Approche orientée optimisation pour un meilleur épandage centrifuge

International audienceThe use of centrifugal spreaders for application of granular fertilizers raises concern about application accuracy. These spreaders enable to distribute almost uniform deposits with regularly spaced parallel tramlines but lead over and under fertilizer application when distances separating the successive tractor trajectories are not constant or if paths are not parallel between them. The aim of this study is to propose an optimization-based method to compute optimal variables for uniform fertilizer application. Mechanical constraints are also introduced so that the calculated parameters can be afterwards used as reference variables for the control of the spreader. The resulting improvements are illustrated by numerical examples for a field with geometrical singularities

Optimisation spatiale de l'application de fertilisants par épandage centrifuge

We study an approach for the optimization of spreading performed by centrifugal spreaders in order to minimize environmental effects due to application errors. Faced with a large scale problem, we divide the domain of study into subdomains so that each tramline is individually dealt with. In order to take into account the mechanical limits of the device, some inequality constraints are introduced. After cost function discretization, we use an augmented lagrangian algorithm associated with a L-BFGS technique to solve the problem. Results are presented for parallel and non parallel paths

Une méthode orientée optimisation pour la réduction des erreurs d'application d'engrais par épandage centrifuge

Centrifugal spreaders are very popular for application of granular fertilizers. Nevertheless, their use raises issues about application accuracy. Indeed, they enable to distribute almost uniform deposits with regularly spaced parallel tramlines but lead to adverse environmental and economical effects when distances separating the successive tractor trajectories are not constant or if paths are not parallel between them. Moreover, irregular applications occur also for start and end of fields. The resulting over-applications mostly lead to an over nitrate enrichment and with ground lixiviation, can cause problems of excessive growth of algae in surface waters. This phenomenon known as eutrophication result then in numerous aquatic animals disappearances. In case of under-applications, productivity losses can be very important. To solve these issues, some works such as were done to find optimal paths followed by the spreader according to the transverse distribution. Unfortunately, these kinds of methods cannot be applied when tramlines are already imposed by other agricultural operations like sowing for example. Furthermore, the search for the best transverse distribution overlappings cannot reduce the application errors because it does not deal with the actual phenomenon occurring during spreading operation: spread patterns overlappings. Therefore, it is important to know how best arrange the placement and the shape of these spatial distributions during the spreading process in the presence of imposed paths. This adjustment should be continuously carried out for each GPS position of the applicator by changing its settings. The spread patterns have a model relying on the product of the mass flow rate by two gaussians which parameters are the medium radius and the medium angle. The medium radius corresponds to the distance between the spinning disc centre and the spread pattern centre, while the medium angle specifies the angle between the travel direction and the axis passing by the disc centre and the spread pattern one. From this model, this study discusses an optimization-based approach to compute optimal variables for uniform fertilizer application. A cost function reflecting the application errors is formalized and its discretization is carried out. In order to take into account the mechanical and dynamical limits of the machine, bound constraints on the decision parameters and their discrete time derivatives are introduced. Thanks to this procedure, the optimal parameters can then be afterwards used as reference variables for the control of the spreader in the future. Faced with a large scale problem owing to the applied discretization scheme, the spatial domain is divided into subdomains to handle each trajectory separately by considering the spreading symmetry properties. The resulting sub-problems are then solved by applying an augmented Lagrangian technique which permits to severely penalize unacceptable parameters. Besides, in view of the costly computational time caused by the cost function and gradients evaluations, we choose to implement also a L-BFGS technique shown to be efficient in this case. To illustrate the improvements given by using this approach, numerical simulations for a field with parallel and non parallel tramlines are presented. After optimization, the obtained results are very satisfying in comparison with absolute application errors reaching more than 100% when traditional settings are used

Application de techniques d'optimisation pour une fertilisation optimale par épandage centrifuge

Mineral fertilizers application is an agricultural task widely performed by centrifugal spreaders. These machines give satisfying results with regularly spaced parallel tractor trajectories but lead to over and under-applications when geometrical singularities occur (non-parallel paths, start and end of spreading,...). The application errors result then in watercourses pollution and important yield losses. In this study, in order to improve fertilizer application by centrifugal spreading, an optimization problem is considered. The optimal parameters are computed by taking into account the mechanical constraints of the machine so that they can be used as reference variables to control the spreader in the future. Faced with a large scale constrained problem, an augmented lagrangian algorithm using a l-bfgs technique is implemented. The improvements provided by this new method are exposed through simulation results for parallel and non parallel paths in the field

Spatial optimization of fertilizer application by a centrifugal spreader

Fertilisation practice using centrifugal spreaders generally consists in the mass flow rate regulation thanks to the simple mathematicl relation D=Q.L.V/600 where Q is the prescribed fertilization rate, L the working width and V the tractor speed. Modern machines equipped with DPAE device can thereby continuously control the mass flow rate with respect to the working width that is in most cases considered as constant during spreading. When computing the previous equation, one reasons as if fertilizer was homogeneously distributed by the machine onto a rectangular area which length is equal to the wished working width. This practice gives satisfying results with regularly spaced parallel travel direction but is very inefficient when geometrical singularities are met in the field (pointed end of field, irregularly spaced parallel travel path, bends, start and end of spreading) and then can produce some local application errors. Indeed, the broadcasted amount of fertilizer is often higher than the local crop requirements. In some cases, it can be lower and then results in smaller crop productions. Thus, spreading process is more and more considered as a source of pollution of groundwater and watercourses