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Blade Tip Timing Technology (BTT) is a new type of blade vibration measurement method with non-contact measurement capabilities, which is associated with high efficiency and convenience. However, due to under-sampling feature of the BTT signal, the method can only measure part of the vibration information. Therefore, various BTT spectral reconstruction algorithms have been developed based on the under-sampling feature and sparsity of the blade vibration spectrum. Because of the harsh working environment of the blades, BTT signal typically contains high-level Gaussian noise in actual measurement, which significantly reduces frequency-domain sparsity and even aliases the vibration modals, resulting in a decrease in the performance of sparse reconstruction algorithms. In this paper, a multi-sequences BTT signal noise reduction method is proposed, which is based on sparse representation to suppress Gaussian noise. Through appropriately modifying the constraint in the ℓ0 optimization problem, the method filters out the noise elements in the sparse vector of the BTT signal. Then, denoising is completed by sparse inverse transformation. Finally, a global average-based singular value decomposition dictionary learning algorithm (GA-K-SVD) is proposed to generate an over-complete sparse dictionary which is adaptable to the original signal, to increase the effectiveness of GA-K-SVD. At last, simulation and experience are carried out to verify the performance optimization effect for sparse reconstruction algorithm and the effectiveness of proposed noise reduction method. [ABSTRACT FROM AUTHOR]

Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities. [ABSTRACT FROM AUTHOR]