Gridless compressed covariance sensing for parameter identification of nonuniform and undersampled blade tip timing data

Due to the harsh working environments, rotating blades are susceptible to failures, which endanger the operational safety of turbomachinery; thus, it is important to monitor rotating blades to promptly detect incipient failure. Blade tip timing (BTT) is a promising approach for monitoring the health of rotating blades owing to its noncontact nature, high measurement efficiency, and long service life. However, the large gap between the high vibration frequency and low sampling frequency results in severe undersampling of the BTT signal. Although advanced methods have been proposed to reconstruct the spectrum or identify parameters from BTT signal, almost all of them face basis mismatch issue caused by frequency discretization and suffers from inevitable reconstruction errors. To overcome these limitations, we developed a gridless compressed covariance sensing (GCCS) approach for the sparse spectral estimation and parameter identification of BTT data. Unlike existing methods relying on frequency discretization, GCCS directly performs a continuous range of spectrum reconstruction and parameter estimation. We derived that GCCS is equivalent to a weighted atomic norm minimization (ANM) with the weight function linked to the Capon spectrum, which implies the advantages of GCCS over methods based on conventional ANM. GCCS involves two core steps, first, covariance (matrix) recovery from compressive samples is formulated as a semidefinite programming; second, the extended Prony's method is employed as a postprocessing technique to retrieve vibration parameters from the covariance estimations, thereby achieving continuous parameter estimation. The quantitative comparison in the simulations and experiments shows the effectiveness of GCCS in overcoming basis mismatch and improving the accuracy and consistency of the parameter estimation.