Abstract: Despite the wide application of the blade tip timing as a non-contact measurement technique, its acquired displacement signal is undersampled in many situations. Compressed sensing is an effective means to reconstruct the undersampled signal. However, the reconstruction process introduces the regularization penalty to achieve sparsity, reducing the amplitude accuracy of the reconstructed signal at the same time, and affecting the accurate identification of blade vibration amplitude, which is highly significant in reconstructing the dynamic stress of the blade. This paper combines the design matrix of the blade vibration equation and the compressed sensing dictionary to identify parameters of the blade vibration equation without prior information. First, a compressed sensing dictionary is constructed according to the form of design matrix elements and the maximum vibration frequency of interests. Second, atoms are extracted from the dictionary according to the indices of non-zero elements in the sparse representation of the blade tip timing signal, and parameters of the vibration equation are calculated. Third, Blade Tip Timing (BTT) simulation results demonstrate that the proposed method can accurately identify parameters of the vibration equation with both single-mode and multi-mode vibrations. Finally, experimental results of rotor blades show that the relative error of the identified natural frequency between using strain gage and using blade tip timing with compressed sensing is only 0.14%; the transmissibility of blade tip displacement to certain points strain of the four blades is compared and the maximum percentage of deviation from the mean is only 2.15%.

Key words: blade tip timing, compressed sensing, amplitude identification, natural frequency identification, rotor blades