3.2.2. Multi-Variable Regression Model

Through preferentially selecting the main factors affecting the feeding rate by correlation analysis in the silage harvester, the least squares multiple regression model [27] between multi-power data and feeding quantity is developed to achieve multi-parameter calibration and fused feeding rate detection, as shown in Formula (16).

$$\begin{cases} \begin{array}{c} q\_{\mathfrak{m}} = b\_0 + b\_1 \mathfrak{x}\_1 + \dots + b\_2 \mathfrak{x}\_i + \dots + b\_{\mathfrak{m}} \mathfrak{x}\_{\mathfrak{n}} + \varepsilon\_{\mathfrak{m}}\\ \varepsilon\_{\mathfrak{m}} \in N(0, \sigma^2) \end{array} \tag{16}$$

where *b*0, *b*1, ... , and *bn* are model regression parameters, *ε<sup>m</sup>* is the residual of the multiregression.

#### **4. Results and Discussion**

To verify the availability of the feeding rate detection model, harvesting tests are carried out in Rizhao, Shandong Province with a self-propelled silage harvester. First, the real-time power monitoring sensors are integrated into the test prototype, covering both the mechanical driving parts and hydraulic driving parts. Secondly, by adjusting the harvesting speed between 1 km/h and 4 km/h, seven groups of field experiments are designed and conducted under different feeding rates, where condition monitoring data under different operating status is simultaneously collected and stored. Thirdly, the raw monitoring data is preprocessed by the combination of the Mann-Kendall data filtering algorithm and the Grubbs exception handling algorithm. Finally, the univariate and multivariate model based on the power data is applied to realize the feeding rate measurement.
