Compressed Sensing-based Blade Tip-timing Vibration Reconstruction under Variable Speeds

Blade tip-timing (BTT) has been regarded as a promising solution of on-line blade vibration monitoring. The rotating speed is often considered to be constant in traditional BTT methods. In practice, this assumption is hardly satisfied, so that BTT vibration monitoring under variable speeds faces is a big problem to be solved. Moreover, BTT vibration signals are always under-sampled due to the limited number of BTT probes and multi-band with less prior knowledge due to system's nonlinearity and complicated aerodynamic excitations. Thus blind multi-band vibration reconstruction under variable speeds is a key challenge by using under-sampled BTT signals. To deal with it, a novel compressed sensing (CS) method in angular domain is proposed to overcome the challenge in this paper. First, angular-domain sampling model of BTT signals is built and its multi-coset sampling scheme is first presented. Then the CS model of BTT signals is derived in order domain. Two metrics of the support reconstruction ratio and the relative root mean square are defined to characterize the reconstruction performance in order and angular domains, respectively. In next simulations, the performances of four reconstruction algorithms are compared, i.e., Orthogonal Matching Pursuit, Multiple Signal Classification, Modified Focal Under-determined System Solver and Basis Pursuit Denoising algorithms. Influences of different algorithms and measurement noises on the reconstruction performance are simulated.

[1]  Minghao Pan,et al.  Sparse Representation Based Frequency Detection and Uncertainty Reduction in Blade Tip Timing Measurement for Multi-Mode Blade Vibration Monitoring , 2017, Sensors.

[2]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[3]  Craig Lawson,et al.  Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearanc , 2005 .

[4]  Yongmin Yang,et al.  Damage detection in high-speed rotated blades by blade tip-timing method based on compressed sensing , 2017, 2017 Prognostics and System Health Management Conference (PHM-Harbin).

[5]  Y. Bresler Spectrum-blind sampling and compressive sensing for continuous-index signals , 2008, 2008 Information Theory and Applications Workshop.

[6]  Zheng Hu,et al.  Sparse reconstruction of blade tip-timing signals for multi-mode blade vibration monitoring , 2016 .

[7]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[8]  P. Tappert,et al.  Health monitoring and prognostics of blades and disks with blade tip sensors , 2000, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484).

[9]  Marc Berthillier,et al.  Identification of modal parameters and aeroelastic coefficients in bladed disk assemblies , 2009 .

[10]  Yoram Bresler,et al.  Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals , 2001, IEEE Trans. Signal Process..

[11]  Hu Zheng,et al.  Blade damage prognosis based on kernel principal component analysis and grey model using subsampled tip-timing signals , 2014 .

[12]  Moslem Rashidi,et al.  Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio , 2010, ArXiv.

[13]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[14]  Zhongsheng Chen,et al.  A comprehensive review on blade tip timing-based health monitoring: status and future , 2021 .

[15]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[16]  Yongmin Yang,et al.  Nonlinear Dynamic Behaviors of Rotated Blades with Small Breathing Cracks Based on Vibration Power Flow Analysis , 2016 .

[17]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[18]  Zhongsheng Chen,et al.  Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades , 2017 .

[19]  Yongmin Yang,et al.  A Non-Uniformly Under-Sampled Blade Tip-Timing Signal Reconstruction Method for Blade Vibration Monitoring , 2015, Sensors.

[20]  Rodrigo Nicoletti,et al.  Applying Compressed Sensing to Blade Tip Timing Data: A Parametric Analysis , 2018 .

[21]  Anindya Ghoshal,et al.  Structural health monitoring techniques for wind turbine blades , 2000 .

[22]  David L. Donoho,et al.  Precise Undersampling Theorems , 2010, Proceedings of the IEEE.

[23]  Jing He,et al.  Reconstructed Order Analysis-Based Vibration Monitoring under Variable Rotation Speed by Using Multiple Blade Tip-Timing Sensors , 2018, Sensors.

[24]  Zheng Hu,et al.  Non-contact crack detection of high-speed blades based on principal component analysis and Euclidian angles using optical-fiber sensors , 2013 .

[25]  Moslem Rashidi Avendi Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio , 2010 .