## 1 Introduction  
As internal combustion type rotating power machinery, gas turbines are the core components of power equipment in industrial fields, and have rapidly developed and been widely used in other fields such as aerospace, industrial power generation, navigation, and land transportation. The reliability and safety of gas turbines are receiving more and more attention. Due to various unavoidable factors, the gas turbine has various failures, and the predetermined function is reduced or even completely lost. As a result, serious or even catastrophic accidents occur, and huge economic losses are felt by enterprises and even industries [1]. Common gas turbine faults are divided into two categories. The first is related to aerodynamics or performance-based faults, such as thermal distortion, compressor erosion and corrosion, compressor fouling, turbine fouling, turbine erosion and corrosion, blade rubbing, etc. Gas Path Analysis (GPA) is an effective technical means for forecasting these faults [2]. At present, data-driven machine learning has been used for gas path diagnosis based on fault sample sets, such as Artificial Neural Network (ANN) [3], Support Vector Machine (SVM) [4], Bayesian network [5], and fuzzy logic [6]. The second type of common gas turbine faults is related to mechanical properties, such as shaft misalignment, rotor dynamic imbalance, bearing defects, and oil film instability [7]. For such faults, there are many technical means, such as oil chip analysis, vibration analysis, acoustic analysis, thermal aging, load analysis, metal temperature, stress analysis, and so on. Vibration monitoring [8] is one of the commonly used methods for gas turbine condition monitoring and fault diagnosis. Effective condition monitoring, fault diagnosis, and maintenance are effective means to ensure the safe, reliable, and stable operation of gas turbines. Through vibration sensors arranged in the casing and other parts of the gas turbine, the vibration signals of the gas turbine are obtained and analyzed with certain signal processing technology to extract the vibration characteristics for locating the fault and finding out the cause of the fault, thereby providing a basis for the diagnosis, evaluation, and decision making concerning the gas turbine. Vibration condition monitoring can reduce downtime for maintenance, reduce maintenance costs, reduce safety accidents, and ensure the normal operation of equipment to improve its reliability [9]. The rotor system is the most important component in a gas turbine. Due to the complex structure of the gas turbine rotor system and strict assembly process, it plays a vital role in the healthy operation of the gas turbine. The rotor system runs under harsh working environments with high temperatures, high pressure, and high speeds, and it is easy to collide with the internal structure. Once a failure occurs, the rotor will deviate from the normal working state, and it will cause significant damage to the gas turbine in severe cases [10]. In gas turbine rotor systems, rotor imbalance faults, rotor misalignment faults, rotor rub impact faults, rotor thermal bending, and other faults emerge. Through vibration monitoring and by analyzing the vibration signal of the rotor, fault diagnosis and condition evaluation can be carried out to provide suggestions for maintenance personnel that are of great significance to ensure the safe and reliable operation of gas turbine rotor systems. The development of gas turbine condition monitoring and fault diagnosis methods can be divided into three categories: methods based on qualitative experience knowledge, methods based on model analysis, and data-driven methods. The method based on qualitative empirical knowledge relies on the manual judgment of field experts and entails simple processing of the monitoring data.