# Distributed Kernel Extreme Learning Machines for Aircraft Engine Failure Diagnostics
## 6 Conclusions  
The study of failure diagnostics is crucial for improving the safety and economic performance of aircraft engine, and KELM has attracted extensive attention in the field of failure diagnostics. Aiming for the disadvantages of original KELM algorithm such as excessive network size and high computational complexity, this paper proposes an innovative DKELMs algorithm. DKELMs makes the scale of the network controllable through distributed subnetworks. In addition, the fusion layer is designed for regression problems and classification problems respectively through likelihood probability and DS evidence theory. The accuracy of fusion result is similar to or higher than the original KELM, and the distributed architecture can effectively reduce the computational complexity. Simulations on benchmark datasets show that compared with KELM and SVM, the proposed \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Failure Patterns** & **Algorithm** & \begin{tabular}{c} **Correct** \\ **Rate** \\ \end{tabular} & \
\begin{tabular}{c} **Training** \\ **Time/s** \\ \end{tabular} &
\begin{tabular}{c} **Testing** \\ **Time/s** \\ \end{tabular} \\ \hline \multirow{3}{*}{Single component failure} & KELM & 91.35\% & 3.1905 & 0.2325 \\  & DKELMs & 92.70\% & 0.4408 & 0.0976 \\  & C-SVC & 90.70\% & 0.9507 & 0.1178 \\ \hline \multirow{3}{*}{Double components failure} & KELM & 89.95\% & 21.6213 & 0.9943 \\  & DKELMs & 91.05\% & 0.9743 & 0.2549 \\ \cline{1-1}  & C-SVC & 90.21\% & 3.6765 & 2.7751 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comprehensive performance comparison for component failure recognition. \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 d1 & LPC, HPC & - & d12 & HPC, HPT & HPC \\ d2 & HPC & LPC & d13 & HPC & HPT \\ d3 & LPC, HPC & LPC & d14 & - & HPC, HPT \\ d4 & LPC & HPC & d15 & HPC & HPC, HPT \\ d5 & - & LPC, HPC & d16 & HPC, HPT & HPT \\ d6 & LPC & LPC, HPC & d17 & HPT & HPC, HPT \\ d7 & LPC, HPC & HPC & d18 & HPC, HPT & HPC, HPT \\ d8 & HPC & LPC, HPC & d19 & HPT, LPT & - \\ d9 & LPC, HPC & LPC, HPC & d20 & LPT & HPT \\ d10 & HPC, HPT & - & d21 & HPT, LPT & HPT \\ d11 & HPT & HPC & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Failure patterns of concurrent component failure. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pattern** & **Number of Misclassification** & **Pattern** & \multicolumn{2}{c}{**Number of Misclassification**} \\
**Code** & **KELM** & **DKELMs** & **C-SVC** & **Code** & **KELM** & **DKELMs** & **C-SVC** \\ \hline d1 & 31 & 13 & 11 & d12 & 12 & 28 & 41 \\ d2 & 11 & 6 & 5 & d13 & 40 & 20 & 9 \\ d3 & 15 & 16 & 12 & d14 & 4 & 3 & 6 \\ d4 & 39 & 15 & 17 & d15 & 15 & 15 & 26 \\ d5 & 14 & 13 & 3 & d16 & 22 & 24 & 15 \\ d6 & 14 & 29 & 22 & d17 & 19 & 8 & 26 \\ d7 & 23 & 41 & 38 & d18 & 6 & 17 & 21 \\ d8 & 17 & 10 & 25 & d19 & 21 & 23 & 10 \\ d9 & 10 & 24 & 43 & d20 & 20 & 11 & 0 \\ d10 & 24 & 13 & 25 & d21 & 34 & 25 & 27 \\ d11 & 31 & 22 & 29 & total & 422 & 376 & 411 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Misclassification of each concurrent component failure pattern through different algorithms. algorithm can generate more compact network structure and higher learning speed for both regression problems and classified problems. Experiment results in estimating gradual component performance degradation and recognizing abrupt failure patterns show that DKELMs can effectively reduce training time and testing time while maintaining similar or even generating higher network accuracy practically. [PERSON] and [PERSON] conceived the main idea, [PERSON] and [PERSON] designed the diagnosis structure, [PERSON] carried out the experiments, [PERSON] and [PERSON] analyzed the data, [PERSON] and [PERSON] wrote the paper.