Block-MUSIC in blade tip timing: Performance study of block snapshot matrix

Periodic nonuniform sampling can be viewed as a combination of uniform sampling and non-uniform sampling. Blade tip timing (BTT) technique conforms to this sampling pattern, where non-uniformity and uniformity are caused by non-uniform probe layout and rotational motion, respectively. By introducing block structure into multiple signal classification (MUSIC) for the extension of snapshot matrix, Block-MUSIC has been proved to be anti-aliasing and can filter out synchronous frequency in BTT application. However, the theoretical justification of the block structure is lacking. In this paper, a performance study of Block-MUSIC is conducted from three aspects: identifiability, stability, and resolution. Additionally, a pseudo 2-dimensional signal model is proposed to represent the periodic nonuniform sampled signal under the assumption of equally spaced probes. To support the performance study, simulations and experiments are carried out to demonstrate how the size of the snapshot matrix, the noise level, and the amplitude of sinusoidal signals affect algorithm performance. Simulation codes are available at https://github.com/superjdg/block-music4btt.