# Distributed Kernel Extreme Learning Machines for Aircraft Engine Failure Diagnostics
## 5 Failure Diagnostics for Aircraft Engine
### Failure Patterns Recognition  
In addition to gradual performance degradation, abrupt failure also often occurs in the service life of the aircraft engine, which would unexpectedly endanger the reliability and safety. Besides estimating the gradual degradation, failure diagnostics of aircraft engine also needs to be able to recognize the abrupt failure patterns, that is, to identify and classify the mode of abrupt failure according to observable parameters. It is assumed that the value range of each health parameter after abrupt failure is 30% to 100% of degradation after 3000 flight cycles. Because the magnitude of LPT efficiency change is too small, the change is almost submerged in the measurement noise. Therefore, abrupt failure of LPT efficiency is ignored and abrupt failure of other health parameters are considered in this subsection. For single component failure, 10 failure patterns and corresponding fault health parameters are listed in Table 8. The misclassification number of each single component failure pattern, through original KELM algorithm, proposed DKELMs algorithm and C-SVC algorithm are listed in Table 9, where the testing samples are 200. Since all failure patterns are included in the training set, the error of all samples is considered when optimizing the loss function. When testing a characteristic failure pattern, it may occur that sometimes DKELMs algorithm has a greater misclassification number than the other two algorithms. Therefore, the accuracy of the algorithm should be measured by the total misclassification number. As can be seen from Table 9, the total misclassification number of proposed DKELMs algorithm is less than that of original KELM algorithm and C-SVC algorithm. The comprehensive performance comparison for single component failure recognition is listed in Table 10. It can be seen from the table that the correct rate of DKELMs algorithm is higher than KELM algorithm and C-SVC algorithm, and the training time and testing time are lower than the other two classification algorithms. For concurrent component failure patterns, it is assumed that it only occurs on two adjacent components, that is, only three groups of components are considered, i.e., LPC & HPC, HPC & HPT, and HPT & LPT. Then, 21 failure patterns and fault health parameters of each pattern are listed in Table 11. Table 12 lists the misclassification number of each concurrent component failure pattern, through original KELM algorithm, proposed DKELMs algorithm and C-SVC algorithm, and the testing samples are 200. It can be found that the proposed DKELMs has lower total misclassification number than original KELM algorithm and C-SVC algorithm. Table 10 lists the comprehensive performance comparison for concurrent component failure recognition. It is clear that the DKELMs algorithm has \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pattern** & **Efficiency** & **Flow Capacity** & **Pattern** & **Efficiency** & **Flow Capacity** \\
**Code** & **Failure** & **Failure** & **Code** & **Failure** & **Failure** \\ \hline s1 & LPC & - & s6 & HPC & HPC \\ s2 & - & LPC & s7 & HPT & - \\ s3 & LPC & LPC & s8 & - & HPT \\ s4 & HPC & - & s9 & HPT & HPT \\ s5 & - & HPC & s10 & LPT & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Failure patterns of single component failure. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Pattern** & **Number of Misclassification** & **Pattern** & **Number of Misclassification** & **C-SVC** & **Code** & **KELM** & **DKELMs** & **C-SVC** \\ \hline s1 & 22 & 25 & 19 & s6 & 1 & 0 & 1 \\ s2 & 26 & 20 & 28 & s7 & 29 & 24 & 23 \\ s3 & 15 & 7 & 28 & s8 & 15 & 9 & 21 \\ s4 & 7 & 5 & 8 & s9 & 7 & 9 & 17 \\ s5 & 1 & 0 & 3 & s10 & 50 & 47 & 38 \\ total & 173 & 146 & 186 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Misclassification of each single component failure pattern through different algorithms. higher correct rate and lower training time and testing time than the other two classification algorithms for recognizing concurrent component failure as well.