Spatial transformation of general sampling-aliasing frequency region for rotating-blade parameter identification with emphasis on single-probe blade tip-timing measurement

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.

Improved minimum variance distortionless response spectrum method for efficient and robust non-uniform undersampled frequency identification in blade tip timing

The noncontact blade tip timing(BTT)measurement has been an attractive technology for blade health monitoring(BHM).However,the severe undersampled BTT signal causes a significant challenge for blade vibration parameter identification and fault feature extraction.This study proposes a novel method based on the minimum variance distortionless response(MVDR)of the direction of arrival(DoA)estimation for blade natural frequency estimation from the non-uniformly undersampled BTT signals.First,based on the similarity between the general data acquisition model for BTT and the antenna array model in DoA estimation,the circumferentially arranged probes on the casing can be regarded as a non-uniform linear array.Thus,BTT signal reconstruction is converted into the DoA estimation problem of the non-uniform linear array signal.Second,MVDR is employed to address the severe undersampling issue and recover the BTT undersampled signal.In particular,spatial smoothing is innovatively utilized to enhance the estimation of covariance matrix of the BTT signal to avoid ill-condition or singularity,while improving efficiency and robustness.Lastly,numerical simulation and experimental testing are employed to verify the validity of the proposed method.Monte Carlo simulation results suggest that the proposed method behaves better than conventional methods,especially under a lower signal-to-noise ratio condition.Experimental results indicate that the proposed method can effectively overcome the severe undersampling problem of BTT signal induced by physical limitations,and has a strong potential in the field of BHM.