# Bearing Fault Diagnosis Using a Vector-Based Convolutional Fuzzy Neural Network
## 4 Experimental Results
### Evaluation of Fault Diagnosis  
The vibration signals were randomly divided into training (70%) and testing (30%) datasets to assess the stability and generalization capabilities of the vector-CFNN. Additionally, during model training, the training data (70% of datasets) were split into 8:2 for model training and validating. Following that, k-fold cross-validation was employed to validate the efficiency of the model across various subsets. The architecture of the developed vector-CFNN is displayed in Table 2, and the layer of the fusion method was adjusted corresponding to GAP, GMP, CAP, CMP, and network mapping. Finally, the performance of the vector-CFNN was compared with that of ANN, FNN, conventional CNN, and CFNN. The total parameters used in the models are provided and improvement in the accuracy of different fusion methods is also presented in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Numbers of Fragments** \\ \hline Normal bearing & 1657 \\ Fault in inner race & 1893 \\ Fault in ball & 1894 \\ Fault in outer race & 3324 \\ Total & 8768 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Total number of fragments in each category. Figure 7: A processed fragment and the corresponding images in each category. The average accuracy of ANN and FNN were 75.78% and 88.76%, respectively; however, the average accuracy of CNN reached 92.43%, which revealed a 3.67% improvement. The images formed by the time domain signals (Figure 7) have been clearly distinguished by their image pattern, as the CNN series algorithms showed superior performance than those of ANN and FNN because of their capacities for strong correlation and characteristic extraction in image classification tasks. By contrast, CFNN, a combination of CNN and FNN, increased the classification ability, and achieved around 96-99% average accuracy when using different fusion methods due to the fuzzy logic's ability to mimic human reasoning. Although network mapping fusion method showed 99.49% average accuracy in CFNN, it needed more parameters than other fusion methods. In order to decrease the parameter usage in a model, the developed vector-CFNN was evaluated against CFNN; the accuracy of vector-CFNN improved by 2.16%, 1.05%, 3.51%, 1.60%, and 0.20% while using GAP, GMP, CAP, CMP, and network mapping fusion methods, respectively. Moreover, vector-CFNN reduced the number of parameters by 66.07% in comparison with CFNN. Additionally, various sizes of damage diameter classification (including 0.007, 0.014, and 0.021 inches) provided by the bearing dataset of Western Reserve University were examined by vector-CFNN. The lowest, highest, and average accuracy were 95.13%, 98.02%, and 96.69%, respectively, and the confusion matrix is given in Figure 8. Overall, while diagnosing the bearing faults, without the addition of a fusion method, the average accuracy of vector-CFNN was 98.89%, and with fusion methods, the average accuracy of vector-CFNN was over 99%, which was higher than that of other models. Moreover, in classifying bearing faults based on different fault diameters, the vector-CFNN can also reach over 95% average accuracy, which showed the capability of fault diagnosis. Specifically, the