## 4 Discussion of the Fault-Diagnosis Results
### Performance under Noise Environment  
In order to comprehensively investigate the performance of the model, three commonly used indicators, namely accuracy, precision, and recall, are used in this section to measure the fault-classification performance of the MSFFCNN model, and the stability of the model is further evaluated through repeated tests. The definition of accuracy, precision, and recall are shown in Equations (15)-(17):  
\[\mathrm{P}_{Acc}\ =\frac{TP+TN}{TP+FN+FP+TN}, \tag{15}\]  
\[\mathrm{P}_{Pre}= \frac{TP}{TP+FP}, \tag{16}\]  
\[\mathrm{P}_{Rec}\ = \frac{TP}{TP+FN}, \tag{17}\]  
where _TP_, _FP_, _TN_, and _FN_ represent the number of true cases, false-positive cases, true-negative cases, and false-negative cases, respectively; \(\mathrm{P}_{Acc}\), \(\mathrm{P}_{Pre}\), and \(\mathrm{P}_{Rec}\) represent accuracy, precision, and recall, ranging from 0 to 1; the higher the value, the better the model performance.  
In practice, signals collected by EMA sensors are easily contaminated by ambient noise. Therefore, in this section, Gaussian white noise of different signal-to-noise ratios (SNR) is added to the original signal to simulate noise interference in the aviation environment. The definition of SNR is as follows:  
\[\mathrm{SNR}=10\mathrm{log}_{10}\left(\frac{P_{\mathrm{signal}}}{P_{\mathrm{ noise}}}\right) \tag{18}\]  
where \(P_{\mathrm{signal}}\) and \(P_{\mathrm{noise}}\) represent the energy of signal and noise, respectively. The more noise contained in the signal, the smaller the SNR value.  
In order to verify the anti-noise performance of the proposed MSFFCNN, the model was tested in five noise environments with SNR of \(-10\) dB, \(-5\) dB, \(0\) dB, \(5\) dB, and \(10\) dB, respectively. The fault diagnosis results are shown in Figure 12. In the environment of SNR = 5 dB with weak noise, the accuracy, precision, and recall of MSFFCNN can reach more than 98%; in the environment of SNR = \(-10\) with strong noise, the three performance indicators can also maintain at about 77%.  
Furthermore, the performance difference between MSFFCNN and 1 DCNN as well as the current representative MSCNN and WDCNN under the three noise environments of SNR = \(-5\), SNR = 0, and SNR = 5 were compared. The results are shown in Figure 12.  
Figure 12: Performance comparison under noise environment: (**a**) performance of MSFFCNN under different SNR; (**b**) comparison with other methods under different SNR.  
As can be seen, the accuracy, precision, and recall of MSFFCNN are significantly higher than those of other reference methods under three different noise environments. MSCNN has the second-best anti-noise performance, and its three indexes can reach more than 90% when SNR = 0. WDCNN and 1 DCNN can achieve a similar level of diagnostic performance, with slightly worse anti-noise performance than MSCNN.  
In addition, although the diagnostic performance of all algorithms decreases to varying degrees with the increase of noise, MSFFCNN still shows excellent anti-noise ability, which means that MSFFCNN has better fault feature learning ability and recognition ability. In summary, MSFFCNN has good robustness to noise and can meet the diagnostic requirements in the actual industrial environment of environmental noise and measurement interference.