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Statistical Approach for Nondestructive Incipient Crack Detection and Characterization Using Kullback-Leibler Divergence

This paper is a contribution to the detection and characterisation of small cracks using Eddy Current Testing in the Non Destructive Evaluation framework. Small cracks are considered as incipient faults defined as gradual faults whose signature is weak and concealed by the noise. They are characterized by high signal to noise ratio and low fault to noise ratio. The detection and diagnosis of such faults is still an open challenge. For complex systems, model-based incipient fault detection and diagnosis (FDD) methods usually fail because of the inaccuracy of the model to describe all the phenomena and their interactions. Data-driven methods using statistical features are very promising as long as historical data are available. However in the case of incipient faults, there is not a significant variation of a single feature. The fault signature lies in the global variation of the signal properties. The proposed method relies on the Kullback-Leibler Divergence (KLD) as a nonparametric fault indicator. It measures the slight dissimilarities between the probability density functions of the current signal compared to the faultless or healthy one. Through experimental results, the KLD exhibits a higher sensitivity than the usual statistical features for the detection of small cracks (with dimensions in the order of 0.1 mm) realized in a nickel-based superalloy plate. Moreover, the detection is done with zero missed detection probability. Furthermore, the fault severity is assessed through the characteristics of the crack (surface, length, and depth). In the principal component analysis framework, the analysis of four statistical features (KLD, mean, variance, and maximum) dependency to the excitation frequency allows to discriminating among the cracks.