Sparsity-based Compressed Covariance Sensing for Spectrum Reconstruction in Blade Tip Timing

Rotating blades play a functional role during the operation of an aero-engine. To ensure safety, it is urgently needed to monitor the blade condition. Blade tip timing (BTT) is a potential vibration measurement technique for rotating blades owing to its non-contact and efficiency. However, the undersampling characteristic of BTT signal hinders the sub-sequent signal processing for condition monitoring and fault diagnosis. In this paper, the autocorrelation/covariance samples replaced signal samples for spectrum reconstruction. On this basis, we proposed a sparsity-based compressed covariance sensing for spectrum reconstruction of BTT signals. Because of the additional correlation operation, obtainable autocorrelation samples are denser than signal samples. Furthermore, the same sparsity of BTT signal and its autocorrelation in the frequency domain ensures the correctness of sparse representation model for autocorrelation samples. Additionally, owing to the dense autocorrelation samples, the proposed method can overcome the problem of the lack of probes. Both simulation and experiment demonstrated the effectiveness of the proposed method.