# Quantitative Analysis of Droplet Size Distribution in Plant Protection Spray Based on Machine Learning Method

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## Abstract

**:**

_{c}= 0.9974, R

_{p}= 0.9929), while multi-layer perceptron (MLP) had the best effect for RS (R

_{c}= 0.9504, R

_{p}= 0.9537). The correlation coefficient of the prediction set is higher than 0.95, showing the excellent ability of machine learning on predicting the droplet size distribution. In addition, the visualization images of the droplet size distribution were obtained based on the optimal models, which provided intuitive guidance for realizing the uniform distribution of pesticide deposition. In conclusion, this study provides a novel and feasible method for quantitative evaluation of droplet size distribution and offers a theoretical basis for further determining appropriate operation parameters according to the optimal droplet size.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Instrument

#### 2.2. Experimental Method

#### 2.3. Performance Evaluation

_{90}and D

_{10}are the respective droplet diameter such that 10% and 90% of the spray liquid volume consists of droplets smaller than that value. The smaller the RS is, the narrower the droplet size spectrum is, indicating that the uniformity of the droplet size distribution is better.

_{c}and R

_{p}represent the correlation coefficient of the calibration set and prediction set, respectively. The calculation formula of R is as follows:

#### 2.4. Data Treatment

## 3. Results and Discussion

#### 3.1. Influence of Different Factors on the Droplet Size Distribution

#### 3.1.1. Droplet Size Distribution of Different Nozzle Orifice Diameters

#### 3.1.2. Droplet Size Distribution of Different Flow Rates

#### 3.1.3. Droplet Size Distribution of Different Spatial Positions

#### 3.2. Quantitative Model of Atomization Parameter

#### 3.2.1. VMD Quantitative Prediction Model

_{c}and R

_{p}reached 0.95. Polynomial regression is currently the most commonly used method to fit the relationship between VMD and spray parameters. However, the error of polynomial regression model was relatively large, of which the RMSEC and RMSEP were 13.5316 μm and 15.3068 μm, respectively. Compared with other methods, the prediction effect was poor. The VMD prediction scatter plot of each model was shown in Figure 4. It could be seen from Figure 4b that the calibration set of the DT model had a better fitting effect while the prediction set had a larger deviation, indicating poor stability. In addition, both the MLP model and the RBFNN model had good fitting results, of which R

_{c}and R

_{p}were above 0.98. It was worth noting that the fitting results of the ELM model and the SVR model were relatively close, and the R

_{c}and R

_{p}were both above 0.99. The R

_{c}and R

_{p}of the SVR model were 0.9974 and 0.9929, respectively, while the RMSEC and RMSEP were 3.4790 μm and 6.0690 μm, respectively. Compared with the other five models, the SVR model had higher R

_{p}and smaller RMSE, which proved that this method was more suitable for predicting VMD.

#### 3.2.2. RS Quantitative Prediction Model

_{p}and RMSEP of polynomial regression were 0.5989 and 0.1055, respectively, indicating that the model had poor fitting effect with large prediction errors. In addition, although the SVR method achieved good results in establishing the VMD evaluation model, the effect in predicting RS was not ideal and the R were less than 0.9. As for RBFNN, ELM, DT models, good results were achieved in calibration while the prediction errors of these models were relatively large. It could be seen from Figure 5c–e that the scatter points of prediction set deviated from the fitting curve more obviously, which indicated that these models were not appropriate to predict RS. Although the R

_{c}and R

_{p}of DT model were both greater than 0.9, the sensitivity of this method to variables was poor. When the spray parameter was within a certain range, the predicted RS value was constant while the actual value changed in real time, so the applicability of DT model was poor. Compared with the other five models, MLP achieved the best modeling result, of which the R

_{p}and RMSEP were 0.9537 and 0.0398, respectively. Therefore, MLP model was more suitable for predicting RS.

#### 3.2.3. Visualization of Droplet Size Distribution

## 4. Conclusions

_{p}and RMSEP were 0.9929 and 6.0690, respectively. For RS, MLP model achieved a better result in predicting RS, of which R

_{p}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 R

_{p}was only 0.5989.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Scatter plot of measured value and predicted value of VMD: (

**a**) polynomial regression; (

**b**) DT; (

**c**) MLP; (

**d**) RBFNN; (

**e**) ELM; (

**f**) SVR.

**Figure 5.**Scatter plot of measured value and predicted value of RS: (

**a**) polynomial regression; (

**b**) SVR; (

**c**) RBFNN; (

**d**) ELM; (

**e**) DT; (

**f**) MLP.

Nozzle Types | Diameter of Nozzle Orifice (mm) | Flow Rates (L/min) |
---|---|---|

TR8001 | 1.0 | 0.4, 0.5, 0.6 |

TR80015 | 1.2 | 0.5, 0.6, 0.7 |

TR8002 | 1.4 | 0.6, 0.8, 1.0 |

TR8003 | 1.8 | 0.8, 1.0, 1.2 |

Nozzle Types | Orifice Diameter (mm) | Height (m) | ||
---|---|---|---|---|

0.50 | 0.75 | 1.00 | ||

TR8001 | 1.0 | 101.07 ± 1.91 ^{c} | 105.66 ± 2.49 ^{c} | 104.74 ± 2.63 ^{c} |

TR80015 | 1.2 | 118.42 ± 2.49 ^{b} | 134.21 ± 4.21 ^{b} | 135.05 ± 3.4 ^{b} |

TR8002 | 1.4 | 163.8 ± 2.01 ^{a} | 160.31 ± 5.4 ^{a} | 179.48 ± 4.35 ^{a} |

Nozzle Types | Orifice Diameter (mm) | Height (m) | ||
---|---|---|---|---|

0.50 | 0.75 | 1.00 | ||

TR8001 | 1.0 | 1.2794 ± 0.0366 ^{a} | 1.3591 ± 0.055 ^{a} | 1.4114 ± 0.0236 ^{a} |

TR80015 | 1.2 | 1.235 ± 0.0357 ^{b} | 1.3037 ± 0.0463 ^{b} | 1.3597 ± 0.0297 ^{b} |

TR8002 | 1.4 | 1.2338 ± 0.0263 ^{b} | 1.301 ± 0.0612 ^{b} | 1.2656 ± 0.0237 ^{c} |

Flow Rate (L/min) | Height (m) | ||
---|---|---|---|

0.50 | 0.75 | 1.00 | |

0.5 | 138.19 ± 1.76 ^{a} | 147.67 ± 2.16 ^{a} | 153.32 ± 3.21 ^{a} |

0.6 | 118.42 ± 2.49 ^{b} | 134.21 ± 4.21 ^{b} | 135.05 ± 3.4 ^{b} |

0.7 | 114.13 ± 2.52 ^{c} | 126.53 ± 3.53 ^{c} | 134.75 ± 4.52 ^{b} |

Flow Rate (L/min) | Height (m) | ||
---|---|---|---|

0.50 | 0.75 | 1.00 | |

0.5 | 1.248 ± 0.0374 ^{b} | 1.2633 ± 0.0289 ^{c} | 1.2459 ± 0.0381 ^{b} |

0.6 | 1.235 ± 0.0357 ^{b} | 1.3037 ± 0.0463 ^{b} | 1.3597 ± 0.0297 ^{a} |

0.7 | 1.3127 ± 0.025 ^{a} | 1.3541 ± 0.0437 ^{a} | 1.3358 ± 0.0629 ^{a} |

Evaluation Index | Calibration Set | Prediction Set | ||||
---|---|---|---|---|---|---|

Range | Average | SD | Range | Average | SD | |

VMD (μm) | 101.07–322.58 | 196.29 | 48.00 | 104.74–307.91 | 196.58 | 50.49 |

RS | 0.8738–1.4313 | 1.0164 | 0.1318 | 0.8675–1.4114 | 1.0164 | 0.1315 |

Model | Parameter [a] |
---|---|

Polynomial regression | 2 |

DT | 11 |

MLP | 10, 5 |

RBFNN | 1.69 |

ELM | 162 |

SVR | 1000, 10 |

Model | Parameter [a] |
---|---|

Polynomial regression | 2 |

SVR | 1000, 6.173 |

RBFNN | 2.06 |

ELM | 148 |

DT | 5 |

MLP | 10, 5 |

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**MDPI and ACS Style**

He, Y.; Wu, J.; Fu, H.; Sun, Z.; Fang, H.; Wang, W.
Quantitative Analysis of Droplet Size Distribution in Plant Protection Spray Based on Machine Learning Method. *Water* **2022**, *14*, 175.
https://doi.org/10.3390/w14020175

**AMA Style**

He Y, Wu J, Fu H, Sun Z, Fang H, Wang W.
Quantitative Analysis of Droplet Size Distribution in Plant Protection Spray Based on Machine Learning Method. *Water*. 2022; 14(2):175.
https://doi.org/10.3390/w14020175

**Chicago/Turabian Style**

He, Yong, Jianjian Wu, Haoluan Fu, Zeyu Sun, Hui Fang, and Wei Wang.
2022. "Quantitative Analysis of Droplet Size Distribution in Plant Protection Spray Based on Machine Learning Method" *Water* 14, no. 2: 175.
https://doi.org/10.3390/w14020175