5. Conclusion

The evaluation parameters calculated for the ANN MLP 4-3-1-1 can be verified in Table 4.

The most important to evaluate the optimized model are the parameters obtained for the test dataset, since these samples simulate a real application with data not used to build nor optimize the model. The RMSEP was 0.67 and the MAPE for test samples was 6.89%, which means that the predicted oxidative stabilities for real samples differed in 0.67 h from the

Still for the test samples, the correlation coefficient was 0.9769, indicating a high correlation between the actual and the predicted values of oxidative stability. The determination coefficient was also high, meaning that the ANN MLP 4-3-1-1 explained 95.44% of the total data

The correlation plot for samples of all the three steps can be seen in Figure 3, in which the samples are well distributed along the line, especially the validation and test samples, leading

In residual plot (Figure 4), it is important to have approximately the same quantity of samples with positive and negative residuals, and the closer to the central line (y=0) the smaller the RMSEs. In this case study, the majority of samples had residual lower than 1.5 h and they are well divided with positive and negative residuals. The higher residuals belong to the training

These parameters can be interpreted as in Section 3.2.

196 Advanced Applications for Artificial Neural Networks

actual values and deviated about 6.89%, related to their actual values.

variance, and the prediction errors represents 4.56% of the total variance.

Figure 4. Residual plot the biodiesel oxidative stability values predicted by the ANN MLP 4-3-1-1.

to correlation coefficients higher than 0.96 for the three steps.

samples, which indeed had the highest RMSE (1.31 h).

The literature presents a variety of published works involving the feasibility of the application of artificial neural networks to biofuels. In this way, the increasing importance of the biofuels theme becomes more evident in the global energetic scenario.

The ANNs proved to be a promising tool in the development of more efficient and costeffective alternative methods to control and monitor the quality of biofuels, when compared to official methods.

In addition, a presented case study allowed to understand, in practice, the procedures to be performed in the process of predicting a physical-chemical property of biodiesel, the oxidative stability, since data preprocessing, ANN setup and training and calculating and interpretation of the evaluation criteria.

Although the practical development was carried out by a regression approach, this work also explained about classifiers and procedures for both the construction and evaluation of models. Therefore, the present work can be helpful to instruct the basic procedures in the application of ANNs to the quality of biofuels.
