# Impact Load Sparse Recognition Method Based on Mc Penalty Function
## 5 Recognition and Analysis of Gas Turbine Rotor System Impact Load Signals  
A new vibration and shock sparse identification method, based on MC penalty function sparse decomposition vibration and shock signal identification method, is proposed. This method can not only separate the shock components in the early fault signal of the gas turbine rotor system, but also effectively suppress the impact of noise on the sparse decomposition process. Interference has a good noise reduction effect, and better preserves high-amplitude amplitude components [36,37].  
In order to further verify the adaptability of the method, the basic parameters of the test bench of a certain type of gas turbine rotor system are as follows: working speed of 9000 rpm, sensor test records the frequency of high-pressure shaft rotation, sampling frequency f_s is 6000 Hz, and the operating speed is kept at 0.1 working condition (about 7462 rpm). The structure of a certain type of gas turbine rotor system is shown in Figure 15. During the test, the speed is slowly increased from low speed to the 0.1 condition, and the sensor detects that the amplitude of the rotor bearing at the rear point obviously increases. The vibration signal is recorded by the INTEDER data acquisition and analyzer of Yiheng. The acquisition channel is 16 channels. The time domain diagram of the signal collected by the acquisition equipment after data compression and analysis processing is shown in Figure 16.  
Figure 14: Sparse decomposition simulation amplitude/envelope results. (**a**) sparse decomposition amplitude map, and (**b**) sparse decomposition envelope spectrum.  
The test and analysis results of the gas turbine rotor system test bench data show that the method can effectively identify the vibration and shock components in the gas turbine rotor system, and provide an effective shock fault identification method for the gas turbine rotor system fault diagnosis.  
Vibration shock time domain and envelope spectrum analysis extracted based on L1 penalty function and MC penalty function are shown in Figure 16. As can be seen from the comparison in Figure 17a, under the condition of multiple vibration and shock, the adaptability gap of noise of the two methods is very obvious. The vibration and shock phenomenon mainly occurs around the four time points of 0.1 s, 0.24 s, 0.49 s, and 0.87 s. In addition to the above four time points, the results of L1-regularized sparse decomposition show obvious amplitude of abnormal noise interference, the impact recognition is not obvious, and the processing effect is not ideal. However, the sparse decomposition results based on MC penalty function have no obvious abnormal noise interference, and the noise is well controlled. The vibration and impact identification effects are obvious at the four time points of 0.1 s, 0.24 s, 0.49 s, and 0.87 s, and the amplitude retention component with high amplitude is obviously better than the L1-regularization method. Additionally, the difference between the two can be well seen from the envelope spectrum analysis in Figure 17b.  
Through the experiment, in the case of multiple vibration impact, the advantage of MC penalty function to the shock signal sparse decomposition algorithm, in order to control noise interference ability, is more prominent; the noise control is in a reasonable range and there is low intrusive process of sparse decomposition. Secondly, the advantage in retaining high-amplitude amplitude components is more apparent. The experiments further proved the effectiveness and adaptivity of the proposed method.  
Figure 16: Time domain diagram of the original vibration signal after preprocessing.  
Figure 15: Structure of a certain type of gas turbine rotor system. (**1**) ball bearing for low pressure compressor; (**2**) cylindrical roller bearing for low pressure compressor; (**3**) ball bearing for high pressure compressor; (**4**) cylindrical roller bearing for high pressure compressor; (**5**) cylindrical roller bearing for low pressure turbine.