop canopy is MJ/(m) 2 D) a step of; t is the average air temperature at the height of 2m, and the unit is the temperature; u (u) 2 Wind speed at the height of 2m is expressed in m/s; e, e s Saturated water vapor pressure is given in kpa; e, e a The unit is kpa for the actual water vapor pressure; delta is the slope of the saturated water vapor pressure versus temperature curve, and the unit is kpa/°c; gamma is the dry-wet thermometer constant in kpa/°c.
The step 3 specifically comprises the following steps:
step 3.1, for each meteorological factor X in the P-M formula i Disturbance is applied, the changed meteorological factors are substituted into a P-M formula, and the meteorological factors X are calculated i Reference crop evapotranspiration value ET at variation delta 0ΔXi ；
Step 3.2 ET obtained according to step 3.1 0ΔXi And ET obtained in step 2 0 label Exhibiting reference crop evapotranspiration versus meteorological factor X i As shown in formula (3):
in formula (3), P (ΔET) 0 -ΔX i ) For reference crop evapotranspiration to meteorological factor X i Sensitivity of (2), i.e. meteorological factor X i When the variation of (a) is delta, the reference crop evapotranspiration is relative to ET 0 label Is a variable amount of (a);
step 3.3, selecting weather factors { X }, { X } = { X according to the sensitivity degree of each weather factor obtained in step 3.2 from high to low 1 ,X 2 ,...,X n ,n≥1}。
The step 4 specifically comprises the following steps:
step 4.1, obtaining training samples, namely, meteorological data obtained in step 1 and ET obtained in step 2 0 label Dividing the training set and the testing set together;
and 4.2, inputting the meteorological factors { X } obtained in the step 3 into a training set to construct an integrated ELM model, setting a model precision threshold value, and optimizing the model by using test set data, wherein the specific steps are as follows:
step 4.2.1, inputting weather factors { X } = { X with top sensitivity ranking 1 Respectively measuring the data and ET obtained in the step 2 0 label The data were normalized as shown in equations (4) and (5):
in the formula (4), X' is a data measured value after normalization processing, X is a data measured value, X max ,X min Respectively a maximum value and a minimum value of the data measured values;
in the formula (5), ET' is normalized ET 0 label Calculating a value; ET is ET 0 label Calculating a value; ET (electric T) max And ET min ET respectively 0 label Maximum and minimum of (2);
step 4.2.2,Randomly generating three groups of input weights W 1 ，W 2 ，W 3 The method comprises the following steps:
in the formula (6), A, B, C is the number of three ELM hidden layer nodes respectively;
step 4.2.3, respectively obtaining three corresponding hidden layer node inputs according to the three ELM models, wherein the three hidden layer node inputs are as follows:
step 4.2.4, respectively obtaining corresponding three activation functions which are 'Sigmoid', 'Relu', 'Radbas' functions according to the three ELM models;
step 4.2.5, obtaining the output of the hidden layer of the ELM model according to the three activation functions obtained in step 4.2.4, wherein the output is as follows:
in the formula (8), g (x) 1 )，g(x 2 )，g(x 3 ) Three activation functions respectively;implicit layer node bias for three ELM models, a=1, 2,3, a; b=1, 2, B; c=1, 2,;
step 4.2.6, obtaining weights between the hidden layer and the input layer by using Moore-Penrose generalized inverse according to an ELM algorithm, wherein the weights are as follows:
in the formula (9), H + Moore-Penrose generalized inverse matrix for H;
step 4.2.7, obtaining an ELM model output according to the ELM network model formed by training, wherein the ELM model output comprises the following steps:
then carrying out inverse normalization treatment to obtain the predicted value of the evapotranspiration of the reference crops
The beneficial effects of the invention are as follows: the reference crop evapotranspiration prediction method based on the integrated extreme learning machine solves the problems that basic data of a reference crop evapotranspiration model is insufficient, required parameters are more and data are not easy to obtain, and an optimization prediction method based on a machine learning model is established. Investigation of ET by sensitivity analysis 0 The sensitivity degree of different meteorological factors is reduced, the meteorological factors are analyzed and selected, the model calculation complexity is reduced, and the ET is optimized 0 And the training samples are predicted, so that the prediction accuracy is improved.
Drawings
FIG. 1 is a flow chart of a reference crop evapotranspiration prediction method based on an integrated extreme learning machine of the present invention;
FIG. 2 is a schematic diagram of the building and training process of an integrated ELM model in the reference crop evapotranspiration prediction method based on an integrated extreme learning machine of the present invention;
FIG. 3 is a schematic diagram of a building flow of an integrated ELM model in the reference crop evapotranspiration prediction method based on an integrated extreme learning machine;
FIG. 4 is a diagram of ET from Shanxi province under meteorological factor analysis in the reference crop evapotranspiration prediction method based on an integrated extreme learning machine of the present invention 0 Schematic of the response curve to the main meteorological factors.
Detailed Description
The invention will be described in detail with reference to the accompanying drawings and detailed description.
The invention provides a reference crop evapotranspiration prediction method based on an integrated extreme learning machine, which is shown in fig. 1 and comprises the following steps:
step 1, collecting meteorological data collected by each meteorological station in a research domain, including a daily maximum temperature (T) max ) Minimum daily temperature (T) min ) Average daily temperature (T) mean ) Sun hours (n), relative Humidity (RH), wind speed (u), etc.; for the missing data of a small part, the space analysis module in the Arc GIS software is utilized to carry out the space analysis of factors, the inverse distance weight method is adopted to carry out the space interpolation acquisition, and the point to be interpolated in the simulation range is assumed to be P (x) p ,y p ,z p ) P point adjacent in-range point Q i (x i ,y i ,z i ) I=1, 2,..n, correlation value Z for P point using distance weighting method p And (5) interpolation analysis. The calculation formula is as follows:
wherein: d, d i Is the distance between the interpolation point and the ith point in the adjacent range.
Step 2, adopting ET proposed by the United nations grain and agriculture organization (FAO) according to the meteorological data obtained in the step 1 0 Standard calculation formula Penman-Monteth (P-M) formula for calculating standard reference crop evapotranspiration ET 0 label The formula is as follows:
wherein: ET (electric T) 0 label The unit is mm/d for the standard reference crop evapotranspiration; g is soil heat flux, and the unit is MJ/(m) 2 ·d)；R n The unit of the net radiation quantity of the crop canopy is MJ/(m) 2 D) a step of; t is the average air temperature at the height of 2m, and the unit is the temperature; u (u) 2 Wind speed at the height of 2m is expressed in m/s; e, e s Saturated water vapor pressure is given in kpa; e, e a The unit is kpa for the actual water vapor pressure; delta is the slope of the saturated water vapor pressure versus temperature curve, and the unit is kpa/°c; gamma is the dry-wet thermometer constant in kpa/°c.
Step 3, sensitivity analysis is adoptedResearch on meteorological factors on ET by law 0 By analysis of ET from response curves and sensitivity matrices 0 The sensitivity degree of different meteorological factors is further analyzed and selected for the meteorological factors in the P-M formula.
Step 3.1, response curve: applying [ -20% to each meteorological factor]Disturbance of the range, substituting the changed meteorological factor parameters into a P-M formula, and calculating a reference crop evapotranspiration value ET under parameter variation 0ΔXi 。
Step 3.2, sensitive matrix: exhibit ET 0 The sensitivity to a certain meteorological factor is expressed as follows:
wherein: p (DeltaET) 0 -ΔX i ) For reference crop evapotranspiration to meteorological factor X i Sensitivity of (2), i.e. meteorological factor X i When the variation of (a) is delta, the reference crop evapotranspiration is relative to ET 0 label Is a variable amount of (a).
Step 3.3, selecting a meteorological factor { X } according to the sensitivity level from high to low according to the analysis result of the step 3.2, wherein { X } = { X 1 ,X 2 ,...,X n N is greater than or equal to 1}, and is used as an input variable of the model.
Step 4, constructing an integrated ELM model based on the sensitive meteorological factors obtained in the step 3, and optimizing to obtain a reference crop evapotranspiration predicted valueAs shown in fig. 2 and 3, the integrated ELM model building and training process is specifically as follows:
step 4.1, obtaining training samples, namely, meteorological data obtained in step 1 and ET obtained in step 2 0 label Dividing the training set and the testing set together;
and 4.2, inputting the meteorological factors { X } obtained in the step 3 into a training set to construct an integrated ELM model, setting a model precision threshold value, and optimizing the model by using test set data, wherein the specific steps are as follows:
step 4.2.1, inputting weather factors { X } = { X with top sensitivity ranking 1 Respectively measuring the data and ET obtained in the step 2 0 label The data were normalized as follows:
wherein X' is the normalized data measurement value, X is the data measurement value, X max ,X min Respectively a maximum value and a minimum value of the data measured values;
wherein ET' is normalized ET 0 label Calculating a value; ET is ET 0 label Calculating a value; ET (electric T) max And ET min ET respectively 0 label Maximum and minimum of (2);
step 4.2.2, randomly generating three groups of input weights W 1 ，W 2 ，W 3 The method comprises the following steps:
wherein A, B, C is the number of nodes of three ELM hidden layers respectively;
step 4.2.3, respectively obtaining three corresponding hidden layer node inputs according to the three ELM models, wherein the three hidden layer node inputs are as follows:
step 4.2.4, respectively obtaining corresponding three activation functions which are 'Sigmoid', 'Relu', 'Radbas' functions according to the three ELM models;
step 4.2.5, obtaining the output of the hidden layer of the ELM model according to the three activation functions obtained in step 4.2.4, wherein the output is as follows:
wherein g (x 1 )，g(x 2 )，g(x 3 ) Three activation functions respectively;implicit layer node bias for three ELM models, a=1, 2,3, a; b=1, 2, B; c=1, 2,;
step 4.2.6, obtaining weights between the hidden layer and the input layer by using Moore-Penrose generalized inverse according to an ELM algorithm, wherein the weights are as follows:
β 1 ＝(H 1 ) + ET′
β 2 ＝(H 2 ) + ET′
β 3 ＝(H 3 ) + ET′
wherein H is + Moore-Penrose generalized inverse matrix for H;
step 4.2.7, obtaining an ELM model output according to the ELM network model formed by training, wherein the ELM model output comprises the following steps:
then carrying out inverse normalization treatment to obtain the predicted value of the evapotranspiration of the reference crops
Step 4.3, checking ET of the Integrated ELM model 0 If the simulation accuracy does not reach the threshold value, the meteorological factors selected in the step 3 are sequentially increased by factors (namely { X } = { X) 1 ,X 2 -2) training the model, repeating step 4.2, until the accuracy requirement is met, and determining an integrated ELM model for the investigation region when the model accuracy requirement is met;
and 4.4, evaluating the integrated ELM model.
Including but not limited to using Root Mean Square Error (RMSE), mean Absolute Error (MAE), coefficient of determination (R 2 ) The index is used as the index of the quality of the judging algorithm. The specific calculation formula of each index is as follows:
root Mean Square Error (RMSE):
mean Absolute Error (MAE):
determining coefficient (R) 2 )：
Wherein: y is Y i The ith daily value of the model simulation;the mean value of the model simulation on the ith day; z is Z i An ith daily standard value calculated for the P-M model; />The ith mean value calculated for the P-M model; n is the total amount of data samples.
In building neural network based models, accuracy and stability are typically chosen as two main criteria for judging the performance of the model. The smaller the values of the RMSE and the MAE in the model evaluation method, the more stable the model is; r is R 2 The closer to 1 the value of (c) is, the higher the agreement between the model predicted value and the calculated value is.
Through the mode, the reference crop evapotranspiration prediction method based on the integrated extreme learning machine can accurately predict the reference crop evapotranspiration in data-missing areas and data-incomplete areas, and is specifically characterized in that:
(1) The invention solves the problems of insufficient basic data, more required parameters and difficult acquisition of data of a reference crop evapotranspiration model calculated based on a P-M formula, and establishes an optimization prediction method based on a machine learning model;
(2) The invention explores ET by a sensibility analysis method 0 The sensitivity degree of different meteorological factors is analyzed and selected, the calculation complexity of a model is reduced, and ET is optimized 0 Predicting training samples, and improving prediction accuracy;
(3) The invention builds an integrated ELM model based on a machine learning algorithm, and provides a method capable of remarkably improving calculation accuracy of the evapotranspiration of reference crops under the condition of lacking meteorological factors;
(4) The invention has good portability, can be applied to various environment monitoring systems, is used for estimating the crop evapotranspiration of crops in research areas lacking complete meteorological data, and provides basis for estimating the crop yield, making decisions for accurate irrigation and making irrigation systems.
Examples
The invention takes Shaanxi province as a research areaAn explanation is given. Meteorological data of 32 meteorological sites 1990-2019 of Shaanxi province are collected in a China meteorological science sharing service network. Computing ET based on P-M formula 0 As a standard value, regarding weather factors and ET day by day 0 The data divides the training samples and the analog samples. The training sample data are taken from 1990 to 2013, and the simulation set data are taken from 2014 to 2019.
Average day ET of 1990-2019 of Shaanxi province through a step 3 method 0 The sensitivity analysis is carried out on the main meteorological factors, and the specific flow is as follows:
1) Calculating the average value of each climate factor according to the daily meteorological data (comprising average temperature, wind speed, sunshine hours and relative humidity) based on 1990-2019;
2) The average value of the meteorological factors is brought into a P-M formula to obtain ET 0 Is a standard value of (2);
3) Setting one factor to float up and down for disturbance of + -5%, + -10% and + -20% respectively, and simultaneously controlling other factors to be unchanged, so that the ET under the single meteorological factor change is obtained by using a P-M formula 0 Value and ET calculated in the second step 0 Comparing the standard values to obtain ET 0 The relative rate and absolute value of the change;
4) Drawing a sensitivity analysis table and an analysis chart;
5) Analyzing and evaluating the result;
the sensitivity analysis chart and the sensitivity analysis table show that FIG. 4 is ET of Shaanxi province 0 Response curves to major meteorological factors, table 1 ET for regions of Shaanxi province 0 A sensitivity analysis table for climate influencing factors; from FIG. 4, it can be seen that ET of Shaanxi province 0 The air conditioner is most sensitive to average air temperature, relative humidity and sunlight hours, and is least sensitive to wind speed. From table 1, the sensitivity was found to be, in order from high to low, average temperature, relative humidity, number of sunshine hours, and wind speed. The response curve and the sensitivity matrix result show that the sensitivity has consistency, and weather factors which are sequentially input by the integrated ELM model are obtained according to the sensitivity degree analysis.
TABLE 1 ET for Shaanxi provinces 0 Sensitivity analysis table for climate influence factors
After the model is built according to the method of the step 4, a single standard ELM model built by 3 activation functions such as Sigmoid, relu, radbas and the like is compared with an integrated ELM model based on three different activation functions adopted by the invention to predict the day ET under the same meteorological factor combined input 0 Precision. The simulation results for ELM-Sigmoid, ELM-Relu, ELM-Radbas, and integrated ELM are shown in Table 2: from the table, the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) of the ELM integrated model are smaller than those of the other three models, and the coefficient (R 2 ) The method is higher than the other three models, so that the integration method proposed by the research is more accurate and more stable.
TABLE 2 simulation result accuracy comparison of different ELM models
The input parameters are combined by 2-4 different meteorological factors, an integrated ELM model is built, the influence on the simulation precision of the integrated ELM model under the condition of lacking one or more meteorological factors is studied, and the result is shown in Table 3.
TABLE 3 simulation accuracy of ET0 for extreme learning machine models under different meteorological factors
As can be seen from the table, the model (No. 5 and No. 2) for inputting the meteorological factors according to the sensitivity degree in the region under the conditions of average temperature, relative humidity, sunshine hours and wind speed according to the sensitivity analysis has higher precision, higher stability and better prediction effect. Indicating that good prediction accuracy can be achieved even in the absence of partial weather factors; meanwhile, the more meteorological factors are not (number 4 and number 5), the better the prediction effect is; therefore, the method can be used for well predicting the evapotranspiration of the reference crops in the areas lacking complete meteorological data.
Claims (5)
1. The reference crop evapotranspiration prediction method based on the integrated extreme learning machine is characterized by comprising the following steps of:
step 1, acquiring meteorological data of a research area and preprocessing the meteorological data;
step 2, calculating the standard reference crop evapotranspiration ET by adopting a P-M formula according to the meteorological data obtained in the step 1 0 label ；
Step 3, based on the ET obtained in step 2 0 label Disturbance is applied to each meteorological factor in the P-M formula, so that the sensitivity degree of the reference crop evapotranspiration to different meteorological factors is obtained, and meteorological factors are selected;
step 4, constructing an integrated ELM model based on the sensitive meteorological factors obtained in the step 3, and optimizing to obtain a reference crop evapotranspiration predicted value
2. The method for predicting the evapotranspiration of a reference crop based on an integrated extreme learning machine as set forth in claim 1, wherein said step 1 specifically comprises the steps of:
step 1.1, collecting daily meteorological data collected by each meteorological station in a research area, wherein the daily meteorological data comprise a daily maximum temperature T max Minimum temperature T min Average temperature T of day mean The sunshine duration n, the relative humidity RH and the wind speed u;
when missing data exists in the time sequence of the meteorological data collected in the step 1.2 and the step 1.1, the space analysis module is utilized to carry out space analysis, and the inverse distance weight method is adopted to carry out space interpolation, and the method specifically comprises the following steps:
assume that the point to be interpolated in the analog range is P (x p ,y p ,z p ) P point adjacent in-range point Q i (x i ,y i ,z i ) I=1, 2,..n, correlation value Z for P point using distance weighting method p Interpolation analysis, the calculation formula is:
in the formula (1), d i Is the distance between the interpolation point and the ith point in the adjacent range.
3. The reference crop evapotranspiration prediction method based on an integrated extreme learning machine as set forth in claim 1, wherein the formula P-M adopted in the step 2 is as follows:
in formula (2), ET 0 label The unit is mm/d for the standard reference crop evapotranspiration; g is soil heat flux, and the unit is MJ/(m) 2 ·d)；R n The unit of the net radiation quantity of the crop canopy is MJ/(m) 2 D) a step of; t is the average air temperature at the height of 2m, and the unit is the temperature; u (u) 2 Wind speed at the height of 2m is expressed in m/s; e, e s Saturated water vapor pressure is given in kpa; e, e a The unit is kpa for the actual water vapor pressure; delta is the slope of the saturated water vapor pressure versus temperature curve, and the unit is kpa/°c; gamma is the dry-wet thermometer constant in kpa/°c.
4. The method for predicting the evapotranspiration of a reference crop based on an integrated extreme learning machine according to claim 1, wherein said step 3 specifically comprises the steps of:
step 3.1, for each meteorological factor X in the P-M formula i Disturbance is applied, the changed meteorological factors are substituted into a P-M formula, and the meteorological factors X are calculated i Reference crop evapotranspiration value ET at variation delta 0ΔXi ；
Step 3.2 ET obtained according to step 3.1 0ΔXi And ET obtained in step 2 0 label Exhibiting reference crop evapotranspiration versus meteorological factor X i Sensitivity of (B) as shown in the formula%3) The following is shown:
in formula (3), P (ΔET) 0 -ΔX i ) For reference crop evapotranspiration to meteorological factor X i Sensitivity of (2), i.e. meteorological factor X i When the variation of (a) is delta, the reference crop evapotranspiration is relative to ET 0 label Is a variable amount of (a);
step 3.3, selecting weather factors { X }, { X } = { X according to the sensitivity degree of each weather factor obtained in step 3.2 from high to low 1 ,X 2 ,...,X n ,n≥1}。
5. The method for predicting the evapotranspiration of a reference crop based on an integrated extreme learning machine according to claim 1, wherein said step 4 specifically comprises the steps of:
step 4.1, obtaining training samples, namely, meteorological data obtained in step 1 and ET obtained in step 2 0 label Dividing the training set and the testing set together;
and 4.2, inputting the meteorological factors { X } obtained in the step 3 into a training set to construct an integrated ELM model, setting a model precision threshold value, and optimizing the model by using test set data, wherein the specific steps are as follows:
step 4.2.1, inputting weather factors { X } = { X with top sensitivity ranking 1 Respectively measuring the data and ET obtained in the step 2 0 label The data were normalized as shown in equations (4) and (5):
in the formula (4), X' is a data measured value after normalization processing, X is a data measured value, X max ,X min Respectively a maximum value and a minimum value of the data measured values;
in the formula (5), ET' is normalized ET 0 label Calculating a value; ET is ET 0 label Calculating a value; ET (electric T) max And ET min ET respectively 0 label Maximum and minimum of (2);
step 4.2.2, randomly generating three groups of input weights W 1 ，W 2 ，W 3 The method comprises the following steps:
in the formula (6), A, B, C is the number of three ELM hidden layer nodes respectively;
step 4.2.3, respectively obtaining three corresponding hidden layer node inputs according to the three ELM models, wherein the three hidden layer node inputs are as follows:
step 4.2.4, respectively obtaining corresponding three activation functions which are 'Sigmoid', 'Relu', 'Radbas' functions according to the three ELM models;
step 4.2.5, obtaining the output of the hidden layer of the ELM model according to the three activation functions obtained in step 4.2.4, wherein the output is as follows:
in the formula (8), g (x) 1 )，g(x 2 )，g(x 3 ) Three activation functions respectively;implicit layer node bias for three ELM models, a=1, 2,3, a; b=1, 2, B; c=1, 2,;
step 4.2.6, obtaining weights between the hidden layer and the input layer by using Moore-Penrose generalized inverse according to an ELM algorithm, wherein the weights are as follows:
in the formula (9), H + Moore-Penrose generalized inverse matrix for H;
step 4.2.7, obtaining an ELM model output according to the ELM network model formed by training, wherein the ELM model output comprises the following steps:
then carrying out inverse normalization treatment to obtain the predicted value of the evapotranspiration of the reference crops
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