*Consiglio per la Ricerca in Agricoltura e l'Analisi dell'Economia Agraria (CREA) - Centro di Ricerca Ingegneria e Trasformazioni Agroalimentari, Via della Pascolare 16, 00015 Monterotondo (Rome), Italy.*

*Consiglio per la Ricerca in Agricoltura e l'Analisi dell'Economia Agraria (CREA) - Centro di Ricerca Ingegneria e Trasformazioni Agroalimentari, Via della Pascolare 16, 00015 Monterotondo (Rome), Italy.*

*Consiglio per la Ricerca in Agricoltura e l'Analisi dell'Economia Agraria (CREA) - Centro di Ricerca Ingegneria e Trasformazioni Agroalimentari, Via della Pascolare 16, 00015 Monterotondo (Rome), Italy.*

The aim of this study was to find a model able to extract the net time per unit of net worked area from different agricultural field basic
shapes (square, circle, rectangle and triangle) considering the following variables: field gross area, working speed, number of turnings
(these depending on the effective working width), side length parallel and orthogonal to working direction, and working direction type.
Being this a non-linear problem, an approach based on artificial neural networks is proposed. The model was trained using an artificial
dataset calculated for the various shapes (internal test) and then tested on 47 different agricultural operations extracted by a real field
dataset for the estimation of the net time (external test). The net time records obtained from both, the trained model and the external
test, were correlated and the performance parameter

_{area}(headland area);

The shape structure of agricultural fields significantly affects the farm profitability. Proper setup and arrangement of farm parcels is the primary criterion enabling an efficient production strategy (

The efficiency of field operations has traditionally been analyzed by manually measuring the time spent for each agricultural field operation such as the number of turnings, distance travelled in headlands, vehicle characteristics (for example the larger the turning radius is the larger the headlands and the larger the overhead would be) etc. The estimation of operating costs of agricultural and forestry machineries is a key factor in both planning agricultural policies and farm management, and, for this estimation, the time spent in field operations is strictly necessary (

Generally, agricultural field is not uniform in shape. As reported by

In this study, only several items of the

The aim of this study was to find a model able to extract the NT from different agricultural fields of basic shapes and other variables to be easily collected by the farmer. Being this a non-linear problem, an artificial neural networks (ANNs) approach is proposed. This method allows a higher performance in predicting NT when compared with a multivariate linear approach and could serve to implement other similar multivariate approaches used to estimate, costs, consumes and emissions. The model was trained using an artificial dataset calculated for different shapes and then was tested on a real field dataset.

An artificial model was constructed to calculate the NT. The concept of artificial model has been developed by
^{2}
), working speed (WS; m s
^{-1}
), effective working width (EWW; m) and the tractor speed during the return without working (RWWS; m s
^{-1}
). The qualitative variables are: field shape (FS; ^{-1}
), turning length (TL; 15 m) and headland width (HW; 5 m). For the sake of simplicity, each turning was considered to have a length of 15 m, empirically estimated considering the tractor manoeuvring in the headland, for any type of work. All these independent variables and constants have been used to calculate the NT per unit of net worked area (h ha
^{-1}
). Ten basic shapes have been chosen. The fixed values for each independent variable/constant used for the construction of the artificial dataset are reported in

For each basic shape, the artificial estimation of NT was conducted based on the following formulas and on the

where, PN is the passes number and SL is the side length orthogonal to the working direction (AB in

where TN is the turnings numbers.

where H
_{area}
is the headland area, SLO is the opposite side length orthogonal to the working direction (CD in _{1}
or CC
_{1}
(equal to 5 m) in

where NW
_{area}
is the net worked area (A
_{1}
, B
_{1}
, C
_{1}
, D
_{1}
area in

where TPL is the total pass length.

In some field shapes (1 to 4, 6, 8, 9 in

For the construction of the artificial dataset used to build the model, have been assigned some fixed values for each variable/constant (

From calculation obtained by the artificial dataset only 7 variables were chosen. Those variables were not directly related with the NT estimation but they have been chosen to build the model because they could be easily known by farmers or easily empirically determined (
^{-1}
) (y-block). The NT estimation of basic shapes could be combined to obtain NT of complex ones.

The model for NT estimation was built using an ANN approach, a non-linear regressive solution. Being the database composed by a series of qualitative and quantitative variables, the best way of finding a regressive solution is a non-linear approach. ANN was built basing on the input layer (x-block) to estimate the output layer (y-block). Between the input and the output layers, one or more hidden layers was built by the ANN procedure basing on its architecture. The type and the complexity of the process or experimentation usually iteratively determine the optimal number of the neurons in the hidden layers (

The ANN model was developed using a generalized regression neural network structure (GRNN), method often used for function approximation (

The GRNN model performance (

^{2}
= 0.98). Also, the RMSE (training and test) resulted to be very low being equal to 1.008 and 1.020 respectively. The comparison with the

Regarding the variable impact on the GRNN model (

^{2}
= 0.63). It is possible to observe as the points that move away from the bisectrix belong to a shredding and two kinds of plowing (simple and two furrow plow - one-way working). This is probably due to the work being carried out on a small area with a particular shape (quarter circle).

This work gives an important contribute in predicting the effective working time needed considering different basic field shapes and the main agricultural operations. The working time calculation is directly related with the farm productivity. The ability to predict in advance the operational agricultural efficiency (

Furthermore, the work reports the advantage of using a non-linear approach when compared with a liner one. As confirmed by the comparison of the ANN approach with the MLR one, the relationship between independent variables and the dependent one (

Generally, shape analysis of agricultural fields is of interest in many agricultural and farm management areas and most of the few studies in the literature concern the analysis of the land fragmentation for rural control and administration purposes.

The shapes taken into consideration, are very simple (

As conclusions, in this scenario, the presented study finds a model for extracting the NT (directly proportional to the previously mentioned agricultural efficiency) starting from basic field shapes (square, circle, rectangle and triangle) and from other easily collected parameters (