Identification of breathing cracks in a beam structure with entropy

A cantilever beam with a breathing crack is studied to detect and evaluate the crack using entropy measures. Closed cracks in engineering structures lead to proportional complexities to their vibration responses due to weak bi-linearity imposed by the crack breathing phenomenon. Entropy is a measure of system complexity and has the potential in quantifying the complexity. The weak bi-linearity in vibration signals can be amplified using wavelet transformation to increase the sensitivity of the measurements. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain dynamic responses. The bi-linearity in time domain signals due to the crack breathing are amplified by wavelet transformation first, and then the complexities due to bi-linearity is quantified using sample entropy to detect the possible crack and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% with the increase in the entropy values more than 10% compared with the healthy beam. The current study extends the entropy based damage detection of rotary machines to structural analysis and takes a step further in high-sensitivity structural health monitoring by combining wavelet transformation with entropy calculations. The proposed technique can also be applied to other types of structures, such as plates and shells.

[1]  Zhengjia He,et al.  Generalised local entropy analysis for crack detection in beam-like structures , 2014 .

[2]  F. Ismail,et al.  Identification of fatigue cracks from vibration testing , 1990 .

[3]  Jamshid Ghaboussi,et al.  Genetic algorithm in structural damage detection , 2001 .

[4]  A. M. R. Ribeiro,et al.  A review of vibration-based structural health monitoring with special emphasis on composite materials , 2006 .

[5]  Charles R. Farrar,et al.  A summary review of vibration-based damage identification methods , 1998 .

[6]  Young-Shin Lee,et al.  A study on crack detection using eigenfrequency test data , 2000 .

[7]  T. Chondros,et al.  Vibration of a Cracked Cantilever Beam , 1998 .

[8]  Wei-Xin Ren,et al.  Structural damage identification by using wavelet entropy , 2008 .

[9]  Quan Wang,et al.  Experimental studies on damage detection of beam structures with wavelet transform , 2011 .

[10]  Y. Yana,et al.  Development in vibration-based structural damage detection technique , 2007 .

[11]  Ka-Veng Yuen,et al.  On the complexity of artificial neural networks for smart structures monitoring , 2006 .

[12]  A. Shiryayev.  New Metric Invariant of Transitive Dynamical Systems and Automorphisms of Lebesgue Spaces , 1993 .

[13]  Robert X. Gao,et al.  Mechanical Systems and Signal Processing Approximate Entropy as a Diagnostic Tool for Machine Health Monitoring , 2006 .

[14]  Nan Wu,et al.  Study of forced vibration response of a beam with a breathing crack using iteration method , 2015 .

[15]  T. Chondros,et al.  VIBRATION OF A BEAM WITH A BREATHING CRACK , 2001 .

[16]  Tony Szturm,et al.  Using entropy measures to characterize human locomotion. , 2014, Journal of biomechanical engineering.

[17]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[18]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[19]  Paul Gerard Ducksbury.  Target detection and intelligent image compression , 2000, SPIE Defense + Commercial Sensing.

[20]  G. Owolabi,et al.  Crack detection in beams using changes in frequencies and amplitudes of frequency response functions , 2003 .

[21]  Oluremi Olatunbosun,et al.  A proposed method for fatigue crack detection and monitoring using the breathing crack phenomenon and wavelet analysis , 2007 .

[22]  Alessandro De Stefano,et al.  A novel approach to detecting breathing-fatigue cracks based on dynamic characteristics , 2013 .

[23]  S. Cheng,et al.  VIBRATIONAL RESPONSE OF A BEAM WITH A BREATHING CRACK , 1999 .

[24]  Long Zhang,et al.  Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference , 2010, Expert Syst. Appl..

[25]  Ya. G. Sinai,et al.  On the Notion of Entropy of a Dynamical System , 2010 .

[26]  W. Ostachowicz,et al.  Modelling and vibration analysis of a cantilever composite beam with a transverse open crack , 1995 .

[27]  Casimer M. DeCusatis,et al.  Wavelets and Subbands: Fundamentals and Applications , 2002 .

[28]  Antonino Morassi,et al.  Crack‐Induced Changes in Eigenparameters of Beam Structures , 1993 .

[29]  J. A. Brandon,et al.  The modelling of the opening and closure of a crack , 1995 .

[30]  Nikos A. Aspragathos,et al.  Identification of crack location and magnitude in a cantilever beam from the vibration modes , 1990 .

[31]  Xiaomin Deng,et al.  Damage detection with spatial wavelets , 1999 .