Theoretical Study of Frequency Ambiguity in Rotor Blade Tip Timing for Vibration Monitoring

Abstract Blade tip timing (BTT) is a non-contact monitoring technology for rotor blade vibrations. Due to its severe undersampling, anti-aliasing spectral analysis has become a key focus. We identified certain specific frequencies that cannot be recognized during spectral analysis, a phenomenon we have termed frequency ambiguity. To investigate its mathematical basis, we assume constant rotational speed and neglect blade vibration effects on sampling time, hereby modeling BTT sampling as periodic non-uniform sampling. The time-domain multiplication of the original signal and sampling pulses corresponds to a convolution in the frequency domain. Frequency ambiguity arises from the uncertainty introduced by the complex weighted sum of two spectral peaks of the original signal. Then, building on the ambiguous frequency defined by this phenomenon, we propose the synchronous filtering using block spatial smoothing for subspace-based methods, which can be explained through the collapse of the signal subspace dimension. Simulation and experimental results demonstrate that subspace-based methods, such as multiple signal classification (MUSIC) and estimating signal parameter variational invariance techniques, exhibit synchronous filtering property that effectively suppresses ambiguous frequencies, thereby improving the accuracy of blade natural frequency identification. Notably, MUSIC exhibits superior noise immunity.