## 4 Results and Discussion
### Intelligent Analysis Based on a Unit Parameter Entropy and the BP Neural Network  
The measured signal requires further analysis to accurately identify the health state of the engine. The BP neural network is an intelligent method with a function of multi-layer feed-forward, identifying the signal through its logic operations. It is very important for the BP neural network to ensure the effectiveness of the input parameters.  
Based on the characteristics of the AE signals, 12 kinds of AE parameters were selected initially in this paper, including the amplitude, the RMS, the signal strength, the initial frequency, and the eight frequency bands' energy after the signal was decomposed by the three-layer wavelet packet. Based on Equation (6), the unit parameter entropy of the 12 AE parameters was calculated, with the results shown in Table 2.  
From Table 3, it can be seen that the value of the unit parameter entropy of the initial frequency, Energy 1, Energy 3, Energy 5, Energy 7, and Energy 8 are smaller than the rest of the parameters. This indicates that the parameters with a smaller value are unevenly distributed over the length of the unit interval with large fluctuations, which are not suitable for input into the BP neural network. The value of the unit parameter entropy of the remaining parameters is larger, indicating that the parameter distribution is more uniform in the unit interval. Therefore, the amplitude, the RMS, the signal strength, Energy 2, Energy 4, and Energy 6 are selected as the input parameters and imported into the BP neural network for intelligent analysis.  
Sixty sets of input parameters were selected for the normal state of the engine and the inlet distortion state of the engineer, respectively. Forty sets of data were randomly selected as training samples to be imported into the BP neural network. The remaining 20 sets of data were used as test samples to test the training effect of the BP neural network. To verify the validity of the unit parameter entropy, the excluded parameters and the selected parameters were imported into the BP neural network, respectively, for comparative analysis. The results are shown in Tables 4 and 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & \
\begin{tabular}{c} **Unit Parameter** \\ **Entropy** \\ \end{tabular} & **Parameter** &
\begin{tabular}{c} **Unit Parameter** \\ **Entropy** \\ \end{tabular} \\ \hline Amplitude & 115.17 & Energy 3 & 43.17 \\ RMS & 131.34 & Energy 4 & 119.91 \\ Signal Strength & 148.23 & Energy 5 & 61.70 \\ Initial Frequency & 4.54 & Energy 6 & 104.27 \\ Energy 1 & 35.69 & Energy 7 & 19.89 \\ Energy 2 & 100.64 & Energy 8 & 58.24 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Unit parameter entropy of 12 AE parameters.  
From Tables 4 and 5, it can be concluded that the total accuracy for identifying the engine's operating status through the AE parameters that are selected by the unit parameter entropy method is up to 97.5%, which is higher than that of the AE parameters excluded by the unit parameter entropy. This result proves that the unit parameter entropy method is an effective method to evaluate the effectiveness of the AE parameters in identifying the engine's operating status.