Dynamic Voltage-Response Estimation for Blade-Tip Timing Sensors Based on EHHO-BP Network and Waveform Mapping

Blade-tip timing (BTT) sensor technology is widely used for non-contact blade vibration measurement. However, conventional BTT methods mainly rely on sparse time-of-arrival (TOA) information, which limits continuous sensor-domain characterization of blade vibration. To address this limitation, this paper proposes a dynamic voltage-response estimation framework combining an Elite Harris Hawks Optimization-based backpropagation neural network (EHHO-BP) with waveform mapping. Zero-speed static calibration experiments are used to establish the nonlinear relationships among blade-tip radial clearance, relative angular position, and sensor voltage, and the EHHO-BP model is employed to estimate the calibration response. Blade vibration displacement obtained from numerical models or reconstructed from BTT TOA measurements is then mapped to a continuous dynamic voltage response under a quasi-static transfer assumption. Single-harmonic and multi-harmonic simulations demonstrate the response-estimation process. In the static calibration comparison, EHHO-BP achieves a median RMSE of 8.92 mV, CVRMSE of 0.56%, MAE of 6.34 mV, and R2 of 0.99982. Rotating experiments at 400, 600, 800, 1200, and 1500 rpm further evaluate the transferability of the zero-speed calibration model without retraining or speed-dependent correction. Across the tested speed range, the correlation coefficient remains between 0.9868 and 0.9989 and R2 remains between 0.952 and 0.997; however, the FWHM error increases from 1.469% at 400 rpm to 22.662% at 1500 rpm. These results demonstrate the good transferability of the proposed quasi-static mapping at low-to-moderate rotational speeds while revealing a progressive deterioration in temporal waveform consistency at higher speeds. The proposed framework, therefore, provides a continuous sensor-domain representation of BTT-derived blade vibration displacement and an experimentally supported assessment of its speed-dependent applicability.