Due to the harsh operating environment, turbine blades are highly susceptible to failures, posing significant risks to equipment safety. Therefore, research on blade monitoring and diagnosis is of critical importance. Blade Tip-Timing (BTT) is a promising measurement technique that enables the monitoring of all blades within a stage using only a small number of probes. However, due to the limited number of probes, BTT signals often suffer from severe undersampling, making high-accuracy signal reconstruction a key research focus in this field. Gridless frequency estimation methods based on continuous compressed sensing have been considered an effective solution to this issue. However, these traditional methods are limited to ideal signals obtained under uniform probe layouts, significantly restricting their applicability to real-world BTT signals. To address this limitation, this paper proposes a gridless frequency estimation method that is independent of probe layout, overcoming the constraints of traditional gridless approaches. First, a manifold separation-based Vandermonde decomposition is developed, effectively eliminating the impact of irregular probe layouts on the signal covariance matrix, enabling accurate frequency recovery from irregular Toeplitz matrices. Based on this, an alternating projection algorithm is proposed to achieve gridless frequency estimation under irregular layouts. Finally, extensive simulations and experiments demonstrate that the proposed method exhibits significant advantages in robustness, high resolution, and estimation accuracy.

Blade tip timing (BTT) is a non-contact measurement method for rotor blades. Its non-uniform sampling pattern is determined by the physical probe placement and rotational speed. Due to the lack of sampling probes and uneven placement, the anti-aliasing spectrum analysis for non-uniformly sampled signals becomes a hotspot in the BTT field. In this paper, a forward backward spatial smoothing (FBSS) method is used to estimate the autocorrelation matrix more accurately, which enables a better frequency identification ability for the autocorrelation matrix-based methods. Additionally, the relationship between the exponential complex steering vector and real-valued steering vectors is revealed. The peak significance is proposed to measure the quality of the pseudo spectrum. By taking multiple signal classification and minimum variance distortionless response as two example methods, the superiority of FBSS is demonstrated by simulations and experiments.

Blade-health monitoring is intensely required for turbomachinery because of the high failure risk of rotating blades. Blade-Tip Timing (BTT) is considered as the most promising technique for operational blade-vibration monitoring, which obtains the parameters that characterize the blade condition from recorded signals. However, its application is hindered by severe undersampling and stringent probe layouts. An inappropriate probe layout can make most of the existing methods invalid or inaccurate. Additionally, a general conflict arises between the allowed and required layouts because of arrangement restrictions. For the sake of economy and safety, parameter identification based on fewer probes has been preferred by users. In this work, a spatial-transformation-based method for parameter identification is proposed based on a single-probe BTT measurement. To present the general Sampling-Aliasing Frequency (SAFE) map definition, the traditional time–frequency analysis methods are extended to a time-sampling frequency. Then, a SAFE map is projected onto a parameter space using spatial transformation to extract the slope and intercept parameters, which can be physically interpreted as an engine order and a natural frequency using coordinate transformation. Finally, the effectiveness and robustness of the proposed method are verified by simulations and experiments under uniformly and nonuniformly variable speed conditions.