Coprime and nested samplings-based spectrum reconstruction in blade tip timing

Blades are crucial components of turbomachinery with high failure risk due to harsh working conditions. Therefore, it is urgently necessary to monitor blade condition. Blade tip timing (BTT) is a potential technique for blade vibrating monitoring owing to its noncontact and efficiency. However, inherent undersampling is a brake on the application of BTT. How to identify the parameters characterizing blade condition from severe undersampled samples is the main hot topic in the BTT field. Here, we proposed coprime sampling-based BTT (CS-BTT) and nested sampling-based BTT (NS-BTT) methods for spectrum reconstruction and parameter identification. The proposed method focuses on reconstructing autocorrelation/covariance in-formation rather than the signal waveform, which improves computational efficiency owing to the elimination of phase information in the autocorrelation function. The proposed method can reconstruct the spectrum without loss of frequency and amplitude information by generating dense lags to improve the decimated rate of autocorrelation function to satisfy the Nyquist criterion. In CS-BTT and NS-BTT, coprime and nested layouts are used to achieve sub-Nyquist sampling, respectively. Moreover, an extended nested sampling was introduced to expand spectrum sensing range. We listed the optimal layouts for coprime, nested, and extended nested samplings in the case that the probe number was given. Compared with the existing BTT methods, the proposed method has a wider applicability and lower computational complexity. The effectiveness and robustness of the proposed method were validated by both simulations and experiments.