# Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network
## 4 Validating the Prediction Accuracy of RBF Neural Network
### Predicted Static Radial Characteristic Curve
Figure 5: Prediction curves of RBF model, Kriging model, BP model and polynomial function with static radial characteristic curve about clearance \(x\) for angle 17.825\({}^{\circ}\), and comparison of prediction curves of Kriging model, BP model and RBF model. **(a)** Comparing the RBF model and static radial feature curve. **(b)** Comparing the Kriging model and static radial characteristic curve. **(c)** Comparing the BP model and static radial feature 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 graph of the polynomial function curve and static radial characteristic curve. The output voltage reaches its maximum value where the centerline of the blade coincides with that of the sensor, at which \(\alpha=35.65^{\circ}\). Figure 9a-f show the correlations among the RBF model prediction curves, Kriging model prediction curves, BP model and polynomial function fitting curves versus the ratio of static radial characteristic curves. The RBF model prediction curves in Figure 9a basically match with the data measured from the data points. The RBF model prediction curves are shown in Figure 9b. The RBF model prediction curves are shown in Figure 9c. The RBF model prediction curves are shown in Figure 9d. The RBF model prediction curves are shown in Figure 9e. experiments. Combining this to Figure 5a, the overall prediction trend and the overlap of the prediction curves are the same even though the selected blade cutting angle of the magnetic induction line is different. Similarly, in Figure 9b, the degree of variation in the prediction curves is still not significant. In Figure 9c, the prediction curve of the BP model has a significant overlap with the static radial characteristic curve between 0.2 and 0.35 mm, and a small overlap in the gap range other than this range, which indicates that the BP model has a local optimal feature. Figure 9d,e show the comparison plots between the models, and it is found that their prediction curves are consistent as a whole, but locally their overlap at various points is low and there are large fluctuations. Figure 9f proves that the polynomial curves predicted from the experimental data are well-aligned with the static radial characteristic curves. The predictive curves of each model at \(\alpha=35.65^{\circ}\) are shown in Figure 10 to have a high degree of overlap with the static calibration data, and their predictions have the best results at that angle. In Figures 11 and 12, the prediction errors are shown under the angle \(\alpha=35.65^{\circ}\). The predictive precision of the RBF model and Kriging model are higher as seen in Figure 11, but the RBF model is less accurate. Moreover, the accuracy at wide clearances is also superior. While the accuracy of the polynomial in Figure 11c is lower  
Figure 9: Prediction curves of the RBF model, Kriging model, BP model and polynomial function versus static radial characteristic curve about clearance \(x\) and comparison of the prediction curves of the Kriging model, BP model and RBF model for angle \(35.65^{\circ}\). (**a**) Comparing the RBF model and the static radial feature curve. (**b**) Comparing the Kriging model and the static radial characteristic curve. (**c**) Comparing the BP model and the static radial feature 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 graph of the polynomial function curve and static radial characteristic curve.