# Classification of Belts Status Based on an Automatic Generator of Fuzzy Rules Base System
## 3 Results  
In order to develop this study, 26 belts in different states of use were used; therefore, there were 26 vibration patterns, each one with the signals of the three Cartesian axes. Firstly, the signal processing is conducted to obtain the frequency signature of each vibration measurement, and then they are divided into bands and the average is obtained for each band. In order to check the generalization capacity of the GNF system after training, 25% of the patterns are reserved. This involves that the algorithm has been trained with 75%  
Figure 5: Flowchart of the process. of the signals, indicating in each case what type of belt each pattern corresponds to. Once the three phases of the algorithm, which have been explained in the previous section, are completed, the classifier is ready. The trained system is now capable of determining the status of the belt from the vibration signals captured by a sensor. Figure 6 shows the results after the GNF phase. As it can be seen, while the iterations or generations are growing, the average distance between individuals is decreasing, and this involves a reduction in the rule number that is necessary to build the classifier. This can be tested with Figure 7, where the initial 100 rules are reduced to 43 rules that correspond to the nodes marked in red. This figure also shows which input activates each node. If only one input activates a particular node, its number is marked in red but if there is a second input linked to the same node, its number is marked in green and finally, if there is a third input, it is marked in pink. The confusion matrix is an adequate method for visualizing the learning capacity of an algorithm. This tool shows as many columns as the number of predictions of each class and as many rows as the instances of the real class. With this representation, the successes and the errors that the classifier makes after training can be observed. In this work, there are three values to predict, and therefore, the confusion matrix will have dimension 3 \(\times\) 3. The diagonal values represent the true positives, that is, those labels that the classifier has identified correctly, while the rest of the elements of the matrix show the erroneous identifications, and depending on the location, it is verified which erroneous label it is. Figure 6: Evolution of average distance between individuals in Genetic algorithm phase. Figure 7: Rules activation network after the genetic algorithm phase. Figure 8 presents the confusion matrix obtained after the training process. As can be seen, label 1 and label 2 have 100% accuracy, whereas label 3, corresponding to close-to-breaking belts, has an accuracy of 88.9% since there was a pattern that the classifier identified as class 2 (half-used belt) and the actual label was 3 (close-to-breaking belt). Green numbers correspond to percentage of right classified samples, whereas red ones correspond to percentage of wrong classified samples. Figure 9 shows the confusion matrix for the generalization patterns, that is, the introduced signals have not been used for training, and therefore, they are unknown data for the classifier. It can be seen that a satisfactory result has been achieved since the classifier has correctly identified each generalization pattern, which means 100% accuracy for the three classes. Green numbers correspond to percentage of right classified samples, whereas red ones correspond to percentage of wrong classified samples. Figure 8: Confusion matrix with training patterns. Figure 9: Confusion matrix with generalization patterns. The good training results obtained could be indicative of over-fitting; however, the classifier also shows good results when test data are introduced, that is, unknown patterns. In this way, it is possible to affirm that the trained algorithm has achieved an adequate level of generalization, and therefore, an over-fitting problem can be overcome. Another technique to check the capacity of a classifier is through the ROC curve (acronym for Receiver Operating Characteristic).