Dependency measures for the diagnosis of local faults in application to the heavy-tailed vibration signal

Abstract

The extraction of the informative frequency band from the signal with heavy-tailed noise is introduced to detect local damage. The algorithm for the vibration signal from a bearing installed in the ore crusher is proposed. From a signal processing point of view, this is related to the detection and recognition of cyclic and non-cyclic impulsive components in the signal. It is assumed that the non-periodic impulses have amplitudes significantly higher than the cyclic impulses – usually fully hidden in the non-Gaussian noise - which makes the diagnosis difficult. As both components are non-Gaussian, a periodicity detector can be used as an alternative to the impulsiveness criteria. In this paper, the proposed informative frequency band selectors utilize the dependency measures, i.e., the Pearson, Spearman and Kendall correlations. These dependency measures are applied to the time–frequency domain representation of the signal to find similarities between sub-signals associated with frequency bands. Three types of frequency bands are expected – the first one – with just Gaussian noise, the second one – with cyclic impulsive behavior, and the last one - with non-cyclic impulsive behavior. For simplicity, it is assumed that frequency bands occupied by cyclic and non-cyclic impulses are different. Finally, one may obtain a map of similarities between all frequency bands, and based on this map the 1D selector for informative frequency band identification can be estimated. The main contribution of the paper is the introduction of the holistic procedure of the fault diagnosis containing the time–frequency representation of vibration signal, including the estimation of the dependency map (D-map) using three different dependency measures, D-map de-noising, and the integration of D-map to one-dimensional (1D) selector. The introduced procedure is applied to the complex simulated data and then to real vibrations from the heavy-duty machine.