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

Abstract

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.

Graphical abstract

Keywords

blade tip timing (BTT) / frequency identification / minimum variance distortionless response (MVDR) / undersampled / blade health monitoring (BHM)

References

[1] Oakley S Y, Nowell D. Prediction of the combined high- and low-cycle fatigue performance of gas turbine blades after foreign object damage. International Journal of Fatigue, 2007, 29(1): 69–80

[2] Yang L H, Yang Z S, Mao Z, Wu S M, Chen X F, Yan R Q. Dynamic characteristic analysis of rotating blade with transverse crack—part I: modeling, modification, and validation. Journal of Vibration and Acoustics, 2021, 143(5): 051010

[3] Yang L H, Yang Z S, Mao Z, Wu S M, Chen X F, Yan R Q. Dynamic characteristic analysis of rotating blade with transverse crack—part II: a comparison study of different crack models. Journal of Vibration and Acoustics, 2021, 143(5): 051011

[4] Lawson C P, Ivey P C. Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearance probes. Sensors and Actuators A: Physical, 2005, 118(1): 14–24

[5] Di Maio D, Ewins D J. Experimental measurements of out-of-plane vibrations of a simple blisk design using blade tip timing and scanning LDV measurement methods. Mechanical Systems and Signal Processing, 2012, 28: 517–527

[6] ChanaK SCardwell D N. The use of eddy current sensor based blade tip timing for FOD detection. In: Proceedings of the ASME Turbo Expo 2008: Power for Land, Sea, and Air. Berlin: ASME, 2008, 169–178

[7] RusshardP. The rise and fall of the rotor blade strain gauge. In: Sinha J K, ed. Vibration Engineering and Technology of Machinery. Cham: Springer, 2015, 27–37

[8] Kadambi J R, Quinn R D, Adams M L. Turbomachinery blade vibration and dynamic stress measurements utilizing nonintrusive techniques. Journal of Turbomachinery, 1989, 111(4): 468–474

[9] RusshardP. Development of a blade tip timing based engine health monitoring system. Dissertation for the Doctoral Degree. Manchester: The University of Manchester, 2010

[10] KharytonVDimitriadis GDefiseC. A discussion on the advancement of blade tip timing data processing. In: Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Charlotte: ASME, 2017, V07BT35A002

[11] Chen Z S, Sheng H, Xia Y M, Wang W M, He J. A comprehensive review on blade tip timing-based health monitoring: status and future. Mechanical Systems and Signal Processing, 2021, 149: 107330

[12] Campbell W. Elastic-fluid turbine rotor and method of avoiding tangential bucket vibration therein. US Patent, 1502904, 1924-07-29

[13] ZablotskiyI YKorostelevY A. Measurement of Resonance Vibrations of Turbine Blades with the Elura Device. Technical Report NTIS 197915, 1978

[14] Dimitriadis G, Carrington I B, Wright J R, Cooper J E. Blade-tip timing measurement of synchronous vibrations of rotating bladed assemblies. Mechanical Systems and Signal Processing, 2002, 16(4): 599–622

[15] Carrington I B, Wright J R, Cooper J E, Dimitriadis G. A comparison of blade tip-timing data analysis methods. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2001, 215(5): 301–312

[16] JoungK KKang S CPaengK SParkN GChoiH J YouY Jvon Flotow A. Analysis of vibration of the turbine blades using non-intrusive stress measurement system. In: Proceedings of the ASME 2006 Power Conference. Atlanta: ASME, 2006, 391–397

[17] ZhangY GDuan F JFangZ QYeS HShiX H. Frequency identification technique for asynchronous vibration of rotating blades. Journal of Vibration and Shock, 2007, 12: 106–108, 106–108 (in Chinese)

[18] VercoutterABerthillier MTalonABurgardtBLardiesJ. Estimation of turbomachinery blade vibrations from tip-timing data. In: Proceedings of the 10th International Conference on Vibrations in Rotating Machinery. London: Woodhead Publishing, 2012, 233–245

[19] Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306

[20] Lin J, Hu Z, Chen Z S, Yang Y M, Xu H L. Sparse reconstruction of blade tip-timing signals for multi-mode blade vibration monitoring. Mechanical Systems and Signal Processing, 2016, 81: 250–258

[21] Wu S M, Zhao Z B, Yang Z B, Tian S H, Yang L H, Chen X F. Physical constraints fused equiangular tight frame method for blade tip timing sensor arrangement. Measurement, 2019, 145: 841–851

[22] Li H Q, Yang Z B, Wu S M, Wang Z K, Tian S H, Yan R Q, Chen X F. Adaptive iterative approach for efficient signal processing of blade tip timing. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1–13

[23] Chen S Y, Yang Y M, Hu H F, Guan F J, Shen G J, Bian Z F, Guo H N. Blind interpolation for multi-frequency blade tip timing signals. Mechanical Systems and Signal Processing, 2022, 172: 108946

[24] Dong J N, Li H K, Fan Z F, Zhao X W, Wei D T, Chen Y G. Characteristics analysis of blade tip timing signals in synchronous resonance and frequency recovery based on subspace pursuit algorithm. Mechanical Systems and Signal Processing, 2023, 183: 109632

[25] StéphanCBerthillierMLardiès JTalonA. Tip-timing data analysis for mistuned bladed discs assemblies. In: Proceedings of the ASME Turbo Expo 2008: Power for Land, Sea, and Air. Berlin: ASME, 2008, 447–455

[26] Liu Z B, Duan F J, Niu G Y, Ye D C, Feng J N, Cheng Z H, Fu X, Jiang J J, Zhu J, Liu M R. Reconstruction of blade tip-timing signals based on the MUSIC algorithm. Mechanical Systems and Signal Processing, 2022, 163: 108137

[27] Wang Z K, Yang Z B, Wu S M, Li H Q, Tian S H, Chen X F. An improved multiple signal classification for nonuniform sampling in blade tip timing. IEEE Transactions on Instrumentation and Measurement, 2020, 69(10): 7941–7952

[28] Wang P, Karg D, Fan Z Y, Gao R X, Kwolek K, Consiglio A. Non-contact identification of rotating blade vibration. Mechanical Engineering Journal, 2015, 2(3): 15–00025

[29] Capon J. High-resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 1969, 57(8): 1408–1418

[30] Lacoss R T. Data adaptive spectral analysis methods. Geophysics, 1971, 36(4): 661–675

[31] Benesty J, Chen J D, Huang Y T. A generalized MVDR spectrum. IEEE Signal Processing Letters, 2005, 12(12): 827–830

[32] Liepin’Sh V Y. An algorithm for evaluating a discrete Fourier transform for incomplete data. Automatic Control and Computer Sciences, 1996, 30: 20–29

[33] Shan T J, Wax M, Kailath T. On spatial smoothing for direction-of-arrival estimation of coherent signals. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985, 33(4): 806–811

[34] Wu S M, Russhard P, Yan R Q, Tian S H, Wang S B, Zhao Z B, Chen X F. An adaptive online blade health monitoring method: from raw data to parameters identification. IEEE Transactions on Instrumentation and Measurement, 2020, 69(5): 2581–2592

[35] GreitansM. Multiband signal processing by using nonuniform sampling and iterative updating of autocorrelation matrix. In: Proceedings of the 2001 International Conference on Sampling Theory and Application. Orlando, 2001, 85–89

[36] PatiY CRezaiifar RKrishnaprasadP S. Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers. Pacific Grove: IEEE, 1993, 40–44

[37] Bouchain A, Picheral J, Lahalle E, Chardon G, Vercoutter A, Talon A. Blade vibration study by spectral analysis of tip-timing signals with OMP algorithm. Mechanical Systems and Signal Processing, 2019, 130: 108–121

[38] Boyd S, Parikh N, Chu E, Peleato B, Eckstein J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Foundations and Trends, 2011, 3(1): 1–122

[39] Stoica P, Li H, He H. Spectral analysis of nonuniformly sampled data: a new approach versus the periodogram. IEEE Transactions on Signal Processing, 2009, 57(3): 843–858

[40] Hajnayeb A, Nikpour M, Moradi S, Rossi G. A new reference tip-timing test bench and simulator for blade synchronous and asynchronous vibrations. Measurement Science & Technology, 2018, 29(2): 025203

[41] Beauseroy P, Lengellé R. Nonintrusive turbomachine blade vibration measurement system. Mechanical Systems and Signal Processing, 2007, 21(4): 1717–1738

[42] Wang Z K, Yang Z B, Li H Q, Cao J H, Tian S H, Chen X F. Automatic tracking of natural frequency in the time–frequency domain for blade tip timing. Journal of Sound and Vibration, 2022, 516: 116522

RIGHTS & PERMISSIONS

Higher Education Press