# Distributed Kernel Extreme Learning Machines for Aircraft Engine Failure Diagnostics
## 5 Failure Diagnostics for Aircraft Engine  
Safety and reliability of aircraft engines cannot be overemphasized throughout the service life. Fouling, abrasion and erosion may lead to gradual deterioration of the performance of gas-path components, and some abrupt failure patterns may be caused by foreign object damage and internal object damage. The CBM system of aircraft engine is mainly to evaluate component performance degradation degree, identify fault mode, and provide technical guidance for inspection and maintenance. The purpose of this section is to verify the effectiveness of the proposed DKELMs algorithm in the practical application of failure diagnostics for aircraft engine. As mentioned above, KELM is an efficient machine learning approach, and SVM is one of the most popular data-driven methods, both of which are major techniques for failure diagnostics. Therefore, the original KELM algorithm, the proposed DKELMs algorithm, n-SVR and C-SVC are investigated for failure diagnostics for aircraft engine.  
In the current study, rotating components such as low pressure compressor (LPC), high pressure compressor (HPC), high pressure turbine (HPT) and low pressure turbine (LPT) are usually considered as the main failure components, and the performance degradation and failure degree are often reflected by two kinds of health parameter, namely efficiency coefficient and flow capacity coefficient. On account of the correlation of thermodynamics, the decline of health parameters will cause the observed parameters such as spool speed, exit temperature and pressure of sections to deviate from the normal state. The deterioration and failure degree of gas-path components are described by eight health parameters, including four regarding efficiency and four regarding flow capacity; Table 5 lists the symbols. The observable parameters used to estimate the variation of health parameters are listed in Table 6, and the signal-to-noise ratio of each observable parameter is given. The sensor noise form and the flight environment are respectively assumed to be Gaussian noise and ground test condition. The degradation and failure simulations for aircraft engine are conducted on a commercial modular aero-propulsion system simulation test-bed.  
\begin{table}
\begin{tabular}{l l c} \hline \hline
**Measurements** & **Symbol** & **Single Noise Ratios** \\ \hline Low pressure spool speed & \(N_{L}\) & 1000 \\ High pressure spool speed & \(N_{H}\) & 1000 \\ LPC outlet temperature & \(T_{22}\) & 600 \\ LPC outlet pressure & \(P_{22}\) & 800 \\ HPC outlet temperature & \(T_{3}\) & 600 \\ HPC outlet pressure & \(P_{3}\) & 800 \\ HPT outlet temperature & \(T_{45}\) & 650 \\ HPT outlet pressure & \(P_{45}\) & 650 \\ LPT outlet temperature & \(T_{5}\) & 800 \\ LPT outlet pressure & \(P_{6}\) & 800 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Measurements and single noise ratio of one aircraft engine.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & & \multicolumn{4}{c}{**Degradation after**} \\
**Health** & & \multicolumn{2}{c}{**Different Flight Cycles**} \\
**Parameter** & **Symbol** & **0** & **3000** & **6000** \\ \hline LPC efficiency & \(SE1\) & \(-0.18\%\) & \(-1.5\%\) & \(-2.85\%\) \\ LPC flow & \(SW1\) & \(-0.26\%\) & \(-2.04\%\) & \(-3.65\%\) \\ HPC efficiency & \(SE2\) & \(-0.61\%\) & \(-2.94\%\) & \(-9.40\%\) \\ HPC flow & \(SW2\) & \(-0.41\%\) & \(-3.91\%\) & \(-14.06\%\) \\ HPT efficiency & \(SE3\) & \(-0.48\%\) & \(-2.63\%\) & \(-3.81\%\) \\ HPT flow & \(SW3\) & \(+0.08\%\) & \(+1.76\%\) & \(+2.57\%\) \\ LPT efficiency & \(SE4\) & \(-0.10\%\) & \(-0.54\%\) & \(-1.08\%\) \\ LPT flow & \(SW4\) & \(+0.08\%\) & \(+0.26\%\) & \(+0.42\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Degradation of gas-path components after different flight cycles.