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Mathematical Problems in Engineering
Volume 2015, Article ID 535398, 14 pages
Research Article

Incipient Gearbox Fault Diagnosis Based on the Reverse State Transformation of the Chaotic Duffing Oscillator and Sampling Integral Technology

1Department of Basic Courses, Mechanical Engineering College, Shijiazhuang 050003, China
2Department of Management, Mechanical Engineering College, Shijiazhuang 050003, China

Received 31 October 2014; Revised 20 January 2015; Accepted 3 February 2015

Academic Editor: Miguel A. F. Sanjuan

Copyright © 2015 Li Jie and Zhao Jianmin. 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.


Incipient fault for a gearbox diagnosis is difficult because the signals with low signal-to-noise ratio (SNR) are corrupted with background noise. A method based on chaos theory and sampling integral technology will be presented to detect the incipient fault of gearbox according to the characters of the gearbox vibration signals. Sampling integral technology was used to improve the tracking ability of fault signals with lower SNR. The small changes in the sidebands of meshing frequency can be detected by the transformation of chaotic phase diagram and its Hu moment invariants, and on this basis the incipient faults can be diagnosed. The results based on gearboxes experiment justify the effectiveness of the method.