# Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms
## 5 Conclusions  
A blade vibration parameter identification method based on the mapping matching between the static waveform of the sensor and the dynamic waveform of the blade tip-timing is proposed in this paper. First, the standard waveform of the non-vibration blade passing through the sensor is obtained by the static calibration simulation experiment of the sensor. Secondly, the blade tip-timing modulation waveform output by the sensor when the blade vibrates is presented through the dynamic measurement simulation experiment. Finally, the blade vibration parameters are identified based on the mapping matching between the static standard waveform of the sensor and the blade tip-timing modulation waveform. The influences of vibration displacements, velocities and vibration amplitudes on the tip-timing waveform of sensor are analyzed. The vibration displacement and velocity \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Identification Methods** & **SNR** & **Number of Sensors** & \
\begin{tabular}{c} **Identification Accuracy** \\ **of Excitation Order** \\ \end{tabular} &
\begin{tabular}{c} **Relative Error of** \\ **Vibration Frequency** \\ **Identification** \\ \end{tabular} \\ \hline Waveform method in Ref. [29] & Infinity & 1 & Unidentification & 14.10\% \\ \hline \multirow{4}{*}{Waveform mapping method} & Infinity & 1 & 100\% & 0\% \\  & 90 db & 1 & 100\% & 0\% \\ \cline{1-1}  & 80 db & 1 & 99.23\% & 0\% \\ \cline{1-1}  & 70 db & 1 & 95.05\% & 0\% \\ \cline{1-1}  & 60 db & 1 & 91.23\% & 0\% \\ \cline{1-1}  & 50 db & 1 & 86.42\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of identification accuracy of excitation order and vibration frequency between the waveform mapping method and the waveform method in reference. Figure 16: Average relative error of constant offset. of the blade tip passing through the sensor are presented by the waveform mapping matching method, and then the vibration parameters of blade are identified. The influence of the number of blade tip-timing sensors on the identification accuracy of blade vibration parameters identification algorithm is observed based on waveform mapping matching theory. The conclusions are as follows:  
1. When the vibration is in positive or negative synchronization, the highest point of the tip-timing waveform of the vibration blade coincides with that of the non-vibration blade. With the increase of amplitude, the waveform shrinks inward or expands outward; that is, the time interval between the blade tip passing through the sensing range of the sensor becomes smaller or larger. When the vibration is ahead or in hysteresis, the highest point of the tip-timing waveform of vibration blade does not coincide with that of non-vibration blade. With the increase of amplitude, the time interval of the waveform moving left or right is larger, but the time interval of blade tip passing through the sensing range of the sensor is basically unchanged;
2. The identification accuracy of vibration amplitude is the highest, followed by the initial vibration phase and finally the constant offset, whether it a single-sensor, double-sensor and three-sensor waveform mapping method is employed. As the SNR increases, the accurately identified initial excitation order decreases. For a certain SNR, with the increase of excitation order, the relative error of amplitude, relative error of constant offset and relative error of initial phase are all smaller; that is, the identification accuracy of the vibration amplitude, constant offset and initial phase is higher. When the excitation order is the same, the larger the SNR, the smaller the relative error of amplitude, the relative error of constant offset and the relative error of initial phase;
3.