Robust sparse representation model for blade tip timing

Blade tip timing (BTT) is one of the most important non-contact monitoring methods for blade vibration estimation. BTT predominantly consists of two steps: 1) acquiring the original pulse signal generated by the rotating blade through optical probes. 2) Obtaining the arrival time of the original pulses through a high-precision counter and then transforming it to deflection. Multiple noise is involved in BTT measurement, which is further complicated by the variable operating environment owing to the complexity and multiplicity of blade vibration and the transmission path. With the introduction of prior knowledge, sparse representation has proved a promising tool for the reconstruction of blade vibration features. However, the classical sparse representation model applied in BTT, is mostly formulated and conducted based on the simple assumption that the noise follows a Gaussian distribution. The assumption, too idealized for real practices, restricts the performance promotion of sparse representation in BTT. To address this problem and to represent the unknown noise, a robust sparse representation model based on a mixture of Gaussians (MoG) is proposed in this work. The solution algorithm of the proposed model is then derived from the perspective of the expectation maximization (EM) algorithm. To validate the effectiveness of the present method, the performance of the developed methodology is discussed in terms of different regular items.