Statistical blade tip timing measurement, Part I: Covariance architecture

Blade tip timing (BTT) is a promising vibration measurement technique for rotating blades owing to its non-contact nature, high efficiency, and long service life. However, due to the mismatch between the high vibration frequency of blades and the low achievable sampling frequency, BTT signal is undersampled and thus it is hard to extract characteristic parameters. To address this critical issue in the application of BTT technique, we shift the attention from the signal itself to its statistics and propose the concept of statistical BTT measurement. In the first part of series papers, we focus on the second-order statistic, i.e., covariance, and develop a covariance architecture containing two aspects: deterministic layout optimization and covariance-based parameter identification. We prove that the covariance carries the vibration parameters (frequency and amplitude) of the signal itself and the consecutive covariance samples are estimable from the sub-Nyquist samples. Inspired by these two findings, we derive a special family of layouts referred to as universal covariance layout (UCL) that physically guarantees the estimability of consecutive covariance samples. To facilitate application, a series of concrete UCLs are designed for users. Owing to UCLs, subsequent parameter identification can be efficiently implemented. The proposed method overcomes the undersampling issue of BTT and shows a higher computational efficiency in parameter identification than existing BTT methods.