# Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network
## 4 Validating the Prediction Accuracy of RBF Neural Network
### Predicting Static Circumferential Characteristic Curves  
Comparison analysis is performed based on the RBF neural network model, Kriging model, BP model, and polynomial function to predict static circumferential characteristic curves at 0.15 mm and 0.2 mm blade tip clearance. Comparison plots between the predicted curves of the RBF model, Kriging model, BP model, and the polynomial function fitted curves against the static circumstantial characteristic curves are shown in Figure 13a-f for the BTC of 0.2 mm. In Figure 13a-c, the RBF model prediction curves, Kriging model prediction curves, and BP model prediction curves are highly consistent with the static circumferential feature curves. There is also a high consistency of the prediction curves across the comparison plots for each model. It is shown in Figure 14 that the four models at all angles when the BTC is at 0.2 mm have an extremely high degree of overlap with the static calibration data, which shows excellent performance. Forecasting errors when blade tip clearance is 0.2 mm are shown in Figures 15 and 16. For the RBF, Kriging, and BP models, their prediction accuracies are high  
Figure 13: Plots of the RBF model, Kriging model, BP model and polynomial function against static circumferential characteristic curve about the angle at 0.2 mm for clearance, together with the curves of the Kriging model, BP model and RBF model. (**a**) Comparing the RBF model and static circumferential characteristic curves. (**b**) Comparing the Kriging model and static circumferential characteristic curve. (**c**) Comparing the BP model and static circumferential characteristic curve. (**d**) Comparing the prediction curves of the Kriging model and RBF model. (**e**) Comparing the prediction curves of the BP model and RBF model. (**f**) Comparative graphs of polynomial function curves and static circumferential characteristic curves. over the range of sampled data, with absolute errors within 20 mV. In Figure 15a,b,d, the RBF model demonstrates highly precise. There is higher fitting accuracy of the polynomial function when there are more data points, but its accuracy is lower than the other three models for fewer sample points, however the errors are all within the allowable range for the sensors. The training curve of the BP model is shown in the upper part of Figure 16, which has good accuracy and good overlap among the various data sets. Figure 16: Where \(x=0.2\) mm, training curves of the BP model dataset under six groups of data points and absolute errors. Figure 14: Where \(x=0.2\) mm, the RBF model, Kriging model, BP model and polynomial function fitting prediction curve compared with the static radial feature curve. Figure 15: The prediction error comparison of different prediction models at a clearance of 0.2 mm: (**a**) with ten groups of data points using Kriging models; (**b**) with six groups of data points using Kriging models; (**c**) the polynomial function fitting model under ten groups of data points; (**d**) with six groups of data points using RBF models. When the clearance \(x=0.15\) mm, the comparison plots as shown in Figure 17a-f among the RBF model prediction curves, Kriging model prediction curves, BP model prediction curves, and polynomial function curves against the static circumferential characteristic curves. In Figure 17a, the curves of the RBF model coincide with the static circumferential characteristic curves due to the static calibration data at the BTC of \(0.15\) mm being used for the prediction of the RBF model. The curves of the Kriging model in Figure 17b have minor fluctuations in the curves at \(15^{\circ}\) and \(55^{\circ}\), which still have a high degree of overlap. Some errors exist in the BP model in Figure 17c at \(20-50^{\circ}\) when it is slightly lower than the static circumferential characteristic curve measured from the experiment. The comparative plots in Figure 17d,e with the RBF model compared with the Kriging model and BP model revealed that their prediction curves have a high overlap at a clearance of \(0.15\) mm.