## 3 Results  
### Evaluation of Droplet Size for TEEJET XR110015 VS Nozzle  
The volume medium diameter (VMD) distribution was shown in Figure 5; standard deviations were labeled as error bars; the VMD values of XR110015 VS nozzle were increased with the horizontal position and spray height. For the same spray height, when the absolute value of the horizontal position was greater than 26, the tendency of increase for droplet size along the direction becamemore obvious. The influence of height on droplet size is less than that of horizontal position. This distribution indicated that the proportion of small droplets decreases with the increasing distance of measuring point and nozzle.  
According to the Jet theory in the cross-flow environment, the droplet sector spreading with the increase of spray height, more and more small droplets drift away from the spray fan with the velocity of droplet and entrainment air flow attenuates, resulting in the overall increase of VMD. Because of the porous media structure of droplet sector, the entrainment of airflow and the velocity distribution of small droplets, transverse airstream will invade the two flanks of the droplet sector, producing forces on small droplets and blow the droplets off the spray fan, leading to the increase of VMD at the edge of horizontal position.  
Quantitative evaluation models based on REGRESS, LS-SVM, ELM, and RBFNN were built to quantify the relationship between spray height, horizontal position, and the droplet size of the nozzle. The number of the calibration set and prediction set was 46 and 15, respectively, with a scale of 3:1. The results of the different models are shown in Table 3. Models based on REGRESS, LS-SVM, and RBFNN all had good modeling performance, with \(Rc^{2}\) values above 0.92 and RMSEp within 2 \(\upmu\)m, indicating these models were capable of predicting VMD values. At the significant level \(\alpha=0.05\), the F value of 70.2383 was greater than its corresponding critical value, showing the accuracy and robustness of the model based on REGRESS. However, ELM performed bad; the results of the calibration and prediction were worse than the other three models. In the study, we used the model obtained by the REGRESS method to express the VMD distribution. The formula was as follows:  
\[\text{z}=147.3650+15.5766x+0.0661y-17.0732x^{2}-0.0776x\cdot y+0.0073y^{2}+7.001 x^{3}+0.0222x^{2}\cdot y-0.0022x\cdot y^{2} \tag{4}\]  
where \(x\) stands for spray height (m), \(y\) stands for the horizontal position (cm), and z stands for VMD (\(\upmu\)m) (four decimal places are reserved for each coefficient).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Parameter [a]**} & \multicolumn{2}{c}{**Accuracy of Calibration Set**} & \multicolumn{2}{c}{**Accuracy of Prediction Set**} \\ \cline{3-5}  & & \(R_{C}\)\({}^{2}\) & **RMSEC (\(\upmu\)m)** & \(R_{P}\)\({}^{2}\) & **RMSEP(\(\upmu\)m)** \\ \hline REGRESS & 3 & 0.9382 & 2.2011 & 0.9201 & 1.9761 \\ LS-SVM & (24.169, 2.445 × 10\({}^{4}\)) & 0.9378 & 2.2026 & 0.9201 & 1.8939 \\ ELM & 9 & 0.7413 & 4.1362 & 0.6795 & 3.8519 \\ RBFNN & 763 & 0.9395 & 1.9960 & 0.9253 & 1.9183 \\ \hline \hline \end{tabular} Parameters of different models: the highest degree of the polynomial for REGRESS, the bandwidth of kernel function (sig2), and the trade-off between minimum model complexity and minimum training error(gam) for LS-SVM, the number of hidden nodes for ELM, the spreading coefficient for RBFNN.  
\end{table}
Table 3: Results of VMD modeling for TEEJET XR110015 VS nozzle.  
Figure 5: Volume medium diameter (VMD) distribution of TEEJET XR110015 VS nozzle.