Time delay-based spectrum reconstruction for nonuniform and sub-Nyquist sampling in blade tip timing

Rotating blades play a functional role during the working process of turbomachinery, but they are prone to failure due to harsh working conditions. Blade tip timing (BTT) is a potential technique for operational blade health monitoring due to its noncontact feature and efficiency. The critical issue in the application of BTT is extracting vibration parameters or reconstructing the spectrum for subsequent fault diagnosis. However, the nonuniform and undersampling characteristics of the BTT signal challenge signal processing. In this work, we developed an effective and efficient time delay-based spectrum reconstruction method. On this basis, we proposed the conditions (minimal probe number and delay sampling criterion) for the spectrum reconstruction. The proposed reconstruction conditions apply to most BTT methods for parameter identification or spectrum reconstruction and provide guidance for BTT measurement. Finally, the effectiveness of the proposed method and the correctness of the reconstruction conditions were demonstrated by a series of simulations and experiments.