## 4 Vibration Fault Diagnosis
### Cooperative GA-Neural Network Based Fault Diagnosis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Predicted Class**} \\ \cline{3-8}  & & **Healthy Bearing** & **Inner Ring Fault** & **Ball Fault** & **Outer Ring Fault** & **Recall** \\ \hline \multirow{4}{*}{**Actual Class**} & Healthy Bearing & 33 & 0 & 0 & 0 & 100\% \\  & Inner Ring Fault & 0 & 59 & 0 & 0 & 100\% \\  & Ball Fault & 0 & 0 & 53 & 1 & 98.15\% \\  & Outer Ring Fault & 0 & 0 & 1 & 62 & 98.41\% \\ \cline{2-8}  & Precision & 100\% & 100\% & 98.15\% & 98.41\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Classification rate for Cooperative GA- neural network based Fault Diagnosis (Validation data). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Predicted Class**} \\ \cline{3-8}  & & **Healthy Bearing** & **Inner Ring Fault** & **Ball Fault** & **Outer Ring Fault** & **Recall** \\ \hline \multirow{4}{*}{**Actual Class**} & Healthy Bearing & 34 & 0 & 0 & 0 & 100\% \\  & Inner Ring Fault & 0 & 66 & 0 & 0 & 100\% \\ \cline{1-1}  & Ball Fault & 0 & 0 & 54 & 1 & 98.18\% \\ \cline{1-1}  & Outer Ring Fault & 0 & 1 & 0 & 53 & 98.15\% \\ \cline{1-1}  & Precision & 100\% & 98.51\% & 100\% & 98.15\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Classification rate for Cooperative GA- neural network based Fault Diagnosis (Test data). Figure 8: Cooperative Genetic Algorithm-neural network: Best Validation Performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Predicted Class**} \\ \cline{3-8}  & & **Healthy Bearing** & **Inner Ring Fault** & **Ball Fault** & **Outer Ring Fault** & **Recall** \\ \hline \multirow{4}{*}{**Actual Class**} & Healthy Bearing & 113 & 0 & 0 & 0 & 100\% \\  & Inner Ring Fault & 0 & 163 & 0 & 0 & 100\% \\  & Ball Fault & 0 & 0 & 179 & 0 & 100\% \\ \cline{1-1}  & Outer Ring Fault & 0 & 0 & 0 & 171 & 100\% \\ \cline{1-1}  & Precision & 100\% & 100\% & 100\% & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Classification rate for Cooperative GA-neural network based Fault Diagnosis (Training data). results have been validated by test data with a F1-Score of 99.12%. The global score for training, validation and testing data is 99.65%. These results are obtained thanks to this approach which has the capacity to optimize the architecture of the neural network. All experiments were performed with Matlab R2017b software on a machine having the following characteristics: Intel Core i5 2.4 GHz processor with 4.0 GB of RAM. The execution time of the algorithm is 13 min 15.03 s.  
It should be noted that this time which has been calculated is not the diagnosis time, but the time which is necessary for the optimization and the learning of the neural network. This operation is carried out only once to build the model. In addition to its ability to accurately classify defects, this method provides a quick diagnosis for making decisions in time. This ability is very useful for flight systems which require a high operational safety. This model is validated to ensure an automatic diagnosis of the vibration defects of the aircraft air compressor bearings.