Damage identification method based on fractal dimension and Shannon entropy

Fractal geometry has been widely used to describe irregular phenomena such as damage in the structure as a new mathematical tool. However, most of structural damage identification methods based on fractal theory have the drawback of being sensitive to noise which restricts their practical application. A new high noise robustness damage identification method based on fractal dimension and Shannon entropy is presented in this paper. The damage index was deduced from the Katz's fractal dimensions of certain sampling points with arithmetic of Shannon entropy. The selection of the number of sampling points for calculating the proposed damage index is also studied in this paper and it can be regarded as a trade-off between the peak value generated by the damage and the stability of the curve of the proposed damage index. As a validation, the proposed method is applied to detect damage in simply supported beams by numerical and experimental study. The successful detection of the damage in the beam demonstrates that the method is capable of estimating the location of the damage. And tests with measurement noise in simulated and the laboratory tested beams demonstrate the strong robustness of the method under the influence of noise with appropriate number of sampling interval for calculating the proposed damage index.