# In-the-Loop Simulation Experiment of Aero-Engine Fault-Tolerant Control Technology
## 2 Materials and Methods  
### Performance Degradation Simulation of Engine Gas Circuit Components  
The use of a mathematical model can greatly reduce the economic cost of a real engine experiment, avoid the huge loss caused by test failure, speed up the cycle of algorithm research, and promote the research progress. In addition, this model needs to be able to set the degradation quantity and sensor fault to simulate the real engine, so as to carry out the simulation research of engine fault diagnosis and fault-tolerant control. The basis of the aeroengine airborne adaptive real-time model is also a component-level model. Therefore, the component level model of turbofan engine is established and studied in this paper. Component-level modeling methods are widely used, so it is not repeated here. Mechanical fatigue, foreign matter inhalation damage, wind sand wear, chemical corrosion, and other conditions can easily lead to engine performance degradation or sensor failure, thus affecting the flow and efficiency of gas path components [35]. According to the data provided by NASA, as shown in Table 1, the degradation amount of efficiency and flow of gas circuit components increase with the increase in the number of working cycles. Therefore, the corresponding performance degradation can be simulated by using efficiency and flow degradation coefficients. In this paper, the flow and efficiency degradation coefficients of four rotating components are selected to simulate the performance degradation of corresponding gas path components, and the health parameters are used to characterize the degradation degree. From Table 2, it can be seen that after injecting the corresponding performance degradation amount at 3000 working cycles, the values of the selected parameters have increased to a certain extent compared with the normal working state, which is in line with the law of performance degradation. The closed-loop control of an aeroengine requires the sensor to provide the corresponding feedback, so that the controller can provide the correct control command. In this paper, the following nine sensors are selected for simulation: high- and low-pressure rotor speed; total outlet pressure and total temperature of fan, compressor, and LTP; total pressure at the inlet of the external culvert. The corresponding accuracy and signal-to-noise ratio of different sensors vary greatly. Referring to [36] in this paper, the noise level of high- and low-pressure rotating speed is higher than that of references, and the noise level of total temperature and total pressure are the same, as shown in Table 3, adding different degrees of noise to the sensor. For sensor faults, this paper refers to [37], as shown in Table 4, the sensor value characterizes the fault by setting the offset. As shown in Table 5, the measured value of the sensor has changed after the introduction of noise, select points with large deviation in a period of time, and its ratio to the measured value before the introduction of noise conforms to Table 3, which can prove that the model meets the requirements in the setting of introducing noise. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of Cycles**} & \multicolumn{2}{c}{**Fan**} & \multicolumn{2}{c}{**Compressor**} & \multicolumn{2}{c}{**HPT**} & \multicolumn{2}{c}{**LPT**} \\ \cline{2-9}  & **Efficiency/\%** & **Flow/\%** & **Efficiency/\%** & **Flow/\%** & **Efficiency/\%** & **Flow/\%** & **Efficiency/\%** & **Flow/\%** \\ \hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
3000 & \(-1.50\) & \(-2.04\) & \(-2.94\) & \(-3.91\) & \(-2.63\) & \(1.76\) & \(-0.54\) & \(0.26\) \\
4500 & \(-2.18\) & \(-2.85\) & \(-6.17\) & \(-8.99\) & \(-3.22\) & \(2.17\) & \(-0.81\) & \(0.34\) \\
6000 & \(-2.85\) & \(-3.65\) & \(-9.40\) & \(-14.06\) & \(-3.81\) & \(2.57\) & \(-1.08\) & \(3.42\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variation of performance degradation of turbofan engine with the number of working cycles.