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Shock and Vibration
Volume 2016 (2016), Article ID 2375859, 17 pages
Research Article

Multicrack Localization in Rotors Based on Proper Orthogonal Decomposition Using Fractal Dimension and Gapped Smoothing Method

1School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2School of Engineering, University of Liverpool, Liverpool L69 3GH, UK
3The State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, China

Received 30 May 2016; Revised 2 August 2016; Accepted 4 September 2016

Academic Editor: Marcello Vanali

Copyright © 2016 Zhiwen Lu 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.


Multicrack localization in operating rotor systems is still a challenge today. Focusing on this challenge, a new approach based on proper orthogonal decomposition (POD) is proposed for multicrack localization in rotors. A two-disc rotor-bearing system with breathing cracks is established by the finite element method and simulated sensors are distributed along the rotor to obtain the steady-state transverse responses required by POD. Based on the discontinuities introduced in the proper orthogonal modes (POMs) at the locations of cracks, the characteristic POM (CPOM), which is sensitive to crack locations and robust to noise, is selected for cracks localization. Instead of using the CPOM directly, due to its difficulty to localize incipient cracks, damage indexes using fractal dimension (FD) and gapped smoothing method (GSM) are adopted, in order to extract the locations more efficiently. The method proposed in this work is validated to be effective for multicrack localization in rotors by numerical experiments on rotors in different crack configuration cases considering the effects of noise. In addition, the feasibility of using fewer sensors is also investigated.