# Fault Diagnosis Method for Aircraft EHA Based on FCNN and MSPSO Hyperparameter Optimization
## 6 Typical Fault Diagnosis of EHA
### Results and Discussion  
The optimal FCNN network obtained in Section 6.1 is used to diagnose the typical faults of aircraft EHA, and ten repetitions of the experiment are conducted. The average result of ten repetitions is selected as the final fault diagnosis result of the MSPSO-FCNN fault diagnosis method for aircraft EHA. To illustrate that FCNN has a better fault diagnosis effectiveness than traditional 1 DCNN and 2 DCNN, we use the completed training 1 DCNN and 2 DCNN models for fault diagnosis of EHA. The test results are shown in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layers** & **Filter Size** & **Filter Number** & **Feature Size** & **Activation Function** \\ \hline Input layer & - & - & \(576\times 1\times 6\) & - \\ Convolutional layer 1 & \(11\times 1\) & 18 & \(566\times 1\times 6\) & Sigmoid \\ Pooling layer 1 & \(2\times 1\) & 18 & \(283\times 1\) & - \\ Convolutional layer 2 & \(7\times 1\) & 26 & \(277\times 1\) & Sigmoid \\ Pooling layer 2 & \(2\times 1\) & 26 & \(139\times 1\) & - \\ Fully connected layer & \(1\times 1\) & 3614 & 3614 & Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The structural parameters of 1 DCNN. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Particle** & **Searching Range** & **Gbest** & **Particle** & **Searching Range** & **Gbest** \\ \hline \(x_{1}\) & 4–64 (step: 2) & 22 & \(x_{11}\) & Sigmoid, Tanh, Relu & Relu \\ \(x_{2}\) & 4–64 (step: 2) & 28 & \(x_{12}\) & Sigmoid, Tanh, Relu & Sigmoid \\ \(x_{3}\) & 4–64 (step: 2) & 40 & \(x_{13}\) & Sigmoid, Tanh, Relu & Sigmoid \\ \(x_{4}\) & 4–64 (step: 2) & 18 & \(x_{14}\) & 64–1024 (step: 2) & 482 \\ \(x_{5}\) & 4–64 (step: 2) & 26 & \(x_{15}\) & Sigmoid, Tanh, Relu & Sigmoid \\ \(x_{6}\) & 2–8 (step: 1) & 3 & \(x_{16}\) & Adam, Adagrad, SGD & Adam \\ \(x_{7}\) & 2–8 (step: 1) & 3 & \(x_{17}\) & 0.05–1 (step: 0.02) & 0.36 \\ \(x_{8}\) & 2–8 (step: 1) & 2 & \(x_{18}\) & 0.2–0.8 (step: 0.1) & 0.5 \\ \(x_{9}\) & 4–20 (step: 1) & 11 & \(x_{19}\) & 25, 40, 50, 100, 150 & 50 \\ \(x_{10}\) & 4–20 (step: 1) & 7 & & & \\ \multicolumn{5}{c}{**Fitness: 0.9758**} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal hyper-parameters of FCNN. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layers** & **Filter Size** & **Filter Number** & **Feature Size** & **Activation Function** \\ \hline Input layer & - & - & \(576\times 1\times 6\) & - \\ Convolutional layer 1 & \(11\times 1\) & 18 & \(566\times 1\times 6\) & Sigmoid \\ Pooling layer 1 & \(2\times 1\) & 18 & \(283\times 1\) & - \\ Convolutional layer 2 & \(7\times 1\) & 26 & \(277\times 1\) & Sigmoid \\ Pooling layer 2 & \(2\times 1\) & 26 & \(139\times 1\) & - \\ Fully connected layer & \(1\times 1\) & 3614 & 3614 & Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The structural parameters of 1 DCNN. To intuitively show the classification effect of the proposed fault diagnosis method on the typical faults of EHA, the confusion matrix of the above six methods is given in Figure 15.  
From Table 6, it is easy to find that MSPSO has better optimization results for all three types of convolutional neural networks compared with PSO. Among them, the accuracy of 1 DCNN, 2 DCNN, and FCNN after optimization of MSPSO is 4.6%, 8.3%, and 8.6% higher than that after optimization of PSO, respectively. The performance of MSPSO does not degrade due to the increase in optimization parameters, which reflects the great potential of the MSPSO algorithm for multi-objective optimization problems. In addition, 1 DCNN has poor recognition of fault 1 (78.1%), fault 3 (76.1%), and fault 6 (83.4%), especially for fault 1 and fault 3, which are two types of faults with relatively close characteristics. In Figure 15d, 23 sample sets belonging to fault 1 are classified as fault 3, and 24 sample sets belonging to fault 3 are classified as fault 1. But in 2 DCNN, the recognition accuracy of fault 1, fault 3, and fault 6 was significantly improved, and the