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Sensors 2015, 15(2), 2419-2437; doi:10.3390/s150202419

A Non-Uniformly Under-Sampled Blade Tip-Timing Signal Reconstruction Method for Blade Vibration Monitoring

1
Science and Technology on Integrated Logistics Support Laboratory, National University of Defense Technology, Changsha 410073, China
2
Hunan Province Key Laboratory of Health Maintenance of Mechanical Equipment, Hunan University of Science and Technology, Xiangtan 411100, China
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 1 December 2014 / Accepted: 16 January 2015 / Published: 22 January 2015
(This article belongs to the Section Physical Sensors)
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Abstract

High-speed blades are often prone to fatigue due to severe blade vibrations. In particular, synchronous vibrations can cause irreversible damages to the blade. Blade tip-timing methods (BTT) have become a promising way to monitor blade vibrations. However, synchronous vibrations are unsuitably monitored by uniform BTT sampling. Therefore, non-equally mounted probes have been used, which will result in the non-uniformity of the sampling signal. Since under-sampling is an intrinsic drawback of BTT methods, how to analyze non-uniformly under-sampled BTT signals is a big challenge. In this paper, a novel reconstruction method for non-uniformly under-sampled BTT data is presented. The method is based on the periodically non-uniform sampling theorem. Firstly, a mathematical model of a non-uniform BTT sampling process is built. It can be treated as the sum of certain uniform sample streams. For each stream, an interpolating function is required to prevent aliasing in the reconstructed signal. Secondly, simultaneous equations of all interpolating functions in each sub-band are built and corresponding solutions are ultimately derived to remove unwanted replicas of the original signal caused by the sampling, which may overlay the original signal. In the end, numerical simulations and experiments are carried out to validate the feasibility of the proposed method. The results demonstrate the accuracy of the reconstructed signal depends on the sampling frequency, the blade vibration frequency, the blade vibration bandwidth, the probe static offset and the number of samples. In practice, both types of blade vibration signals can be particularly reconstructed by non-uniform BTT data acquired from only two probes. View Full-Text
Keywords: blade tip-timing; non-uniformly sampled signal; under-sampled signal reconstruction; on-line vibration; band-pass sampling blade tip-timing; non-uniformly sampled signal; under-sampled signal reconstruction; on-line vibration; band-pass sampling
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Hu, Z.; Lin, J.; Chen, Z.-S.; Yang, Y.-M.; Li, X.-J. A Non-Uniformly Under-Sampled Blade Tip-Timing Signal Reconstruction Method for Blade Vibration Monitoring. Sensors 2015, 15, 2419-2437.

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