## 4 Conclusions  
In this study, machine learning methods were applied to accomplish droplet size and deposition distribution quantitative evaluation for TEEJET XR110015 VS nozzle. REGRESS and LS-SVM achieved good performance for droplet size quantitative evaluating of single and twin nozzles, with \(Rc^{2}\) and \(Rp^{2}\) values both above 0.9. The droplet size distribution of twin nozzles was visualized by formula obtained from REGRESS, the principles leading to the droplet size distribution of single and twin nozzles were also explained. Additionally, RBFNN showed great effectiveness for deposition distribution quantitative evaluation for twin nozzles condition with the best \(Rp^{2}\) value of 0.7994 and RMSEP value of 0.2183 mL/cm\({}^{2}\). The results of Models for deposition distribution were inferior to models for droplet size distribution but still promising. Finally, the model of a single nozzle based on REGRESS was  
\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{3-6}  & & \(R_{\text{C}}\)\({}^{2}\) & **RMSEC (\(\upmu\)m)** & \(R_{p}\)\({}^{2}\) & **RMSEP(\(\upmu\)m)** \\ \hline LM-UGO & / & 0.7430 & 3.7959 & 0.6838 & 4.1984 \\ LS-SVM & (0.599, 22.789) & 0.9116 & 2.1398 & 0.7714 & 3.5471 \\ ELM & 36 & 0.8120 & 3.2470 & 0.7415 & 3.8389 \\ RBFNN & 35 & 0.9567 & 1.5578 & 0.8616 & 3.2595 \\ \hline \hline \end{tabular} Parameters of different models: 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 6: Results of VMD modeling for the overlapping areas of the twin nozzles condition.  
Figure 10: Scatter plot of measured VMD values vs. predicted VMD values of overlapping area for twin nozzles condition. (**a**) LM-UGO (**b**) LS-SVM; (**c**) ELM; (**d**) RBFNN.  
used to predict the droplet size in the overlapping area of twin nozzles; RBFNN showed the best performance for quantitatively predicting, with an \(Rc^{2}\) value of 0.9567 and RMSEP of 3.2595 \(\upmu\)m.  
This study provided a novel and precise method for effective quantitative evaluation of droplet size and deposition distribution for UAV spray nozzle. The quantitative determination of droplet size distribution for UAV spray nozzle can help to control the spray drift and provide a basis for realizing uniform deposition and efficacy of UAV spraying. Furthermore, the study showed the feasibility to predict droplet size of the overlapping area by using the model based on machine learning methods, providing a basis for studying the droplet size distribution of a multi-nozzle spray. In future studies, more types of UAV spray nozzles and more measuring points will be studied under different conditions, the effect of the wind field and the interaction between droplets and crop leaves also need to be investigated in the future experimental design.  
The work presented here was carried out in collaboration between all authors. [PERSON] and [PERSON] conceived the idea. [PERSON] and [PERSON] co-worked on associated data collection and carried out the experimental work. [PERSON], [PERSON], and [PERSON] contributed to the data processing of this paper. [PERSON] drafted the manuscript, [PERSON] and [PERSON] provided their experience and co-wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Program of China (2017 YED0701002) and Key Research and Development Program of Ningxia Hui Autonomous Region (2017 BY067).  
The authors declare no conflict of interest.