## 3 Neural Model of Water Consumption  
Water consumption tests were carried out in large processing plants in the fruit and vegetable industry that used similar technologies and diversified processing products. For the construction of neural models, 634 data sets of water consumption in fruit and vegetable processing plants were used--all were normalized to obtain values in the range [0,1] by dividing them by maximum values. The purpose of modeling was to prepare the objective function for optimization. In order to select the optimal structure of the neural network, 35 numerical simulations (Table 4) were carried out in the MATLAB program [27]. The variable parameters were divided into the training, validation, and test sets (column 2); activation functions in the hidden and output layer (columns 3 and 5); and the number of neurons in the hidden layer (column 4). The assessment criteria for the conducted numerical simulations were the smallest root mean square error (MSE), correlation coefficient \(R\) for the validation set, and \(R\)--adjusted value (columns 6, 7, and 8). All tested models were implemented in the MATLAB neural network and trained according to Levenberg-Marquardt learning algorithm. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Simulation No.**} & **Division of Each** & **Activation** & **Number of** & **Activation** & \multicolumn{2}{c}{**Statistical Performance**} \\  & **Sample into** & **Function in the** & **Neutrons in the** & **Function in the** & & & \\  & **Train-Valid-** & **Test Sets** & **Hidden Layer** & **Hidden Layer** & **Output Layer** & **MSE** & \(R\)**-Value** & \(R\)**—Adjusted** \\ \hline
1 & 60-20-20 & log-sig & 10 & log-sig & 0.00909 & 0.92052 & 0.94955 \\ \hline
2 & 60-20-20 & log-sig & 14 & log-sig & 0.01295 & 0.85946 & 0.80006 \\ \hline
3 & 60-20-20 & log-sig & 6 & pureline & 0.00882 & 0.90510 & 0.92124 \\ \hline
4 & 60-20-20 & log-sig & 10 & pureline & 0.01115 & 0.89047 & 0.93475 \\ \hline
5 & 60-20-20 & log-sig & 14 & pureline & 0.00569 & 0.93186 & 0.92554 \\ \hline
6 & 60-20-20 & tansig & 6 & pureline & 0.01105 & 0.87170 & 0.93544 \\ \hline
7 & 60-20-20 & tansig & 10 & pureline & 0.01012 & 0.88376 & 0.98881 \\ \hline
8 & 60-20-20 & tansig & 14 & pureline & 0.00724 & 0.94758 & 0.96594 \\ \hline
9 & 60-20-20 & tansig & 6 & log-sig & 0.01227 & 0.85771 & 0.84561 \\ \hline
10 & 60-20-20 & tansig & 10 & log-sig & 0.01046 & 0.90830 & 0.83945 \\ \hline
11 & 60-20-20 & tansig & 14 & log-sig & 0.01151 & 0.91263 & 0.94033 \\ \hline
12 & 70-15-15 & log-sig & 6 & log-sig & 0.00656 & 0.94070 & 0.88573 \\ \hline
13 & 70-15-15 & log-sig & 10 & log-sig & 0.00839 & 0.90687 & 0.99758 \\ \hline
14 & 70-15-15 & log-sig & 14 & log-sig & 0.01024 & 0.91473 & 0.96854 \\ \hline
15 & 70-15-15 & log-sig & 6 & pureline & 0.00779 & 0.88962 & 0.88017 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimization of the neural network architecture. The conducted simulations show that neural network no. 24 demonstrated the smallest root mean square error (MSE = 0.00411) and the highest correlation coefficient (R = 0.95967) (see Table 4). In this case, the samples were randomly divided into the following sets: for training, 80 % of samples; for validation, 10% of samples; and for testing, 10% of samples. Figure 1 shows ANN regression plots between outputs and target samples. The \(R\) values in each case are greater than 91%. Therefore, the fit is reasonably good for all data sets. Additionally, \(R\) for the water consumption was estimated as 0.90774 for training, 0.88705 for testing, and 0.95967 for validation data sets. Figure 2 presents the optimal structure of the neural network. The neural network consisted of three layers (input, hidden, output). The input layer contained six decision variables: frozen products (\(x_{1}\)), concentrates (\(x_{2}\)), juices and drinks (\(x_{3}\)), other products (\(x_{4}\)), total power (\(x_{5}\)), and total production (\(x_{6}\)). Water consumption (\(y\)) was in the output layer.