# A New Engine Fault Diagnosis Method Based on Multi-Sensor Data Fusion
## 4 Applications
### Motor Motor Fault Diagnosis
For case 3: \((\bar{X}_{H_{F_{1}}},\sigma_{H_{F_{1}}})=(0.1619,0.0101)\), \((\bar{X}_{H_{F_{1}}},\sigma_{H_{F_{1}}})=(0.1481,0.0164)\), \((\bar{X}_{H_{F_{1}}},\sigma_{H_{F_{1}}})=(0.1131,0.0071)\), \((\bar{X}_{H_{F_{1}}},\sigma_{H_{F_{1}}})=(4.3035,0.3204)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(0.1848,0.0109)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(0.3320,0.0106)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(0.2492,0.0342)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(4.7851,0.4010)\), \((\bar{X}_{H_{F_{3}}},\sigma_{H_{F_{3}}})=(0.3271,0.0050)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(0.3446,0.0141)\), \((\bar{X}_{H_{F_{3}}},\sigma_{H_{F_{3}}})=(0.1367,0.0113)\), \((\bar{X}_{H_{F_{4}}},\sigma_{H_{F_{4}}})=(9.8182,0.1090)\), \((\bar{X}_{H_{F_{1}}},\sigma_{H_{F_{1}}})=(0.1696,0.0096)\), \((\bar{X}_{H_{F_{2}}},\sigma_{H_{F_{2}}})=(0.3187,0.0041)\), \((\bar{X}_{H_{F_{3}}},\sigma_{H_{F_{3}}})=(0.2131,0.0053)\), \((\bar{X}_{H_{F_{4}}},\sigma_{H_{F_{4}}})=(4.4358,0.4015)\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Category** & \(\boldsymbol{m}\left(\{\boldsymbol{F_{1}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{2}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{3}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{1}},\boldsymbol{F_{2}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{1}},\boldsymbol{F_{3}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{2}},\boldsymbol{F_{3}}\}\right)\) & \(\boldsymbol{m}\left(\{\boldsymbol{F_{1}},\boldsymbol{F_{2}},\boldsymbol{F_{3}}\}\right)\) \\ \hline \(BPA_{1}\) & 0.0773 & 0.8452 & 0 & 0.0775 & 0 & 0 & 0 \\ \(BPA_{2}\) & 0 & 0.4052 & 0.2974 & 0 & 0 & 0.2974 & 0 \\ \(BPA_{3}\) & 0 & 0.9995 & 0.0002 & 0 & 0 & 0.0003 & 0 \\ Final BPA & 0.0020 & 0.9973 & 0.00056 & 0.0001 & 0 & 0.0004 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: \(BPA_{i}\) (\(i=1,2,3\)) and final BPA. Figure 5: Intersection area of fault models and test model under feature 4 (\(Shifting\)). (**a**), (**b**), (**c**) shows the \(Area\{F_{1}\}\), \(Area\{F_{2}\}\), \(Area\{F_{1},F_{2}\}\), respectively. For case 3: \((\bar{X}_{H_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.1619,0.0107)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.1481,0.0164)\), \((\bar{X}_{\mu_{\rm{F_{3}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.1114,0.0050)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(4.3241,0.3240)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.1790,0.0101)\), \((\bar{X}_{\mu_{\rm{F_{2}}}},\sigma_{\mu_{\rm{F_{2}}}})=(0.3320,0.0106)\), \((\bar{X}_{\mu_{\rm{F_{2}}}},\sigma_{\mu_{\rm{F_{2}}}})=(0.2492,0.0342)\), \((\bar{X}_{\mu_{\rm{F_{2}}}},\sigma_{\mu_{\rm{F_{2}}}})=(4.6484,0.4402)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.3299,0.0079)\), \((\bar{X}_{\mu_{\rm{F_{3}}}},\sigma_{\mu_{\rm{F_{3}}}})=(0.3446,0.0141)\), \((\bar{X}_{\mu_{\rm{F_{3}}}},\sigma_{\mu_{\rm{F_{3}}}})=(0.1367,0.0113)\), \((\bar{X}_{\mu_{\rm{F_{3}}}},\sigma_{\mu_{\rm{F_{3}}}})=(9.8220,0.1010)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.3275,0.0023)\), \((\bar{X}_{\mu_{\rm{F_{2}}}},\sigma_{\mu_{\rm{F_{2}}}})=(0.3409,0.0135)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(0.1341,0.0113)\), \((\bar{X}_{\mu_{\rm{F_{1}}}},\sigma_{\mu_{\rm{F_{1}}}})=(9.7652,0.0953)\).