*4.1. Field Experiment Design*

Field experiments are realized group by group, as shown in Figure 5, while the harvested crops are upright maize at the wax ripeness stage with a moisture content of 65–70%.

**Figure 5.** The experiment process of harvesting in the field(where *R*1, *R*2, ... , and *Rn* are harvesting crop rows); (**A**) Grouping schematic; (**B**) Picture of the field test.

As shown in Figure 5A, during each group, the silage harvester is adjusted to a predetermined harvesting velocity under the rated working state in the pre-acceleration area (the area between position a and position b in test group no.1). After that, the normal harvesting progress is carried out in the harvesting area (the area between position b and position c in test group no.1) according to the setting velocity and cutting height of 150 mm, while simultaneously all of the silage materials thrown from the outlet of the throwing cylinder were collected manually. Reaching point c, the harvester was parked and shut down in the stopping area (the area between position c and position d in test group no.1). As shown in Figure 5B, the raw material harvested and processed by the silage harvester all falls on the aggregate canvas. After manual collection, it is weighed with a platform scale with an accuracy of 0.01 kg to obtain the cumulative mass of the harvested material. After that, the true value of the feeding rate is calculated with the harvesting time.

#### *4.2. Test Results Analysis*

#### 4.2.1. Data Pre-Processing Results

First, the Mann-Kendall algorithm is used to screen the effective data segments. The detection results of the mutation boundary on both sides of the data area are shown in Figure 6. It can be seen that the algorithm can accurately capture the rising and falling edge of the torque monitoring value. Moreover, the data fluctuations related to the dynamic load changes during the harvesting have less influence on the mutation boundary detection.

Meanwhile, the power data of all components are subjected to effective boundary detection, and the test results are shown in Table 1. The boundary extraction accuracy of the shedding data and blowing data are 100%, while that of the inside header, outside header, and feeding part are 64.3%, 71.4%, and 85.7%, respectively. The reason for the analysis is that the header and the feeding part are the front-end mechanisms in plant feeding, which have the characteristics of strong operating vibration, frequency data fluctuations, and small amplitude changes between different working conditions; the accuracy of edge detection is lower compared with the rear-end mechanism. Considering that, the timedelay model described in Formula (10) is applied to achieve data filtering for front-end mechanisms.

Then, through Grubbs Criterion anomaly detection and neighborhood interpolation, the processing results of field test data are finally obtained, as shown in Table 2.

**Figure 6.** Results of data filtering; (**A**) The rising boundary of the shredding data; (**B**) The descending boundary of the shredding data; (**C**) The rising boundary of the blowing data; (**D**) The descending boundary of the blowing data.


**Table 1.** Results of boundary detection for data filtering.

**Table 2.** Pre-processed data of field harvesting.


4.2.2. Correlation Analysis Results

Correlation analysis between the monitored variables and feeding rate is performed based on the field trial data, and the correlation R is calculated by Formula (17) through the Pearson correlation coefficient [28].

$$R = \frac{\sum\_{i=1}^{n} x\_i y\_i - \frac{\sum\_{i=1}^{n} x\_i \sum\_{i=1}^{n} y\_i}{n}}{\sqrt{\left(\sum\_{i=1}^{n} x\_i^2 - \frac{\left(\sum\_{i=1}^{n} x\_i\right)^2}{n}\right) \left(\sum\_{i=1}^{n} y\_i^2 - \frac{\left(\sum\_{i=1}^{n} y\_i\right)^2}{n}\right)}} \tag{17}$$

where X = {*x*1, *x*<sup>2</sup> ... , *xn* } and Y = {*y*1, *y*<sup>2</sup> ... , *yn* } are the sampled data sets of the two monitored variables respectively; *R* is the correlation coefficient between the variable X and Y; and *n* is the sample set size.

The heat map of the correlation among variables is shown in Figure 7. The results show that the influence of each operating part on the feeding rate, in descending order, is the shredding rollers, the throwing blower, the outside header, the inside header, and the hydraulic feeding part. The correlation coefficient of the outside header, the shredding rollers, and the throwing blower relative to the feeding rate is 0.87, 0.97, and 0.90, respectively. All of the above correlation coefficients are greater than 0.85, presenting a strong correlation relationship with the feeding rate. The correlation coefficient of the inside header and the feeding part relative to the feeding rate is 0.63 and 0.54, respectively, showing a weak correlation with the feeding rate.

**Figure 7.** Heatmap of the variable correlation coefficient.

4.2.3. Feeding Rate Measurement Results

(1) single-variable regression results

The univariate linear regression models between the feeding rate and the power data of key components in maize silage harvester are respectively established by using the single factor analysis method, and the model results are shown in Figure 8. Along with the increase in feeding rate, the power of each working part shows an increasing trend. According to the modeling performance, they are ranked into shredding roller, throwing blower, outside-header, inside-header, and hydraulic feeding part power, which are consistent with the correlation analysis results. The linear relationship between the shredding power and the feeding rate is the most significant, with a model coefficient of determination *R2* of 0.94, while the coefficient of determination *R2* for the feeding rate

model based on the blowing power is 0.82. Therefore, if a single-factor measurement is considered, a shredding-power-based feeding rate model can achieve better detection results.

**Figure 8.** Results of the single-variable regression model; (**A**) The model between inside-header power and feeding rate; (**B**) The model between outside-header power and feeding rate; (**C**) The model between feeding power and feeding rate; (**D**) The model between shredding power and feeding rate; (**E**) The model between blowing power and feeding rate.

(2) multiple-variable regression results

The first three factors that affect the feeding rate, including the inside-header power, the shredding power, and the blowing power, are selected as model inputs to develop a multivariate least squares regression model for the detection of the feeding rate. The result is shown in Formula (18), where the parameter *b0* is −4.0326 within the confidence interval of [−12.0817, 4.0165], the parameter *b1* is 7.9867 within the confidence interval of [−8.5042, 24.4776], the parameter *b2* is 0.2353 within the confidence interval [−0.0564, 0.5271], and the parameter *b3* is 0.1315 within the confidence interval [−0.0817, 0.3446]. While the model coefficient of determination *R2* is 0.9792, the model statistic *F* is 73.8684, and the significance factor *P* is 0.00035 (far less than 0.05). The multiple-variable model is reliable.

$$q\_m = -4.0326 + 7.9867 \cdot p\_2 + 0.2353 \cdot p\_4 + 0.1315 \cdot p\_5 \tag{18}$$

where *p*2, *p*4, and *p*<sup>5</sup> are the power of the outside header, shredding rollers, and blower, respectively.

Furthermore, a residual analysis is made for the model and the results are shown in Figure 9. The residual value of the data in the samples is close to zero, while the confidence interval of the residual includes zero and there are no exceptions, indicating that the model can better fit the original data.

Meanwhile, the accuracy of the multiple regression feeding rate model is analyzed, and the results are shown in Table 3. The maximum absolute error of the model is 0.58 kg/s, and the maximum relative error is ±5.84%, which meets the requirements of the field feeding rate measurement and evaluation. Furthermore, the influence factors of feeding rate measurement accuracy are analyzed. There are primarily two aspects that contribute to the detection error. Firstly, as the compositions of maize forage plants in the machine vary, the working power of key components changes dynamically during harvesting, and the feeding rate measurement is modeled based on the average value of the power consumption, which introduces detection errors. Secondly, although the variation range in the crop moisture content during the field harvesting is slight with a range of 65%~70%, the crop moisture content has a direct influence on chopping power

consumption, which is the core parameter of feeding rate detection, and thus increases the measurement error.

**Figure 9.** The plot of residual case order.

**Table 3.** Results of the multi-variable regression model error analysis.

