# Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network
## 1 Introduction
[PERSON] [18] combined the BTT measurement technique and convolutional neural network, which yielded blade crack data. The project by [PERSON] [19] proposed a spatial transformation-based parameter identification method based on fewer probes with single-probe BTT measurements. [PERSON] [20] linearly fitted the multi-probe data of the BTT and linearly corrected the blade arrival time so as to correct the nonlinear vibration in a way that reduces the error of the vibration displacement analysis method. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **General Introduction and Causes of Development** \\ \hline Strain gauge method & The contact measurement method directly reflects the magnitude of the strain at the affixed position; however, it is constrained by the high-speed airflow scouring caused by the high-speed rotation of the blade rotor, dynamic balance and other issues, and there are greater requirements for the installation of the strain gauges and wires. \\ \hline Frequency modulation method & Utilizing frequency modulation grids for frequency modulation of vibration signals according to the principle of electromagnetic induction has played a positive role in the development of early rotating blade vibration detection technology, but magnets embedded in the tip of the blade change the vibration characteristics of the blade, so this method is difficult to popularize and apply. \\ \hline Laser holography & The holographic irradiation is used to measure the blade vibration, which has the advantages of intuition, full-field accuracy, and allows for the measurement of very small amplitudes, but it is more demanding in terms of blade vibration mode, making it suitable for laboratory work only. \\ \hline Acoustic response method & Monitoring of blades in real time is based on the Doppler effect of the acoustic signals generated by the blades, where background noise will cause serious interference with the signals, and the mechanical noise cannot be filtered out. \\ \hline Blade Tip Timing & The blade’s elapsed time is measured by the BTT sensor on the magazine, with different BTT processing algorithms for the blade vibration detection signal arrival time of the overrun or hysteresis processing, to obtain the blade vibration information, which is the hot spot of the current non-contact blade vibration detection technology. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The development history of blade vibration detection methods. [PERSON] et al. [18] applied a Convolutional Neural Network (CNN) combined with the BTT measurement technique to analyze the rotating blade crack data, linking the CNN and BTT measurements, thus providing an online real-time diagnosis of blade crack faults. [PERSON] et al. [21] proposed the feature learning method based on a CNN to learn new fault-sensitive features from the under-sampled raw data to address the shortcomings of the traditional BTT method. [PERSON] et al. [22] applied a CNN to alternative aerodynamic wind turbine blades, and the alternative aerodynamic blade model was trained with high-precision data to predict the aerodynamic loads of the wind turbine blades; this approach is more accurate and creates a more precise proxy model. However, RBF NN approximates any continuous function with arbitrary accuracy compared to CNN when applied to BTT measurement data, which is more suitable for waveform prediction of BTT sensors. [PERSON] et al. [23] used three rotational frequency mode sets of helicopter rotor blades under flap, hysteresis and elastic torsion motions obtained from finite element analysis to detect structural damage of helicopter rotor blades with RBF NN, which obtained good damage detection results. However, this method, using RBF NN, does not fit its characteristics better, and RBF NN is more suitable for function approximation-type problems. [PERSON] et al.