Due to the harsh operating environment, turbine blades are highly prone to failure, posing significant risks to equipment safety. Therefore, research on blade monitoring and diagnosis is of critical importance. Blade Tip-Timing (BTT) is a promising measure-ment 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 lay-outs, 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.
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