# Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network
## 1 Introduction  
Rotating blades are an important functional part of impeller machinery. However, severe operating conditions such as high speeds, extreme temperatures and heavy loads can very easily lead to blade failure. Therefore, the application of blade monitoring is very important for the safety and integrity of impeller machinery. Vibration-based condition monitoring is a practical method to analyze the vibration of a blade to obtain a more comprehensive understanding of the current state of the blade. Vibrations in impeller machinery produce continuous stresses on the material, which deteriorate its properties. As a result, fatigue damage, especially High Circumference Fatigue (HCF), may occur. This can lead to the failure of components and, in extreme cases, cause the failure of the entire engine, which must be prevented. Due to their geometry and arrangement, rotor blades are susceptible to fatigue damage. Hence, a lot of research has been conducted in this area to understand and analyze blade vibrations to develop measurement methods [1]. The fundamental concept of Blade Tip Timing (BTT) is to take the rotational speed signal measured by the rotational speed sensor installed near the rotating shaft as the reference signal for each revolution, record the blade arrival moment by using the sensorto detect the rotating blade through the pulse signal generated, and obtain the vibration information of the blade by analyzing the blade sweeping through the sensor time sequence. At the moment, in the field of blade vibration mode identification research based on BTT technology, a variety of modal analysis algorithms have been proposed, such as the single-parameter method, two-parameter method, sinusoidal fitting method, autoregressive method, compression perception, etc. [2]. As the accurate measurement of the tiny displacement of the blade tip is the basis for the reconstruction of the rotating blade vibration mode by BTT technology, it is urgent to improve the measurement accuracy of the blade tip displacement to ensure the accuracy of vibration mode reconstruction and health diagnosis [3]. Research on BTT vibration measurement technology has achieved great results after a long period of development and its evolution is shown in Table 1. Initially this was due to research by the United States WESTHOUSE corporation on the rotating blade vibration online measurement, and on the basis of this appeared the strain gauge detection method [4; 5]. [PERSON] and [PERSON] used holographic interference metric technology applied to vibration testing, leading to the emergence of the laser holographic method [6; 7], using holographic irradiation to measure blade vibration. However, it requires a high degree of blade vibration mode monitoring, which is only possible in laboratory settings. After that, the American Electric Power Research Institute (EPRI) and Liberty Technology Center proposed to monitor the blade in time according to the Doppler effect of the acoustic signal generated by the blade acoustic response method [8; 9], leading to the application of the acoustic response system to measure the vibration information of the blade. However, the operating environment of the actual rotating blade is a complex magnetic field with a wide frequency range, and the background noise can cause great interference. The BTT vibration measurement method appeared only afterwards; domestic research in this field started later. [PERSON] et al. [10; 11; 12; 13; 14; 15; 16] form the earliest team in China to carry out research in the field of blade tip vibration measurement, and they have conducted a lot of pioneering work in system simulation modeling, system design and development, data analysis algorithms, etc. [PERSON] [17] has conducted related research in the field of blade tip synchronous signal processing. In recent years, blade tip synchronization measurements have been combined with rotating blade dynamics analysis to study the identification of blade micro-damage.