## 2 Materials and Methods
### Model Development
#### 2.5.1 ANN Model 1  
Firstly, the soiling losses were modeled in the absence of the short-circuit current of the unmaintained panel. Figure 3 shows the structure of the initial network. The first step was to model the variables related to the unmaintained panel (Tpanel and Iglo) and those common to the plant installation. Tables 3 and 4 present the different tests. Observing the first table, the results of the 16 tests carried out are appreciated, divided into three blocks according to the number of variables that have been eliminated as possible entries. The first block includes network 1 to 7, the second from network 8 to 12, and the last from 13 to 16. The idea was to know those dispensable variables and eliminate them. In the case of the first block, the network that offered the best result was 3, and therefore the pressure was eliminated as an input variable. This choice is due to the fact that the mean square errors present values close to 3% and regression coefficients very close to or higher than 0.72. In the second block, network 10 was selected as the most suitable since it has the highest regression values in the three training phases. Therefore, in the third block, pressure and relative humidity would be excluded as inputs. In the third block networks 13 and 16 showed very similar results, although slightly better by eliminating the panel temperature as an input. It was not considered to model without this temperature or the solar altitude by decreasing the R parameter and increasing the RMS error, as well as the number of iterations, so grid 10 was chosen before grid 16. In conclusion, the network to model the losses without using the short circuit current was going to include as inputs the panel temperature, the global irradiance, the ambient temperature, and the solar altitude. Figure 3: Initial Model 1 network. Once the input variables to the network were chosen, other results were studied by altering the number of neurons in the hidden layer of the network. Tests were made from 10 to 50 neurons as shown in Table 4 (each row represents a new network with 10 neurons plus), being the last network the one selected. Although it had a longer duration, R values of the order of 0.71 were obtained to work with values higher than 0.77 in the training process, so the network was more adjusted to the data. Figure 4 shows the final network with the selected input variables. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**NET** & \multicolumn{4}{c}{**INPUTS**} & \multicolumn{4}{c}{**TRAINING**} & **VALIDATION** & \multicolumn{4}{c}{**TESTING**} \\ \hline  & **Tpanel** & **Iglo** & **RH** & **Tamb** & **P** & \(\mathbf{\alpha}\) & **MSE** & **R** & **MSE** & **R** & **MSE** & **R** & **Duration** & **Iterations** \\ \hline
10 & x & x & x & x & x & 2.9 & 0.74 & 2.81 & 0.75 & 2.99 & 0.74 & 0.00:20 & 177 \\
10\_3 & x & x & x & x & 2.82 & 0.75 & 2.91 & 0.76 & 2.87 & 0.76 & 0.00:13 & 83 \\
10\_4 & x & x & x & x & x & 2.73 & 0.76 & 2.63 & 0.76 & 2.76 & 0.77 & 0.00:29 & 117 \\ \hline
**10\_5** & **x** & **x** & **x** & **x** & **x** & **2.57** & **0.77** & **2.71** & **0.77** & **2.67** & **0.785** & **0.00:59** & **162** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANN Model \(1\) results with more than 10 neurons. Figure 4: Final Model 1 network.