Measures of Dependence for α-Stable Distributed Processes and Its Application to Diagnostics of Local Damage in Presence of Impulsive Noise

Abstract

Local damage detection in rotating machinery is simply searching for cyclic impulsive signal in noisy observation. Such raw signal is mixture of various components with specific properties (deterministic, random, cyclic, impulsive, etc.). The problem appears when the investigated process is based on one of the heavy-tailed distributions. In this case the classical measure can not be considered. Therefore, alternative measures of dependence adequate for such processes should be considered. In this paper we examine the structure of dependence of alpha-stable based systems expressed by means of two measures, namely, codifference and covariation. The reason for using alpha-stable distribution is simple and intuitive: signal of interest is impulsive so its distribution is heavy-tailed. The main goal is to introduce a new technique for estimation of covariation. Due to the complex nature of such vibration signals applying novel methods instead of classical ones is recommended. Classical algorithms usually are based on the assumption that theoretical second moment is finite, which is not true in case of the data acquired on the faulty components. Main advantage of our proposed algorithm is independence from second moment assumption.