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Article

Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis

by
Tareq Al-hababi
1,2,†,
Nizar Faisal Alkayem
2,3,†,
Huaxin Zhu
4,
Li Cui
5,
Shixiang Zhang
6 and
Maosen Cao
1,*
1
Department of Engineering Mechanics, Hohai University, Nanjing 210098, China
2
Anhui Provincial International Joint Research Center of Data Diagnosis and Smart Maintenance on Bridge Structures, Chuzhou University, Chuzhou 239000, China
3
College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
4
Jiangsu Zhongji Engineering Technology Research Co., Ltd., Nantong 226001, China
5
College of Civil and Architecture Engineering, Chuzhou University, Chuzhou 239000, China
6
College of Civil Engineering, Southeast University, Nanjing 210000, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2022, 10(11), 1853; https://doi.org/10.3390/math10111853
Submission received: 12 March 2022 / Revised: 22 May 2022 / Accepted: 25 May 2022 / Published: 28 May 2022
(This article belongs to the Section E: Applied Mathematics)
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Abstract

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities.
Keywords: breathing cracks; multiple cracks; damage localization; non-Gaussianity; random vibration; statistical methods; Shannon entropy breathing cracks; multiple cracks; damage localization; non-Gaussianity; random vibration; statistical methods; Shannon entropy

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MDPI and ACS Style

Al-hababi, T.; Alkayem, N.F.; Zhu, H.; Cui, L.; Zhang, S.; Cao, M. Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis. Mathematics 2022, 10, 1853. https://doi.org/10.3390/math10111853

AMA Style

Al-hababi T, Alkayem NF, Zhu H, Cui L, Zhang S, Cao M. Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis. Mathematics. 2022; 10(11):1853. https://doi.org/10.3390/math10111853

Chicago/Turabian Style

Al-hababi, Tareq, Nizar Faisal Alkayem, Huaxin Zhu, Li Cui, Shixiang Zhang, and Maosen Cao. 2022. "Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis" Mathematics 10, no. 11: 1853. https://doi.org/10.3390/math10111853

APA Style

Al-hababi, T., Alkayem, N. F., Zhu, H., Cui, L., Zhang, S., & Cao, M. (2022). Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis. Mathematics, 10(11), 1853. https://doi.org/10.3390/math10111853

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