Analysis of the Effect of Bivariate Fertilizer Discharger Control Sequence on Fertilizer Discharge Performance

Abstract

Fertilization stability is an important index for evaluating the operational performance of variable fertilizer dischargers. To study the influence law of the combination of fertilizer discharge wheel rotational speed n and opening L on the fertilizer discharge performance, this paper firstly constructs a fertilizer amount prediction model based on a radial basis function neural network (RBFNN) through a calibration test, and after verification, its determination coefficient reaches 0.99965 with a mean relative error (MRE) of 3.88%. Then the discrete element simulation software (EDEM) was used to simulate the fertilizer discharge process under different control sequences for each of the three target fertilizer application amounts. The simulation results show that at the target fertilizer discharge rate of 944.92 g/min, when the control sequence is 18.3 r/min and 25 mm, the uniformity coefficient of variation (CV) of fertilizer discharge is the smallest. In the other control sequences, σ was higher than 20%, the stability of fertilizer discharge was poor, and the phenomenon of broken strips appeared; under the target fertilizer discharge rate of 2101.47 g/min, σ was the smallest at (24.2 r/min, 45 mm) 4.34%; under the target fertilizer discharge rate of 3842.87 g/min, σ was less than 4% in all cases, and at the control sequence (44.7 r/min, 45 mm), σ reached a minimum of 2.01%. Finally, using the simulation results and the prediction model of fertilizer amount based on RBFNN, the optimization model of fertilizer discharge control sequence based on the differential evolutionary (DE) algorithm was established, and a bench test was conducted to verify the optimization results, which showed that the accuracy and uniformity of fertilizer discharge met the operational requirements.

1. Introduction

The application of chemical fertilizers is an important measure to improve crop yields, and production and the use of chemical fertilizers are inevitable products of the development of agricultural production and scientific research to a certain stage. Fertilizers as food for crops can increase crop yields, improve soil fertility, bring into play the potential of good seeds, and compensate for the shortage of arable land. According to the Food and Agriculture Organization (FAO) of the United Nations, the contribution of chemical fertilizer to crop yield increases is 40–60%. In addition, according to the survey, fertilizer application contributes 41.43% to land productivity improvement and 53.89% to labor productivity growth [1].

Variable fertilizer application technology can put fertilizer on demand according to soil nutrient status, effectively reduce fertilizer use, improve the fertilizer utilization rate, and reduce environmental pollution at the same time, which is an important part of fine agricultural practice and one of the important directions of modern agricultural development [2,3]. Nowadays, there are two main types of variable fertilization technologies: GIS-prescription map-based and sensor-based variable fertilization technologies. Among them, the GIS-prescription map-based variable fertilization technology is used to generate a fertilization prescription map through soil nutrient and crop yield analysis and then they use this prescription map to control variable fertilization [4]. The single-variable fertilizer applicator based on the outer grooved wheel type fertilizer discharger mainly adjusts the fertilizer amount by changing the rotational speed of the discharge wheel. For example, the variable fertilizer spreader developed by Kyoto University in Japan [5] works on the principle that each spreader mechanism is driven by its connected motor, and the size of the spreader volume is adjusted by the rotational speed of the driving motor; Zhang et al. [6] designed a fertilizer spreader that combines GPS and GIS to make decisions on fertilizer application and achieves precise automatic variable fertilizer application by controlling the rotational speed of the spreader shaft on the spreader. However, this single variable control method has disadvantages such as obvious pulsation at low speeds and poor uniformity of fertilizer discharge, which affect the operational performance of the variable fertilizer applicator [7]. However, since each application volume of the dual variable fertilizer applicator corresponds to an infinite set of speed and opening combinations, a non-optimal sequence of speed and opening combinations will reduce the uniformity and accuracy of fertilizer application. For this reason, domestic and foreign research teams have conducted a lot of research on dual variable fertilizer applicators.

Yuan et al. [8] conducted a systematic study of control sequence optimization methods, proposed a bivariate fertilizer discharge prediction model based on the Gauss process (GP), and obtained an optimized control sequence list using the weighted sum method, which laid the foundation for the study of bivariate control sequence optimization methods. Chen et al. [9] used the Bisquare estimation robust value regression method to construct a bivariate control model, analyzed three control strategies—speed priority control, openness priority control, and bivariate adaptive control—and constructed a query table of variable fertilization control sequences to provide a basis for realizing bivariate adaptive control. Zhao et al. [10] studied the factors affecting the fertilizer filling performance of a bivariate fertilizer discharge device and proposed a segmentation control method by using the relationship model between the rotational speed, opening, and the amount of fertilizer discharged and achieved better control accuracy. Su et al. [11,12] transformed a Kuhn air-suction spot seeder with a manually adjustable opening into a variable fertilizer applicator with an effective working length automatically adjustable by a servo motor and verified experimentally that the coefficient of variation of the average fertilizer discharge uniformity for each row of seven dischargers was 8.4% at five different openings. Zhang et al. [13] developed a MOEA/D-DE-based control sequence optimization (CSO) method of fertilizer discharge rotational speed and opening, which can greatly improve the accuracy and uniformity of fertilizer discharge.

This study focuses on the variable fertilizer applicator used for cotton in large fields in Xinjiang. The cotton fields in Xinjiang have large plots and an uneven distribution of soil nutrient contents, which will result in wasted fertilizer if fertilizer is applied according to uniform standards. In this paper, we mainly study the influence of the combination of the rotational speed and the opening degree of the outer groove wheel fertilizer discharger on the fertilizer discharge performance and combine the RBFNN-based fertilizer discharge volume prediction model and the differential evolutionary algorithm with each other to establish an optimization-seeking model for the fertilizer discharge control sequence. The accuracy of fertilizer discharge using the optimization-seeking results can be within 6%, which is obviously better than other studies (about 10%) [14,15]. This paper can provide a reference for realizing the optimal control of a bivariate fertilizer application system.

2. Materials and Methods

2.1. Bivariate Fertilizer Discharger

2.1.1. Working Principle of Bivariate Fertilizer Discharge Device

The working principle of the bivariate regulating device is shown in Figure 1. The bivariate fertilizer discharging device mainly consists of the outer groove wheel discharger, the rotational speed adjusting mechanism, and the opening adjusting mechanism. The rotational speed regulating mechanism includes a stepper motor, a motor bracket, and a coupling, in which the output shaft of the stepper motor is connected to the drive shaft of the outer groove wheel through a coupling, and the stepper motor drives the outer groove wheel to rotate when it turns to realize the adjustment of the speed n of the fertilizer discharge wheel. The opening adjusting mechanism is a set of ball screw slide modules, and the rotational speed adjusting mechanism is fixed on the slider. When the slider moves, it drives the stepping motor and the outer groove wheel to move to realize the adjustment of the opening L of the fertilizer discharge wheel. In actual operation, the fertilizer discharge system automatically adjusts the size of the rotational speed n and the opening L according to the volume of fertilizer to be applied, so as to realize the regulation of the fertilizer amount.

2.1.2. Advantages of the Bivariate Fertilizer Discharge Device

For the univariate control fertilizer applicator, there is a univariate relationship between the fertilizer amount q per unit time and the rotational speed n, i.e., q = F(n), and the functional relationship can be obtained through several experimental calibrations. In the actual fertilization process, the speed value can be calculated based on the fertilizer amount to achieve fertilization control. However, there is pulsation in the outer groove wheel fertilizer discharger, and its pulsation will reduce the uniformity of fertilizer application, and the uniformity of fertilizer application gradually becomes worse with the decrease in fertilizer application volume (i.e., the decrease in rotational speed). At the same time, when the fertilizer application volume is small, the rotational speed is also small, and the small control error of the rotational speed can have a substantial impact on the fertilizer application accuracy and uniformity. Although the univariate control method is simple and easy to implement and meets the requirements of precision agriculture, its precision and range of fertilizer application adjustment are small, and the uniformity is not good enough at low speeds.

For the bivariate fertilizer applicator, the fertilizer amount q per unit time is a function of the rotational speed n and the opening L, i.e., q = F(n, L), and the functional relationship can also be obtained by multiple experimental calibrations. Compared with the univariate fertilizer applicator, each application amount of the bivariate fertilizer applicator corresponds to an infinite number of combinations of rotational speed and openness. At a certain amount of fertilizer application, the pulsation of fertilizer application can be reduced, and the uniformity of fertilizer application can be improved by reducing the opening and increasing the rotational speed. The bivariate fertilizer applicator can improve fertilizer application accuracy and uniformity by reasonably setting the combination of speed and opening parameters according to the different fertilizer application volumes [16].

2.2. Fertilizer Discharge Prediction Model Construction

2.2.1. Fertilizer Discharge Calibration Test

To construct a prediction model for the fertilizer amount of the outer groove wheel fertilizer discharger, the fertilizer amount is now calibrated for different speeds and opening conditions. The calibration test was carried out on a bivariate fertilizer discharge test bench in the laboratory of Shihezi University. The urea produced by Shihezi Voda Agricultural Technology Co., Ltd. (Shihezi, China) is used as the object of fertilizer discharge, with a nitrogen content of 46.4%, a spherical rate of 93.6%, and a density of 1341 kg/m³. To meet the minimum opening requirement of fertilizer discharge and the minimum working speed requirement of a stepper motor, the adjustment range of the fertilizer wheel opening is set from 15 to 55 mm, and the adjustment range of fertilizer wheel speed is 10 to 60 r /min, and the adjustment step is 5, totaling 99 groups. The fertilizer amount was measured for 5 min under each combination of conditions, and each group was repeated 3 times to take the average value, then the amount of fertilizer discharged per minute by the discharger was calculated.

The contour curve of the fertilizer amount at different fertilizer discharge wheel speeds n and openings L were obtained by fitting the surface to the calibration test data with Origin software (Figure 2).

From Figure 2, it can be seen that the same target fertilizer amount can correspond to numerous combinations of rotational speeds and openings.

2.2.2. Fertilizer Discharge Prediction Model Construction

Radial basis function neural network (RBFNN) is a feed-forward neural network with the best approximation and global optimum performance and a simple and fast training method, which makes RBFNN widely used in nonlinear sequence prediction. RBFNN is generally divided into three layers, i.e., the input layer, hidden layer, and output layer [17,18].

The kernel function of RBFNN usually uses a Gaussian function [19,20]:

$$R_i\left(t\right)=exp\left(-\frac{||\overrightarrow{x}\left(t\right)-{\overrightarrow{c}}_i{\left(t\right)}^2||}{2{\sigma }_i^2}\right), i=1,2,\dots ,m$$

(1)

where $R_i\left(t\right)$—output of the ith node in the hidden layer; $\overrightarrow{x}\left(t\right)$—input parameter vector, ${\overrightarrow{c}}_i\left(t\right)$ is the $\overrightarrow{x}\left(t\right)$ homo-dimensional vector and is the center of the radial basis function; ${\sigma }_i^2$—width of the Gaussian basis function; m—number of nodes in the hidden layer.

The output of the neural network is:

$$y_j\left(t\right)={\displaystyle \sum }_{i=1}^m{w}_{ij}{R}_i\left(t\right), j=1,2,\cdots ,n$$

(2)

where $w_{ij}$—network weights from the hidden layer to the output layer, and there are i input nodes and j output nodes in the hidden layer; n—number of output nodes; $y_j\left(t\right)$—output result of the neural network.

The structure of the RBFNN-based fertilizer amount prediction model is shown in Figure 3, with the fertilizer discharge wheel speed n and opening L as model inputs and the fertilizer amount q as model outputs. The 185 sets of sample data obtained from calibration were substituted into Matlab software for training, and finally, the prediction model of fertilizer amount under different combinations of rotational speeds and openings was obtained.

$$g\left(n,L\right)=q$$

(3)

2.2.3. Prediction Model Accuracy Analysis

To verify the accuracy of the fertilizer discharge prediction model, 14 samples that did not participate in training (

Table 1. Test Sets.

Number	Rotation Speed N/r·min−1	Opening L/mm	Fertilizer Amount q/g·min−1
1	30	20	1261.8
2	40	45	3436.1
3	40	55	4155.2
4	60	40	4596.0
5	35	55	3644.3
6	10	35	699.6
7	40	35	2720.1
8	60	30	.3510.9
9	25	25	1277.6
10	30	45	2594.3
11	50	35	3388.6
12	10	55	1050.0
13	25	30	1493.6
14	40	40	3086.2

) were selected as the test set to test the model. The mean relative error (MRE) between the predicted and tested values of the model and the model coefficient of determination was calculated to evaluate the accuracy of the model.

The results of the fertilizer discharge prediction model test are shown in Figure 4.

As can be seen from Figure 4, the error between the model predictions and the experimental values is small. Therefore, RBFNN can be used for the prediction of fertilizer discharge for bivariate external slotted wheel dischargers under different control sequences.

2.3. Discrete Element Simulation Test

The discrete element method (DEM) is a method used to study how to calculate the motion of a large number of particles under a given condition [21]. It enables the simulation of particle motion behavior by building a discrete-element parametric model of the particle system and is widely used in the optimization of structural parameters of the outer groove wheel fertilizer discharger [22,23]. EDEM is the world’s first multi-purpose discrete element simulation software and one of the most widely used discrete element software products on the market today.

2.3.1. Simulation Model Establishment and Parameters Setting

When conducting discrete, it is favored by users for its absolute leading solution speed, simple and friendly modeling means, flexible and versatile multi-field coupling, and various post-processing tools [24]. For element simulation tests, the simulation models of urea particles and fertilizer dischargers are first established separately.

To build the discrete element model of fertilizer particles, the physical and mechanical characteristic parameters of the fertilizer need to be obtained first. A sample of 5000 urea particles was selected, and their length, width, and thickness were measured using vernier calipers (accuracy 0.01 mm) to calculate their equivalent diameter D:

$$D=\sqrt[3]{lWT}$$

(4)

where l—length of fertilizer particles, mm; W—width of fertilizer particles, mm; T—thickness of fertilizer particles, mm.

The fertilizer particle sphericity φ is calculated as:

$$\phi =\frac{D}{l}\times 100\%$$

(5)

The particle size distribution of urea particles can be derived from the equivalent measurement of the particle’s diameter size (Figure 5).

The particle size distribution of urea particles was calculated to be normally distributed, and the mean and standard deviation of particle size were 2.13 mm and 0.21 mm, respectively, and the sample sphericity was greater than 90%. The overall estimation of the sample indicates that the fertilizer particles as a whole have high spherical distribution characteristics, so a spherical shape can be selected as the 3D model of fertilizer particles in the simulation process [25] (Figure 6). In this study, the spherical particle filling method was used to establish the urea particle simulation model [26].

The urea particle and fertilizer discharger were modeled in 3D using SolidWorks 2019, and the size of the fertilizer wheel opening was adjusted during assembly in SolidWorks and imported into EDEM simulation software.

The physical characteristics parameters [27,28,29] required for the simulation tests (

Table 2. Simulation test parameters.

Parameters		Value
Density/(kg·m−3)	Urea particles	1341
	Fertilizer discharger	1418
	Ground	2523
Poisson’s ratio	Urea particles	0.25
	Fertilizer discharger	0.32
	Ground	0.35
Elastic modulus/Pa	Urea particles	6.72 × 107
	Fertilizer discharger	4.22 × 109
	Ground	1.85 × 109
Restitution coefficient	Urea particle-particle	0.26
	Urea particles-fertilizer discharger	0.35
	Urea particles-ground	0.22
Static friction coefficient	Urea particle-particle	0.27
	Urea particles-fertilizer discharger	0.32
	Urea particles-ground	0.88
Dynamic friction coefficient	Urea particle-particle	0.11
	Urea particles-fertilizer discharger	0.27
	Urea particles-ground	0.15

) were entered into the EDEM software, respectively, and the urea particle size distribution was set to normal distribution. Since there is almost no adhesion on the fertilizer particle surface, the Hertz–Mindin no-slip contact model [30] can be used to simulate the interaction between the urea particles and the fertilizer discharge device.

To simulate the actual fertilizer discharging process and observe the distribution of fertilizer particles on the horizontal ground surface, a flat surface with a length of 2500 mm and a width of 500 mm was set at a position of 300 mm from the lower end of the fertilizer discharge box to simulate the ground surface. The particle factory was set to generate 50,000 g of particles per second, generating a total of 15,000 g of particles; then, different rotational speeds of the fertilizer discharge wheel and ground movement (v = 1 m/s) were set for the simulation of the fertilizer discharge process.

2.3.2. Simulation Test Design

According to the iso-discharge volume curve of the outer groove wheel fertilizer discharger, a target discharge volume (940.26, 2100.35, 3840.42 g/min) was selected in three gradients of low, medium, and high, as shown in Figure 7. In order to obtain the control parameters of the same target fertilizer application volume, i.e., different combinations of L and n, the speed n corresponding to the opening L at 15 to 55 mm (in increments of 10 mm), respectively, was marked in the figure, and the sequence combinations were obtained as in

Table 3. Control sequence combinations.

Control Sequence	Target Fertilizer Amount q/g·min−1
	944.92	2101.47	3842.87
L/mm		15
n/(r·min−1)	26.9	-	-
L/mm	25
n/(r·min−1)	18.3	41.4	-
L/mm	35
n/(r·min−1)	13.3	30.6	57.4
L/mm	45
n/(r·min−1)	11.0	24.2	44.7
L/mm	55
n/(r·min−1)	-	20.3	36.9

.

2.3.3. Fertilizer Discharge Performance Evaluation Index

Referring to the method specified in JB/T 9783-2013, “Seeder outer groove wheel fertilizer discharger”, to evaluate the fertilizer discharging performance of the EDEM simulation test, the coefficient of variation (CV ≤ 8%) of fertilizer discharging uniformity was adopted as the evaluation index of the fertilizer discharging performance of the fertilizer discharger.

After the fertilizer discharge simulation test, a 15,000 mm area of the simulated ground was selected as the sampling area for the fertilizer discharge effect; a Grid Bin Group was set up on the simulated ground to divide the area horizontally and uniformly into 10 identical cell grids, each with a size of 600 mm × 150 mm × 50 mm; the total mass of fertilizer particles in each cell grid was counted, and the CV of fertilizer discharge of the fertilizer discharger was calculated as follows [31]:

$$\sigma =\frac{\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(m_i-\overline{m}\right)}^2}{n-1}}}{\overline{m}}\times 100\%$$

(6)

$$\overline{m}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n{m}_i$$

(7)

where $m_i$—mass of fertilizer in the ith grid cell, g; $\overline{m}$—average mass of fertilizer particles within the grid cell, g; n—number of sampled grid cells, where n is taken as 10; σ—variation coefficient of fertilizer uniformity of the fertilizer discharger, %.

The CV of fertilizer discharge uniformity σ is used as an index to evaluate the stability and uniformity of fertilizer discharge; the smaller σ is, the better the stability and uniformity of fertilizer discharge.

3. Results

3.1. Analysis of Simulation Results

Simulation tests were conducted on the discharge process of the combination of different control sequences of three target fertilizer amounts (Figure 8), and the uniformity of the discharge was analyzed and calculated to obtain the coefficient of variation of the discharge of the outer slotted wheel discharger, as shown in Figure 9.

As can be seen from Figure 9, the CV of fertilizer uniformity at the control sequence of 18.3 r/min and 25 mm is the smallest, at 6.27%, when the target fertilizer discharge rate is 944.92 g/min, and the best stability of fertilizer discharge is achieved at this time. Under the control sequence (26.9 r/min, 15 mm), σ is 53.67%; at this time, the opening is small, the speed is relatively high, and the fertilizer filling performance of the outer groove wheel is poor, resulting in low stability of fertilizer discharge and even causing broken bars in the process of fertilizer discharge. Under the control sequence (11.0 r/min, 45 mm), σ was 38.10%, when the opening was larger and the rotational speed was lower, leading to the pulsation of the fertilizer discharge process and poorer stability of fertilizer discharge. Therefore, at the q₁ target fertilizer amount, the control sequence selection has a greater impact on the fertilizer discharge performance.

When the target fertilizer amount is 2101.47 g/min, the stability of fertilizer discharge from the outer groove wheel shows a decreasing trend with decreasing speed and increasing opening, and σ is the smallest at 4.34% under the control sequence of n = 24.2 r/min and L = 45 mm, and the best stability of fertilizer discharge at this time. When the target fertilizer amount was 3842.87 g/min, the coefficients of variation of fertilizer discharge uniformity σ were all less than 4%, the overall fertilizer discharge stability was high, and σ was the smallest at 2.01% with the control sequence n = 44.7 r/min and L = 45 mm. When the target fertilizer amount is larger, the corresponding combination of speed and opening will also be slightly larger; the fertilizer filling performance is better, and the discharge stability will be relatively improved. Therefore, at q₂ and q₃ target fertilizer discharge, the effect of control sequence selection on fertilizer discharge stability was small.

3.2. Control Sequence Optimization

By analyzing the CV of fertilizer discharge, l₀: L = 0.61n + 15.1L = 0.63n + 15.4 was fitted in Figure 9, which means that the control sequence (n, L) close to the line l₀ shows a small CV for a given target fertilizer discharge, indicating good fertilizer application uniformity.

In this paper, we use the differential evolution (DE) algorithm and a constructed RBFNN-based fertilizer discharge prediction model to find the best combination of speed and opening. DE is an efficient global optimization algorithm and a population-based heuristic search algorithm, where each individual in the population corresponds to a solution vector [32,33]. The evolutionary process of a differential algorithm is similar to that of a genetic algorithm (GA), which contains mutation, crossover, and selection operations [34].

To obtain the best combination of speed n and opening L for the same target fertilizer application, we define the minimization of the distance between the control sequence position (n, L) and the line l₀ as the fertilizer uniformity objective function. Thus, the multi-objective model including fertilizer discharge accuracy and uniformity can be defined as Equation (8):

$$\left\{\begin{array}{c}min{f}_1\left(n,L\right)=\left|\frac{q_p-q_t}{q_t}\right|\times 100\%\\ min{f}_2\left(n,L\right)=\left|\frac{0.63n-L+15.4}{1.18}\right|\end{array}\right.$$

(8)

$$s.t.\left\{\begin{array}{c}n\in \left[10,60\right]\\ L\in \left[15,55\right]\end{array}\right.$$

(9)

where f₁ is the accuracy objective function between the target and predicted fertilizer application. Here, q_p and q_t are the fertilizer amounts (g) obtained from the fertilizer application prediction model and prescription map, respectively, where f₂ is the uniformity objective function. The constraint condition is defined in Equation (2).

The target fertilizer application Q in the prescription chart is in kg/ha, while the fertilizer collected from the experiment is in g. To facilitate calculations comparing the target and actual fertilizer discharge, we used the following conversion:

$$q_t=10QBb$$

(10)

where Q—target fertilizer application volume in the prescription map, kg/ha; B—Operating width, m, and this paper takes B = 7 m; b—length of fertilizer application cell, m, and this paper takes b = 1 m.

After the DE algorithm code is written, the objective function is weighted, Q is set to 500 kg/ha, the number of iterations is 100, and its convergence curve is shown in Figure 10.

3.3. Bench Test Verification

In the fertilizer prescription map, Q was randomly selected as 560, 370, and 575 kg/ha, i.e., q_t as 39,200, 25,900, and 40,250 g. The optimal control sequences of 33.9 r/min, 35.8 mm; 23.9 r/min, 29.7 mm; and 44.6 r/min, 42.3 mm were obtained after the optimization search by the DE algorithm. For this result, a bench test was conducted in the laboratory of Shihezi University to check.

The opening adjustment mechanism (ball screw slide) used in the test bench has a repeat positioning error of ≤0.003 mm, the stepping angle accuracy of the speed adjustment motor is ≤0.09°, and the response time of the transistor type PLC controller is about 0.2 ms. The fertilizer discharger adopts the external slotted wheel-type fertilizer discharger, and its discharge outlet is 80 cm from the ground (Figure 11).

As can be seen from

Table 4. Test results.

Control Sequence (N/r·min−1, L/mm)	Predicted Value/g	True Value/g	MRE/%	CV/%
(33.9, 35.8)	39,200	39,515	0.80	4.12
(23.9, 29.7)	25,900	25,634	1.02	5.27
(44.6, 42.3)	40,250	40,058	0.47	2.88

, the relative error of fertilizer discharge using the control sequence derived after the algorithm search is less than 2% and the coefficient of variation is less than 6%, and this result is a great improvement compared with other studies. This indicates that the DE algorithm combined with RBFNN for fertilizer discharge control sequences in this study is reliable.

However, since there is no formed machine for actual operation at this stage, the effect of fertilizer applicator vibration and field slope on fertilizer application is ignored, and we will follow up with an in-depth study on this issue.

4. Conclusions

(1)

A fertilizer discharge calibration test with different fertilizer wheel speeds and openings was conducted on a bivariate outer groove wheel fertilizer discharge device. An RBFNN-based fertilizer discharge prediction model was constructed, and 14 samples that did not participate in the training were selected as the test set to validate the model. The results showed that the prediction model coefficient of determination reached 0.99965 with a mean relative error of 3.88%.

(2)

The influence law of the control sequence of outer groove wheel fertilizer discharger on fertilizer discharging performance was studied, and a simulation model was constructed by applying the EDEM software. A simulation test of fertilizer discharging with different control sequences under the same target fertilizer application volume was conducted. The simulation results show that when the target fertilizer application volume is small, the control sequence with a large rotational speed and a small opening combination has poor fertilizer filling performance and low fertilizer discharge stability; the control sequence with a small rotational speed and a large opening combination has significant pulsation and low fertilizer discharge stability. When the target fertilizer application volume is large, the control sequence selection has less influence on the outer groove wheel discharge stability.

(3)

Using the simulation test results and the RBFNN fertilizer discharge prediction model, a DE algorithm-based control sequence for finding a model with the target fertilizer discharge as input was established. Three target fertilizer discharge amounts of 560, 370, and 575 kg/ha were selected as inputs, and the corresponding optimal control sequences were calculated by the model and verified by bench tests. The results show that the optimal control sequence obtained by the DE algorithm has good fertilizer discharge accuracy and uniformity.