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Mathematical Problems in Engineering
Volume 2018, Article ID 3494785, 10 pages
Research Article

A Novel Multidimensional Frequency Band Energy Ratio Analysis Method for the Pressure Fluctuation of Francis Turbine

1Key Laboratory of Transients in Hydraulic Machinery, Wuhan University, Ministry of Education, Wuhan 430072, China
2Jiangxi Province Key Laboratory of Precision Drive & Control, Nanchang 330029, China
3Zhejiang Energy Beihai Hydropower Co., Ltd., Hangzhou 320002, China

Correspondence should be addressed to Qijuan Chen; nc.ude.uhw@nehcjq

Received 27 August 2017; Revised 27 November 2017; Accepted 26 December 2017; Published 21 January 2018

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2018 Weiyu Wang et al. 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.


The pressure fluctuation has multiple influence on the steady operation of Francis turbine, and the impact degree varies with the operation condition. In this paper, for the analysis of pressure fluctuation in the Francis turbine, a novel feature extraction method of multidimensional frequency bands energy ratio is proposed based on Hilbert Huang Transform (HHT). Firstly, the pressure fluctuation signal is decomposed into intrinsic mode functions (IMFs) by EEMD. Secondly, the Hilbert marginal spectrum is utilized to analyze the frequency characteristics of IMFs. Then, according to the inner frequency of IMFs, each of them is divided into high, medium, or low frequency band which are constructed based on the frequency characteristic of the pressure fluctuations in the Francis turbine. Afterward, the energy ratio of each frequency band to the original signal is calculated, which is to realize the feature extraction of multidimensional frequency band energy ratio. Actual applications verify that this method not only can extract the time-frequency characteristics but also can analyze the condition feature of the pressure fluctuation. It is a novel method for extracting the feature of pressure fluctuation in the Francis turbine.