Fig. 1. (Left) situation of tractors in Italy in the last 60 years (total number of tractors, registration of new units); graphical trend of the turnover rate (ratio new tractors/tot: tractors) in the same period (right). * As tractor A but with a different injection regulation. > At max-power engine speed and full load; n.a.: not available data. Engine main specifications of the farm tractors employed in this study (taken from OECD technical bulletins). Table 1 ‘ig. 2. (Left) experimental test layout (between brackets: the instrumental resolution); (right) example of operative points recorded in a bench test (tractor B; note thé oints are already subdivided in the two datasets used in the Artificial Neural Network Analysis). Fig. 3. Interactions among the principal independent and dependent variables characterizing the “diesel engine” system. * Respectively for: tractor A, tractor B, tractor C, tractor D. > Where two hidden layers are present, first data are referred to first layer (closer to input neurons), second data to second layer. Structural parameters of the ANN models inquired for each set. Table 3 Fig. 4. ANNA approach; use of the experimental data with an ANN regarding a single engine performance indicator (the torque, in this example) and then, use of this tool for obtaining indirectly the values of the performance indicator (engine torque) in a second moment (parallelograms/rectangles: input/output quantities; ellipses: tools involved in the computations). Different regression equations for estimating ANNs training time (DS: dataset size; TN: total number of hidden layer nodes; IC: number of initial connections). Values of the determination coefficients obtained for the torque and the BSFC as a function of rpms and EG temperature. Table 5 Fig. 5. Example of calculation of R? in the validation phase for the 4 tractors; the points are referred to the experimental and predicted values of the torque in ANN nr. 10 ANN inputs were rpms and EG temperature. p-Values for the analysed factors (p-values lower than 0.05 are evidenced in bold and indicate significant model terms). Table 6 ANN predictive correlation mean values and percentage differences among the different transfer functions and tractors. Table 7 * This training dataset lacks of 4 data, one of them related to the motor in idle condition, so the two datasets including all the values and the selected values for tractor D are equal except for a single datum. Values of the determination coefficients obtained for the torque and the BSFC as a function of rpms and motor oil temperature (All: all experimental data; Filt.: filterec experimental data, i.e. without data referred to idle). Fig. 6. Example of calculation of R? in the validation phase for the 4 tractors; the points are referred to the experimental and predicted values of the torque in ANN nr. 5; ANN inputs were rpms and motor oil temperature (left: all experimental data; right: filtered experimental data); note that the filtering of training and validation datasets has effects on all the predictions.
