# A New Engine Fault Diagnosis Method Based on Multi-Sensor Data Fusion
## 4 Applications
### Motor Motor Fault Diagnosis  
In this section, the proposed method is applied in practical engine fault diagnosis, and experimental data is from actual measurement data of the motor rotor [77]. Feature \(j\) under fault \(i\) is denoted as \(F_{ij}\), where \(i=1,2,3\), respectively, on behalf of the three kinds of faults: rotor imbalance, rotor misalignment and the base loose. In addition, \(j=1,2,3,4\), respectively, on behalf of the four features: the amplitude of fundamental harmonic (\(1X\)), the amplitude of second harmonic (\(2X\)), and the amplitude of the third harmonic (\(3X\)) in the frequency spectrum of the rotor vibration acceleration sensor signal and shifting of rotor vibration (\(Shifting\)). For example, \(F_{11}\) means feature \(1X\) of fault rotor imbalance. The frame of discernment should be \(\Theta=\{F_{1},F_{2},F_{3}\}\). There are five sets of measured data for specific \(i\) and \(j\) and each set of measured data is composed of forty continuous measurements in sixteen seconds. Step 1: Establish fault models \(\mu_{F_{ij}}\). For specific \(i\) and \(j\), four sets of feature data are randomly selected as fault samples to generate fault model \(\mu_{F_{ij}}\); thus, a total of 12 fault models can be established for all \(i\) and \(j\). For example, \((\bar{X}_{\mu_{F_{i4}}},\sigma_{\mu_{F_{i4}}})\) is shown in Table 5 and the function curve of \(\mu_{F_{i4}}\) is shown in Figure 4a. Step 2: Generate test models \(\mu_{T_{j}}\). Assuming the left four sets of feature data in \(F_{2j}\) are selected as the test sample, which can be used to generate test models \(\mu_{T_{j}}\), the final diagnostic result should be \(F_{2}\). For example, \((\bar{X}_{\mu_{T_{4}}},\sigma_{\mu_{T_{4}}})\) is shown in Table 5 and the function curve of \(\mu_{T_{4}}\) is shown in Figure 4b. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Test Times** & **Identification Accuracy** \\ \hline \(S\) & 10,000 & 100\% \\ \(E\) & 10,000 & 99.95\% \\ \(V\) & 10,000 & 99.99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The identification accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Category** & \(Sup\left\{\{\$\}\right\}\) & \(Sup\left\{\{\$\}\right\}\) & \(Sup\left\{\{\$\}\right\}\) & \(Sup\left\{\{\$,E\}\right\}\) & \(Sup\left\{\{\$,V\}\right\}\) & \(Sup\left\{\{\$,V\}\right\}\) & \(Sup\left\{\{\$,E,V\}\right\}\) \\ \hline \(SL\) & 0.1086 & 0.8324 & 0.7254 & 0.1086 & 0.0595 & 0.5934 & 0.0595 \\ \(SW\) & 0.2982 & 0.9919 & 0.6336 & 0.2974 & 0.2980 & 0.6289 & 0.2974 \\ \(PL\) & \(2\times 10^{-9}\) & 0.9196 & 0.2416 & \(1.9\times 10^{-9}\) & \(2\times 10^{-11}\) & 0.2385 & \(2\times 10^{-11}\) \\ \(PW\) & \(1.2\times 10^{-5}\) & 0.9660 & 0.2470 & \(1.1\times 10^{-5}\) & \(5.5\times 10^{-6}\) & 0.2471 & \(5.5\times 10^{-6}\) \\ \hline \hline \end{tabular} \(SL\): legal length; \(SW\): legal width; \(PL\): petal length; \(PW\): petal width.  
\end{table} 
Table 2: Support degrees. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Category** & \(m\left\{\{\$\}\right\}\) & \(m\left\{\{\$\}\right\}\) & \(m\left\{\{\$\}\right\}\) & \(m\left\{\{\$,E\}\right\}\) & \(m\left\{\{\$,E\}\right\}\) & \(m\left\{\{\$,V\}\right\}\) & \(m\left\{\{\$,E,V\}\right\}\) & \(m\left\{\{\$,E,V\}\right\}\) \\ \hline \(BPA_{SL}\) & 0.0437 & 0.3346 & 0.2916 & 0.0437 & 0.0239 & 0.2385 & 0.0239 \\ \(BPA_{SW}\) & 0.0865 & 0.2879 & 0.1839 & 0.0863 & 0.0865 & 0.1825 & 0.0863 \\ \(BPA_{PL}\) & \(1.4\times 10^{-9}\) & 0.6570 & 0.1726 & \(1.3\times 10^{-9}\) & \(1.4\times 10^{-11}\) & 0.1704 & \(1.4\times 10^{-11}\) \\ \(BPA_{PW}\) & \(8.2\times 10^{-6}\) & 0.6616 & 0.1692 & \(8.2\times 10^{-6}\) & \(3.8\times 10^{-6}\) & 0.1692 & \(3.8\times 10^{-6}\) \\ Final BPA & \(4.9\times 10^{-4}\) & 0.8798 & 0.1130 & \(3.3\times 10^{-5}\) & \(2.2\times 10^{-6}\) & 0.0066 & \(1.5\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: BPA (basic probability assignment) under each attribute and final BPA. Step 3: Generate \(BPA_{j}\).