Detection of cracks in shafts with the Approximated Entropy algorithm

Abstract

The Approximate Entropy is a statistical calculus used primarily in the fields of Medicine, Biology, and Telecommunication for classifying and identifying complex signal data. In this work, an Approximate Entropy algorithm is used to detect cracks in a rotating shaft. The signals of the cracked shaft are obtained from numerical simulations of a de Laval rotor with breathing cracks modelled by the Fracture Mechanics. In this case, one analysed the vertical displacements of the rotor during run-up transients. The results show the feasibility of detecting cracks from 5% depth, irrespective of the unbalance of the rotating system and crack orientation in the shaft. The results also show that the algorithm can differentiate the occurrence of crack only, misalignment only, and crack + misalignment in the system. However, the algorithm is sensitive to intrinsic parameters p (number of data points in a sample vector) and f (fraction of the standard deviation that defines the minimum distance between two sample vectors), and good results are only obtained by appropriately choosing their values according to the sampling rate of the signal.