# Research on Real-Time Model of Turboshaft Engine with Surge Process
## 3 Real-Time Surge Model of Turboshaft Engine
### Model Confidence Verification  
In order to further verify the confidence of the simulated surge signal, the aero-engine surge detection method in [29], which has benefitted dozens of core engine surge tests, is applied to the surge real-time model in this paper. The main steps of the aero-engine surge detection method based on fluctuating pressure change rate are as follows  
Step 1. Use Butterworth filter for dynamic pressure low-pass filtering and reserve the pressure component below 150 Hz. Step 2. Remove the steady-state pressure component \(P_{3 CLM}\) and extract the pulsating pressure component \(\Delta P_{3 CLM}\). The steady-state pressure component is calculated by the front-end point moving average method:  
\[\overset{-}{P}_{3 CLM}=\frac{1}{N}\sum_{i=1}^{N}P_{3 CLM}(k+i),\ (k=1,2,\cdots,n) \tag{25}\]  
\[\Delta P_{3 CLM}(k)=P_{3 CLM}(k)-\overset{-}{P}_{3 CLM}(k) \tag{26}\]  
where \(N\) is the size of the sliding window and \(n\) is the length of the signal sequence. Step 3. Take the engine control cycle, i.e., 20 ms, as the calculation cycle and calculated \(|\Delta P_{3 CLM}|\) which is the absolute value of the pulsating pressure change rate. Step 4. Detect the \(|\Delta P_{3 CLM}|\) and judge whether it exceeds the detection threshold. Step 5. If \(|\Delta P_{3 CLM}|\) is greater than the detection threshold for two times or more in three consecutive detection cycles, it is determined that the engine is surging and a surge alarm signal is sent. In order to simulate the compressor outlet static pressure signal collected in the real operating environment, white noise with a signal-to-noise ratio of 20 is added to the compressor outlet pressure signal in the multi surge dynamic process in Section 4.2. Using the above surge detection algorithm, the steady-state pressure component \(\overset{-}{P}_{3 CLM}\) and the pulsating pressure component \(\Delta P_{3 CLM}\) are shown in Figure 15. Obviously, with the occurrence of the surge, the amplitude of fluctuating pressure component increases and the amplitude of the deep surge is greater than that of the classical surge. Figure 14: The engine’s operating trajectory in the surge dynamic process at multiple operating points. As shown in Figure 16, the change rate of pulsating pressure component is further obtained, and the surge detection results are given in combination with the threshold. In Section 4.2, set the model to generate two surges, one for classical surge and one for deep surge and the \(|\Delta P_{3 CLM}^{\prime}|\) increases greatly during the surge. According to the simulation settings in Section 4.2 and the detection results of engine surge, the dynamic pressure at the compressor outlet begins to fluctuate and the first surge occurred at \(t=5\) s. The surge alarm signal appears at 5.08 s while the absolute value of fluctuating pressure change rate sharply increases to 15,000 kPa/s. The surge alarm signal is sent about 0.08 s after the pressure begins to fluctuate. When \(t=10\) s, the dynamic pressure fluctuation at the compressor outlet ends. The surge alarm signal disappears in 10.04 s, and the surge disappears in about 0.04 s after the pressure fluctuation ends. The second surge occurred at \(t=35\) s (after accelerating to 100% Ng speed), the dynamic pressure at the compressor outlet begins to fluctuate and the surge alarm signal appears at \(t=35.10\) s where the absolute value of the fluctuation pressure change rate increased sharply to 30,000 kPa/s. The surge alarm signal is sent out about 0.10 s after the pressure begins to fluctuate. After the dynamic pressure fluctuation at the compressor outlet ends at 40 s, the surge alarm signal disappears at 40.06 s.  
Figure 16: The absolute value of fluctuating pressure change rate (\(|\Delta P_{3 CLM}^{\prime}|\)) and the surge detection results. Figure 15: The steady-state pressure component \(\vec{P}_{3 CLM}\) and the the pulsating pressure component \(\Delta P_{3 CLM}\) of simulated pressure \(P_{3 CLM}\).