# Blade Crack Diagnosis Based on Blade Tip Timing and Convolution Neural Networks
## 1 Introduction  
Turbomachine blades are subjected to centrifugal force, airflow excitation, and thermal stress when working in high-temperature, high-pressure, and corrosive environments. Therefore, it is easy for cracks, wear, corrosion, and other risks to develop on the blades, which would hasten high-cycle fatigue failure or potential fracture, shorten the service life, and endanger the safety and operational stability of the turbine [1]. The aircraft compressor blade of China Southern Airlines flight CZ3739 cracked in 2014, causing the engine to catch fire in the air. An engine explosion on a United Boeing 777 happened in February 2021, caused by the fatigue fracture of two fan blades of the PW4000 engine, which damaged the magazine and caused the explosion. According to statistics, blade damage caused 70% of forced-stop accidents in turbines in the United States until 2008 [2]. There are many ways to monitor the real-time status of blade crack faults. [PERSON] et al. [3] measured the change in potential difference by placing three electrodes on the specimen's surface to obtain the shape parameters of the crack. However, this method required attaching electrodes to the surface of the specimen, and the measurement in the rotating state was not independently verified. [PERSON] et al. [4] detected damage to wind turbine rotor blades by using audio classification techniques, but the technique was ineffective for monitoring blades with progressive cracks or in a cabinet with loud airflow. [PERSON] et al. [5] proposed the empirical decomposition characteristic strength level (EDFIL) method for the diagnosis of blade cracks by measuring the real-time vibration of the wind turbine. However, this method was an indirect measurement, which was not able to measure vibration energy concentrated in the blade, such as in a blade-impeller system with a strong rotor stiffness. The acquisition sensors are not in contact with test blades but are installed around the blades, which is called the non-contact vibration measurement method. This method, which is simple in structure and does not affect the original blade quality, stiffness, and other performance parameters, can detect the vibration state of all circled blades and hasgradually become a research focus in the field of blade vibration detection. Intermittent phase [6], laser holography [7], acoustic response [8], and blade tip timing [9] are some examples. Blade tip timing (BTT) technology is developed on the basis of the frequency modulation method. The arrival times of the blade to the displacement sensor mounted on the casing are recorded, and the vibration parameters of the blade can be obtained by analyzing the difference between the recorded times. BTT has the advantages of a simple structure and easy installation. It only needs to arrange the sensor in the casing to monitor the vibration status of all circled blades and does not affect the blades. Due to the sparsity of sampling, the BTT signal is severely undersampled, so it needs a recognition algorithm for data processing to further obtain the vibration parameters, which is also the main drawback of the blade tip timing technology. In recent years, enterprises, research institutions, and universities have invested significant resources in the research of BTT technology in the field of turbomachinery, resulting in a wealth of research results and extensive experience in theoretical methods and engineering practice [10]. General Electric, Pratt &Whitney, and Rolls-Royce all applied BTT technology to the safety detection of engine blades [11]. At the Politecnico di Torino, the latest generation of BTT systems was used to identify the dynamic properties of rotating blade discs [12]. [PERSON] et al. [13] adopted BTT to measure the abnormal vibration of an aeronautical gas turbine blade and applied it to detect blade damage. [PERSON] et al.