Machine Learning for Prediction of Energy Consumption and Broken Force in the Chopping Process of Maize Straw

Abstract

The main causes of high productional costs and greenhouse gas emissions in the chopping process of maize straws are high energy consumption and breaking force. Addressing these issues, this paper proposes a solution that leverages machine-learning algorithms to select appropriate operational parameters for chopping devices, thereby reducing energy consumption and the cutting force. In this study, the peak breaking force of the stalk (PB), the energy consumption of the stalk chopping (EC) and the slide-cutting momentum of the disc blade (SM) were set as dependent variables, and the rotation speed of the Y-type blade (RSY), transmission ratio (TR) and slide-cutting angle (SA) were set as independent variables. Various techniques, including back-propagation (BP), a radial basis function (RBF), an artificial neural network (ANN), support vector regression and a stepwise polynomial regression model, were applied using a 6-fold cross-validation approach to determine the most effective predictive models. The results indicated that the BP-ANN model performs best in predicting the PB (R²_Test = 0.9860) and SM (R²_Test = 0.9561), while the RBF-ANN model yields the highest accuracy in predicting the EC (R²_Test = 0.9255) under the optimal parameters. Subsequently, a verification test was conducted using randomly selected training and testing data based on the selected predicted functions. The results demonstrated that the R²_Train and R²_Test data for PB, EC and SM are all above 0.95, indicating that the BP and RBF neural networks are capable of accurately predicting the nonlinear relationship between the dependent variables (EC, SM and PB) and independent variables (RSY, TR and SA) in practical applications.

1. Introduction

Maize straw is widely acknowledged as a significant byproduct of maize production and contains essential elements like carbon, nitrogen, phosphorus and potassium, making it suitable for use as both fodder and fertilizer [1,2,3,4]. A common agricultural practice involves chopping maize straws and returning them to the field, as this has been found to improve soil structure, enhance fertility and increase crop yields [5,6,7]. Consequently, this method also helps to reduce the need to burn maize straws openly, thereby limiting environmental pollution. The primary agricultural machine used to conduct the chopping and returning of maize straws is the maize straw-chopping machine [8]. However, the operational requirements of the chopping process, such as ensuring that the length and spreading rate of the chopped straw are less than 10 cm and 30%, respectively, mandate a high rotational velocity of the blades (e.g., Y-type blade, hammer blade and straight blade) [8,9]. Consequently, energy consumption and carbon emissions were increased.

In response to these energy consumption challenges, researchers worldwide have conducted a series of studies. For the structure optimization of fixed blades and chopping blades, Zhang et al. (2018) focused on the optimization of fixed and chopping blades and developed a sliding cutting blade for banana stalks and found that a sliding cutting angle of 45° yielded the best results [10]. Zhao et al. (2020) designed a high-performance stubble cutting device for a no-tillage planter, incorporating the structure of locust mouthparts and top incisor lobes, demonstrating significant reductions in cutting torque and energy consumption [11]. Furthermore, Jiang et al. (2013) discovered a field reciprocating cutting test bench for maize stalks and discovered that the maximum cutting force and energy consumption were inversely related to the cutting speed and cutting angle of the chopping blade, reaching their minimum values at a cutting angle of 20° [12]. In addition, various operational parameters of chopping devices, such as static force, simulation and bench and field tests, have been utilized to reduce energy consumption. For example, Xie et al. (2022) determined the optimal parameters for cutting citrus stems to minimize energy consumption and cutting force [13]. Koc and Liu (2018) achieved a significant reduction in cutting energy through ultrasound-assisted cutting [14]. Additionally, the physical properties of crop stalks, such as water content, diameter and sampling location, were studied for the reduction in cutting force and energy consumption [15,16,17].

Some researchers have also developed regression functions to establish relationships between energy consumption and operational parameters. For example, Xie et al. (2018) constructed a quadratic polynomial function among the energy consumption of cutting sugarcane, rotational speed of the chopping blades, the overlapping length of the upper and lower blades and the bevel angle [18]. Gao et al. (2017) developed an exponential function to predict changes in the cutting force of a greenhouse vegetable harvester [19].

While the aforementioned studies offered valuable insights into the impact of the structural and operational parameters of chopping devices on energy consumption and cutting force, it is essential to consider the limitations of these findings. The complex field conditions and variations in the physical properties of the straw may limit the applicability of these research results to the optimization of energy consumption in the chopping process of maize stalks. Additionally, measuring the cutting force of the chopping blade presented challenges due to the high rotational speed of the blades and the intricate field environment. Thus, developing an accurate predictive model to forecast changes in energy consumption and cutting force during the maize straw chopping process is crucial for designing and optimizing chopping devices for crop straw.

Currently, machine-learning algorithms have been increasingly utilized to provide an accurate prediction service, such as a quadratic dynamic thresholding segmentation algorithm based on multi-channel fusion for seed cotton color measurement, artificial neural networks for weed–plant discrimination and K-nearest neighbors for dry bean seeds classification [20,21,22,23]. Furthermore, to elucidate the change principles governing energy consumption and cutting force during the maize straw chopping process, data from a finite element simulation test were validated by an actual field test using a self-designed maize stalk chopping device with double rollers [24,25,26]. Consequently, the objectives of this study aimed to (1) construct a predictive model for energy consumption and cutting force using machine-learning algorithms; (2) determine the most effective algorithm; and (3) verify the accuracy of the selected algorithm’s predictions.

2. Materials and Methods

2.1. Structure of the Maize Stalk Chopping Device with Double Rollers

The self-designed maize stalk chopping device with double rollers (SCD) mainly included 11 slide-cutting disc blades, 20 Y-type blades, a Y-type blade shaft, a disc blade shaft, a suspension device, a transmission device, and a shell [24,25,26] (Figure 1). The Y-type blades were fixed onto the shaft in a spiral pattern, while the disc blades are arranged parallel on the shaft. In the chopping process, two slide-cutting disc blades, along with one Y-type blade, work together to support and chop the maize stalks. Hence, the SCD is equipped with 10 chopping units (Figure 1c).

2.2. Chopping Test of Maize Stalks

To address the challenges posed by the complex field environment and high rotational speed of the Y-type blade and disc blades, a combination of finite element simulation and field verification tests were employed. In order to enhance the efficiency of the finite element method (FEM) simulation, some simplifications were made. Specifically, the maize stalk was treated as an isotropic material, and the influences of the stem, leaves, and moisture content were disregarded. Moreover, due to the significant difference in stiffness between the stalk and chopping blade, the deformation of the chopping blade was ignored. Additionally, some unimportant components, such as the Y-type blade holder, bolt and nut, were excluded from the simulation. Furthermore, the simulation model primarily focused on a single spiral-type cutting edge of the disc blade (1/12 disc blade) and one chopping unit, considering the spiral arrangement of the Y-type blades and the symmetric distribution of the spiral-type cutting edge on the disc blade. The outer circle diameter of the pith and rind was 18 and 20 mm, respectively, and the length of both the pith and rind was 500 mm [27].

The simulation model (type: .stp) was imported into LS-Prepost software (Version 4.1, ANSYS Corporation, Canonsburg, PA, USA) to obtain the calculated mesh, set material, boundary and contacting conditions. Subsequently, 2.79 × 10⁵ elements were meshed based on the cell unit length of stalk (1.6 mm) and chopping unit (2 mm), presented in

Table 1. Material and boundary properties of FEM model.

	Material Model	Density (kg/m3)	Elastic Modulus (MPa)	Poisson Ratio	Yield Strength (MPa)	Shear Modulus (MPa)	Segment
Rind/Pith	MAT_PLASTIC_KINEMATIC	1120/660	850/26	0.35/0.35	67.2/30	1.89/0.87	Slave
Y-type and disc blade	MAT_ELASTIC	7850	2 × 105	0.30	-	-	Master
Shaft of Y-type and disc blade	MAT_RIGID	7850	2 × 105	0.30	-	-

. To illustrate the chopping and breaking process of maize stalk, the contacting model of ERODING_SURFACE_TO_SURFACE was applied. The static and dynamic friction coefficient between the maize stalk and chopping unit were 0.4 and 0.1, respectively.

In the FEM simulation, parameters including the rotation speed of the Y-type blade (RSY), the transmission ratio between the Y-type blade and disc blade (TR) and the sliding-cutting angle of the disc blade (SA) were selected (

Table 2. Material and boundary properties of the FEM model.

Parameters	Values
Rotation speed of Y-type blade (RSY, rpm)	1400, 1600, 1800, 2000, 2200, 2400
Transmission ratio (TR, constant)	0.25, 0.50, 0.75, 1.0
Slide-cutting angle (SA, °)	30, 40, 50, 60

). A .K format file was then generated for computational analysis using LS-DYNA (Version R11, Canonsburg, Pennsylvania, USA) [24,25,26]. Finally, 96 sets of peak broken force of stalk (PB, unit: N), energy consumption of stalk chopping (EC, unit: W) and slide-cutting momentum of the disc blade (SM unit: N·S) data were obtained by LS-Prepost software for use in machine learning. The results accuracy of FEM simulation had been verified by a field stalk chopping experiment in Zhuozhou Science and Technology Park of China Agricultural University National Institute for Conservation Tillage (39°28′ N, 115°56′ E) showing an error of less than 15% [24].

2.3. Methods

2.3.1. Back-Propagation Artificial Neural Network Model

The back-propagation artificial neural network (BP-ANN) model is one of the most popular artificial neural network models to deal with the approximation of nonlinear maps [28]. The BP-ANN model consists one input layer, one output layer and one or more hidden layers to build the relationship between the factors and index. The topology of the BP-ANN model is shown in Figure 2.

The transformation process during BP-ANN model training was expressed as follows:

$$O{v}_j=f(ne{t}_j)=f({\displaystyle \sum _i{\omega }_{ji}I{n}_i-{\theta }_j})$$

(1)

$$Ou{t}_l=f(ne{t}_l)=f({\displaystyle \sum _i{\tau }_{jl}O{v}_j-{\theta }_l})$$

(2)

where In_i, Ov_j and Out_l are the input data of input layer, output data of hidden layer and output layer, respectively; f(net) is the transfer function; ω and τ are the weight value of hidden layer and output layer, respectively; θ is the threshold value of the neuron. To improve the performance, the bipolar sigmoid activation function was adopted as follows:

$$f(x)=\frac{2}{1+e^{(-x)}}-1$$

(3)

The newff function in MATLAB 2018 was selected for the BP-ANN model: net = newff (P, T, S, TF, BTF), where P and T are the input and target vector, respectively; S is the number of the hidden layers; TF is the transfer function and the functions of the tansig and purelin were used for the hidden layer and output layer; BTF is the back-propagation network training function. To obtain the optimum performance, the 13 back-propagation network training functions were explored in MATLAB (

Table 3. The back-propagation network training functions for the BP-ANN model.

TF Types	Abbreviation	Code
Levenberge–Marquardt back-propagation	Trainlm	T1
Bayesian regularization back-propagation	Trainbr	T2
Scaled conjugate gradient back-propagation	Trainscg	T3
Gradient descent back-propagation	Traingd	T4
Gradient descent with momentum back-propagation	Traingdm	T5
Gradient descent with adaptive learning rate back-propagation	Traingda	T6
Gradient descent with momentum and adaptive learning rate back-propagation	Traingdx	T7
Resilient back-propagation	Trainrp	T8
Conjugate gradient back-propagation with Fletcher–Reeves updates	Traincgf	T9
Conjugate gradient back-propagation with Polak–Ribiere updates	Traincgp	T10
Conjugate gradient back-propagation with Powell–Beale restarts	Traincgb	T11
Bfgs quasi-newton back-propagation	Trainbfg	T12
One-step secant back-propagation	Trainoss	T13

). Moreover, the BP-ANN model was configured with specific settings, including a learning rate of 0.01, 1000 iterations, a minimum error value of 10, and a minimum error threshold of 0.0001. Additionally, the number of hidden layers was systematically varied from 1 to 20 (the interval was 1).

2.3.2. Radial Basis Function Artificial Neural Network Model

The radial basis function artificial neural network (RBF-ANN) model, known for its capability to construct nonlinear functions, was employed [29]. This model is structured with an input layer, a hidden layer and an output layer (Figure 3). The number of neurons in the hidden layer can be adjusted according to the actual demand. Notably, the activation function for the RBF-ANN model was specified as the Gaussian function (Equation (4)).

$$g(x)={\mathrm{e}}^{-\frac{{(x-h)}^2}{2{\sigma }^2}}$$

(4)

where h and σ² are the center and variance of the Gaussian function, respectively. The output network y_m is computed by a derivable non-linear function (Equation (5)):

$$y_m={\displaystyle {\sum }_i{\omega }_{mi}{\nu }_i}$$

(5)

where ω_i is the weight vector in the output layer for the nth output node and v_i is the radial basis function of the ith node.

To optimize the model performance, the newrb function in MATLAB was selected: net = newrb (P, T, goal, spread, MN), where P and T are the input and target vector, respectively; goal is the mean squared error goal and is set as 0.0001; spread is the distribution density of radial basis functions; MN is the maximum number of neurons (set as the maximum number of the column vectors of the input and target vector). The study systematically adjusted the spread (ranging from 1 to 100 with an interval of 1) and MN (from 1 to 100 with an interval of 1) to determine the RBF-ANN model’s optimal performance.

2.3.3. Support Vector Regression

Support vector regression (SVR) has been widely applied in the agricultural sector to handle limited data and nonlinear problems [30]. The model involves the construction of a hyperplane that minimizes the expected risk and error by ensuring the proximity of sample data points to the plane. Notably, the forecasting accuracy and efficiency of SVR are influenced by key parameters, including the kernel functions (KFs), coefficient of kernel function (g), and penalty factor (c). In this study, a linear function (line, Equation (6)), polynomial function (poly, Equation (7)), radial basis function (rbf, Equation (8)) and sigmoid function (sig, Equation (9)) were considered as kernel functions. The values of g (ranging from 0.1 to 10 with an interval of 0.1) and c (ranging from 0.1 to 10 with an interval of 0.1) were determined based on the selected index of 6-fold cross-validation.

$$k_{line}(x_i,x_j)=x_i^T·x_j$$

(6)

$$\begin{array}{cc}{k}_{poly}(x_i,x_j)={\left(x_i^T·x_j\right)}^d& d\ge 0\end{array}$$

(7)

$$\begin{array}{cc}{k}_{rbf}(x_i,x_j)=\exp (-\frac{{\Vert x_i-x_j\Vert }^2}{2{\sigma }^2})& \sigma >0\end{array}$$

(8)

$$\begin{array}{ccc}{k}_{sig}(x_i,x_j)=\tanh (\beta x_i^T{x}_j+\theta )& \beta >0& \theta <0\end{array}$$

(9)

2.3.4. Stepwise Polynomial Regression Model

The stepwise polynomial regression model (SPRM) has been widely utilized in agriculture due to its effectiveness in addressing the complexities of nonlinear relationships [28]. In this model, the rotational velocity of the Y-type chopping blade, the transmission ratio between the Y-type chopping blade and disc blade and the sliding-angle of the disc blade were set as independent variables; the cutting energy, the cutting momentum and the peak breaking force of the stalk were set as dependent variables. Then, a second-order multiple linear regression model was used as Equation (10):

$$y_j=b_j+{\displaystyle \sum _{i=1}^3{a}_i{x}_i}$$

(10)

where b and a were constants. In the stepwise regression process, some parameters would be deleted, so the parameters in the LRM depend on the actual calculation.

2.3.5. Data Processing

In order to optimize the performance of the BP-ANN, RBF-ANN and SVR models, the input layers of the artificial neural network model were designed using a randomized complete block design with k-fold cross-validation. Six (k = 6) different dataset blocks for the training and testing phases were created. Each block included 16 data resulting in the random division of the original datasets into 6 sub-samples. In each simulation run, one single sub-sample was utilized for testing the artificial neural network model, and another k-1 sub-samples were utilized for training the artificial neural network model. This process was repeated k times in the simulation, employing each sub-sample as the testing dataset. In this study, the 96 samples were divided into the training phase data (n = 80) and test phase data (n = 16) with a ratio of 5:1 considering the effect variables.

2.3.6. Performance Evaluation

The performance of the predication model was evaluated using five statistical functions, which include the relative error (RE), mean absolute deviation (MAE), root mean square error (RMSE), coefficient of determination (R²) and accuracy (ACC). Each statistical index was calculated as follows:

$$R{E}_i=\frac{\left|p_i-y_i\right|}{y_i}\times 100\%$$

(11)

$$ACC=1-{\displaystyle \sum _{i=1}^n\left|\frac{p_i-y_i}{y_i}\right|}$$

(12)

$$RMSE=\sqrt{{\displaystyle \sum _{i=1}^n\frac{{(p_i-y_i)}^2}{n}}}$$

(13)

$$MAE={\displaystyle \sum _{i=1}^n\left|\frac{p_i-y_i}{n}\right|}$$

(14)

$$R^2=\frac{{\displaystyle \sum _{i=1}^n{(p_i-\overline{p})}^2{(y_i-\overline{y})}^2}}{{\displaystyle \sum _{i=1}^n{(p_i-\overline{p})}^2{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}}$$

(15)

where, p and y was the predicted and actual value in the test phase, respectively; n was a constant; $\overline{p}$ and $\overline{y}$ were the mean of the predicted and actual value in the test phase, respectively.

N₂₀ was defined as the percentage of cases in which the RE value of the prediction was smaller than 20%, respectively. The predictive performance of the models was assessed by the value of the ACC, N₂₀, R², MAE and RMSE. The model with the smallest MAE and RMSE and the highest ACC, N₂₀ and R² was preferred.

3. Results and Discussion

3.1. Results of SPRM

The SPRM was used to obtain the nonlinear relationship between independent variables (RSY, SA and TR) and dependent variables (PB, EC and SM), as shown in

Table 4. The results of SPRM.

	Intercept	RSY	TR	SA	RSY·TR	RSY·TR·SA	TR2	MAE	RMSE	R2Train	R2Test
PB	40.84 NS	−0.051 ***	−414.33 ***	1.35 ***	0.43 ***	−0.0039 ***	177.80 ***	6965.0	8231.7	0.71	0.71
EC	918.34 NS	−1.58 ***	−15742.3 ***	59.72 ***	11.77 ***	−0.099 ***	6480.34 ***	5045.3	5879.9	0.76	0.81
SM	0.012 ***	-	-	-	3.79 × 10−5 ***	−3.65 × 10−7 ***	-	7073.5	8361.8	0.73	0.64

Notes: “***” represents an extremely significant effect (p ≤ 0.001); “^NS” represents an insignificant effect (p > 0.1).

. The results indicated that the significant indexes were RSY, TR, SA, RSY·TR, RSY·TR·SA and TR² for PB and EC, and were RSY·TR and RSY·TR·SA for SM. Extremely significant positive influences on PB and EC of increased SA and decreased RSY and TR were found, and the interactive item of RSY·TR and RSY·TR·SA positively and negatively affected SM, respectively. These results indicated a significant nonlinear relationship between independent variables and dependent variables. In the training phase, all R²_Train values were higher than 0.7 and in the testing phase, the R²_Test values for PB, EC and SM were 0.71, 0.81 and 0.64, respectively. The results indicated that the SPRM had a limited stability and generalization ability for prediction. Consequently, the SPRM can be employed to predict the relationship between independent and dependent variables. The combination of RSY, TR, SA, RSY·TR, RSY·TR·SA and TR² could be utilized to forecast changes in force and energy consumption during the chopping process.

3.2. Results of the BP-ANN Model

The training function (TF) and number of hidden layers (NHL), key parameters of the BP-ANN model, directly impacted the calculated efficiency and precision of the network. Therefore, the Kruskal–Wallis test was conducted to analyze the effect of TF and NHL on the evaluation factors (MAE, RMSE, ACC, train phase R² and test phase R²) (

Table 5. Kruskal–Wallis test for performance criteria of BP-ANN model.

Parameter		MAE		RMSE		ACC		R2test		R2train		N20
		CS	p	CS	p	CS	p	CS	p	CS	p	CS	p
PB	Block	54.32	***	125.54	***	199.22	***	92.42	***	8.33	NS	59.76	***
	NHL	63.18	***	64.89	***	16.66	NS	65.84	***	13.22	NS	31.40	**
	TF	733.70	***	650.18	***	210.28	***	677.18	***	870.48	***	676.23	***
EC	Block	92.29	***	163.61	***	201.06	***	203.71	***	12.96	**	61.11	***
	NHL	71.36	***	53.12	***	18.11	NS	50.91	***	12.20	NS	48.35	***
	TF	559.00	***	517.94	***	159.36	***	510.40	***	694.32	***	446.47	***
SM	Block	31.10	***	65.92	***	77.37	***	181.46	***	10.94	*	101.04	***
	NHL	48.79	***	55.84	***	19.24	NS	45.87	**	11.82	NS	61.53	***
	TF	604.71	***	535.19	***	187.41	***	484.93	***	752.24	***	459.66	***

Notes: “***” represents an extremely significant effect (p ≤ 0.001); “**” represents a highly significant effect (p ≤ 0.05); “*” represents a significant effect (p ≤ 0.1); “^NS” represents an insignificant effect (p > 0.1); “CS” represents the number of Chi square.

). The results indicated that the block of datasets significantly influenced the performance of the BP-ANN model, with most p-values being less than 0.001. Moreover, the training function had an extremely significant effect on all performance criteria, illustrating the efficiency and accuracy of the prediction relying on the type of training function. Furthermore, the number of hidden layers had an extremely significant influence on most performance criteria, such as MAE and RMSE for PB and EC. Therefore, the predicted performance of the BP-ANN model was hinged on the type of training and test dataset and the number of hidden layers, not just the training function, although the influence level was TF > block > NHL.

After a series of training and testing when each block was set as the testing dataset, the results of the comparison of average values (MAE, RMSE, R²_Train and R²_Test) between the predicted and actual values under different application parameters for the BP-ANN model are shown in Figure 4. Notably for PB, the trainbr training function (T₂) and 19 hidden layers had the best performance (MAE < 8, RMSE < 11.01, R²_Train > 0.99, R²_Test > 0.98, Figure 4a–d) compared with other training functions. On the other hand, for EC, the results indicated that the predicted performance under the traingd training function (T₄) was better than other functions (Figure 4e–h), and when number of hidden layer was 7, both MAE and RMSE were reached their minimum value, and R²_Train and R²_Test were 0.9672 and 0.9445, respectively. Similarly, for SM, the trainbr training function (T₂) with 14 hidden layers was also found to be the most suitable function among 14 training functions, and the corresponding values for MAE, RMSE, R²_Train and R²_Test were 0.00168, 0.00249, 0.9764 and 0.9561, respectively.

3.3. Results of the RBF-ANN Model

In the RBF-ANN model, the parameters of spread and MN have a direct impact on the smoothing characteristics and accuracy of the predicted model. The Kruskal–Wallis test was undertaken to assess the influence of the block of datasets, spread, and MN on the prediction performance criteria. The results of the test revealed that all three factors had a highly significant influence (p < 0.001) on the prediction performance, as determined by a random complete block design (

Table 6. Kruskal–Wallis test for performance criteria of the RBF-ANN model.

Parameter		MAE		RMSE		ACC		R2test		R2train		N20
		CS	p	CS	p	CS	p	CS	p	CS	p	CS	p
PB	Block	39,804	***	39,385	***	10,873	***	20,260	***	4963	***	25,379	***
	Spread	2882	***	2773	***	8157	***	6768	***	2629	***	4571	***
	MN	7470	***	6790	***	10,231	***	13,369	***	43,981	***	14,287	***
EC	Block	28,427	***	28,345	***	9140	***	18,570	***	11,723	***	24,304	***
	Spread	5108	***	4859	***	9034	***	9127	***	2511	***	5698	***
	MN	12,332	***	10,806	***	9308	***	13,390	***	36,050	***	12,936	***
SM	Block	42,263	***	41,998	***	16,139	***	21,101	***	18,666	***	36,002	***
	Spread	3116	***	3104	***	8491	***	9688	***	1490	***	4785	***
	MN	5831	***	5141	***	7274	***	10,872	***	28,709	***	7417	***

Notes: “***” represents an extremely significant effect (p ≤ 0.001); “CS” represents the number of Chi square.

). According to the results, the influence level was block > MN and spread. Consequently, it is imperative to meticulously select the values of spread and MN to attain an optimal performance of the RBF-ANN model, given their direct impact on the model’s smoothing characteristics and accuracy.

In order to assess the expected performance of the RBF-ANN model, a comprehensive experimental test was conducted, involving 100 levels of MN (ranging from 1 to 100 with an interval of 1) and spread parameters (ranging from 1 to 100 with an interval of 1). The appropriate values of spread and MN were determined based on the results of the experimental test (see Figure 5). The experimental test results showed that for PB, when the spread and MN were set to 46 and 27, R²_Test reached the maximum value of 0.9356, and R²_Train was just smaller than the highest R²_Train by 1.31%. For EC, the results showed that the RBF-ANN model exhibited the highest predicted accuracy (R²_Train = 0.9771 and R²_Test = 0.9255) when the spread and MN were set to 27 and 22, respectively, and the RMSE and MAE were also the lowest compared to the other parameters. In the case of SM, the best predicted performance (R²_Test > 0.97, R²_Train > 0.92 and minimum RMSE) was reached under a spread of 27 and MN of 22, respectively, outperforming the other combinations of spread and MN parameters.

3.4. Results of SVR

The results of the Kruskal–Wallis test indicated that both the kernel function and block of dataset had an extremely significantly influence on the predicted performance of the SVR model (p < 0.001) for three dependent variables (

Table 7. Kruskal–Wallis test for the performance criteria of the SVR model.

Parameter		MAE		RMSE		ACC		R2test		R2train		N20
		CS	p	CS	p	CS	p	CS	p	CS	p	CS	p
PB	KF	15,028	***	14,542	***	13,064	***	15,118	***	19,903	***	15,523	***
	Block	2271	***	3107	***	4623	***	1337	***	245.3	***	1350	***
	C	52.5	***	51.8	***	41.3	***	49.5	***	302.7	***	8.2	***
	G	1587.8	***	1225.9	***	589.5	***	1597.5	***	191.2	***	1294	***
EC	KF	13,596	***	13,649	***	12,948	***	13,666	***	18,678	***	12,132	***
	Block	3014	***	3493	***	5415	***	1242	***	389	***	2590	***
	C	51.0	***	47.1	***	44.0	***	39.1	***	185.0	***	2.8	NS
	G	1139	***	907	***	493	***	1200	***	119	*	1224	***
SM	KF	16,514	***	15,787	***	14,058	***	16,701	***	20,762	***	16,473	***
	Block	1146	***	1614	***	3084	***	607	***	188	***	1531	***
	C	53.9	***	55.5	***	30.0	***	51.7	***	161.3	***	2.2	NS
	G	1524	***	1378	***	664	***	1535	***	134	***	937	***

Notes: “***” represents an extremely significant effect (p ≤ 0.001); “*” represents a significant effect (p ≤ 0.1). “^NS” represents an insignificant effect (p > 0.1); “CS” represents the number of Chi square.

). Moreover, the value of C and G also was significant on the evaluation factors (MAE, RMSE, ACC, train phase R² and test phase R²) with most p-values being less than 0.001. Notably, the influence level was found to be KF > block > G > C for the three dependent variables. Therefore, the appropriate kernel function was crucial for improving the performance of the SVR model.

Figure 6 displays the results of a comparison of mean values for the performance criteria of the SVR model during the testing and training phases. The results from both phases were simultaneously analyzed to determine the most effective kernel function. The sigmoid kernel function had a much lower MAE, RMSE and standard deviation, as well as a higher R²_Test compared to the other kernel functions. These findings suggested that the sigmoid kernel function was more proficient than the other kernel functions in predicting various block datasets. In conclusion, considering all the factors that influence the prediction process, the sigmoid kernel function demonstrated the best performance among the four kernel functions.

The performance of the SVR model with a sigmoid kernel function was assessed through a comprehensive test involving a test of 100 levels of parameters c (ranging from 0.1 to 10) and g (ranging from 0.1 to 10) to ascertain the optimal values. Figure 7 displays the performance evaluation criterion (MAE, RMSE, R²_test and R²_train) of the combination of c and g during both the training and test phases. The results indicated that a lower value of c and g leads to a lower MAE and RMSE and a higher R²_test and R²_train. Specifically, for PB, the optimal values of c = 0.2 and g = 0.3 yielded the best predicted performance (MAE = 26.73, RMSE = 38.95, R²_test = 0.84 and R²_train = 0.81). For EC, the best predicted performance was found under the values of c = 1.1 and g = 0.1 (MAE = 925.54, RMSE = 1199.59, R²_test = 0.7525 and R²_train = 0.7061), surpassing the performance of other parameter combinations. For SM, the SVR model performed most accurately with c = 0.1 and g = 0.4, achieving the highest R² values (R²_Train = 0.8768 and R²_Test = 0.8790), while also exhibiting the lowest RMSE and MAE compared to other values of c and g.

4. Discussion

The comparative results of the BP-ANN model, RBF-ANN model, SVR and SPRM were analyzed and presented in

Table 8. The comparative results of the predicted model.

Parameter	Predicted Model	MAE	RMSE	R2Train	R2Test
PB	BP-T2	7.88	11.01	0.9936	0.9860
	RBF	269.65	345.08	0.9869	0.9359
	SVR-Sigmoid	26.73	38.95	0.81	0.84
	SPRM	6965.0	8231.7	0.71	0.71
EC	BP-T4	351.73	475.39	0.9672	0.9445
	RBF	286.090	406.00	0.9771	0.9255
	SVR-Sigmoid	925.54	1199.59	0.7061	0.7525
	SPRM	5045.3	5879.9	0.76	0.81
SM	BP-T2	0.00168	0.00249	0.9764	0.9561
	RBF	220.97	297.86	0.9705	0.9178
	SVR-Sigmoid	0.0032	0.0043	0.8768	0.8790
	SPRM	7073.5	8361.8	0.73	0.64

. The results indicated that the R²_Train of BP-T₂ in predicting PB and SM, of RBF in predicting EC based on the nonlinear function were greater than 0.97, while R²_Test were greater than 0.92. Additionally, the MAE and RMSE of BP-T₂ were smaller compared to those of the other predicted models. These findings were indicated that the BP-T₂ for PB and SM, and RBF for EC, were more appropriate for predication of energy and force change in the stalk chopping process compared with other predicted algorithms. Consequently, the BP-T₂ ANN model for PB and SM, and RBF ANN model for EC were selected as the best predicted function based on the RSY, TR and SA.

The performances of the selected models were further illustrated using the randomly selected training data (N_Train = 80) and testing data (N_Test = 16, 56, 96). Evaluation indexes, such as R²_Train, R²_Test, N₂₀ and ACC, were utilized to assess the models’ performance. The comparative predicted performances of the BP-ANN and RBF-ANN models, based on the optimal parameters, are presented in Figure 8. Despite the random selection of training and testing data, all the R²_Train, R²_Test and ACC values were larger than 0.95, and the N20 values for PB, EC and SM were larger than 93%, 67% and 93%, respectively, indicating the effectiveness of the selected models in predicting the changes of PB, EC and SM (Figure 8).

5. Conclusions

In this study, the change in PB, EC and SM based on the rotation speed of a Y-type blade, transmission ratio and slide-cutting angle was forecasted using various models including BP-ANN, RBF-ANN, SVR and SPRM models. These models were further developed by adjusting key parameters, such as training functions and the number of hidden layers for a BP-ANN model, the spread and MN for an RBF-ANN, and kernel functions, c and g for SVRM, in order to improve the accuracy of the predictions. In addition, stepwise polynomial regression was employed to capture the nonlinear relationship between PB, EC and SM and RSY, TR and SA. The analysis results shown that the BP-Trainbr ANN model performed better in predicting PB and SM, while the RBF ANN model was more accurate in predicting EC compared to the other models. Furthermore, a vertical experiment was conducted using randomly selected training and testing data, and it was found that R²_Train, R²_Test and ACC of PB, EC and SM were all higher than 0.95, demonstrating the superior predictive accuracy of the selected models. However, given the complexity of the maize stalk chopping process, it is recommended to incorporate additional independent variables in future studies to further enhance the accuracy and applicability of the predictive model.