## 4 Gas Turbine Test Bench Experiment and Fault Diagnosis  
### Experiment and Data Acquisition  
To further verify the performance of the proposed method, the gas turbine rotor system fault experiment from the test bench is adopted. The rotor system of a gas turbine is shown in Figure 5, which is mainly composed of a compressor, turbine, rotating shaft, and so on. The low-pressure turbine is connected to the low-pressure compressor through the low-pressure rotating shaft, and the high-pressure turbine is connected to the high-pressure compressor through the high-pressure rotating shaft sleeved on the low-pressure rotating shaft. Due to the complex and high-temperature internal environment of gas turbines, the whole machine vibration measurement is often used in the engineering application. Through multiple experiments and analyses at different positions and angles, as shown in Figure 5, a speed sensor (sensor 1) is installed on the radial position at the front end of the low-pressure compressor casing as the front measuring point, a speed sensor (sensor 2) is installed at the radial position of the casing between the high-pressure compressor and the combustion chamber as the back measuring point, and the rotor speed sensor for measuring high- and low-pressure rotor speed is installed inside the gas engine. The numbers 1-5 in the Figure 5 are the support points for high- and low-pressure rotor, among which, 1, 2 and 5 are the low-pressure rotor support points, and 3 and 4 are the high-pressure rotor support points. The sampling frequency is 6000 Hz, and the experiment time lasts 8000 s. In the actual operation of the gas turbine rotor system, the time domain statistics in the vibration signals will change with the change in the working conditions and state of the gas turbine rotor system. Therefore, the time domain analysis of gas turbine rotor system vibration signals can be used to preliminarily observe and judge the state and trend of the rotor system, and further for the gas turbine rotor system fault diagnosis and analysis. The vibration signals  
Figure 5: Schematic diagram of gas turbine vibration test. collected by the gas turbine sensor are shown in Figure 6, and the effective values of gas turbine vibration signals in the time domain can be obtained. From Figure 6, it can be seen that the amplitude of the front measuring point vibration data is large and exceeds the limit in some time periods, and by analysis, it can be concluded that faults may occur. For further analysis, the root mean square (RMS) values of vibration signals are calculated and shown in Figure 7.  
In Figure 7, the high-pressure rotor speed changes continuously under multiple working conditions; the dotted line is the change in the high-pressure rotor frequency, the green line is the vibration limit value, the red line is the RMS for the front measuring point, and the blue line is the RMS for the back measuring point. It can be found from the gas turbine sensor data analysis that the speed was constantly changing in various working conditions during the experiment. The effective value of the front measuring point vibration signals and the effective value of the back measuring point vibration signals change with the working conditions. Among them, the effective value of the front measuring point vibration signals has the phenomenon of vibrations exceeding the limit for several time periods, and the effective value of the back measuring point vibration signals has never exceeded the limit. It can be found that in multiple periods of time, due to the structure and assembly of the gas turbine, the gas turbine stalls due to the rotation of the high-pressure compressor  
Figure 6: Gas turbine vibration signals at front measuring point. Figure 7: RMS for gas turbine vibration signals. during the speed-up condition, resulting in air flow excitation, further causing temporary unbalance of the high-pressure rotor, resulting in vibration overrun.