Plant protection spray has been widely used to prevent and control diseases and pests due to its high efficiency, rapidity and economy. It plays an irreplaceable role in ensuring food security [1
]. During the spraying process, a fraction of pesticides are lost in the air due to the droplet drift [2
]. In addition, pesticides also exist in the soil on account of the run-off and rebound of droplets. The volatilization and wind erosion of soil particles will increase the pesticide content in the atmosphere, which causes air pollution and poses a threat to human health and safety [3
]. The imperfect plant protection spraying technology not only leads to the low utilization rate of pesticides, but also seriously endangers the agricultural product safety and the environment [5
]. With the increasing awareness of global environmental protection, how to maximize the effectiveness of pesticides has attracted widespread attention. It is necessary to improve pesticide utilization and reduce human exposure to atmospheric pesticides [4
Studies have found that it is necessary to ensure the uniformity of pesticide spray coverage for maximum efficacy [6
]. The droplet size of pesticides is the main factor that directly affects the distribution uniformity on the target crop [8
]. In the spray process, large droplets are not easy to drift or evaporate but are likely to bounce or roll off. As a result, liquid loss, pollution of soil and water, as well as poor coverage density and uniformity of droplets can occur, which greatly reduces the effectiveness of pesticide spray effect [9
]. On the contrary, the small droplets have excellent adhesion, coverage density and uniformity on the crop surface. However, they are prone to drift, which causes environmental pollution as well as damage to other crops nearby [10
]. According to the theory of Biological Optimum Droplet Size (BODS), the range of droplet size captured by different biological targets is different. Only droplets within the optimal size range are effective for specific target organisms [14
]. Therefore, reasonable droplet size is key to achieve the best prevention and control effect with the least amount of pesticides and to reduce environmental pollution. In order to achieve the expected prevention and control effect, appropriate pesticides should be sprayed to the target crops to obtain optimal droplet coverage density [6
]. This conclusion negates the possibility of blindly increasing the dosage to improve the prevention and control effect. Washington [18
] indicated that the linkage change of the spray coverage density can be realized by controlling the volume median diameter (VMD) of droplets so as to obtain the optimal control effect of diseases and pests. The size directly affects the adhesion, slippage or drift of pesticide droplets, which are important indicators to measure the quality of spray [19
]. Therefore, based on the atomization parameters of VMD and RS, the research on the influence factors and laws of the spatial distribution of the droplet size is of great significance for controlling spray operations, improving the utilization of pesticides and reducing pesticide residues.
In the spray operation, the droplet size is affected by meteorological conditions, pesticide characteristics, spray parameters, spatial parameters and so on [21
]. In order to precisely control the spatial distribution of droplet size, it is necessary to study the correlation between different influence factors and droplet size. Among them, spray parameters and spatial parameters are easy to control during the operation. Therefore, many researchers focus on the analysis of these parameters. The nozzle type and the flow rate are the focus of attention in spray parameters. The nozzle is the main component to atomize the sprayed liquid, and its type and structure directly determine the characteristics of the droplet spectrum [25
]. Kang et al. [26
] obtained atomization models of different nozzles, which was validated by actual test method and showed a high degree of confidence. Kooij et al. [27
] studied the liquid film generated by nozzles of different shapes. In many studies, the droplet size distribution between different nozzles was compared [25
]. In order to improve the utilization rate of pesticides, low-volume spray mode is widely used [30
]. The spraying flow rate also becomes an important parameter in the spraying operation. A suitable droplet size distribution can be achieved with the proper selection of the nozzle and the flow rate. Balsari et al. [32
] measured droplet size parameters and RS in different combinations between flow rates and air speed. The spatial parameters refer to the spray height and the horizontal distance between the target crop and the nozzle. Studies have shown that there are significant differences in the droplet size distribution at different locations [8
]. During the unmanned aerial vehicle (UAV) spraying operation, the flying height directly affects the droplet deposition effect [34
]. The droplet deposition effects at different horizontal positions are also different, which is an important factor in determining the nozzle position and the horizontal distance between the two flight routes [35
]. In variable spraying process, the uniformity of droplet deposition is often improved by adjusting the spatial parameters [36
]. In summary, the spray parameters and spatial parameters should be considered comprehensively to achieve a better spraying effect.
Most of the current studies only focus on single or dual factors when establishing analysis models without comprehensive consideration of spray parameters and spatial parameters. In order to guide spraying operations, it is necessary to establish a prediction model of droplet size distribution considering multiple factors. In addition, polynomial regression models were mainly used, of which the accuracy needs to be improved (determination coefficients were all less than 0.85) [8
]. Machine learning is an important research field of artificial intelligence, which can be used to mine the potential laws behind data and achieve effective use of data through independent learning. Its basic principle is to build a model according to the effective information provided by the calibration set, and then realize the prediction of the newly input sample information. During the plant protection spray, the droplet size distribution is affected by many factors, which also interact with each other. The influences of spray parameters and spatial parameters on droplet size are different and nonlinear, so the polynomial regression has a poor fitting effect. In this case, the machine learning methods can transform the problem from low-dimensional nonlinearity to high-dimensional linearity, thereby making the prediction results better. Among them, multi-layer perceptron (MLP) can effectively self-learn the interaction between factors while extreme learning machine (ELM) has a fast learning speed. Decision tree (DT), support vector regression (SVR) and radial basis function neural network (RBFNN) have a strong ability to deal with nonlinear issues. These methods combined with spectral technology have achieved good results in detection of crop diseases [37
], determination of crop origins [38
] and prediction of physiological indexes [40
]. It confirms the superiority of machine learning in mining the relationship between variables. However, as far as we know, machine learning methods have not been widely used in quantitative analysis of droplet size distribution of plant protection spray. Therefore, the main purpose of this study is to investigate the influence of multiple factors on the droplet size distribution as well as the establishment of prediction model based on machine learning. Specifically, that is to (1) investigate the effects of nozzle orifice diameter, flow rate, spray height, horizontal position on VMD and RS; (2) establish quantitative prediction models of VMD and RS, and explore the feasibility of machine learning methods to predict the droplet size distribution; (3) realize the visualization distribution of VMD and RS based on the optimal prediction model. According to the results of the droplet size distribution and the optimal droplet size for the target, the optimal spray parameters and spatial parameters can be determined to realize the uniform distribution of pesticide deposition and exert the best effect of pesticides.
The quantitative analysis of droplet size distribution is crucial to the effectiveness of spray operations. In this research, VMD and RS were selected as the atomization indexes to evaluate the distribution of droplet size. The influence of nozzle orifice diameter, flow rate, spray height and horizontal position on the spatial distribution of droplet size was investigated. In addition, quantitative evaluation models were established for predicting RS and VMD based on machine learning methods. The specific conclusions are as follows: (1) as the orifice diameter increased or flow rate decreased, VMD increased and RS decreased. (2) Spatial parameters (spray height and horizontal position) had an impact on the distribution of droplet size. The variation curves of VMD and RS were approximately symmetrically distributed around the centerline of the spray fan. With the increase of spray height and horizontal distance, VMD showed an increasing trend. There was an obvious turning of RS reduction rate at some horizontal position. RS decreased with the increasing horizontal distance or the decreasing height within this value while the influence of spatial parameters on RS was not obvious when the horizontal distance was larger than this value. (3) The models based on machine learning for predicting VMD all achieved a better result than polynomial regression. Among them, SVR model had the best prediction effect, of which Rp and RMSEP were 0.9929 and 6.0690, respectively. For RS, MLP model achieved a better result in predicting RS, of which Rp and RMSEP were 0.9537 and 0.0398 respectively, while there was overfitting in the other models. Compared with machine learning methods, the polynomial regression model had a large error in predicting RS, and its Rp was only 0.5989.
The results show that machine learning methods have provided a novel and feasible method for quantitative evaluation of droplet size distribution. The accurate prediction model of droplet size distribution provides an important basis for optimizing nozzle installation parameters, and the visualization results based on models can provide intuitive guidance for spray operations. Combining the optimal droplet size of the target crop with the visual distribution, the nozzle parameters and operating parameters, such as the selection of nozzle type, nozzle position arrangement, spray height and flow rate, can be modified in a targeted manner, providing a basis for realizing the uniform distribution of pesticide deposits and further research on droplet distribution during multi-nozzle operation. Therefore, it is very meaningful to apply the prediction model based on machine learning to the variable spraying system for prediction of droplet size distribution.