Enhanced matrix completion technique for blade tip timing signal

Blade tip timing (BTT) is a potential non-contact vibration measurement for rotating blades. Identifying characteristic parameters or recovering the (power) spectrum of vibrations for condition monitoring from BTT data is a critical issue in the actual application. However, due to the measurement principle and installation restrictions, BTT signal is severely undersampled and then is hard to be analyzed by traditional signal processing methods. To clear the obstacle caused by undersampling on the application of BTT, we proposed an enhanced matrix completion technique (EMCT) for BTT signal post-processing. EMCT contains two procedures: covariance (matrix) reconstruction and followed by parameter estimations. First, based on the finding that the covariance matrix of BTT data is a low-rank and symmetric positive semidefinite Toeplitz matrix, we develop a matrix completion algorithm to reconstruct covariance. Then, based on the reconstructed covariance matrix, we extract frequency and amplitude/power parameters using root-MUSIC and least square algorithms. Due to dual structural prior, EMCT performs better than covariance-based methods relying on a single prior in estimation accuracy and precision. More importantly, EMCT also shows potential in reducing the number of probes. In addition, due to its gridless nature, EMCT is free from the basis mismatch issue and can achieve continuous parameter estimation. Finally, the effectiveness of EMCT has been repeatedly validated by both simulations and experiments.