Analysis of the Influence of Parameters of a Spraying System Designed for UAV Application on the Spraying Quality Based on Box–Behnken Response Surface Method

Abstract

With the development of precision agriculture (PA), low-altitude and low-volume spraying based on unmanned aerial vehicles (UAVs) is playing an increasingly important role in the control of crop diseases, pests, and weeds. However, the aerial spraying quality and droplet drift are affected by many factors, some of which are controllable (e.g., flight and spraying parameters) and some of which are not (e.g., environmental parameters). In order to study the influence of spraying parameters on the UAV-based spraying performance, we propose a UAV-compatible spraying system and a customized experimental platform in this work. Through single-factor test and Box–Behnken response surface methods, four influencing factors, namely spraying height, flow rate, distance between nozzles, and pulse width modulation (PWM) duty cycle, were studied under indoor conditions. Variance analysis and multiple quadratic regression fitting were performed on the test data by using Design-Expert 8.0.5B software, and quadratic polynomial regression models of effective spraying width, droplet coverage density, coefficient of variation, and droplet coverage rate were established. Based on the Z-score standardization, a mathematical model of the comprehensive score with four factors was established to evaluate the spraying quality and predict optimal spraying parameters. Test results indicate that the effect intensity of four influencing factors from strong to weak is PWM duty cycle, flow rate, distance between nozzles, and spraying height, and their optimal values are 98.65%, 1.74 L/min, 1.0 m, and 1.60 m, respectively. Additionally, verification experimental results demonstrate that the deviation between the predicted comprehensive score and the actual value was less than 6%. This paper can provide a reference for the design and optimization of UAV spraying systems.

1. Introduction

Over the past few decades, traditional agriculture has been evolving towards precision agriculture (PA), which is characterized by applying the right treatment in the right place at the right time [1,2]. Throughout the whole growth circle of crops, labor-intensive and high-risk agrochemical spraying is one of the most indispensable operations to control the emergence and spread of pests, diseases, or weeds. However, the abuse of agrochemicals, especially pesticides, has caused great damage to the agricultural ecosystem. Determining how to suppress the increase in pesticide usage by improving the application efficiency and then promoting the sustainable development of agriculture is a worldwide challenge in this century [3]. Although terrestrial agricultural machinery plays the main role in field spraying, its accessibility in unstructured farmland, especially with late-stage high-stem crops, limits its efficiency in curbing disease, pest, or weed outbreaks.

With the advance of robotics and sensing technologies, agricultural robots (Agri-robots) have shown great potential in closing the crop yield gap and promoting sustainable agricultural development [4,5]. With the unique characteristics of high flexibility and maneuverability, unmanned aerial vehicles (UAVs) stand out among various Agri-robots and have proven to be a powerful platform to conduct field surveys and aerial management [6,7,8]. For example, UAVs have been widely used in different agricultural applications, such as soil mapping, crop identification, and biotic/abiotic monitoring [9,10,11,12,13]. Specifically, UAV-based agrochemical spraying has drawn extensive attention in the agricultural community [14,15]. Generally, there are two strategies for UAV-based spraying, namely uniform spraying and spot spraying. Uniform spraying aims to cover the entire area with the same dosage of agrochemicals. Most of the previous research work can be classified into this category. For instance, to achieve the highest droplet deposition volume and droplet uniformity, Guo et al. [16] conducted an orthogonal experiment to find the optimal combination of flight parameter, drop size, and crop phenotype. Furthermore, some researchers have focused on applying adaptive methods to aerial pesticide spraying. Faiçal et al. [17] introduced a series of optimization algorithms, such as genetic algorithm, particle swarm algorithm, and hill-climbing algorithm, to optimize the UAV’s flight route according to the dynamically changing weather conditions. Variable-rate application is another adaptive approach to achieve area-even spraying [18,19,20]. Wang et al. [21] realized the dynamic adjustment of flow rate following the real-time change of flight speed and improved the uniformity of the deposition distribution. With the development of agricultural information technology, spatial and temporal variabilities of farmland are becoming more and more accessible. Spot spraying takes the spatiotemporal variabilities into account and only performs appropriate treatment on specific sites. Richardson et al. [22] developed a UAV spot spraying system for applying pesticides to individual plants and proposed a method for quantifying and analyzing the 2D pattern of droplet deposition. Compared to uniform spraying, spot spraying is more conducive to improving agrochemical utilization and reducing dosage. For both uniform spraying and spot spraying, it is necessary to study the influence of operating parameters on spraying quality.

Spraying width, size of droplets, volume of deposition, droplet coverage density, droplet distribution uniformity, and droplet coverage rate are among the main metrics used to evaluate the UAV-based spraying quality. However, they can be affected by many factors, which can be roughly divided into three aspects: environmental parameters, flight parameters, and spraying parameters. Among them, in-situ environmental parameters, including crosswind speed and direction, are usually uncontrollable and have a direct impact on droplet deposition and drift [23,24]. Flight parameters, such as flight speed, flight height, and downwash, determine the deposition and distribution of droplets [25,26,27]. Additionally, some spraying parameters, such as spraying flow and nozzle specifications, directly influence the characteristics of droplets and spraying efficiency [28,29,30].

Agricultural scientists have carried out many studies to investigate the impact of different operating parameters on the quality of UAV spraying. Chen, et al. [24] studied the impact mechanism of the wind field in X-, Y-, and Z-directions on the distribution characteristics of aerial spraying droplet deposition on a rice canopy. Field experimental results demonstrated that the wind field in the Z-direction has the most significant effect on droplet deposition, followed by the Y-direction and then the X-direction. Ahmad et al. [25] and Tang et al. [26] investigated the influences of flight parameters, such as flight speed and flight height, on the droplet deposition and off-target drift. At present, most of the studies with field experiments only focused on a few influencing factors, such as flight speed, flight height, and spraying flow [31,32]. The main reason is that many factors cannot be precisely controlled in a real field environment. Additionally, it has been proven that the interactions of various factors also have a significant impact on UAV-based spraying quality.

Another limitation of previous studies is that most of the relevant works are based on specific spraying systems with fixed spraying parameters to study the impact of flight parameters and environmental parameters on spraying quality, while ignoring the optimization of spraying system parameters. However, the optimization of the spraying system is fundamental and critical for UAV spraying.

This work specifically focused on the analysis of the influence of parameters of a spraying system designed for UAV spraying application on the spraying quality based on Box–Behnken response surface method. A customized platform was constructed for simulating the flight of UAVs. Four-factor–three-level factorial tests were conducted to investigate the interaction of four spraying parameters, namely spraying height, flow rate, distance between nozzles, and pulse width modulation (PWM) duty cycle, on spraying quality. This study aims to provide a reference for the design and optimization of UAV spraying systems.

2. Materials and Methods

2.1. Design and Control Methods of Spraying System

In order to study the influence of different operating parameters on spraying quality, a spraying system for UAV spraying application was designed as shown in Figure 1. The spraying system is mainly composed of a tank, a micro diaphragm pump (MDP) (PLD-1206, max pressure: 1 MPa, max flow: 4 L/min), a pressure sensor (KY-3, measure range: 0–1 MPa, precision: ±0.25%), a flow sensor (MJ-HW41C, measure range: 0.25–2.5 L/min, precision: ±5%), two electric centrifugal nozzles (ECNs) (LXPT-03, nominal voltage: 12 V, max speed: 16,000 r/min), and the spraying controller (STM32F407, STMicroelectronics). The MDP is responsible for transporting the spray material from the tank to the ECNs. The ECN atomizes the spraying material into droplets with a minimum diameter of less than 100 μm through the centrifugal force generated by the high-speed rotation of the embedded motor. The main reason for choosing this type of nozzle is that the size of the droplet diameter can be controlled by adjusting the duty cycle of the PWM control signal. Additionally, droplets with 100–150 μm diameter are generally required for ultra-low-volume UAV spraying according to [33] other related works.

For the spraying system we designed, the spraying height, flow rate, distance between nozzles, and rotation speed of ECNs are the four controllable parameters. The spraying height and flow rate are set with reference to the values commonly used in other works. The selection of installing space between the two ECNs is mainly based on common UAV sizes. Motor speed inside ECN directly determines the centrifugal force and indirectly affects the droplet diameter and spraying width. It can be controlled by configuring the duty cycle of the PWM signal.

The control method of spraying system is shown in Figure 2. A microcontroller unit (MCU) with ARM Cortex-M4 kernel is used as the spraying controller. Two Ultra battery elimination circuit (UBEC) modules are deployed to stabilize the output voltage of the 6S lithium battery into constant 5 and 12 V, respectively. The 5 V powers the MCU, wireless data transmission module, pressure sensor, and flow sensor; the 12 V powers ECNs and MDP. The inputs of the MCU are connected to the flow sensor, pressure sensor and wireless data transmission module, and the outputs are connected to the MDP and ECN through three electronic speed controllers (ESCs). The MCU can output three independent PWM waves with adjustable duty cycle to control the rotational speed of the internal motors of the MDP and ECNs. The wireless data transmission module is used to build a direct communication bridge between the spray controller and the host computer. Based on LabVIEW, a control software running (as shown in Figure 3) on the host computer was developed to monitor the entire system and send control commands.

2.2. Design of Test Platform

As shown in Figure 4, an indoor test platform was designed and constructed to study the effects of spraying height, flow rate, distance between nozzles, and PWM duty cycle on spraying performance of the proposed spraying system. The test platform is 4 m long, 5 m wide, and 3 m high. It is mainly composed of a gantry with nozzles, sliding carrier, liner slide, servo motor, motor controller, and pulleys. The servo motor drives the sliding carrier with water-sensitive paper (WSP) through the wire rope and pulleys to pass through the spraying field at 2.0 m/s. To avoid contamination of the WSP by droplets before the spraying field reaches a steady state, plastic film is used on both ends of the test platform to shield the sliding carrier.

2.3. Test Methods

The multifactor and multilevel orthogonal experiment was the core test method in this work. The spraying height, flow rate, distance between nozzles, and PWM duty cycle of ECNs were the four factors, and the effective spraying width, droplet coverage density, coefficient of variation, and droplet coverage rate were considered as response values. The indoor test is shown in Figure 5. For each test, the spraying height and the distance between nozzles were manually adjusted according to the experimental schedules. The target flow and PWM duty cycle of the nozzles were set by remote control software. The servo motor controller communicated with the spraying controller through the RS232 communication protocol and received the control instruction from the host computer to execute start, accelerate, brake, and stop.

To ensure the safety of indoor tests, all experiments were carried out with water instead of agrochemicals. Pieces of water-sensitive paper (26 × 76 mm, Syngenta, Switzerland) were used to collect the droplets and calculate their coverage density and coverage rate. Twenty-four sampling points were evenly arranged at 20 cm intervals on the sliding carrier, and a single piece of WSP was fixed at each sampling point. After each test, all 24 pieces of WSP were collected, labeled, and sealed separately for subsequent analysis.

In view of the immaturity of UAV-based spraying technology, there is currently no internationally recognized method for evaluating the quality of UAV spraying. According to the definitions in the China civil aviation standard “Agricultural Aviation Operation Quality and Technical Indicators Part I: Spraying Operations-MH/T1002.1-2016”, low-volume and ultra-low-volume spraying means that the usage of agrochemical is 5–30 L/ha and 0–5 L/ha, respectively. Droplet coverage density in ultra-low-volume pesticide spraying is 15–40/cm², and the droplet distribution uniformity is less than 70%. Combining our research experience and methods in related works, in this study, when the droplet coverage density at the sampling point is greater than 15/cm², it is considered an effective sampling point. A WSP sample with sedimentary droplets is shown in Figure 6a, and the corresponding processed image is shown in Figure 6b. The individual droplet size, the droplet distribution, the total number of droplets, the droplet coverage density, and the droplet coverage rate can be extracted by DepositScan, a publicly available scanning program that can quickly evaluate deposit distribution on images of WSP [34].

Droplet coverage density (CD) is the total number of deposited droplets per cm². The droplet distribution uniformity is expressed by the coefficient of variation (CV) of the droplet coverage density. The smaller the CV, the more uniform the droplet distribution is. The calculation formula is as follows:

$$CV=\frac{S}{C{D}_{avg}}\times 100\%$$

(1)

$$S=\sqrt{{{\displaystyle \sum }}_{i=1}^n\raisebox{1ex}{${\left(C{D}_i-C{D}_{avg}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$\left(n-1\right)$}\right.}$$

(2)

where CV is the coefficient of variation, S is the standard deviation of the droplet coverage density, CD is the droplet coverage density of a single sample, and CD_avg is the average droplet coverage density of all samples within a single test.

Droplet coverage rate (CR) is the ratio of total area that droplets covered per cm²; it can be computed by (3):

$$CR=\frac{{{\displaystyle \sum }}_1^n(a_1)}{A}\times 100\%$$

(3)

where CR is the droplet coverage rate, a_i represents the area of a single droplet, and A stands for the entire area of the selected region.

The effective spraying width represents the total spraying width of both left and right ECNs and can be obtained by counting the number of effective sampling points:

$$SW=0.2\times \left(\sum num.sample-1\right)$$

(4)

where SW is the effective spraying width, ∑num.sample represents the total number of samples between the leftmost and rightmost effective samples, and 0.2 refers to the interval between WSP samples with the unit of m. The width of WSP is ignored.

2.4. Analysis Method

The main purpose of this work is to find the optimal combination of four influencing factors which can yield the best spraying quality. This is a typical multifactor, multilevel factorial study. The use of overall experimental methods to solve multifactor and multilevel optimization problems usually results in too many total trials that are unpractical to conduct. Orthogonal experimental design (OED), central composite design (CCD), and Box–Behnken design (BBD) are the three most used factorial experimental design methods. According to the orthogonality, OED selects some representative points from the overall experiments to find the best combination of factors and levels. It pays attention to how to arrange the experiment scientifically and reasonably. However, it cannot find a clear functional expression between the factor and the response value, so it cannot find the optimal combination of factors and the optimal value of the response value in the entire interval. CCD and BBD are the two most important response surface design methods, both of which can construct regression equations between factors and response values. CCD is particularly useful in sequential experiments because it is possible to add pivot points and center points to previous factor experiments to build a new work. BBD usually has fewer design points, so its operating cost is lower than that of CCD with the same number factor. In this work, there was no order requirement for 4-factor and 3-level experiments, and we hoped to establish an accurate regression equation of the four spraying parameters and spraying quality through as few experiments as possible. Therefore, Box–Behnken response surface analysis method was the best option for this study. In addition, Design-Expert 8.0.5B (Stat-Ease Inc., Minneapolis, MN, USA) was introduced to schedule BBD tests and analyze experimental results.

Taking effective spraying width SW_, average droplet coverage density CD_avg, coefficient of variation CV, and droplet coverage rate CR as reference values, the effects of spraying height X₁, flow rate X₂, distance between nozzles (the distance between left and right ECNs) X₃, and PWM duty cycle of ECN X₄ on spraying performance of the spraying system were investigated. In this work, the PWM duty cycle of the left ECN and right ECN is always configured to the same value. Firstly, single-factor tests were designed and conducted to find the maximum and minimum levels of each factor (detailed in Section 3.1). Secondly, BBD was deployed to design the 4-factors and 3-levels test (detailed in Section 3.2). Thirdly, based on the test results, quadratic polynomial mathematical models were obtained with the help of analysis of variance (ANOVA). Then, through Z-score standardization, a mathematical model of comprehensive score that integrates the four response values was established and the optimal operating parameters were solved. The Z-score standardization for the positive correlation response value data can be described as Formula (5), where $x^{*}$ is the standardized data, $\overline{x}$ is the average of raw data x, and σ means the standard deviation. The standardized treatment formula for the negative correlation response value data can be described as Formula (6).

$$x^{*}=\frac{x-\overline{x}}{\sigma }$$

(5)

$$x^{*}=\frac{\overline{x}-x}{\sigma }$$

(6)

Finally, a set of optimal values of the four factors and the corresponding comprehensive score could be solved. The spraying quality with the predicted values was evaluated by the verification tests. The deviation between the predicted comprehensive score and the actual value was used to estimate the prediction accuracy of the model.

3. Results

3.1. Results of Single-Factor Test

We carried out a series of single-factor tests to determine the level scope of each factor. The test results in

Table 1. Design and results of single-factor tests.

Investigating Factor	Fixed Factors	Levels	Response Value
			SW (m)	CDavg (No./cm2)	CV (%)	CR (%)
X1 (m)	X2: 1.0 L/min X3: 1.5 m X4: 100%	0.6	1.8	59.6	38.78	9.81
		0.8	2.2	65.0	34.69	7.84
		1.0	2.6	75.4	44.28	7.02
		1.2	2.6	84.6	34.81	7.86
		1.4	2.6	88.1	32.37	11.81
		1.6	2.6	88.2	29.39	11.05
		1.8	2.4	95.7	30.15	11.47
		2.0	2.4	86.5	32.96	11.05
X2 (L/min)	X1: 1.5 m X3: 1.5 m X4: 100%	0.50	1.6	157.0	50.20	8.54
		0.80	2.4	101.6	51.10	8.46
		1.10	2.8	98.9	35.45	15.20
		1.40	2.8	88.8	32.59	17.60
		1.70	3.2	52.5	36.66	20.88
		2.00	2.8	96.1	37.17	22.05
		2.30	2.8	87.3	47.63	29.75
X3 (m)	X1: 1.5 m X2: 1.0 L/min X4: 100%	0.6	1.8	88.7	53.62	31.17
		0.8	2.2	96.4	47.16	20.72
		1.0	2.6	109.3	30.88	15.74
		1.2	2.6	95.5	30.29	20.27
		1.4	2.8	102	31.63	16.76
		1.6	3.0	95.7	30.32	15.00
		1.8	2.8	102.7	31.85	13.21
		2.0	2.8	96.8	49.30	15.01
		2.2	3.4	84.1	59.63	13.00
		2.4	3.8	62.0	75.33	11.75
X4 (%)	X1: 1.5 m X2: 1.0 L/min X3: 1.5 m	50	2.8	49.6	42.16	9.36
		60	3.0	61.5	51.07	9.14
		70	3.0	71.5	41.26	10.32
		80	2.8	78.2	45.59	12.38
		90	2.8	106.4	39.56	15.27
		100	2.8	108.1	35.02	13.18

show the following: (a) Taking X₁ as the investigating factor, when X₁ increases from 1.0 to 1.8 m, SW is basically stable at 2.6 m, and CD_avg, CR, and the droplet distribution uniformity are improved. When X₁ reaches 2 m, CD_avg and CR begin to decrease, and the uniformity of droplet distribution begins to deteriorate. (b) Taking the flow rate X₂ as the investigating factor, as X₂ increases, the CR gradually increases. However, the maximum value of SW appears when X₂ reaches 1.7 L/min, and the minimum value of the CV occurs when X₂ reaches 1.4 L/min. (c) Taking the distance between nozzles X₃ as the investigating factor, as X₃ increases, SW gradually increases, while CV first decreases and then increases, and the minimum value is taken at 1.6 m. (d) Taking PWM duty cycle X₄ as the investigating factor, with the increase in X₄, SW changes in a small range, and the CD_avg and the uniformity of droplet coverage distribution are improved.

Considering the results of the single-factor test and the limitation of the actual operating environment, the level values of the four factors are configured as follows: spraying height X₁: 1.0–2.0 m, flow rate X₂: 0.50–2.00 L/min, distance between nozzles X₃: 0.8–2.2 m, PWM duty cycle X₄: 50–100%. The final four factors and three levels of the Box–Behnken tests are shown in

Table 2. Factor level of Box–Behnken tests.

Factors	Level Values
	−1	0	1
X1: Spraying height (m)	1.0	1.5	2.0
X2: Flow rate (L/min)	0.50	1.25	2.00
X3: Distance between nozzles (m)	0.8	1.5	2.2
X4: PWM duty cycle (%)	50	75	100

.

3.2. Results Analysis of Response Surface Test

A total of 29 tests were designed by BBD in Design-Expert 8.0.5B. Of these, numbers 1, 11, 15, 24, and 29 are the central point tests, and the others are the factorial tests. All tests were carried out in accordance with the order of the test sequence. The results in

Table 3. Design and results of Box–Behnken tests.

Run	Factors				Response Value				Com. Score
	X1 (m)	X2 (L/min)	X3 (m)	X4 (%)	SW (m)	CDavg (No./cm2)	CV (%)	CR (%)
1	1.5 (0)	1.25 (0)	1.5 (0)	75 (0)	3.6 (1.528)	65.0 (−0.173)	33.77 (0.747)	8.33 (−0.785)	1.316
2	2.0 (1)	2.00 (1)	1.5 (0)	75 (0)	2.6 (−0.249)	60.7 (−0.330)	42.96 (0.128)	17.48 (1.211)	0.760
3	2.0 (1)	0.50 (−1)	1.5 (0)	75 (0)	2.2 (−0.959)	96.5 (0.977)	60.18 (−1.032)	8.57 (−0.733)	−1.747
4	1.0 (−1)	0.50 (−1)	1.5 (0)	75 (0)	2.2 (−0.959)	112.7 (1.569)	61.29 (−1.106)	9.35 (−0.563)	−1.059
5	1.5 (0)	1.25 (0)	0.8 (−1)	50 (−1)	2.2 (−0.959)	40.4 (−1.069)	27.95 (1.139)	10.20 (−0.378)	−1.267
6	1.5 (0)	2.00 (1)	1.5 (0)	100 (1)	3.2 (0.817)	72.4 (0.096)	35.51 (0.629)	17.75 (1.270)	2.813
7	1.0 (−1)	1.25 (0)	1.5 (0)	100 (1)	3.4 (1.173)	77.5 (0.284)	41.01 (0.259)	12.73 (0.174)	1.890
8	1.0 (−1)	2.00 (1)	1.5 (0)	75 (0)	2.6 (−0.249)	64.9 (−0.176)	37.26 (0.511)	17.35 (1.182)	1.269
9	1.5 (0)	2.00 (1)	0.8 (−1)	75 (0)	2.2 (−0.959)	65.6 (−0.151)	42.93 (0.130)	23.03 (2.423)	1.443
10	1.5 (0)	1.25 (0)	2.2 (1)	100 (1)	3.0 (0.462)	85.1 (0.563)	33.37 (0.773)	14.11 (0.475)	2.273
11	1.5 (0)	1.25 (0)	1.5 (0)	75 (0)	3.4 (1.173)	58.3 (−0.418)	52.68 (−0.527)	9.81 (−0.462)	−0.234
12	1.5 (0)	2.00 (1)	2.2 (1)	75 (0)	3.4 (1.173)	47.0 (−0.828)	70.34 (−1.716)	12.33 (0.088)	−1.283
13	1.5 (0)	2.00 (1)	1.5 (0)	50 (−1)	3.0 (0.462)	28.2 (−1.514)	44.86 (0.000)	9.59 (−0.511)	−1.563
14	2.0 (1)	1.25 (0)	1.5 (0)	100 (1)	2.6 (−0.249)	78.4 (0.316)	32.22 (0.851)	17.97 (1.317)	2.236
15	1.5 (0)	1.25 (0)	1.5 (0)	75 (0)	2.8 (0.107)	57.0 (−0.463)	38.70 (0.415)	11.61 (−0.069)	−0.011
16	1.5 (0)	0.50 (−1)	0.8 (−1)	75 (0)	1.6 (−2.025)	127.6 (2.111)	36.14 (0.587)	11.51 (−0.091)	0.582
17	1.5 (0)	0.50 (−1)	1.5 (0)	100 (1)	2.2 (−0.959)	142.9 (2.670)	79.53 (−2.335)	7.64 (−0.936)	−1.560
18	1.0 (−1)	1.25 (0)	0.8 (−1)	75 (0)	2.4 (−0.604)	75.0 (0.193)	35.18 (0.652)	14.06 (0.466)	0.706
19	1.5 (0)	1.25 (0)	2.2 (1)	50 (−1)	3.2 (0.817)	37.2 (−1.186)	34.28 (0.713)	7.13 (−1.048)	−0.704
20	1.0 (−1)	1.25 (0)	1.5 (0)	50 (−1)	2.8 (0.107)	35.5 (−1.250)	31.88 (0.874)	7.64 (−0.936)	−1.205
21	1.5 (0)	1.25 (0)	0.8 (−1)	100 (1)	2.0 (−1.315)	106.3 (1.334)	35.30 (0.644)	21.70 (2.131)	2.794
22	2.0 (1)	1.25 (0)	0.8 (−1)	75 (0)	2.0 (−1.315)	76.0 (0.228)	38.62 (0.420)	16.42 (0.980)	0.312
23	2.0 (1)	1.25 (0)	2.2 (1)	75 (0)	3.6 (1.528)	56.0 (−0.502)	58.28 (−0.904)	7.66 (−0.932)	−0.811
24	1.5 (0)	1.25 (0)	1.5 (0)	75 (0)	3.0 (0.462)	63.2 (−0.237)	31.77 (0.882)	11.21 (−0.158)	0.949
25	1.5 (0)	0.50 (−1)	2.2 (1)	75 (0)	2.6 (−0.249)	88.1 (0.671)	68.25 (−1.575)	7.66 (−0.932)	−2.085
26	1.5 (0)	0.50 (−1)	1.5 (0)	50 (−1)	2.4 (−0.604)	56.9 (−0.466)	76.83 (−2.153)	5.35 (−1.435)	−4.658
27	2.0 (1)	1.25 (0)	1.5 (0)	50 (−1)	2.4 (−06.04)	38.5 (−1.141)	26.32 (1.248)	8.19 (−0.817)	−1.313
28	1.0 (−1)	1.25 (0)	2.2 (1)	75 (0)	3.4 (1.173)	59.2 (−0.383)	46.98 (−0.143)	10.33 (−0.349)	0.298
29	1.5 (0)	1.25 (0)	1.5 (0)	75 (0)	3.6 (1.528)	49.9 (−0.724)	46.39 (−0.103)	9.13 (−0.610)	0.090

Note: The data in brackets are standardized data after Z-score normalization. Com. score means comprehensive score.

were analyzed using the method of quadratic multiple regression fitting.

Through parameter optimization, the quadratic polynomial regression equations of effective spraying width SW, average droplet coverage density CD_avg, coefficient of variation CV, and droplet coverage rate CR were respectively obtained for the true values of spraying height X₁, flow rate X₂, distance between nozzles X₃, and PWM duty cycle X₄.

$$\begin{array}{ll}SW=-1.626+& 1.591 X_1+2.306 X_2+1.769 X_3+1.33\times {10}^{-3}{X}_4\\ & +0.429 X_1{X}_3+0.095 X_2{X}_3-0.993 X_1^2-0.886 X_2^2\\ & -0.66 X_3^2\end{array}$$

(7)

$$R^2=0.8014$$

$$\begin{array}{ll}C{D}_{avg}=76.337& -35.259 X_1-101.649 X_2-43.05 X_3+2.577 X_4\\ & +7.998 X_1{X}_2-3.022 X_1{X}_3-0.042 X_1{X}_4+9.964 X_2{X}_3\\ & -0.558X_2{X}_4-0.256 X_3{X}_4+9.931 X_1^2+33.904 X_2^2\\ & +13.420 X_3^2-0.558 X_4^2\end{array}$$

(8)

$$R^2=0.9587$$

$$\begin{array}{ll}CV=7.521+& 15.999 X_1-74.342 X_2+15.213 X_3+1.406 X_4+4.529 X_1{X}_2\\ & \hspace{1em}\hspace{1em}+5.613 X_1{X}_3-0.065 X_1{X}_4-2.235 X_2{X}_3-0.161 X_2{X}_4\\ & \hspace{1em}\hspace{1em}-0.118 X_3{X}_4-8.14 X_1^2+28.361 X_2^2-0.213 X_3^2\\ & \hspace{1em}\hspace{1em}-5.88\times {10}^{-3} X_4^2\end{array}$$

(9)

$$R^2=0.6354$$

$$\begin{array}{ll}CR=18.56-& 14.86X_1-1.466 X_2-3.373 X_3-4.097\times {10}^{-3} X_4\\ & \hspace{1em}+0.628 X_1{X}_2-3.591 X_1{X}_3+0.094 X_1{X}_4-3.259 X_2{X}_3\\ & \hspace{1em}+0.078 X_2{X}_4-0.065 X_3{X}_4+4.417 X_1^2+1.936 X_2^2\\ & \hspace{1em}+4.396X_3^2\end{array}$$

(10)

$$R^2=0.9242$$

The correlation coefficient R² of equation CD_avg and CR are greater than 0.9, indicating that the quadratic polynomial could accurately represent the effect of changes in operating parameters on droplet coverage density and droplet coverage rate. Z-score standardization was used to standardize the four response values (in Table 3) obtained in each experiment. Then, by adding the four standardized response values, a comprehensive score was obtained, which can be used to represent the spraying performance of the spraying system under different operating parameters. The quadratic polynomial regression equation of comprehensive score (CS) of the true values of X₁, X₂, X₃, and X₄ is as follows:

$$\begin{array}{ll}CR=-8.394-& 0.886 X_1+4.666 X_2+0.228 X_3+0.099 X_4+0.119 X_1{X}_2-0.511 X_1{X}_3+9.083\times {10}^{-3} X_1{X}_4\\ & \hspace{1em}-0.028 X_2{X}_3+0.017 X_2{X}_4 -0.016 X_3{X}_4+0.137 X_1^2-1.812 X_2^2+0.306X_3^2\end{array}$$

(11)

$$R^2=0.8318$$

The results of ANOVA for quadratic regression equations of response surface are listed in

Table 4. ANOVA for quadratic regression equations of response surface.

Variance Source	Sum of Squares	DOF	Mean Square	F	p-Value	Sig.	Variance Source	Sum of Squares	DOF	Mean Square	F	p	Sig.
Model	66.65	14	4.76	4.94	0.0025	*	X3X4	0.29	1	0.29	0.31	0.5893
X1	0.51	1	0.51	0.52	0.4809		X12	0.01	1	0.01	0.01	0.9304
X2	16.25	1	16.25	16.88	0.0011	*	X22	6.74	1	6.74	6.99	0.0192	*
X3	3.95	1	3.95	4.10	0.0624		X32	0.14	1	0.14	0.15	0.7039
X4	37.30	1	37.30	38.74	<0.0001	*	X42	0.18	1	0.18	0.19	0.6731
X1X2	0.01	1	0.01	0.01	0.9288		Residual	13.48	14	0.96
X1X3	0.13	1	0.13	0.13	0.7212		Lack of fit	11.68	10	1.17	2.59	0.1863
X1X4	0.05	1	0.05	0.05	0.8204		Error	1.80	4	0.45
X2X3	0.00	1	0.00	0.00	0.9767		Total	8.87	28
X2X4	0.41	1	0.41	0.42	0.5255		-	-	-	-	-	-	-

Note: The significance level α = 0.05 was used in this work. * represents that the value in variance source has a significant effect.

. The results demonstrate the following: (a) The integrated regression model is correct as the model has a significant p-value. (b) X₂, X₄, and X₂² reach significance level. (c) According to the F value, it can be inferred that the influence intensity of four factors from strong to weak is X₄ > X₂ > X₃ > X₁. (d) Although the interactions between the four factors are not significant, X₂ and X₄ is the main interaction. The interaction effects of X₂X₄, X₂X₃, and X₃X₄ on the comprehensive score are shown in Figure 7a, Figure 7b, and Figure 7c, respectively. In Figure 7a, the comprehensive score increases first and then decreases with the increase in X₂, but it shows a linear change with the changes of X₃ (Figure 7b) and X₄ (Figure 7c), indicating that the interactions of X₂X_4, X₂X_3, and X₃X₄ have a nonsignificant influence on the model.

Taking the highest comprehensive score as the goal of optimization, the optimized operating parameters of the spraying system can be predicted by solving and analyzing the extreme value of the regression model. The optimal parameters are as follows: spraying height X₁, 1.60 m; flow rate X₂, 1.74 L/min; distance between nozzles X₃, 1.0 m; PWM duty cycle in nozzle X₄, 98.65%. The predictive value of the comprehensive score is 3.182.

To facilitate the verification tests, the PWM duty cycle was adjusted to 100%, and the model prediction results were verified according to the above optimal conditions. The test results are shown in

Table 5. Results of verification tests.

Run	Response Value				Test Com. Score	Predicted Com. Score	Relative Error (%)
	SW (m)	CDavg (No./cm2)	CV (%)	CR (%)
1	2.8 (0.107)	67.3 (−0.088)	34.96 (0.667)	23.11 (2.440)	3.124	3.182	−1.81
2	3.0 (0.462)	72.6 (0.105)	30.16 (0.990)	20.20 (1.805)	3.361	3.182	5.64
3	3.0 (0.462)	65.4 (−0.158)	32.84 (0.809)	21.99 (2.195)	3.309	3.182	3.98
AVG	2.9 (0.284)	68.4 (−0.048)	32.65 (0.822)	21.77 (2.147)	3.205	3.182	0.74

Note: The data in brackets are standardized test data after Z-score normalization.

. The experimental data were added after Z-score standardization, and the comprehensive average score was 3.205. Compared with the predicted value of the model, the relative error is 0.74%, which indicates that the regression equation model is reliable and predictable.

4. Discussion

In general, the spraying technology based on UAVs is still in the preliminary research stage. Although some achievements have been made so far, there are still many problems that need to be solved. Firstly, some of the UAVs used in related research are commercialized, and some are privately customized. These UAVs have a variety of shapes, sizes, and driving methods, which increases the difficulty of studying the influence of the UAVs’ flight parameters on the spraying quality. Secondly, except for some commercial agricultural UAVs, such as DJI MG-P and T series, other agricultural UAVs used for scientific research are usually equipped with customized nonstandardized spraying systems. This means that the optimal spraying parameters vary in different studies. Thirdly, UAV-based spraying quality is affected by many factors, and there are no uniform standards that are recognized by the global agricultural community that can be used to evaluate it.

Spraying height, flight speed, flow rate, and drop size are controllable in indoor or outdoor experiments. Their influence on spraying quality is the research focus of most published papers [15,25,26,28,31,32]. For example, in 2016, Xue et al. [15] developed an automatic aerial spraying system for an N-3-type unmanned helicopter. They investigated the performance of UAV spraying through a series of outdoor experiments, in which the main test parameters were set as follows: flight speed 3–6 m/s, flight height 3–7 m, and spraying flow of each centrifugal rotary atomizer (total 2) 0.6–1 L/min. Test results revealed that the CV of UAV-based spraying performance is lower than 60%. However, the spraying quality is sensitive to experimental configurations, and the optimal combination of operating parameters in this study may not be applicable to other UAV-based spraying systems. In addition, downwash and crosswinds also have a significant impact on deposition patterns and off-target drift [23,24,35]. What makes this area of study more complicated is that UAV spraying quality is usually affected by the interaction of multiple factors, and it is unrealistic to accurately reveal the interaction mechanism by conducting real field experiments, especially given the uncertainty of environmental parameters and the instability of flight attitude. For example, the dynamically changing downwash airflow is determined by various factors such as ambient wind, crop canopy, flight speed, flight altitude, flight attitude, and drone modalities. Sometimes, it is necessary or even inevitable to study the influence of some factors in certain specific ideal environments. Although such research results are different from the real situation, they can provide a certain reference for the optimization of system parameters.

Zhang et al. [36] developed an indoor spraying platform to simulate UAV aerial spraying. The system was tested at three different moving speeds, 0.3, 0.6, and 1.0 m/s, during which the wind speed and flow rate remained constant at 5.7 m/s and 1.16 L/min, respectively. Although they introduced the downwash airflow by installing a propeller above each nozzle, the wind speed could not adapt to the change of the moving speed, which would reduce the interpretability of the experimental results.

This work mainly studies the effect of spraying parameters on spraying quality and proposes a spraying parameter optimization method. The influences of other factors, such as downwash and crosswind, are not in the scope of this research. Spraying height, flow rate, distance between nozzles, and PWM duty cycle of ECNs are the four investigating factors, and the effective spraying width, coefficient of variation, droplet coverage density, and droplet coverage rate are the main metrics used to evaluate the spraying quality. Analysis results in Table 5 demonstrate that the optimal parameters are as follows: spraying height, 1.60 m; flow rate, 1.74 L/min; distance between nozzles, 1.0 m; PWM duty cycle of ECN, 98.65%. With these configurations, the effective spraying width SW, average droplet coverage density CD_avg, coefficient of variation CV, and droplet coverage rate CR are 2.9 m, 68.4 No./cm², 32.65%, and 21.77%, respectively. Once the spraying system is mounted on the UAV, the 1.6 m spraying height can not only ensure flight safety, but also help reduce the drift of the droplets. Taking the 2.0 m/s moving speed of the gantry in our designed platform and the 2.9 m effective spraying width (Table 5) into account, the flow rate of 1.74 L/min results in the dosage of agrochemical at 50 L/ha, which is inconsistent with the 15–20 L/ha commonly used for low-volume UAV spraying. However, our research results still can provide a reference for real-field UAV-based spraying, and the flow rate can be further reduced with the increase in flight speed and the involvement of downwash. The 1.0 m nozzle spacing, on the one hand, is compatible with most agricultural UAVs; on the other hand, it can maintain the adjacent overlap of the left and right nozzles. The 98.65% PWM duty cycle means the ECN almost works at the full speed, and the minimum droplet diameter can reach 100 μm or less. This is beneficial to improve the droplet coverage density and coverage uniformity.

There are a few limitations in this work. The first one is that we studied the cross-effects of four spray parameters on spraying quality through simulation experiments in an indoor environment. However, field trials are needed to verify the results because the real farmland environment is more complicated, and many parameters cannot be precisely controlled. Another one is that we did not consider the impact of the downwash airflow. The main reason is that the intensity and distribution characteristics of the downwash airflow are affected by many factors and cannot be accurately simulated.

5. Conclusions

In this work, a specially customized platform and a spraying system designed for UAV spraying applications were proposed. Under indoor environmental conditions, the influence of operating parameters of the spraying system on the spraying quality was studied by combining the single-factor test and Box–Behnken response surface methodology. Test data were standardized by Z-score, and a comprehensive score was used to evaluate the spraying performance. Variance analysis and multiple quadratic regression fitting were performed on the test data by using Design-Expert 8.0.5B software. The mathematical model of the comprehensive score with four factors was established to predict the optimal operating parameters, which can be listed as follows: spraying height, 1.60 m; flow rate, 1.74 L/min; distance between nozzles, 1.0 m; duty cycle of PWM in nozzle, 98.65%. Verification test results showed that the deviation between the predicted comprehensive score and the actual value was less than 6%, which indicated that the response surface method for the working parameters of the application system was reasonable and feasible. Overall, this work will contribute to the design and optimization of spraying systems for UAV spraying applications. In the following research, we will equip this spraying system on a UAV to carry out real field spraying experiments and verify the real spraying performance under this set of optimized parameters.