Corn yield prediction method based on artificial neural network

Through an artificial neural network-based method, a corn yield prediction model is constructed using the flowering period, plant type and ear trait data of corn, which solves the problem of insufficient prediction accuracy of corn yield in the existing technology, and achieves higher prediction accuracy and model stability.

CN119886404AActive Publication Date: 2025-04-25SICHUAN AGRI UNIV
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Patent Information

Application Number
CN202411790069.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-06
Publication Date
2025-04-25
Estimated Expiration
2044-12-06

AI Technical Summary

Technical Problem

The accuracy of existing corn yield prediction methods needs to be improved, mainly because the corn yield is ignored by the influence of a variety of factors.

Method used

Using an artificial neural network-based method, a corn yield prediction model is constructed by obtaining the flowering data, plant-type trait data and ear-type trait data of corn, and the model is trained and tested using the training set and test set to finally obtain the prediction results of corn yield.

Benefits of technology

By considering that corn yield is affected by a variety of factors, the accuracy of the prediction results is improved and the problem of overfitting the model is avoided, thereby enhancing the accuracy of the prediction results.

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Abstract

The invention discloses a corn yield prediction method based on an artificial neural network. The method comprises the following steps: acquiring flowering phase data, plant type character data and ear character data of corn; constructing a corn yield prediction model based on an artificial neural network, constructing a training set and a test set by using flowering phase data, plant type character data and ear character data of corn, and training and testing the corn yield prediction model by using the training set and the test set; and obtaining flowering phase data, plant type character data and ear character data of the to-be-measured corn, and obtaining a corn yield prediction result according to the tested corn yield prediction model and the flowering phase data, plant type character data and ear character data of the to-be-measured corn. According to the method, the influence of various factors on the corn yield is considered, so that the finally obtained prediction result has higher accuracy.
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Description

Technical Field

[0001] The invention relates to the field of crop yield prediction, and in particular to a corn yield prediction method based on an artificial neural network. Background Art

[0002] Crop yield prediction is one of the important contents of modern agricultural scientific research and an important basis for production guidance and agricultural decision-making. In the past, corn yield prediction was mainly done by experienced experts in the industry. With the development of smart agriculture, more and more corn yield prediction models are being applied to the field of crop yield prediction.

[0003] The current corn yield prediction method uses the random forest model to predict corn yield to a certain extent, but because it ignores the impact of multiple factors on corn yield, the accuracy of the final prediction result needs to be improved. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a corn yield prediction method based on artificial neural network.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A corn yield prediction method based on artificial neural network comprises the following steps: S1. Obtaining the flowering period data, plant type trait data and ear trait data of corn; S2. Constructing a corn yield prediction model based on an artificial neural network, using the corn flowering period data, plant type trait data, and ear trait data to construct a training set and a test set, and using the training set and the test set to train and test the corn yield prediction model; S3. Obtain the flowering period data, plant type trait data and ear trait data of the corn to be measured, and obtain the corn yield prediction result according to the tested corn yield prediction model and the flowering period data, plant type trait data and ear trait data of the corn to be measured.

[0006] Further, in step S1, the flowering period data of corn include the tasseling period, the pollen shedding period and the silking period; the plant type trait data of corn include plant height, ear height, the number of leaves on the ear, the length of the main axis of the male ear, the number of branches of the male ear, the length of one leaf under the ear, the width of one leaf under the ear, the leaf length at the ear, the leaf width at the ear, the length of one leaf on the ear, the length of two leaves on the ear, the length of three leaves on the ear, the width of one leaf on the ear, the width of two leaves on the ear, the width of three leaves on the ear, the angle of one leaf on the ear, the angle of two leaves on the ear, the angle of three leaves on the ear, the length of the highest point of one leaf on the ear, the length of the highest point of two leaves on the ear, and the length of the highest point of three leaves on the ear; the ear trait data of corn include ear weight, ear length, ear thickness, ear row, number of grains per row, convex tip, 100-grain weight, and grain weight.

[0007] Furthermore, the flowering period data of corn are obtained. The specific process is as follows: the number of days from the sowing period to the time when the tips of the male tassels of more than half of the plants in the sowing area are exposed from the top leaves is collected to obtain the tasseling period; the number of days from the sowing period to the time when the male tassels of more than half of the plants in the sowing area begin to shed pollen is collected to obtain the pollen shedding period; the number of days from the sowing period to the time when the filaments of more than half of the plants in the sowing area are pulled out from the bracts is collected to obtain the silking period.

[0008] Furthermore, 10 days after the corn powder shedding ended, the length from the plant's surface root to the top of the tassel main axis was measured to obtain the plant height, the length from the plant's surface root to the first ear node was measured to obtain the ear height, the number of leaves at the ear position and above was measured to obtain the number of leaves on the ear, the distance from the highest branch of the tassel to the top of the main axis was measured to obtain the tassel main axis length, the number of all tassel first-level branches was measured to obtain the tassel branch number, the ear position leaves were measured to obtain the length of 1 leaf under the ear, and the length from the ear of the plant leaf to the leaf tip was measured to obtain the length of 1 leaf on the ear, the length of 2 leaves on the ear, and the length of 1 leaf on the ear. The length of 3 leaves on the ear, measure the length of the widest part of the plant leaf to obtain the width of 1 leaf on the ear, the width of 2 leaves on the ear, and the width of 3 leaves on the ear, measure the angle between the main vein of the plant leaf and the stem to obtain the angle of 1 leaf on the ear, the angle of 2 leaves on the ear, and the angle of 3 leaves on the ear, measure the length from the ear to the highest point of the leaf to obtain the length of the highest point of 1 leaf on the ear, the length of the highest point of 2 leaves on the ear, and the length of the highest point of 3 leaves on the ear; collect the ears in the late stage of corn maturity, dry the ears, and measure the dried ears to obtain ear weight, ear length, ear diameter, ear row, number of grains per row, convex tip, 100-grain weight, and grain weight.

[0009] Further, in step S2, the corn yield prediction model includes an input layer, a hidden layer, and an output layer connected in sequence; The input layer includes 31 input neurons; the input layer is used to input the flowering period data, plant type trait data and ear trait data of corn, and the flowering period data, plant type trait data and ear trait data of corn are processed according to the first connection weight to output the first input variable to the hidden layer; The hidden layer includes a set number of internal neurons; the hidden layer is used to perform data processing on the first input variable according to the transfer function to output the second input variable to the output layer; The output layer includes 1 output neuron; the output layer is used to perform data processing on the second input variable according to the second connection weight to obtain a corn yield prediction result.

[0010] Further, in the input layer, the flowering period data, plant type trait data and ear trait data of corn are processed according to the first connection weight to obtain the first input variable, which is expressed as:

[0011] in: For the The first input variable obtained by the internal neuron, is the serial number of the internal neuron, is the serial number of the input neuron, is the total number of input neurons, For the The input neurons and The first connection weight between internal neurons, For the The input of the input neuron is the flowering period data, plant type trait data and ear trait data of corn. For the The input neurons and The bias between the internal neurons.

[0012] Furthermore, in the hidden layer, the first input variable is processed according to the transfer function to obtain the second input variable, which is expressed as:

[0013] in: For the The second input variable is the output of the internal neuron, is the hyperbolic tangent function, For the The first input variable obtained by the internal neuron.

[0014] Further, in the output layer, the second input variable is processed according to the second connection weight to obtain the corn yield prediction result, which is expressed as:

[0015] in: is the predicted value of corn ear weight, is the serial number of the internal neuron, is the number of internal neurons, For the The second connection weight between the internal neurons and the output neuron, For the The second input variable is the output of the internal neuron, For the The bias between the internal neurons and the output neuron.

[0016] Furthermore, the number of internal neurons is set to 32.

[0017] Furthermore, in step S2, the flowering period data, plant type trait data and ear trait data of corn are used to construct a training set and a test set. The specific process is: the flowering period data, plant type trait data and ear trait data of corn are classified by phenotypic traits and sample labels, and the classified flowering period data, plant type trait data and ear trait data of corn are randomly selected in a ratio of 7:3 as the training set and the test set, respectively.

[0018] The present invention has the following beneficial effects: (1) The present invention obtains the flowering period data, plant type trait data and ear trait data of corn, constructs a corn yield prediction model based on an artificial neural network, and obtains the corn yield prediction result according to the tested corn yield prediction model and the flowering period data, plant type trait data and ear trait data of the corn to be measured, taking into account that the corn yield is affected by multiple factors, so that the prediction result finally obtained can have higher accuracy; (2) By setting the number of neurons in the hidden layer to 32, the present invention can avoid the overfitting phenomenon caused by overtraining of the corn yield prediction model while ensuring the prediction fit, thereby enhancing the accuracy of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a corn yield prediction method based on artificial neural network. DETAILED DESCRIPTION

[0020] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0021] like Figure 1 As shown, a corn yield prediction method based on artificial neural network includes the following steps: S1. Obtain the flowering period data, plant type trait data and ear trait data of corn.

[0022] In an optional embodiment of the present invention, the flowering period data of corn include the tasseling period, the pollen shedding period and the silking period; the plant type trait data of corn include plant height, ear height, the number of leaves on the ear, the length of the main axis of the male ear, the number of branches of the male ear, the length of 1 leaf under the ear, the width of 1 leaf under the ear, the leaf length at the ear, the leaf width at the ear, the length of 1 leaf on the ear, the length of 2 leaves on the ear, the length of 3 leaves on the ear, the width of 1 leaf on the ear, the width of 2 leaves on the ear, the width of 3 leaves on the ear, the angle of 1 leaf on the ear, the angle of 2 leaves on the ear, the angle of 3 leaves on the ear, the length of the highest point of 1 leaf on the ear, the length of the highest point of 2 leaves on the ear, and the length of the highest point of 3 leaves on the ear; the ear trait data of corn include ear weight, ear length, ear thickness, ear row, number of grains per row, convex tip, 100-grain weight, and grain weight.

[0023] The present invention obtains the flowering period data of corn, and the specific process is: collecting the number of days from the sowing period to the time when the tips of the male tassels of more than half of the plants in the sowing area are exposed from the top leaves, so as to obtain the tasseling period; collecting the number of days from the sowing period to the time when the male tassels of more than half of the plants in the sowing area begin to shed pollen, so as to obtain the pollen shedding period; collecting the number of days from the sowing period to the time when the filaments of more than half of the plants in the sowing area are pulled out from the bracts, so as to obtain the silking period.

[0024] The invention obtains plant type trait data and ear trait data, and the specific process is: 10 days after corn powder shedding ends, the length from the plant surface root to the top of the male ear main axis is measured to obtain the plant height, the length from the plant surface root to the first ear node is measured to obtain the ear height, the number of leaves at the ear position and above is measured to obtain the number of leaves on the ear, the distance from the highest branch of the male ear to the top of the main axis is measured to obtain the male ear main axis length, the number of first-level branches of all male ears is measured to obtain the number of male ears branches, the ear position leaf is measured to obtain the length of one leaf under the ear, and the length from the ear of the plant leaf to the leaf tip is measured to obtain the length of the ear. 1 leaf length, 2 leaf lengths on an ear, and 3 leaf lengths on an ear; measure the length of the widest part of the plant leaf blade to obtain the width of 1 leaf on an ear, 2 leaf widths on an ear, and 3 leaf widths on an ear; measure the angle between the main vein of the plant leaf and the stalk to obtain the angle of 1 leaf on an ear, the angle of 2 leaves on an ear, and the angle of 3 leaves on an ear; measure the length from the ear to the highest point of the leaf blade to obtain the length of the highest point of 1 leaf on an ear, the length of the highest point of 2 leaves on an ear, and the length of the highest point of 3 leaves on an ear; collect the ears in the late stage of corn maturity, dry the ears in the sun, and measure the dried ears to obtain ear weight, ear length, ear diameter, ear row, number of grains in a row, convex tip, 100-grain weight, and grain weight.

[0025] S2. Construct a corn yield prediction model based on artificial neural network, use corn flowering period data, plant type trait data and ear trait data to construct training set and test set, and use the training set and test set to train and test the corn yield prediction model.

[0026] In an optional embodiment of the present invention, the present invention constructs a corn yield prediction model with corn flowering period, plant type and ear traits as input and ear weight as output. The corn yield prediction model includes an input layer, a hidden layer and an output layer connected in sequence.

[0027] The input layer includes 31 input neurons; the input layer is used to input the flowering period data, plant type trait data and ear trait data of corn, and the flowering period data, plant type trait data and ear trait data of corn are processed according to the first connection weight to output the first input variable to the hidden layer.

[0028] The present invention processes the flowering period data, plant type trait data and ear trait data of corn according to the first connection weight to obtain a first input variable, which is expressed as:

[0029] in: For the The first input variable obtained by the internal neuron, is the serial number of the internal neuron, is the serial number of the input neuron, is the total number of input neurons, For the The input neurons and The first connection weight between internal neurons, For the The input of the input neuron is the flowering period data, plant type trait data and ear trait data of corn. For the The input neurons and The bias between the internal neurons.

[0030] The hidden layer includes a set number of internal neurons, and the number of internal neurons is set to 32; the hidden layer is used to perform data processing on the first input variable using a transfer function to output a second input variable to the output layer.

[0031] The present invention performs data processing on the first input variable according to the transfer function to obtain the second input variable, which is expressed as:

[0032] in: For the The second input variable is the output of the internal neuron, is the hyperbolic tangent function, For the The first input variable obtained by the internal neuron.

[0033] The output layer includes 1 output neuron; the output layer is used to perform data processing on the second input variable according to the second connection weight to obtain a corn yield prediction result.

[0034] The present invention performs data processing on the second input variable according to the second connection weight to obtain a corn yield prediction result, which is expressed as:

[0035] in: is the predicted value of corn ear weight, is the serial number of the internal neuron, is the number of internal neurons, For the The second connection weight between the internal neurons and the output neuron, For the The second input variable is the output of the internal neuron, For the The bias between the internal neurons and the output neuron.

[0036] The present invention utilizes corn flowering data, plant type trait data and ear trait data to construct a training set and a test set. The specific process is: phenotypic trait classification and sample label classification are performed on the corn flowering data, plant type trait data and ear trait data, and the classified corn flowering data, plant type trait data and ear trait data are randomly extracted in a ratio of 7:3 as a training set and a test set, respectively.

[0037] The present invention uses a training set and a test set to train and test a corn yield prediction model. During the whole process, the learning rate of the corn yield prediction model is set to 0.1, and the determination coefficient and root mean square error are used to update the parameters of the corn yield prediction model.

[0038] S3. Obtain the flowering period data, plant type trait data and ear trait data of the corn to be measured, and obtain the corn yield prediction result according to the tested corn yield prediction model and the flowering period data, plant type trait data and ear trait data of the corn to be measured.

[0039] In an optional embodiment of the present invention, the present invention obtains the flowering period data, plant type trait data and ear trait data of the corn to be measured, and inputs the flowering period data, plant type trait data and ear trait data of the corn to be measured into the tested corn yield prediction model to obtain the corn yield prediction result.

[0040] Simulation experiment: The present invention is based on the same corn flowering period data, plant type trait data and ear trait data, and adopts different inputs (flowering period, plant type trait, ear trait as input respectively, and these three parts are taken as input together) and different models (MLR, PLSR, RF and the model of the present invention, wherein MLR is a multiple linear regression model, PLSR is a partial least squares regression model, and RF is a random forest model) to carry out simulation experiments, and the evaluation indicators are selected as the determination coefficient and the root mean square error. The simulation results are shown in Table 1:

[0041] As can be seen from Table 1, the model provided by the present invention, which uses the flowering period data, plant type trait data and ear trait data of corn as input data and is constructed using the present invention, is superior to other prediction methods in terms of the two evaluation indicators of determination coefficient and root mean square error. Therefore, the method provided by the present invention can make the final prediction result have higher accuracy.

[0042] Then the present invention conducts simulation experiments on training sets and test sets with different ratios, and the simulation results are shown in Table 2:

[0043] As can be seen from Table 2, the present invention randomly extracts data in a ratio of 7:3 as training set and test set respectively, which can perform better in the two evaluation indicators of determination coefficient and root mean square error, which is beneficial to improving the prediction accuracy of the model, and thus making the final prediction result have higher accuracy.

[0044] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0045] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0046] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0047] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0048] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A corn yield prediction method based on artificial neural network, characterized in that: The following steps are involved: S1. Obtaining the flowering period data, plant type trait data and ear trait data of corn; S2. Constructing a corn yield prediction model based on an artificial neural network, using the corn flowering period data, plant type trait data, and ear trait data to construct a training set and a test set, and using the training set and the test set to train and test the corn yield prediction model; S3. Obtain the flowering period data, plant type trait data and ear trait data of the corn to be measured, and obtain the corn yield prediction result according to the tested corn yield prediction model and the flowering period data, plant type trait data and ear trait data of the corn to be measured.

2. The corn yield prediction method based on artificial neural network according to claim 1, characterized in that: In step S1, the flowering period data of corn include tasseling period, pollen shedding period and silking period; the plant type trait data of corn include plant height, ear height, number of leaves on ear, length of main axis of male ear, number of branches of male ear, length of leaf under ear, width of leaf under ear, leaf length at ear position, leaf width at ear position, length of leaf on ear, length of leaf 2 on ear, length of leaf 3 on ear, width of leaf 1 on ear, width of leaf 2 on ear, width of leaf 3 on ear, angle of leaf 1 on ear, angle of leaf 2 on ear, angle of leaf 3 on ear, length of highest point of leaf 1 on ear, length of highest point of leaf 2 on ear, length of highest point of leaf 3 on ear; the ear trait data of corn include ear weight, ear length, ear thickness, ear row, number of grains per row, convex tip, 100-grain weight, and grain weight.

3. The corn yield prediction method based on artificial neural network according to claim 2, characterized in that: The flowering period data of corn were obtained by the following process: the tassel emergence period was obtained by collecting the number of days from the sowing period to the time when the tips of the male spikes of more than half of the plants in the sowing area were exposed from the top leaves; the pollen shedding period was obtained by collecting the number of days from the sowing period to the time when the male spikes of more than half of the plants in the sowing area began to shed pollen; the silking period was obtained by collecting the number of days from the sowing period to the time when the filaments of more than half of the plants in the sowing area were pulled out from the bracts.

4. The corn yield prediction method based on artificial neural network according to claim 2, characterized in that: The plant type trait data and ear trait data were obtained. The specific process was as follows: 10 days after the corn powder was released, the length from the plant's surface root to the top of the tassel main axis was measured to obtain the plant height, the length from the plant's surface root to the first ear node was measured to obtain the ear height, the number of leaves at the ear position and above was measured to obtain the number of leaves on the ear, the distance from the highest branch of the tassel to the top of the main axis was measured to obtain the tassel main axis length, the number of first-level branches of all tassels was measured to obtain the number of tassel branches, and the number of leaves at the ear position was measured to obtain the number of leaves on the ear. Obtain the length of the leaf below the ear, measure the length from the ear of the plant leaf to the tip of the leaf to obtain the length of the leaf above the ear, the length of the leaf below the ear, and the length of the leaf below the ear, measure the length of the widest part of the plant leaf to obtain the width of the leaf above the ear, the width of the leaf below the ear, and the width of the leaf below the ear, measure the angle between the main vein of the plant leaf and the stem to obtain the angle of the leaf above the ear, the angle of the leaf below the ear, and the angle of the leaf below the ear, and measure the length from the ear of the plant leaf to the highest point of the leaf to obtain the length of the highest point of the leaf above the ear, the length of the highest point of the leaf above the ear, and the length of the highest point of the leaf above the ear; In the late stage of corn maturity, the ears are collected, dried in the sun, and the dried ears are measured to obtain ear weight, ear length, ear diameter, ear row, number of kernels in a row, convex tip, 100-kernel weight, and kernel weight.

5. The corn yield prediction method based on artificial neural network according to claim 1, characterized in that: In step S2, the corn yield prediction model includes an input layer, a hidden layer, and an output layer connected in sequence; The input layer includes 31 input neurons; the input layer is used to input the flowering period data, plant type trait data and ear trait data of corn, and the flowering period data, plant type trait data and ear trait data of corn are processed according to the first connection weight to output the first input variable to the hidden layer; The hidden layer includes a set number of internal neurons; the hidden layer is used to perform data processing on the first input variable according to the transfer function to output the second input variable to the output layer; The output layer includes 1 output neuron; the output layer is used to perform data processing on the second input variable according to the second connection weight to obtain a corn yield prediction result.

6. The method for predicting corn yield based on artificial neural network according to claim 5, characterized in that: In the input layer, the flowering period data, plant type trait data and ear trait data of corn are processed according to the first connection weight to obtain the first input variable, which is expressed as: in: For the The first input variable obtained by the internal neuron, is the serial number of the internal neuron, is the serial number of the input neuron, is the total number of input neurons, For the The input neurons and The first connection weight between internal neurons, For the The input of the input neuron is the flowering period data, plant type trait data and ear trait data of corn. For the The input neurons and The bias between the internal neurons.

7. The method for predicting corn yield based on artificial neural network according to claim 5, characterized in that: In the hidden layer, the first input variable is processed according to the transfer function to obtain the second input variable, which is expressed as: in: For the The second input variable is the output of the internal neuron, is the hyperbolic tangent function, For the The first input variable obtained by the internal neuron.

8. The method for predicting corn yield based on artificial neural network according to claim 5, characterized in that: In the output layer, the second input variable is processed according to the second connection weight to obtain the corn yield prediction result, which is expressed as: in: is the predicted value of corn ear weight, is the serial number of the internal neuron, is the number of internal neurons, For the The second connection weight between the internal neurons and the output neuron, For the The second input variable is the output of the internal neuron, For the The bias between the internal neurons and the output neuron.

9. The method for predicting corn yield based on artificial neural network according to claim 5, characterized in that: The number of internal neurons is set to 32.

10. The method for predicting corn yield based on artificial neural network according to claim 1, characterized in that: In step S2, the flowering period data, plant type trait data and ear trait data of corn are used to construct a training set and a test set. The specific process is: the flowering period data, plant type trait data and ear trait data of corn are classified by phenotypic traits and sample labels, and the classified flowering period data, plant type trait data and ear trait data of corn are randomly selected in a ratio of 7:3 as the training set and the test set, respectively.

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