# Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network
## 5 Conclusions  
In this paper, we simulated the waveforms of the BTT sensors under different conditions by numerical analysis, which are used to estimate the actual waveforms in the current main method. However, utilizing the theoretical simulation results to estimate the actual BTT waveform is more difficult. For the difficulty of measuring dynamic experimental blade tip clearance data, this paper introduces a waveform prediction method using the BTT sensor based on an RBF neural network and static calibration data. In the first instance, the experimental data is obtained through the established static calibration experiment bench, and the static calibration data is used as sample point data for the real measured value. Later, dividing the measured values into different sample point arrays, the sample point data are predicted by establishing the RBF prediction model, Kriging prediction model, BP prediction model and polynomial function prediction equation, and the prediction curves are compared with the measured actual value fitted curves. It is concluded that the RBF neural network model approaches any nonlinear function with arbitrary accuracy, and it can be globally approximated, which has a high forecasting ability and still has good prediction accuracy with different groups of sampling points. In the case of fewer sample data, the RBF model's fitted curves still have good prediction accuracy. Additionally, forecasting accuracies of the RBF model and Kriging model are essentially identical, while the BP model has a higher local accuracy, which decreases significantly when it is far away from the center of their points. Whereas the polynomial fitting function is less accurate relative to the RBF model, the Kriging model and the BP model, showing more significant prediction errors in some cases.  
Conceptualization, L.Z.; methodology L.Z.; software, C.C.; validation, L.Z.; formal analysis, C.C.; investigation, Y.X.; data curation, C.C.; writing-original draft preparation, L.Z.; writing-review and editing, L.Z., C.C. and J.C.; visualization, Q.S.; supervision, L.Z.; project administration, L.Z. All authors have read and agreed to the published version of the manuscript.  
The work is supported by National Natural Science Foundation of China (Grant no. 51505206), Liaoning Province Applied Basic Research Program Project (Grant no. 2023 JH2/101300227), Key Laboratory of Vibration and Control of Aero-Propulsion System, Ministry of Education, Northeastern University (Grant no. VCAME202211), Liaoning Provincial Natural Science Foundation Guidance Program Project (Grant no. 2019-ZD-0694), Liaoning Provincial Department of Education Scientific Research General Project (Grant no. L2014246) and Liaoning University of Technology Teacher Research Start Fund Project (Grant no. X201202).  
Not applicable.  
Figure 20: Where \(x=0.15\) mm, training curves of the BP model dataset under six groups of data points and absolute errors.  
Data Availability Statement: The data used to support the findings of this paper are available from the corresponding author upon request.  
The authors declared no conflict of interest.