## 2 Materials and Methods
### Artificial Neural Network Development  
An effective analytical technique for modeling complicated, multidimensional, and highly nonlinear interactions is the artificial neural network (ANN) [59]. Thus, ANNs are engaged to aid with explaining the compound practical issues in agricultural endeavors [60]. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Working Parameters**}} & \multicolumn{5}{c}{**Statistical Criteria**} \\ \cline{2-6}  & **Minimum** & **Maximum** & **Mean** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **No. of Data** \\ **Points** \\ \end{tabular} \\ \hline Tractor power (TP), (kW) & 44.75 & 104.44 & 60.77 & 17.47 & 377 \\ Initial soil moisture content (MC),(\% db) & 6.31 & 28.73 & 20.20 & 4.41 & 377 \\ Initial soil bulk density (BD), (g/cm\({}^{3}\)) & 1.07 & 1.78 & 1.32 & 0.12 & 377 \\ Soil texture norm (STN),(-) & 0.03 & 0.84 & 0.50 & 0.27 & 377 \\ Old Fi-parameter (-) & 0.65 & 1.00 & 0.92 & 0.13 & 377 \\ New—Fi-parameter (-) & 0.713 & 1.003 & 0.924 & 0.108 & 377 \\ Tillage depth (d), (cm) & 10.00 & 30.00 & 20.47 & 4.52 & 377 \\ Tillage speed (S), (km/h) & 1.50 & 9.00 & 3.96 & 1.28 & 377 \\ Plow width (L), (cm) & 34.51 & 385.00 & 122.81 & 39.98 & 377 \\ No. of chisel tools (-) & 5 & 15 & 8.04 & 2.75 & 90 \\ Working field criterion (WFC), (-) & 0.019 & 2.328 & 0.134 & 0.213 & 377 \\ Horizontal force determined using & & & & & \\ Equation (1) and new—Fi-parameter & 0.42 & 25.72 & 14.88 & 4.33 & 377 \\ (DD), (kN) & 0.38 & 25.85 & 16.92 & 5.01 & 377 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The statistical criteria of the acquired data used in this study for three different tillage implements (disk, chisel, and moldboard plows). Artificial neurons, which are a huge number of simple processing components that are arranged in layers, constitute an ANN. Multilayer perceptron (MLP), also known as a feed forward network that was trained by using one of the learning methods (specifically a backpropagation algorithm), is the most widely used ANN architecture for predictive modeling. The input layer and output layer are the two primary layers in MLP. Additional (hidden) layers are sandwiched in between the input and output layers. In most cases, synapses fully connect neurons in adjacent layers. The quantity of input and output variables in the model is represented by the number of nodes in the input and output layers, respectively. To create an ANN model, at least three layers--the input layer, the hidden layer, and the output layer--must be present (Figure 1). Nodes that correspond to input variables are present in the input, whereas nodes that relate to output variables are present in the output. The input layer is used to distribute the inputs to a variety of hidden layers, each of whose outputs is linked to an output layer; this is then connected to the inputs of the following layer by connection weight. The weighted connections make it possible for data to pass across layers more simply since the node generates a weighted total of all its net inputs after accepting the data from the layer before it, which is as follows:  
\[\mathrm{t_{i}}=\sum_{j=1}^{n}\left(\mathrm{w_{ij}}\times\mathrm{x_{j}}+ \mathrm{b_{i}}\right) \tag{7}\]  
In Equation (7), the number of inputs is \(n\), the weight of the link between nodes \(i\) and \(j\) is \(w_{ij}\), the input from node \(j\) is \(x_{j}\), and the bias is \(\mathrm{b_{i}}\). The weighted value is then subjected to a transfer function \(f(\mathrm{t_{i}})\) to determine the node output (\(O_{i}\)):  
\[O_{i}=f(\mathrm{t_{i}}) \tag{8}\]  
There is no set rule for how many neurons should be in a hidden layer, yet this has a substantial impact on the quality of the model. Therefore, a trial-and-error method was used in this study to estimate the ideal number of neurons that should be in the hidden layers. The commercial neural network program of Qnet 2000 for Windows was used to run ANN simulations [60].