MOEA/D-DE based bivariate control sequence optimization of a variable-rate fertilizer applicator

https://doi.org/10.1016/j.compag.2019.105063Get rights and content

Highlights

  • An improved GRNN was proposed to improve the fertilization rate prediction model.

  • A three-objective bivariate fertilization-rate optimization model was developed.

  • MOEA/D-DE algorithm was proposed to optimize the control sequence.

Abstract

To realize precise control for a bivariate control system of a variable-rate applicator, it is essential to determine the optimal control sequence, which depends on quantifying the appropriate combination of the active feed-roll length (L) and the rotational speed of the drive shaft (N). This paper presents a novel method to optimize the control sequence (L, N) to improve fertilization accuracy and uniformity, while guaranteeing the rapidity of equipment adjustment. First, the variable-rate fertilization process model was formed using an improved General Regression Neural Network (GRNN), in which the optimum spread parameter (σ=2.0304) was calculated using a differential evolutionary (DE) algorithm. Next, a three-objective problem model was developed, and the Pareto set of the control sequence was obtained using a Multi-Objective Evolutionary Algorithm based on a Decomposition (MOEA/D) algorithm. Finally, a group of control sequences representing different target fertilization rates at the weight vector of (0.90, 0.08, 0.02) was chosen and an indoor test was conducted. Results revealed that the optimized control sequence overall outperformed the traditional method. It decreased the mean relative error (RE) from 8.239% to 5.977% and coefficient of variation (CV) from 13.512% to 13.187%, while constraining the response time to around two seconds.

Introduction

The application of precision agriculture (PA) technology on a global scale could increase agricultural profitability while reducing environment impacts such as greenhouse gas emissions (Fulton et al., 2001, Balafoutis et al., 2017). The excessive fertilization in China is severe. In 2015, fertilizer consumption nationally reached 446.1 kg/ha, which far exceeded the maximum safe rate of 225 kg/ha accepted by international standards (Kong et al., 2018). Variable-Rate technology (VRT), as an important part of PA, could decrease the needed input of fertilizers while maintaining yields. In France, 50% of crop farms have a tractor with a console, and 25% of those farms were able to modulate their provision of fertilizers and pesticides (Tolis, 2017). Recently, a variety of granular spreaders were developed and evaluated in field tests, all performing reasonably well (Fulton et al., 2001, Jones et al., 2008, Kim et al., 2008, Yinyan et al., 2018). However, in modern large-scale farming, most fertilizers need to be accurately applied at a prescribed application rate and at a specific soil depth (Su et al., 2015).

A fluted roller fertilizer distributor is a common application device with a simple structure and is still widely utilized in implementing variable-rate fertilization (Jafari et al., 2010). A simple linear fitting between the fertilizer discharge rate (Q) and the rotational speed of the fluted roller (N) is established, and Q changes by adjusting N at a fixed active feed-roll length (L) in the traditional control method (Ehtesham, 2012). However, this kind of control has disadvantages such as a limited rate adjustment range and pulsed application characteristics, which affect the fertilization accuracy and uniformity (Yuan et al., 2011). To counter this limitation, Liu et al. (2010) developed a bivariate control appliance which could adjust two operational parameters (L and N) automatically by changing the drive power to two DC motors. However, it added complexity to the system. As the flow of seeds or fertilizers through the fluted roller is a nonlinear physical process, modeling the nonlinear features of the L, N, and Q is more difficult than linear fitting between N and Q. Moreover, the control sequence of the bivariate control system is more complex than the traditional one, as the target fertilization rate can be achieved by several different control sequences according to the characteristics of the fertilizer discharge. It is essential to determine the optimal control sequences to meet the accuracy and uniformity requirements efficiently (Yuan et al., 2010).

Currently, variable-rate fertilization (VRF) control schemes focus on controlling one parameter, either N or L. The other parameter is considered as a supplement, and the control model is built on the statistical properties of the fertilizer discharge rates. Tola et al. (2008) developed a VRF applicator with a real-time discharge sensor, in which a DC motor was used to control the movement of a mechanical lever to adjust the fertilization rate. Su et al. (2015) designed a device to adjust the active feed-roll length of a fluted roller, and then applied it to a seed drill (Kuhn Company, France), while N was driven by the ground wheel. Alameen et al. (2019) attached a pneumatic cylinder to the handle of the fertilizer rate adjustment lever of a manual mechanical fertilizer rate system on a seed drill and realized automatic control by adjusting the position of the lever. Yuan et al. (2010) first utilized Gaussian Processes (GP) regression to identify the variable-rate fertilizing process and then optimized the fertilization control sequences using a Genetic Algorithm (GA), in which a weight sum transform minimized two objectives, fertilizer discharge accuracy and uniformity. Field test results indicated that an optimized control sequence could decrease the average error by 4% and decrease the fertilizer-rate response time (Yuan et al., 2011).

Application uniformity and accuracy are important variables used to evaluate the performance of a fertilizer applicator (Fulton et al., 2005, Fulton et al., 2001). The adjustment time of L and N must be considered when optimizing the control sequence since it is an inevitable part of the lag time and can indirectly influence the accuracy of the applicator (Maleki et al., 2008a). Therefore, all three objectives need to be considered to optimize the control sequence. In previous studies, two objectives were considered and solved by transforming the problem into a single objective problem via the weighted sum method (Yuan et al., 2010). Multi-objective models and algorithms have been introduced in decision making problems relating to irrigation and fertilization (Kilic and Anac, 2010, Srinivasa Raju and Nagesh Kumar, 1999, Zheng et al., 2013). Nevertheless, optimizing the control sequence for a bivariate fertilizer applicator as a three-objective problem has not been developed yet.

Recently, Artificial Neural Networks (ANN), such as feedback artificial neural networks (FB-ANN) and general regression neural networks (GRNN) have been utilized for modeling and optimizing nonlinear features to produce reasonable results (Anantachar et al., 2010, Bendu et al., 2016, Majumder and Maity, 2018, Panda et al., 2015, Prasanna Kumar et al., 2009, Taheri-Rad et al., 2017, Topuz, 2010, Zhang et al., 2018). Yip et al. (2014) made a comparison between the GRNN models and Box-Jenkins time series models to predict the maintenance cost of construction equipment. The result revealed that GRNN models can better characterize the maintenance cost. Huang et al. (2016) reported that the developed GRNN model performed better than the linear model in predicting chemical exergy. Taki et al. (2018) compared three soft computing models including ANN (MLP and RBF models) and GP regression (GPR) to predict irrigated versus rainfed wheat output energy, showing that the ANN-RBF model was more accurate than the MLP-ANN and GPR models.

Multi-objective evolutionary algorithms (MOEA) are efficient in obtaining solutions to Multi-objective problems (MOP) (Zheng et al., 2013). The MOEA based on decomposition (MOEA/D) is regularly used in practical problem solving because of its low computational complexity and high efficiency (Lanza-Gutierrez and Gomez-Pulido, 2015, Trivedi et al., 2017, Xu et al., 2018b). Proposed by Zhang and Li in 2007, the method decomposed a MOP into a number of scalar optimization sub-problems and optimized them using an evolutionary algorithm (EA) simultaneously, which allowed them to find the optimal solution set (called the ‘Pareto set’) and the set of the Pareto optimal objective vectors (called the ‘Pareto front’) (Yu et al., 2018, Zhang and Li, 2007). MOEA/D-DE is a new implementation of MOEA/D based on Differential Evolution (DE). It utilizes a DE operator and polynomial mutation to improve the population diversity. Research has revealed that MOEA/D-DE is capable of solving MOP with more complicated Pareto front shapes (Li and Zhang, 2009).

The objective of this study is to model the fertilization discharge process of a variable-rate fertilizer applicator and to optimize its control sequence considering the requirements of fertilization accuracy, uniformity, and equipment adjustment time. Based on the three-objective optimization problem model that was designed, the optimized control sequence set (Pareto Set) can be found by MOEA/-DE. Choosing a control sequence (L and N) from the Pareto Set using a reasonable weight vector can improve the overall performance of the bivariate control system at a specific target fertilization rate.

Section snippets

Material and methods

The flow chart of the control sequence optimization consists of three parts and is shown in Fig. 1. First, the variable-rate fertilization process was modeled. Second, a three-objective model was created which considered the fertilizer discharge accuracy, uniformity, and equipment adjustment speed. Lastly, the three-objective problem was solved via MOEA/D-DE to get the solution set (Pareto Set). Specifically, the available dataset was obtained from a bivariable control test platform. The

Regression analysis of the model

The fertilization-rate process model based on improved GRNN was formed at the optimized σ(2.0304) and trained by 143 samples from calibration. Another m (20) samples from Table 2 were used to test prediction accuracy. The result is shown in Fig. 9.

In Fig. 9 (a), the R2 of the model reached 99.89%. The relative error between the predicted and experimental values stayed within 3%, and the MRE was 2.18%. Fig. 9 (b) shows that there is very good agreement between predicted and experimental values

Conclusion

The control sequence of the rotational speed and active feed-roll length of a fluted-roller bivariate fertilizer applicator was optimized in this study. The fertilization rate model was formed based on an improved GRNN. Additionally, a three-objective optimization problem was created considering the requirements of fertilization accuracy, uniformity, and equipment adjustment rapidity, which was then solved using the proposed MOEA/D-DE algorithm. Experimental tests were conducted and compared

Acknowledgements

This work was supported by the National Key Research and Development Program of China (No. 2017YFD0700503).

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