Local damage detection methods based on the stochastic modeling techniques

Problem of selection of informative frequency band (IFB) for local damage detection using vibration signal is often discussed in the literature. One of the approaches used in this context is based on the analysis of sub-signals obtained in time-frequency representation of the vibration signal. Mentioned sub-signals are analyzed using appropriate statistics (called selectors). Till now, the most popular statistic was kurtosis, one of the measures that can point out these frequency bins on time-frequency map that reveal the most impulsive nature. However for many real signals the spectral kurtosis does not give expected results because it can be sensitive for impulses not related to damage (i.e. artifacts). In this paper we extend the idea of spectral kurtosis. We propose a novel method combining time-frequency representation, namely spectrogram, dependency measure suitable for heavy-tailed distributions, statistical features for novel time-frequency representation and statistical modeling of such features. The new time-frequency representation is based on the measure of dependence appropriate for more general class of distribution, namely heavy tailed. This measure, called autocovariation, is an extension of the classical measures of dependences, namely autocovariance or autocorrelation. The new time-frequency representation was developed in order to enhance informative parts of the signal while reducing inadvisable parts of the signal like artifact or high-energy deterministic parts. Next, the Kuiper statistic is applied to novel time-frequency representation for IFB detection and we design the Alter characteristic. Moreover, we propose also the automatic procedure of filter characteristic thresholding based on the alpha-stable distribution approach.