### Abstract

There are significant changes in the vibration responses of cracked structures when the crack depth is significant in comparison to the depth of the structure. This fact enables the identification of cracks in structures from their vibration response data. However when the crack is relatively small, it is difficult to identify the presence of the crack by a mere observation of the vibration response data. A new approach for crack detection in beam-like structures is presented and applied to cracked simply supported beams in this paper. The approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. These two sets of mode shape data, which constitute two new signal series, are obtained and reconstructed from the modal displacement data of a cracked simply supported beam. They represent the left half and the modified right half of the modal data of the simply supported beam. SWT is a redundant transform that doubles the number of input samples at each iteration. It provides a more accurate estimate of the variances at each scale and facilitates the identification of salient features in a signal, especially for recognising noise or signal rupture. It is well known that the mode shape of a beam containing a small crack is apparently a single smooth curve like that of an uncracked beam. However, the mode shape of the cracked beam actually exhibits a local peak or discontinuity in the region of damage. Therefore, the mode shape ‘signal’ of a cracked beam can be approximately considered as that of the uncracked beam contaminated by ‘noise’, which consists of response noise and the additional response due to the crack. Thus, the modal data can be decomposed by SWT into a smooth curve, called the approximation coefficient, and a detail coefficient. The difference of the detail coefficients of the two new signal series includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams used are computed using the finite element method. For real cases, mode shape data are affected by experimental noise. Therefore, mode shape data with a normally distributed random noise are also studied. The results show that the proposed method has great potential in crack detection of beam-like structures as it does not require the modal parameters of an uncracked beam as a baseline for crack detection. The effects of crack size, depth and location, and the effects of sampling interval are examined.

Original language | English |
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Pages (from-to) | 1853-1884 |

Number of pages | 32 |

Journal | Mechanical Systems and Signal Processing |

Volume | 21 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2007 |

Externally published | Yes |

### Keywords

- cracks
- cracked beams
- crack detection
- damage detection
- stationary wavelet transform

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## Cite this

Zhong, S., & Oyadiji, S. O. (2007). Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform.

*Mechanical Systems and Signal Processing*,*21*(4), 1853-1884. https://doi.org/10.1016/j.ymssp.2006.07.007