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.

叶片尖端定时（BTT）是评估叶片振动的最重要的非接触式监测方法之一。BTT主要包括两个步骤：1）通过光学探针获取旋转刀片产生的原始脉冲信号。2）通过高精度计数器获得原始脉冲的到达时间，然后将其转换为偏转。BTT测量涉及多种噪声，由于叶片振动和传输路径的复杂性和多样性，操作环境的变化使操作更加复杂。通过引入先验知识，稀疏表示已被证明是用于重建叶片振动特征的有前途的工具。但是，在BTT中应用了经典的稀疏表示模型，噪声是根据简单的假设（即噪声遵循高斯分布）来制定和执行的。该假设对于实际实践而言过于理想，限制了BTT中稀疏表示的性能提升。为了解决这个问题并表示未知噪声，在这项工作中提出了一个基于高斯混合（MoG）的鲁棒的稀疏表示模型。然后从期望最大化（EM）算法的角度导出所提出模型的求解算法。为了验证本方法的有效性，针对不同的常规项目讨论了所开发方法的性能。为了解决这个问题并表示未知噪声，在这项工作中提出了一个基于高斯混合（MoG）的鲁棒的稀疏表示模型。然后从期望最大化（EM）算法的角度导出所提出模型的求解算法。为了验证本方法的有效性，针对不同的常规项目讨论了所开发方法的性能。为了解决这个问题并表示未知噪声，在这项工作中提出了一个基于高斯混合（MoG）的鲁棒的稀疏表示模型。然后从期望最大化（EM）算法的角度导出所提出模型的求解算法。为了验证本方法的有效性，针对不同的常规项目讨论了所开发方法的性能。