Construction method of crop leaf age simulation model

Abstract

The invention discloses a method for constructing a crop leaf age simulation model, and the method comprises the following steps: (1) collecting the phenological data of a to-be-simulated crop at a research site, and obtaining the day order of the beginning of the development period of the to-be-simulated crop, all key development stages, and the meteorological data of the research site; (2) according to the data obtained in the step (1), continuously calculating three types of development period process simulation values of the to-be-simulated crop under a day-by-day or hour-by-hour scale through a temperature difference method, a temperature accumulation method and a physiological development time method, and obtaining leaf age simulation values under the three types of development period processes by utilizing a quantitative relation between leaf age and the three types of development period process simulation values; and (3) integrating the leaf age simulation values obtained in the step (2) under the three developmental period processes to obtain a leaf age integrated simulation value of the to-be-simulated crop. The crop leaf age simulation model constructed by the method is high in precision, and technical support is provided for intelligent production management of horticultural crops.

Description

Technical Field

[0001] This invention belongs to the field of agricultural science and technology, and specifically relates to a method for constructing a crop leaf age simulation model. Background Technology

[0002] Leaf age exhibits a strict correlation with root growth and internode elongation, serving as an outward indicator of the growth process and directly impacting photosynthesis, growth, development, and yield formation in plants. In recent years, crop simulation models have been widely applied to optimize farmland production management decisions to improve yield and quality. Leaf age models are a crucial component of crop models, using environmental conditions such as temperature, light, soil, and water as driving variables to quantitatively describe the dynamics of crop leaf growth, providing a theoretical basis for achieving "digitally visible crop leaf age." In agricultural production, for crops where leaf growth is the harvest target, the harvest period is often based on the maturity of leaves at different locations; therefore, improving its accuracy and reliability is paramount.

[0003] Leaf age simulation models can draw on the modeling methods of developmental stage simulation models, using developmental progress as the driving variable to quantitatively simulate leaf age changes. However, when using the time after sowing / transplanting as the driving variable, the unstable crop growth environment fails to reflect the relationship between environmental conditions and leaf emergence, resulting in poor replicability and generalizability of such simulation models. When using accumulated temperature or thermal time as the driving variable, the simulation model is only applicable to crops that are not photoperiod-sensitive, and the impact of extreme temperatures on crop development must also be considered. When using physiological development time or radiative heat accumulation as the driving variable, although light and temperature are considered, it is more suitable for photoperiod-sensitive crops. However, due to the non-linear relationship between crop development rate and temperature, especially under extreme temperatures or large diurnal temperature ranges, different temperature response patterns vary significantly, requiring consideration of the crop's biological limit temperature. Furthermore, the cumulative heat required for a crop to complete a certain developmental stage is not constant, leading to biases in phenological stage simulations.

[0004] To date, while different models have advantages in capturing different aspects of crop growth processes, no single model can guarantee better simulation accuracy than others under all conditions. Building on this, Yang Y et al. combined crop models with genome prediction to achieve multi-model quantitative analysis; Liu W et al. integrated plant-soil-management modules into a single model system to determine the impact of phosphate fertilizer application on yield; the Agricultural Model Comparison and Improvement Project (AgMIP) has compared 27 wheat models, representing the largest ensemble of crop models created to date. These models vary significantly in complexity and crop-environment interaction modeling methods, and leaf age simulation models constructed using developmental process modeling methods for different types of horticultural crops (leafy vegetables, melons and fruits, flowers, shrubs, etc.) also exhibit inconsistent quality.

[0005] Therefore, there is an urgent need to develop a crop leaf age simulation model with high simulation accuracy. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing a crop leaf age simulation model, which can accurately simulate the leaf age of different crops.

[0007] To achieve the above-mentioned objectives, the technical solution of the present invention is as follows:

[0008] A method for constructing a crop leaf age simulation model includes the following steps:

[0009] (1) Collect phenological data of the crop to be simulated at the research site, and obtain the date sequence of the start of the development period of the crop to be simulated, the key development stages, and the meteorological data of the research site.

[0010] (2) Based on the data obtained in step (1), the simulated values ​​of the three types of developmental stages of the crop to be simulated on a daily or hourly scale are calculated continuously using the temperature difference method, accumulated temperature method and physiological development time method, and the simulated values ​​of leaf age under the three types of developmental stages are obtained by using the quantitative relationship between leaf age and the simulated values ​​of the three types of developmental stages.

[0011] (3) Integrate the simulated leaf age values ​​under the three developmental stages obtained in step (2) to obtain the integrated simulated leaf age values ​​of the crop to be simulated.

[0012] This invention utilizes 27 sets of experimental data to establish a leaf age simulation model and 18 sets of independent experimental data to validate the model. It constructs a leaf age simulation model for horticultural crops based on at least three mainstream modeling methods, determines the model parameters, and integrates the simulation results of various algorithm models to improve the accuracy of the model and provide technical support for intelligent production management of horticultural crops.

[0013] The RMSE between the simulated and measured values ​​of the crop leaf age simulation model constructed in this invention is 1-7.23d, the NRMSE is 1.16-8.32%, the R² is 0.99-1, and the D value is 1. It can be seen that the simulated and measured values ​​of crop leaf age constructed in this invention are very close, and the simulated values ​​of crop leaf age can accurately predict the leaf age of the simulated crop.

[0014] Preferably, step (2) further includes continuously calculating the simulated developmental process of the crop to be simulated on a daily or hourly scale using the radiative thermal accumulation method, in order to further improve the simulation accuracy; that is:

[0015] The above-mentioned method for constructing a crop leaf age simulation model includes the following steps:

[0016] (1) Collect phenological data of the crop to be simulated at the research site, obtain the date sequence of the start of the development period of the crop to be simulated and the meteorological data of the research site;

[0017] (2) Based on the data obtained in step (1), the simulated values ​​of the four types of developmental stages of the crop to be simulated on a daily or hourly scale are continuously calculated by the temperature difference method, accumulated temperature method, physiological development time method and radiation heat accumulation method, respectively. The simulated values ​​of leaf age under the four types of developmental stages are obtained by using the quantitative relationship between leaf age and the simulated values ​​of the four types of developmental stages.

[0018] When using the temperature difference method to calculate the simulated value of the developmental process of the crop to be simulated, the cumulative daily maximum temperature difference (ATD) is calculated using the cumulative maximum temperature difference method shown in formula (1). maximum_daily Alternatively, the cumulative diurnal temperature range (ATD) can be calculated using the cumulative diurnal temperature range method shown in formula (2). dif_daily ;

[0019]

[0020]

[0021] In the formula, T i_max The highest daily / hourly temperature, in °C; T i_min The lowest daily / hourly temperature, in °C; T i_day T represents the daily daytime temperature, in °C. i_night is the daily nighttime temperature, °C; DS is the total number of days / hours of the crop growth and development process to be simulated, d / h; i is the i-th day / hour of the crop growth and development to be simulated, d / h.

[0022] When calculating the simulated developmental stages of the crop using the accumulated temperature method, the cumulative effective accumulated temperature (Accu) should be calculated using at least one of the following three extreme temperature response simulation methods: 1), 2), and 3). E Or accumulated activity temperature Accu A ;

[0023] 1) Assumption A: Based solely on the biological lower limit temperature T b As a temperature indicator:

[0024]

[0025]

[0026] 2) Assumption B: Using the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator:

[0027]

[0028]

[0029] 3) Assumption C: Based on the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator:

[0030]

[0031]

[0032] In the formula, T i_ave The value represents the daily average air temperature / leaf temperature, in °C.

[0033] When calculating the simulated value of the developmental process of the crop to be simulated using the physiological development time method, first use at least one of the linear or sinusoidal temperature response modes shown in Equation (9) to calculate the temperature effect factor TE, and then calculate the physiological development time PDT according to Equation (10).

[0034]

[0035]

[0036] In the formula, T ol T ou The optimal temperature for simulating crop growth during this developmental stage is ℃; T b The lower biological limit temperature, in °C; T m The upper limit of biological temperature, in °C.

[0037] When using the radiative heat accumulation method to calculate the simulated value of the development process of the crop to be simulated, the daily relative radiative heat accumulation RTEP is first calculated according to formula (11), and then the daily relative radiative heat accumulation is accumulated according to formula (12) to obtain the cumulative radiative heat accumulation TEP.

[0038] RTEP = TE n ×PAR=TE n ×K×Q,n=1,2,3,4 (11);

[0039]

[0040] In the formula, RTEP is the daily relative radiant heat product, MJ / (m²). 2 ·d); TE is the temperature effect factor; PAR is the daily average photosynthetically active radiation, MJ / (m 2 ·d); Q is the average daily total solar radiation during this period, MJ / (m 2 ·d); K is the proportion of photosynthetically active radiation in total solar radiation.

[0041] As a further optimization, the cumulative daily maximum temperature difference ATD is calculated using formula (1).maximum_daily At that time, T i_max T represents the highest temperature per hour. i_min This represents the lowest temperature per hour. In other words, the temperature difference method is performed on an hourly scale.

[0042] As a further optimization, in equations (3)-(9), T i_ave The average daily leaf temperature;

[0043] As a further preferred option, the formula for calculating the temperature effect factor TE in equations (9) and (11) is as follows:

[0044] The preferred temperature response mode is the sinusoidal temperature response mode.

[0045] After obtaining the simulated values ​​of the four developmental stages, the simulated values ​​of leaf age under the four developmental stages can be obtained by using the quantitative relationship between leaf age and the simulated values ​​of the four developmental stages as shown in equations (13), (14) or (15).

[0046] DP i_n -DP0=a×(N i -N0)+b,n=1,2,…,21(22) (13);

[0047] DP i_n =a×ln(N) i )+b,n=1,2,…,21(22) (14);

[0048] DP i_n =a×N i +b,n=1,2,…,21(22) (15);

[0049] In the formula, N i DP represents the leaf age measurement on day i; N0 represents the initial leaf age measurement; i_n DP0 represents the No. n developmental stage progress on day i; DP0 represents the No. n developmental stage progress at the first harvest; a and b are model parameters; n is the number of methods to calculate the simulated value of the developmental stage progress.

[0050] Formula (13) is applicable to simulating the leaf age of spinach, formula (14) is applicable to simulating the leaf age of tea leaves and parsley, and formula (15) is applicable to simulating the leaf age of other crops.

[0051] (3) Integrate the simulated leaf age values ​​under the four developmental stages obtained in step (2) to obtain the integrated simulated leaf age values ​​of the crop to be simulated;

[0052] Specifically, integration is performed using at least one of the following methods:

[0053] ①Mean method: Maverage =∑ m＝1 DS(16);

[0054] ② (Maximum value + Minimum value) / 2 integration method: M max+min =(min m＝1 DS+max m＝1 DS) / 2(17);

[0055] ③Median method: M median =median m＝1 DS(18);

[0056] ④ Stepwise regression method: M stepregression =a m ×DS m (19);

[0057] In the formula, m is the number of methods or categories of the developmental process algorithm in step (2), and a m The weighting coefficients represent the simulated leaf age values ​​obtained through different methods or categories of developmental process algorithms; DS represents the simulated leaf age values ​​obtained through different methods or categories of developmental process algorithms.

[0058] ⑤ BP Neural Network Method: The BP neural network, also known as the back propagation neural network, is one of the most widely used neural network models. Its design principle is that the signal propagates forward, and the error propagates backward. The input signal propagates forward from the input layer through the hidden layers, processing them layer by layer until the output error is less than a pre-set target error or the number of iterations exceeds the maximum training count; otherwise, it propagates backward. A BP neural network includes an input layer, hidden layers, and an output layer. Let the input layer have n neurons, the output layer have m neurons, and the hidden layer have l neurons; let i be the index of the input layer neuron (i = 1, 2, ..., n); let j be the index of the hidden layer neuron (j = 1, 2, ..., l); let k be the index of the output layer neuron (k = 1, 2, ..., m); and let w be the connection weight from input layer neuron i to hidden layer neuron j. ij The connection weights from hidden layer neuron j to output layer neuron k are w. jk Let the threshold of the j-th hidden layer neuron be a. j Let the threshold of the k-th output layer neuron be b. k Let H be the output of the j-th hidden layer neuron. j Let the value of the i-th neuron in the input layer be x. i The value of the k-th neuron in the output layer is Y. k Let Q be the parameter for adjusting the form of the excitation function, then the calculation method of the unit cell of the BP neural network is shown in formulas (20) to (27).

[0059] Excitation function:

[0060] Calculate the output value of the j-th hidden layer neuron:

[0061] Calculate the predicted output value of the k-th output layer neuron: O k =H j *w ij -b k (twenty two);

[0062] Network prediction error: e k =Y k -Q k (twenty three);

[0063] Update the connection weights between the input layer and the hidden layer:

[0064] Update the connection weights between the hidden layer and the output layer: w jk =w jk +η*H j *e k (25);

[0065] Update the threshold of hidden layer neurons:

[0066] Update the threshold of the output layer neurons: b k =b k +e k (27);

[0067] Repeat the iterations until the output error is less than the preset target error or the number of iterations exceeds the maximum number of training iterations.

[0068] ⑥ Elman Neural Network Method: The Elman neural network is a two-layer BP network structure with feedback, consisting of an input layer, hidden layers (intermediate layers), a receiving layer, and an output layer. The input layer units transmit signals, the output layer units perform linear weighting, and the intermediate layer units can use nonlinear or linear transfer functions, which are transferred from the output of the hidden layer to its input. This feedback method enables the Elman network to detect and identify time-varying patterns. The receiving layer acts as a one-step delay operator, returning the output value of the intermediate layer units from the previous time step to the input. This special two-layer network can approximate any function with arbitrary precision. The only requirement is that its hidden layer must have a sufficient number of neurons. The nonlinear state-space expression describing the Elman neural network is shown in formulas (28) to (31):

[0069] y(k)=g(w 3 x(k))(28):

[0070] x(k)=f(w 1 x c (k)+w 2 (T(k-1)))(29);

[0071] x c (k)=x(k-1)(30);

[0072] Where: T, x, x c y represents the r-dimensional input vector, n-dimensional hidden layer node unit vector, n-dimensional feedback state vector, and m-dimensional output node vector, respectively; w 1 w 2 w 3 These are the connection weights from the state layer to the hidden layer, from the input layer to the hidden layer, and from the hidden layer to the output layer, respectively; f() is the transfer function of the hidden layer neurons, usually using the S-function; g() is the transfer function of the output neurons, which is a linear combination of the outputs of the hidden layers;

[0073] Because of feedback connections in the hidden layers, the final output of the network is influenced by the initial input, and this influence is determined by the connection matrix between nodes. Let the k-th output of the network be yd(k), then the error function is calculated as follows:

[0074]

[0075] For BP neural network and Elman neural network methods, to avoid neuron saturation, the input data is normalized in the input layer, converting each value to the [0,1] interval, and the prediction result is denormalized in the output layer; in this invention, the number of hidden layer neurons in the BP neural network and Elman neural network is set to... (a is a constant between 1 and 10). To improve training efficiency and network generalization performance, a normalization method is used to preprocess the sample data.

[0076] In the method for constructing the crop leaf age simulation model of the present invention, there are 22 methods for the developmental process algorithm on a daily scale, i.e., n = 22 in equations (13)-(15); and 21 algorithms for the developmental process algorithm on an hourly scale, i.e., n = 22 in equations (13)-(15).

[0077] In step (3), the 21 or 22 developmental process algorithms can be integrated step by step, or the average of the 21 or 22 developmental process algorithms can be calculated according to their respective categories before integration. Preferably, in step (3), the average of the 21 or 22 developmental process algorithms is calculated according to their respective categories before integration, and the Elman neural network method is used for integration.

[0078] Under these conditions, the RMSE between the simulated and predicted leaf age values ​​is 1d, the NRMSE is 1.16%, the R² is 1, and the D value is 1, indicating optimal simulation accuracy.

[0079] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0080] (1) This invention uses 27 sets of experimental data to establish a leaf age simulation model and 18 sets of independent experimental data to verify the model. It constructs a leaf age simulation model for horticultural crops based on at least three mainstream modeling methods, determines the model parameters, and integrates the simulation results of various algorithm models to improve the accuracy of the model and provide technical support for intelligent production management of horticultural crops.

[0081] (2) The RMSE between the simulated and measured values ​​of the crop leaf age simulation model constructed in this invention is 1-7.23d, the NRMSE is 1.16-8.32%, the R2 is 0.99-1, and the D value is 1. It can be seen that the simulated and measured values ​​of crop leaf age constructed in this invention are very close, and the simulated values ​​of crop leaf age can accurately predict the leaf age of the simulated crop.

[0082] (3) In this invention, it is preferable to integrate 21 or 22 developmental process algorithms after calculating the mean according to their respective categories, and to use the Elman neural network method for integration; in this case, the RMSE between the simulated and predicted values ​​of leaf age integration is 1d, the NRMSE is 1.16%, the R2 is 1, and the D value is 1; the simulation accuracy is optimal. Attached Figure Description

[0083] Figure 1 The validation results of the leaf age simulation model at different time scales (stepwise ensemble);

[0084] Wherein, Observation(d) represents the measured value (day), Simulation(d) represents the simulated value (day), Timescales represents the time scale, Dailyresults represents the results obtained under the daily scale algorithm, and Hourlyresults represents the results obtained under the hourly scale algorithm; the same applies below.

[0085] Figure 2 Validation results of developmental simulation models for different crop species (stepwise integration);

[0086] In this context, "Cropvariety" refers to crop varieties, "Apium graveolens L." refers to celery, "Spinaciaoleracea Linn." refers to spinach, "Lycopersicum esculentum Mill." refers to tomato, "Cucumis sativus L." refers to cucumber, "Libanotisseseloides Turcz." refers to parsley, and "Tulipa gesneriana L." refers to tulip; the same applies below.

[0087] Figure 3 The validation results of developmental simulation models under different simulation methods (step-by-step integration);

[0088] Wherein, simulationmethod represents the simulation method, temperaturedifferencemethod represents the temperature difference method, active accumulated temperaturemethod represents the active accumulated temperature method, effective accumulated temperaturemethod represents the effective accumulated temperature method, physiological development timemethod represents the physiological development time method, photo-thermal indexmethod represents the photo-thermal index method, and integrationmethod represents the integration method, and the same applies below.

[0089] Figure 4 Validation results (mean ensemble) of leaf age simulation models at different time scales;

[0090] Figure 5 Validation results (mean ensemble) of developmental period simulation models for different crop species;

[0091] Figure 6 Validation results of developmental simulation models under different simulation methods (mean ensemble);

[0092] Among them, Average integration method represents the mean integration method, Maximum and minimum average integration method represents the maximum and minimum average integration method, Median integration method represents the median integration method, Stepwise regression integration method represents the stepwise regression integration method, BP neural network represents the BP neural network integration method, and Elman neural network represents the Elman neural network integration method. Detailed Implementation

[0093] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0094] Example 1

[0095] This embodiment describes a method for constructing a crop leaf age simulation model, which includes the following steps:

[0096] (1) Collect phenological data of the crop to be simulated at the research site, obtain the date sequence of the start of the development period of the crop to be simulated and the meteorological data of the research site;

[0097] Specifically, including:

[0098] 1) Experimental Design

[0099] In this embodiment, cucumber, tulip, celery, spinach, parsley, and tea were used as simulated crops. The cucumber and celery experiments were conducted at the Agricultural Science and Technology Innovation Base Park in Wuqing District, Tianjin (E116.97°, N39.43°, altitude 8m). The tulip experiment was conducted at the B2 solar greenhouse base of Yangzhen International Flower Port in Shunyi District, Beijing (E116.79°, N40.17°, altitude 38m). The celery, spinach, and parsley experiments were conducted at the glass greenhouse base of Lishui University in Lishui City, Zhejiang Province (E119.92°, N28.45°, altitude 61.8m). The tea experiment was conducted at Huangbutou Village in Songyang County, Lishui City, Zhejiang Province (E119.44°, N28.50°, altitude 544.0m) and Xiaoshi Village in Zhaitang Township, Songyang County, Lishui City, Zhejiang Province (E119.44°, N28.49°, altitude 128.0m). The tested horticultural crop varieties, crop rotation sowing dates, and the dates of the beginning and end of the developmental stages are shown in Table 1. Each sowing date has 3 replicates, and a randomized block design is used.

[0100] Table 1. Test varieties and experimental design in this embodiment.

[0101]

[0102]

[0103] Note: Experimental data marked with * are used for model validation, while other experimental data are used for model building.

[0104] 2) Meteorological data acquisition

[0105] Microclimate observations inside the greenhouse were conducted using a CAWS2000 microclimate observation instrument (Beijing Huayun Shangtong Technology Co., Ltd.), which automatically recorded meteorological data such as indoor air temperature, humidity, CO2 concentration, and total solar radiation every 10 minutes. Intensive auxiliary observations were conducted using a Hobo microclimate observation instrument (ONSET, USA), which automatically recorded meteorological data such as indoor air temperature, humidity, and total solar radiation every 5 minutes. Hourly meteorological data provided by the local meteorological station were used for microclimate observations outside the greenhouse.

[0106] (2) Based on the data obtained in step (1), the simulated values ​​of the four types of developmental stages of the crop to be simulated on a daily or hourly scale are continuously calculated by the temperature difference method, accumulated temperature method, physiological development time method and radiation heat accumulation method, respectively. The simulated values ​​of leaf age under the four types of developmental stages are obtained by using the quantitative relationship between leaf age and the simulated values ​​of the four types of developmental stages.

[0107] Specifically, the simulated values ​​of the developmental process are first calculated using the following method:

[0108] 1) Temperature difference method

[0109] The temperature difference method is divided into the daily maximum temperature difference method and the diurnal temperature difference method. The daily maximum temperature difference is calculated by the difference between the highest and lowest temperatures in the greenhouse each day, while the diurnal temperature difference is calculated by the difference between the daytime and nighttime temperatures in the greenhouse each day. Therefore, the accumulated daily maximum temperature difference (ATD) is calculated using formula (1). maximum_daily The cumulative diurnal temperature difference (ATD) is calculated using formula (2). maximum_daily Since hourly meteorological data does not distinguish between day and night, the cumulative diurnal temperature difference method is not considered in the hourly algorithm of this study.

[0110]

[0111]

[0112] In the formula, T i_max The highest daily / hourly temperature, in °C; T i_min The lowest daily / hourly temperature, in °C; T i_dayT represents the daily daytime temperature, in °C. i_night ...

[0113] 2) Accumulated Temperature Method

[0114] The accumulated temperature method is divided into two types: effective accumulated temperature method and active accumulated temperature method. Effective accumulated temperature is calculated from the difference between the daily average air temperature / leaf temperature and the biological lower limit temperature, while active accumulated temperature is calculated from the daily average air temperature / leaf temperature. Furthermore, the effective accumulated temperature (Accu) is calculated under the following three extreme temperature response simulation methods. E ) and accumulated active temperature (Accu A );

[0115] ①Assumption A: Based solely on the biological lower limit temperature T b As a temperature indicator:

[0116]

[0117]

[0118] ②Assumption B: Using the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator:

[0119]

[0120]

[0121] ③ Assumption C: Using the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator:

[0122]

[0123]

[0124] In the formula, T i_ave The value represents the daily average air temperature / leaf temperature, in °C.

[0125] T for different crops at different developmental stages b and T mSince the values ​​of are different, this study collected literature on the cultivation of various crops to be simulated and compiled the three cardinal temperatures of each horticultural crop at different developmental stages, as shown in Table 2.

[0126] Table 2. Three base point temperatures at different developmental stages of different crops to be simulated.

[0127]

[0128] 3) Physiological development time method

[0129] Based on the calculation method of the temperature effector (TE) (see formula (9)), the physiological developmental time (PDT) is divided into four types (see formula (10)): The first type is that TE is calculated using a linear calculation method (TE1), where T i_ave The first method uses the average daily temperature; the second method calculates TE using a sinusoidal formula (TE2), where T... i_ave The third method uses a linear calculation method for TE, where T is the average daily temperature. i_ave The fourth method is to calculate TE using a sinusoidal formula, where T is the average daily leaf temperature. i_ave The average daily leaf temperature is . To clearly explore the effects of temperature response patterns and temperature forms on the leaf age of horticultural crops, this method only considers the effect of TE on the leaf age of horticultural crops, and does not consider the effect of the photoperiod effector (PE) on crop growth and development.

[0130]

[0131]

[0132] In the formula, T ol T ou The optimal temperature for simulating crop growth during this developmental stage is ℃; T b The lower biological limit temperature, in °C; T m The upper limit of biological temperature, in °C.

[0133] 4) Radiation heat accumulation method

[0134] The daily relative product of thermal effectiveness and photosynthetically active radiation (RTEP) is obtained by multiplying the daily temperature effect factor by the corresponding daily average photosynthetically active radiation (see Equation (11)) and then summing them up; the accumulated product of thermal effectiveness and photosynthetically active radiation (TEP) is the accumulation of the daily relative product of thermal effectiveness and photosynthetically active radiation (RTEP) over time (see Equation (12)).

[0135] RTEP = TE n ×PAR=TE n ×K×Q,n=1,2,3,4 (11);

[0136]

[0137] In the formula, RTEP is the daily relative radiant heat product, MJ / (m²). 2 ·d); TE is the temperature effect factor; PAR is the daily average photosynthetically active radiation, MJ / (m 2 ·d); Q is the average daily total solar radiation during this period, MJ / (m 2 ·d); K is the proportion of photosynthetically active radiation in total solar radiation.

[0138] After obtaining the simulated values ​​of the four developmental stages, the simulated values ​​of leaf age under the four developmental stages can be obtained by using the quantitative relationship between leaf age and the simulated values ​​of the four developmental stages as shown in equations (13), (14) or (15).

[0139] DP i_n -DP0=a×(N i -N0)+b,n=1,2,…,21(22) (13);

[0140] DP i_n =a×ln(N) i )+b,n=1,2,…,21(22) (14);

[0141] DP i_n =a×N i +b,n=1,2,…,21(22) (15);

[0142] In the formula, N i DP represents the leaf age measurement on day i; N0 represents the initial leaf age measurement; i_nDP0 represents the No. n developmental stage progress on day i; DP0 represents the No. n developmental stage progress at the first harvest; a and b are model parameters; n is the number of methods to calculate the simulated value of the developmental stage progress.

[0143] Formula (13) is applicable to simulating the leaf age of spinach, formula (14) is applicable to simulating the leaf age of tea leaves and parsley, and formula (15) is applicable to simulating the leaf age of other crops.

[0144] In equations (13)-(15), parameters a and b are determined by the following method:

[0145] Based on the four types of developmental process algorithms mentioned above, the initial parameters of the model were solved using the 27 sets of experimental data in Table 1 for modeling, according to the principle of least squares. By adjusting the parameters, the final parameters of the hourly-scale algorithm and the daily-scale algorithm in the leaf age simulation model were obtained (see Table 3).

[0146] Table 3 Parameters of the simulation model for leaf age of horticultural crops at different time scales

[0147]

[0148]

[0149] Note: No.1 represents ATD maximum_daily No.2 indicates Accu AA (Average daily temperature), No.3 indicates Accu EA (Daily average temperature), No. 4 represents PDT-TE1 (daily average temperature), No. 5 represents PDT-TE2 (daily average temperature), No. 6 represents PTI-TE1 (daily average temperature), No. 7 represents PTI-TE2 (daily average temperature), No. 8 represents Accu AA (Daily average leaf temperature), No.9 indicates Accu EA (Daily average leaf temperature), No. 10 represents PDT-TE1 (daily average leaf temperature), No. 11 represents PDT-TE2 (daily average leaf temperature), No. 12 represents PTI-TE1 (daily average leaf temperature), No. 13 represents PTI-TE2 (daily average leaf temperature), No. 14 represents Accu AB (Average daily temperature), No. 15 indicates Accu EB (Average daily temperature), No. 16 indicates Accu AC (Daily average temperature), No. 17 indicates Accu EC (Average daily temperature), No. 18 indicates Accu AB (Daily average leaf temperature), No. 19 indicates Accu EB (Daily average leaf temperature), No. 20 indicates Accu AC(Daily average leaf temperature), No. 21 indicates Accu EC (Daily average leaf temperature), Method 22 represents ATD diurnal_daily Same as the table below.

[0150] (3) Integrate the simulated leaf age values ​​under the four developmental stages obtained in step (2) to obtain the integrated simulated leaf age values ​​of the crop to be simulated;

[0151] Specifically, integration is performed using at least one of the following methods:

[0152] ①Mean method: M average =∑ m＝1 DS(16);

[0153] ② (Maximum value + Minimum value) / 2 integration method: M max+min =(min m＝1 DS+max m＝1 DS) / 2(17);

[0154] ③Median method: M median =me6ian m＝1 DS(18);

[0155] ④ Stepwise regression method: M steppegpession =a m ×DS m (19);

[0156] In the formula, m is the number of methods or categories of the developmental process algorithm in step (2), and a m The weighting coefficients represent the simulated leaf age values ​​obtained through different methods or categories of developmental process algorithms; DS represents the simulated leaf age values ​​obtained through different methods or categories of developmental process algorithms.

[0157] ⑤ BP Neural Network Method: The BP neural network, also known as the back propagation neural network, is one of the most widely used neural network models. Its design principle is that the signal propagates forward, and the error propagates backward. The input signal propagates forward from the input layer through the hidden layers, processing them layer by layer until the output error is less than a pre-set target error or the number of iterations exceeds the maximum training count. Otherwise, it propagates backward. The BP neural network includes an input layer, a hidden layer, and an output layer. Let the input layer have n neurons, the output layer have m neurons, and the hidden layer have l neurons. Let i be the index of the input layer neuron (i = 1, 2, ..., n); let j be the index of the hidden layer neuron (j = 1, 2, ..., l); let k be the index of the output layer neuron (k = 1, 2, ..., m); and let w be the connection weight from input layer neuron i to hidden layer neuron j. ij The connection weights from hidden layer neuron j to output layer neuron k are w.jk Let the threshold of the j-th hidden layer neuron be a. j Let the threshold of the k-th output layer neuron be b. k Let H be the output of the j-th hidden layer neuron. j Let the value of the i-th neuron in the input layer be x. i The value of the k-th neuron in the output layer is Y. k Let Q be the parameter for adjusting the form of the excitation function, then the calculation method of the unit cell of the BP neural network is shown in formulas (20) to (27).

[0158] Excitation function:

[0159] Calculate the output value of the j-th hidden layer neuron:

[0160] Calculate the predicted output value of the k-th output layer neuron: O k =H j *w ij -b k (twenty two);

[0161] Network prediction error: e k =Y k -Q k (twenty three);

[0162] Update the connection weights between the input layer and the hidden layer:

[0163] Update the connection weights between the hidden layer and the output layer: w jk =w jk +η*H j *e k (25);

[0164] Update the threshold of hidden layer neurons:

[0165] Update the threshold of the output layer neurons: b k =b k +e k (27);

[0166] Repeat the iterations until the output error is less than the preset target error or the number of iterations exceeds the maximum number of training iterations.

[0167] ⑥ Elman Neural Network Method: The Elman neural network is a two-layer BP network structure with feedback, consisting of an input layer, hidden layers (intermediate layers), a receiving layer, and an output layer. The input layer unit transmits signals, the output layer unit performs linear weighting, and the intermediate layer unit can use a nonlinear or linear transfer function, which is from the output of the hidden layer to its input. This feedback method enables the Elman network to detect and identify time-varying patterns. The receiving layer acts as a one-step delay operator, returning the output value of the intermediate layer unit from the previous time step to the input. This special two-layer network can approximate any function with arbitrary precision. The only requirement is that its hidden layer must have a sufficient number of neurons. The nonlinear state-space expression describing the Elman neural network is shown in formulas (28) to (31):

[0168] y(k)=g(w 3 x(k))(28);

[0169] x(k)=f(w 1 x c (k)+w S (T(k-1)))(29);

[0170] x c (k)=x(k-1)(30);

[0171] Where: T, x, x c y represents the r-dimensional input vector, n-dimensional hidden layer node unit vector, n-dimensional feedback state vector, and m-dimensional output node vector, respectively; w 1 w 2 w 3 These are the connection weights from the state layer to the hidden layer, from the input layer to the hidden layer, and from the hidden layer to the output layer, respectively; f() is the transfer function of the hidden layer neurons, usually using the S-function; g() is the transfer function of the output neurons, which is a linear combination of the outputs of the hidden layers;

[0172] Because of feedback connections in the hidden layers, the final output of the network is affected by the initial input, and this effect is determined by the connection matrix between nodes. Let the k-th output of the network be yd(k), then the error function is calculated as follows:

[0173]

[0174] For BP neural network and Elman neural network methods, to avoid neuron saturation, the input data is normalized in the input layer, converting each value to the [0,1] interval, and the prediction result is denormalized in the output layer; in this invention, the number of hidden layer neurons in the BP neural network and Elman neural network is set to... (a is a constant between 1 and 10). To improve training efficiency and network generalization performance, a normalization method is used to preprocess the sample data.

[0175] In the method for constructing the crop leaf age simulation model of the present invention, there are 22 methods of developmental process algorithm on a daily scale, i.e., n = 22 in equations (13)-(15); and 21 algorithms of developmental process algorithm on an hourly scale, i.e., n = 21 in equations (13)-(15). Furthermore, in step (3), the 21 or 22 developmental process algorithms can be integrated step by step, or the 21 or 22 developmental process algorithms can be averaged according to their respective categories and then integrated.

[0176] In particular, for stepwise regression, the weight coefficients of each sub-model are different under stepwise ensemble and mean ensemble, as shown in Table 4.

[0177] Table 4. Weight coefficients of stepwise regression method for leaf age simulation models of different crops under different integration methods.

[0178]

[0179] (4) Model Validation

[0180] 1) Statistical criteria for model testing

[0181] Statistical criteria mainly include the mean. Standard deviation (SD), linear regression coefficient α, intercept β, coefficient of determination R 2 The values ​​of P(t*), root mean square error (RMSE), normalized root mean square error (NRMSE), and conformity index D are also included.

[0182] Among them, the mean This represents the average of the simulated value Xsim and the measured value Xobs;

[0183] The standard deviation (SD) reflects the dispersion of the data's mean.

[0184] Linear regression coefficients α, intercept β, and coefficient of determination R 2 The regression coefficient α is used to demonstrate whether there is a significant linear relationship between measured and simulated values. A closer regression coefficient α is to 1 and a closer intercept β is to 0 indicates a good linear relationship. The degree of linearity is expressed by the coefficient of determination R0. 2 The closer the value is to 1, the more significant the linear relationship.

[0185] The P(t*) value is used to reflect whether there is a difference between the measured value and the simulated value;

[0186] RMSE (see Equation (32)) and NRMSE (see Equation (33)) are used to measure the deviation between the observed value and the measured value, and can also reflect the precision of the measurement well. If NRMSE is below 10%, it means that the model simulation effect is very accurate. If NRMSE is between 10% and 20%, it means that the model simulation effect is relatively accurate. If NRMSE is between 20% and 30%, it means that the model simulation effect is moderately accurate. If NRMSE is greater than 30%, it means that the model simulation effect is poor.

[0187] The consistency index D is a normalization metric (see Equation (34)). The closer the D value is to 1, the higher the consistency between the distribution trend of the simulated value and the observed value, that is, the better the model simulation effect.

[0188]

[0189]

[0190]

[0191] 2) Validation of the 28 leaf age simulation models obtained under the step-by-step integration method

[0192] Using the 18 independent sets of experimental data marked with an asterisk (*) in Table 1, based on different time scales (see results...), Figure 1 Based on different crop species (see results) Figure 2 Based on different simulation methods (see results) Figure 3 The leaf age simulation model was validated, and the validation results are shown in [the table below]. Figures 1 to 3 See Table 5.

[0193] Table of validation statistics for leaf age simulation models based on different modeling methods (step-by-step ensemble)

[0194]

[0195]

[0196] Figures 1 to 3 In the diagram, the solid line represents the 1:1 line, and the dashed line represents the error control range. It can be seen that the simulated leaf age value is close to the measured value of the 1:1 line and is basically within the error range, meaning that the simulated value and the measured value are quite consistent.

[0197] Depend on Figures 1 to 3 As can be seen, the RMSE of the observed values ​​(Xobs±SD=85.01±65.81d) and the simulated values ​​(Xsim±SD=84.91±66.17d) of the overall leaf age simulation model is 16.01d, the NRMSE is 18.83%, and the R² value is [missing information]. 2 The value is 0.97, and the value of D is 0.99.

[0198] As shown in Table 5, the RMSE of the leaf age simulation model ranges from 14.12 to 17.63 days and the NRMSE ranges from 16.62 to 20.73% at different time scales. The NRMSE indicates that the optimal time scale for the leaf age simulation model is the hourly scale.

[0199] For different crop varieties, the RMSE of the leaf age simulation model ranged from 1.37 to 17.69 days, and the NRMSE ranged from 7.90 to 28.02%. Based on the NRMSE, the optimal horticultural crop for the leaf age simulation model is tea.

[0200] Under 28 leaf age simulation methods, the RMSE of the leaf age simulation model ranged from 1.00 to 35.38 days, and the NRMSE ranged from 1.16 to 48.09%.

[0201] Regarding the simulation results of different simulation methods, the ensemble method (mean RMSE 8.59d, mean NRMSE 9.89%, excellent simulation effect) > physiological development time method (mean RMSE 13.08d, mean NRMSE 15.05%, good simulation effect) > accumulated temperature method (mean RMSE 15.34d, mean NRMSE 17.65%, good simulation effect) > temperature difference method (mean RMSE 24.24d, mean NRMSE 27.90%, average simulation effect) > radiative heat accumulation method (mean RMSE 26.62d, mean NRMSE 42.01%, poor simulation effect).

[0202] In terms of temperature response model simulation results, the sinusoidal temperature response model (mean RMSE of 19.39d, mean NRMSE of 27.73%, simulation effect is average) > the linear temperature response model (mean RMSE of 20.30d, mean NRMSE of 29.33%, simulation effect is average).

[0203] Regarding the temperature-related results, air temperature (mean RMSE 16.47d, mean NRMSE 21.40%, simulation effect is average) > leaf temperature (mean RMSE 17.81d, mean NRMSE 22.61%, simulation effect is average).

[0204] Regarding the extreme temperature response results, Hypothesis C (mean RMSE of 12.62d, mean NRMSE of 14.53%, good simulation effect) > Hypothesis B (mean RMSE of 16.01d, mean NRMSE of 18.43%, good simulation effect) > Hypothesis A (mean RMSE of 17.38d, mean NRMSE of 20.00%, average simulation effect).

[0205] In summary, among the 28 leaf age simulation models constructed by different methods, the optimal leaf age simulation model is the Elman neural network ensemble simulation model.

[0206] 3) Validation of the five leaf age simulation models obtained under mean ensemble

[0207] Using the 18 independent sets of experimental data marked with an asterisk (*) in Table 1, based on different time scales (see Table 1...), Figure 4 Different crop varieties (see) Figure 5 Different simulation methods (see) Figure 6 The leaf age simulation model was validated, and the validation results are shown in [the table below]. Figures 4 to 6 See Table 6.

[0208] Table: Validation statistics (mean ensemble) of leaf age simulation models based on different modeling methods.

[0209]

[0210]

[0211] Note: No.1 represents the ATD method, No.2 represents the Accu method, No.3 represents the PDT method, No.4 represents the PTI method, No.5 represents the average ensemble method, No.6 represents the extreme value average ensemble method, No.7 represents the median ensemble method, No.8 represents the stepwise regression ensemble method, No.9 represents the BP neural network ensemble method, and No.10 represents the Elman neural network ensemble method.

[0212] Figures 4 to 6 In the diagram, the solid line represents the 1:1 line, and the dashed line represents the error control range. It can be seen that the simulated leaf age value is close to the measured value of the 1:1 line and is basically within the error range, meaning that the simulated value and the measured value are quite consistent.

[0213] The RMSE of the observed values ​​(Xobs±SD=85.62±66.41d) and simulated values ​​(Xsim±SD=85.62±66.22d) in the overall leaf age simulation model was 12.35d, the NRMSE was 14.42%, and the R² value was [missing value]. 2 The value is 0.99, and the D value is 0.99.

[0214] As shown in Table 6, the RMSE of the leaf age simulation models at different scales ranges from 9.52 to 14.64 days, and the NRMSE ranges from 11.11 to 17.10%. The NRMSE indicates that the optimal leaf age simulation model is an hourly scale.

[0215] The RMSE of different leaf age simulation models ranged from 1.25 to 15.00 days, and the NRMSE ranged from 6.74 to 24.66%. The NRMSE indicates that tea is still the horticultural crop with the optimal leaf age simulation model.

[0216] The RMSE of the four simulation methods during the harvest period ranged from 4.70 to 25.67 days, and the NRMSE ranged from 5.41 to 40.51%.

[0217] Based on the simulation results of the four modeling methods and six ensemble methods, the order is as follows: Elman neural network ensemble (excellent simulation effect) > BP neural network ensemble (relatively good simulation effect) > stepwise regression ensemble (excellent simulation effect) > median ensemble (good simulation effect) > mean ensemble (good simulation effect) > physiological development time method (good simulation effect) > accumulated temperature method (good simulation effect) > (maximum + minimum) / 2 ensemble (good simulation effect) > temperature difference method (average simulation effect) > radiative heat accumulation method (poor simulation effect).

[0218] In conclusion, the optimal leaf age simulation model among the five modeling methods remains the Elman neural network ensemble simulation model.

[0219] 4) Conclusion

[0220] The RMSE of leaf age simulation models at different time scales ranged from 9.52 to 17.63 days, and the NRMSE ranged from 11.11 to 20.73%. The optimal leaf age simulation model was based on an hourly time scale. The RMSE of leaf age simulation models for different varieties ranged from 1.25 to 17.69 days, and the NRMSE ranged from 6.74 to 28.02%. The optimal leaf age simulation model was for tea. The RMSE of leaf age simulation models using different simulation methods ranged from 1.00 to 26.62 days, and the NRMSE ranged from 1.16 to 42.01%. The optimal leaf age simulation model was based on the Elman neural network ensemble method, with the optimal ensemble being a stepwise ensemble. The optimal temperature response mode was a sinusoidal mode, the optimal temperature form was daily average air temperature, and the optimal extreme temperature response was hypothesis C.

Claims

1. A method for constructing a crop leaf age simulation model, characterized in that, Includes the following steps: (1) Collect phenological data of the crop to be simulated at the research site, and obtain the date sequence of the start of the development period of the crop to be simulated, the key development stages, and the meteorological data of the research site. (2) Based on the data obtained in step (1), the simulated values ​​of the three types of developmental stages of the crop to be simulated on a daily or hourly scale are calculated continuously using the temperature difference method, accumulated temperature method and physiological development time method, respectively. The simulated values ​​of leaf age under the three types of developmental stages are obtained by using the quantitative relationship between leaf age and the simulated values ​​of the three types of developmental stages. (3) Integrate the simulated leaf age values ​​under the three developmental stages obtained in step (2) to obtain the integrated simulated leaf age values ​​of the crop to be simulated.

2. The method for constructing a crop leaf age simulation model as described in claim 1, characterized in that, Includes the following steps: (1) Collect phenological data of the crop to be simulated at the research site, obtain the date sequence of the start of the development period of the crop to be simulated and the meteorological data of the research site; (2) Based on the data obtained in step (1), the simulated values ​​of the four types of developmental stages of the crop to be simulated on a daily or hourly scale are continuously calculated by the temperature difference method, accumulated temperature method, physiological development time method and radiation heat accumulation method, respectively. The simulated values ​​of leaf age under the four types of developmental stages are obtained by using the quantitative relationship between leaf age and the simulated values ​​of the four types of developmental stages. (3) Integrate the simulated leaf age values ​​under the four developmental stages obtained in step (2) to obtain the integrated simulated leaf age values ​​of the crop to be simulated.

3. The method for constructing a crop leaf age simulation model as described in claim 2, characterized in that, In step (2), when calculating the simulated value of the developmental process of the crop to be simulated using the temperature difference method, the cumulative daily maximum temperature difference (ATD) is calculated using the cumulative maximum temperature difference method shown in formula (1). maximum_daily Alternatively, the cumulative diurnal temperature range (ATD) can be calculated using the cumulative diurnal temperature range method shown in formula (2). dif_daily ; In the formula, T i_max The highest daily / hourly temperature, in °C; T i_min The lowest daily / hourly temperature, in °C; T i_day T represents the daily daytime temperature, in °C. i_night is the daily nighttime temperature, °C; DS is the total number of days / hours of the crop growth and development process to be simulated, d / h; i is the i-th day / hour of the crop growth and development to be simulated, d / h; When calculating the simulated developmental stages of the crop using the accumulated temperature method, the cumulative effective accumulated temperature (Accu) should be calculated using at least one of the following three extreme temperature response simulation methods: 1), 2), and 3). E or accumulated activity temperature Accu A ; 1) Assumption A: Based solely on the biological lower limit temperature T b As a temperature indicator: 2) Assumption B: Using the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator: 3) Assumption C: Based on the biological lower limit temperature T b and biological upper limit temperature T m As a temperature indicator: In the formula, T i_ave Average daily air temperature / leaf temperature, in °C; When using the physiological development time method to calculate the simulated value of the developmental process of the crop to be simulated, first use at least one of the linear or sinusoidal temperature response modes shown in Equation (9) to calculate the temperature effect factor TE, and then calculate the physiological development time PDT according to Equation (10). In the formula, T ol T ou The optimal temperature for simulating crop growth during this developmental stage is ℃; T b The lower biological limit temperature, in °C; T m The upper limit of biological temperature, in °C.

4. The method for constructing a crop leaf age simulation model as described in claim 3, characterized in that, Calculate the cumulative daily maximum temperature difference (ATD) using formula (1). maximum_daily At that time, T i_max T represents the highest temperature per hour. i_min This represents the lowest temperature per hour.

5. The method for constructing a crop leaf age simulation model as described in claim 3, characterized in that, In equations (3)-(9), T i_ava The average daily leaf temperature; In equation (9), the formula for calculating the temperature effect factor TE is:

6. The method for constructing a crop leaf age simulation model as described in claim 2, characterized in that, In step (2), when calculating the simulated value of the development process of the crop to be simulated using the radiative heat accumulation method, the daily relative radiative heat accumulation RTEP is first calculated according to formula (11), and then the daily relative radiative heat accumulation is accumulated according to formula (12) to obtain the cumulative radiative heat accumulation TEP. RTEP=TE n ×PAR=TE n ×K×Q,n=1,2,3,4 (11); In the formula, RTEP is the daily relative radiant heat product, MJ / (m²). 2 ·d); TE is the temperature effect factor; PAR is the daily average photosynthetically active radiation, MJ / (m 2 ·d); Q is the average daily total solar radiation during this period, MJ / (m 2 ·d); K is the proportion of photosynthetically active radiation in total solar radiation.

7. The method for constructing a crop leaf age simulation model as described in claim 2, characterized in that, In step (2), the simulated leaf age values ​​under the four developmental stages are obtained by using the quantitative relationship between leaf age and simulated values ​​of the four developmental stages as shown in equations (13), (14) or (15). DP i_n -DP0=a×(N i -N0)+b,n=1,2,…,21(22) (13); DP i_n =a×ln(N i )+b,n=1,2,…,21(22) (14); DP i_n =a×N i +b,n=1,2,…,21(22) (15); In the formula, N i DP represents the leaf age measurement on day i; N0 represents the initial leaf age measurement; i_n DP0 represents the developmental stage of No. n on day i; DP0 represents the developmental stage of No. n during the first harvest; a and b are model parameters; Formula (13) is applicable to simulating the leaf age of spinach, formula (14) is applicable to simulating the leaf age of tea leaves and parsley, and formula (15) is applicable to simulating the leaf age of other crops.

8. The method for constructing a crop leaf age simulation model as described in claim 1, characterized in that, In step (3), integration is performed using at least one of the following methods: ①Mean method: M average =∑ m＝1 DS (16); ② (Maximum value + Minimum value) / 2 integration method: M max+min =(min m＝1 DS+max m＝1 DS) / 2 (17); ③Median method: M median =me6ian m＝1 DS (18); ④ Stepwise regression method: M stapragrassion =a m ×DS m (19); In the formula, m is the number of methods or categories of the developmental process algorithm in step (2), and a m Weighting coefficients representing simulated harvest period values ​​obtained through different methods or categories of developmental process algorithms; ⑤ Backpropagation (BP) Neural Network Method: A BP neural network consists of an input layer, a hidden layer, and an output layer. Let the input layer have n neurons, the output layer have m neurons, and the hidden layer have l neurons. Let i be the index of the input layer neuron (i = 1, 2, ..., n); let j be the index of the hidden layer neuron (j = 1, 2, ..., l); let k be the index of the output layer neuron (k = 1, 2, ..., m); and let w be the connection weight from input layer neuron i to hidden layer neuron j. ij The connection weights from hidden layer neuron j to output layer neuron k are w. jk Let the threshold of the j-th hidden layer neuron be a. j Let the threshold of the k-th output layer neuron be b. k Let H be the output of the j-th hidden layer neuron. j Let the value of the i-th neuron in the input layer be x. i The value of the k-th neuron in the output layer is Y. k Let Q be the parameter for adjusting the form of the excitation function, then the calculation method of the unit cell of the BP neural network is shown in formulas (20) to (27). Excitation function: Calculate the output value of the j-th hidden layer neuron: Calculate the predicted output value of the k-th output layer neuron: O k =H j *w ij -b k (twenty two); Network prediction error: e k =Y k -Q k (twenty three); Update the connection weights between the input layer and the hidden layer: Update the connection weights between the hidden layer and the output layer: w jk =w jk +η*H j *e k (25); Update the threshold of hidden layer neurons: Update the threshold of the output layer neurons: b k =b k +e k (27); Repeat the iterations until the output error is less than the preset target error or the number of iterations exceeds the maximum number of training iterations; ⑥ Elman Neural Network Method: The Elman neural network consists of an input layer, hidden layers, a continuation layer, and an output layer. The nonlinear state-space expression describing the Elman neural network is shown in formulas (28) to (31): y(k)=g(w 3 x(k)) (28); x(k)=f(w 1 x c (k)+w 2 (T(k-1))) (29); x c (k)=x(k-1) (30); Where: T, x, x c y represents the r-dimensional input vector, n-dimensional hidden layer node unit vector, n-dimensional feedback state vector, and m-dimensional output node vector, respectively; w 1 w 2 w 3 These are the connection weights from the state layer to the hidden layer, from the input layer to the hidden layer, and from the hidden layer to the output layer, respectively; f() is the transfer function of the hidden layer neurons, usually using the S-function; g() is the transfer function of the output neurons, which is a linear combination of the outputs of the hidden layers; Because of feedback connections in the hidden layers, the final output of the network is influenced by the initial input, and this influence is determined by the connection matrix between nodes. Let the k-th output of the network be yd(k), then the error function is calculated as follows:

9. The method for constructing a crop leaf age simulation model as described in claim 8, characterized in that, There are 22 algorithms for the developmental process on a daily scale and 21 algorithms for the developmental process on an hourly scale. In step (3), the 21 or 22 developmental process algorithms are integrated step by step, or the 21 or 22 developmental process algorithms are integrated after calculating the average value according to their respective categories.

10. The method for constructing a crop leaf age simulation model as described in claim 9, characterized in that, In step (3), the 21 or 22 developmental process algorithms are integrated after calculating the mean according to their respective categories, and the Elman neural network method is used for integration.

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