Time-frequency reassignment of blade tip timing signal

Abstract

The health condition of a rotor blade can be assessed by its dynamic frequency with respect the rotational speed, which can be derived from the time–frequency analysis of the blade vibration signal. Blade tip timing (BTT), as a non-contact measurement technique, provides an alternative to traditional contact strain measurement methods. However, the vibration signal measured by BTT is usually undersampled, which limits the application of conventional time–frequency analysis methods. BTT sparse time–frequency methods utilize the sparsity to reconstruct undersampled BTT signals. Nevertheless, BTT sparse time–frequency representation suffers from poor concentration and inaccurate estimation of the dynamic frequency, especially in the case of fast varying speed and limited BTT sensors. In this paper, a BTT time–frequency reassignment method is proposed to enhance the concentration of the BTT time–frequency spectrum and improve the accuracy of dynamic frequency estimation. Firstly, BTT time–frequency reassignment utilizes the blade natural frequency, obtained from the Campbell diagram, as prior information. The blade dynamic frequency with respect to the rotational speed is estimated by combining the prior frequency with the measured frequency in the Bayesian framework. Subsequently, weights are assigned to both the time–frequency coefficients and the posterior frequency. The time–frequency coefficients are relocated around the posterior frequency according to the weights. The advantages of BTT time–frequency reassignment are demonstrated through a simulation, a laboratory test and a full-scale aeroengine test. Both simulation and experimental results demonstrate that BTT time–frequency reassignment enhances the concentration of the BTT time–frequency spectrum and improves the accuracy of the estimated dynamic frequency when limited BTT sensors are available. The influence of the prior frequency is discussed to evaluate the robustness of BTT time–frequency reassignment. In the full-scale aeroengine test, the reliability of BTT time–frequency reassignment is verified under the fast varying speed.