连续压缩感知叶端定时频率估计方法

doi:10.7527/S1000-6893.2025.31620

Abstract

Abstract:

Due to the harsh operating environment， turbine blades are highly susceptible to failures， posing significant risks to equipment safety. Therefore， research on blade monitoring and diagnosis is of critical importance. Blade Tip-Timing （BTT） is a promising measurement 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 layouts， 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.

Key words: blade vibration, blade tip-timing, gridless frequency estimation, Vandermonde decomposition, manifold separation

CLC Number:

V216.8

Ruochen JIN, Zhibo YANG, Laihao YANG, Baijie QIAO, Junnan FENG, Huan ZHANG, Zhijun YANG, Xuefeng CHEN. Frequency estimation method for blade tip timing using continuous compressed sensing[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(17): 231620.

Figures/Tables 9

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References 27

[1]	HEATH S， IMREGUN M. An improved single-parameter tip-timing method for turbomachinery blade vibration measurements using optical laser probes［J］. International Journal of Mechanical Sciences， 1996， 38（10）： 1047-1058.
[2]	G D， I B C， J R W， et al. Blade-tip timing measurement of synchronous vibrations of rotating bladed assemblies［J］. Mechanical Systems and Signal Processing， 2002， 16（4）： 599-622.
[3]	ZABLOTSKIY I Y， KOROSTELEV Y A. Measurement of resonance vibrations of turbine blades with the elura device［J］. Asia-Pacific Journal of Teacher Education， 1999， 27（4）： 61-75.
[4]	LI H K， FAN Z F， DONG J N， et al. An improved blade vibration difference-based two-parameter plot method for synchronous vibration parameter identification of rotating blades［J］. Measurement， 2023， 207： 112397.
[5]	HEATH S. A new technique for identifying synchronous resonances using tip-timing［J］. Journal of Engineering for Gas Turbines and Power， 2000， 122（2）： 219-225.
[6]	GURU S S， SHYLAJA S， KUMAR S， et al. Pre-emptive rotor blade damage identification by blade tip timing method［J］. Journal of Engineering for Gas Turbines and Power， 2014， 136（7）： 072503.
[7]	BASTAMI A R， SAFARPOUR P， MIKAEILY A， et al. Identification of asynchronous blade vibration parameters by linear regression of blade tip timing data［J］. Journal of Engineering for Gas Turbines and Power， 2018， 140（7）： 072506.
[8]	JOUNG K K， KANG S C， PAENG K S， et al. Analysis of vibration of the turbine blades using non-intrusive stress measurement system［C］∥ASME 2006 Power Conference， New York：ASME， 2008： 391-397.
[9]	YANG L H， MAO Z， CHEN X F， et al. Dynamic coupling vibration of rotating shaft-disc-blade system： Modeling， mechanism analysis and numerical study［J］. Mechanism and Machine Theory， 2022， 167： 104542.
[10]	WU Z Y， YAN H， ZHAO L C， et al. Axial-bending coupling vibration characteristics of a rotating blade with breathing crack［J］. Mechanical Systems and Signal Processing， 2023， 182： 109547.
[11]	VERCOUTTER A， BERTHILLIER M， TALON A， et al. Tip timing spectral estimation method for aeroelastic vibrations of turbomachinery blades［C］∥International Forum on Aeroelasticity and Structural Dynamics （IFASD）. Paris：IFASD， 2011： 26-30.
[12]	WANG P， KARG D， FAN Z Y， et al. Non-contact identification of rotating blade vibration［J］. Mechanical Engineering Journal， 2015， 2（3）： 15-25-15-00025.
[13]	WANG Z K， YANG Z B， TENG G R， et al. Amplitude-identifiable MUSIC （aid-MUSIC） for asynchronous frequency in blade tip timing［J］. IEEE Transactions on Industrial Informatics， 2023， 19（4）： 5732-5742.
[14]	LIU Z B， DUAN F J， NIU G Y， et al. Reconstruction of blade tip-timing signals based on the MUSIC algorithm［J］. Mechanical Systems and Signal Processing， 2022， 163： 108137.
[15]	LIN J， HU Z， CHEN Z S， et al. Sparse reconstruction of blade tip-timing signals for multi-mode blade vibration monitoring［J］. Mechanical Systems and Signal Processing， 2016， 81： 250-258.
[16]	BOUCHAIN A， PICHERAL J， LAHALLE E， et al. Blade vibration study by spectral analysis of tip-timing signals with OMP algorithm［J］. Mechanical Systems and Signal Processing， 2019， 130： 108-121.
[17]	WU S M， RUSSHARD P， YAN R Q， et al. An adaptive online blade health monitoring method： From raw data to parameters identification［J］. IEEE Transactions on Instrumentation and Measurement， 2020， 69（5）： 2581-2592.
[18]	DONG J N， LI H K， FAN Z F， et al. Characteristics analysis of blade tip timing signals in synchronous resonance and frequency recovery based on subspace pursuit algorithm［J］. Mechanical Systems and Signal Processing， 2023， 183： 109632.
[19]	CHI Y J， PEZESHKI A， SCHARF L， et al. Sensitivity to basis mismatch in compressed sensing［C］∥2010 IEEE International Conference on Acoustics， Speech and Signal Processing. Piscataway： IEEE Press， 2010： 3930-3933.
[20]	BERNHARDT S， BOYER R， MARCOS S， et al. Compressed sensing with basis mismatch： performance bounds and sparse-based estimator［J］. IEEE Transactions on Signal Processing， 2016， 64（13）： 3483-3494.
[21]	FANG J， WANG F Y， SHEN Y N， et al. Super-resolution compressed sensing for line spectral estimation： An iterative reweighted approach［J］. IEEE Transactions on Signal Processing， 2016， 64（18）： 4649-4662.
[22]	ZHU H， LEUS G， GIANNAKIS G B. Sparsity-cognizant total least-squares for perturbed compressive sampling［J］. IEEE Transactions on Signal Processing， 2011， 59（5）： 2002-2016.
[23]	PISARENKO V F. The retrieval of harmonics from a covariance function［J］. Geophysical Journal of the Royal Astronomical Society， 1973， 33（3）： 347-366.
[24]	TANG G G， BHASKAR B N， SHAH P， et al. Compressed sensing off the grid［J］. IEEE Transactions on Information Theory， 2013， 59（11）： 7465-7490.
[25]	BHASKAR B N， TANG G G， RECHT B. Atomic norm denoising with applications to line spectral estimation［J］. IEEE Transactions on Signal Processing， 2013， 61（23）： 5987-5999.
[26]	CHI Y J， FERREIRA DA COSTA M. Harnessing sparsity over the continuum： Atomic norm minimization for superresolution［J］. IEEE Signal Processing Magazine， 2020， 37（2）： 39-57.
[27]	JIN R C， YANG L H， YANG Z B， et al. The connection between digital-twin model and physical space for rotating blade： An atomic norm-based BTT undersampled signal reconstruction method［J］. Structural and Multidisciplinary Optimization， 2023， 66（1）： 27.

编号	频率/Hz	幅值/mm
1	121.3	1.2
2	623.1	1.3
3	841.7	0.7

项目	数值	项目	数值
叶盘半径/mm	50	叶片长度/mm	48
叶盘厚度/mm	20	叶片厚度/mm	1
叶片个数	8	叶片宽度/mm	20

Frequency estimation method for blade tip timing using continuous compressed sensing

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