# Prediction of Almond Nut Yield and Its Greenhouse Gases Emission Using Different Methodologies
## 3 Results and Discussion
### Evaluation of ANN Models  
To achieve a model to predict the almond nut yield based on input energies, several ANN algorithms with various topologies and learning structures were proposed. Furthermore, various hidden layers and neurons comprising each layer, as well as transfer functions, were used to produce the architecture of the models. Table 3 lists the performance of the studied ANN networks. As highlighted in the table, the topology of 8-12-1 was found to be the best network structure. The log-sigmoid and linear transfer functions were employed in the hidden and output layers, respectively. The calculated MSE, RMSE, and MAPE for the best algorithm were 0.186, 0.431, and 0.041, respectively. The correlation coefficient between the measured data and the predicted ones by the best ANN model is shown in Figure 5.  
[PERSON] et al. [1] developed various multilayer ANN models to predict grape yield and found the 7-6-1 architecture to be the best model.  
Practicing several artificial neural networks with different topologies and learning algorithms was performed by [PERSON] et al. to predict the amount of consumed energy for tomato production in the greenhouse [23]. The researchers employed several types of activation functions (i.e., logistic sigmoid, tangent sigmoid, and purelin) as well as various hidden layers and neurons in every hidden layer. They reported that the best prediction was obtained by the network topology of 10-20-7-9-1, with the tangent sigmoid and purelin transfer functions employed in the hidden layers and the target layer, respectively. Furthermore, among the different training algorithms, the LM algorithm produced the best result. For sugarcane production in planted or ratoon farms, [PERSON] et al. [41] used ANNs to predict life cycle assessment and output energy, and they found the best ANN model with 9-10-5-11 and 7-9-6-11 topologies, respectively. Furthermore, in training for environmental impacts and output energy, the researchers reported the R\({}^{2}\) in the range from 0.923-0.986 in planted farms and 0.942-0.982 in ratoon farms. Based on obtained data from a time series (1961-2016), [PERSON] et al. [42] practiced the ANN method to estimate some soybean harvest parameters such as the area, yield, and production in Brazil, and compared the results with classical methods of time series analysis. They stated that, in the case of harvest area and production, ANN was the best approach, while a classical linear function was more effective for the yield prediction. [PERSON] et al. [43] employed an ANN approach to predict the maize production in South Africa based on climate variable inputs including precipitation, maximum and minimum temperatures (TMX), potential evapotranspiration, soil moisture, and cultivated land.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Activation Function** & **Training Algorithm** & **Topology** & **MSE** & **RMSE** & **MAPE** \\ \hline Tansig/linear & Trainlm & 8-12-8-1 & 0.2160 & 0.4650 & 0.0462 \\
**Logsig/linear** & **Trainlm** & **8-12-1** & **0.1860** & **0.4310** & **0.0410** \\ Tansig/linear & Traingd & 8-10-10-1 & 38.0381 & 6.1670 & 0.6680 \\ Logsig/linear & Traingd & 8-12-11-1 & 63.0203 & 7.9301 & 0.9010 \\ Tansig/linear & Traingdm & 8-10-10-1 & 30.6861 & 3.1895 & 0.6330 \\ Logsig/linear & Traingdm & 8-21-1 & 31.4830 & 5.6110 & 0.6340 \\ Tansig/linear & Traingdx & 8-16-1 & 0.5977 & 0.7731 & 0.0808 \\ Logsig/linear & Traingdx & 8-10-8-1 & 0.3710 & 0.6090 & 0.0620 \\ Tansig/Tansig & Trainrp & 8-97-1 & 0.2053 & 0.4531 & 0.0435 \\ Logsig/linear & Trainrp & 8-16-11-1 & 0.2454 & 0.4953 & 0.0480 \\ Logsig/linear & Trainscg & 8-10-9-1 & 0.2343 & 0.4840 & 0.0471 \\ Tansig/Tansig & Trainscg & 8-12-13-1 & 0.2148 & 0.4635 & 0.0457 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance of various ANN topologies for predicting output.