## 4 Test Results and Discussion  
Of the 815 samples randomly, 90% were used for training (733 samples) and 10% for validation (82 samples). The samples allocated for validation (82) are those that were not part of the initial training process. In other words, after the training, these samples (input data--gases) were introduced to the network to simulate which of the outputs (1, 2, or 3) the network classified. Two configurations were used for the hidden layer, one with 5 and the other with 10 neurons. Figure 7 shows the training and validation performances of the artificial neural networks (PRN) used in this study. Figure 7a shows the **MSE** for each iteration of the PRN with five neurons in the hidden layer; the value achieved for the **MSE** was 0.0456 for training and 0.0595 for validation. Figure 7b shows the histogram of the error (obtained output \(\mathbf{Y_{ob}}\) relative to the desired output \(\mathbf{Y_{des}}\)), with 20 intervals for the 2445 data in the training and validation related to Figure 7a. The errors were around zero for most of the data. Better  
Figure 6: Flowchart of starting the training program several times (\(n\)) to choose the best configuration. results were found for the PRN with 10 neurons in the hidden layer, **MSE** at 0.0179 for training and 0.0057 for validation, which is close to what was expected (0.001), as shown in Figure 6(c), with higher data accumulation and with errors around zero for the histogram, as shown in Figure 6(d). Table 1 proves these results. The training and validation parameters were iterations, time, performance, and correlation. For the PRN with five neurons in the hidden layer, the values achieved were 10 s, with 113 iterations (10 validation checks achieved with 103 iterations), a correlation between the desired and obtained outputs of 0.8769 and 0.7599 to training and validation, respectively. Similar results are presented for the PRN with 10 neurons in the hidden layer, which are better results but with greater training time and number of iterations. Figure 7(a) displays the results with five neurons in the hidden layer, comprising a comparison between the outputs obtained by the ANN (\(\mathbf{Y_{ob}}\)) and the desired outputs (\(\mathbf{Y_{des}}\)) derived from experiments during the training phase (90%, 733 samples). A notable resemblance between the \(\mathbf{Y_{ob}}\) and \(\mathbf{Y_{des}}\) outputs is observed, indicating effective network training, as illustrated in Figure 7 and described in Table 2. Consequently, the ANN is now capable of estimating data (such as composition) for samples that were not part of the training process. An automated model has been developed to estimate these parameters based on new sets of input data (combustible gases H\({}_{2}\) (hydrogen), CH\({}_{4}\) (methane), C\({}_{2}\)H\({}_{2}\) (acetylene), C\({}_{2}\)H\({}_{4}\) (ethylene) and C\({}_{2}\)H\({}_{6}\) (ethane)). Figure 7(b) presents the results of the network validation phase for 82 samples (10%) of the input data that were not part of the training, with the desired and obtained output values. Again, there is a similarity between the outputs, proving the effectiveness of the model created via ANN. The **MSE** between outputs for this phase was 0.0595, similar to the specified value. Figure 7: PRN performance: (**a**) training and validation performance (**MSE**) for PRN with 5 neurons in hidden layer, (**b**) error histogram (\(\mathbf{Y_{des}}-\mathbf{Y_{ob}}\)) for PRN with 5 neurons in hidden layer and 20 intervals for the 815 output samples, (**c**) training and validation performance (**MSE**) for PRN with 10 neurons in hidden layer, (**d**) error histogram (\(\mathbf{Y_{des}}-\mathbf{Y_{ob}}\)) for PRN with 10 neurons in hidden layer and 20 intervals for the 815 output samples. Figure 8c represents the results for 100% of the samples (815 in total), encompassing both the training and validation phases simultaneously.