Blind equalization using combined skewness–kurtosis criterion for gearbox vibration enhancement

Abstract

In this paper a method for vibration signal enhancement is presented. It incorporates an idea that the signal acquired on the machine housing is a convolution of an informative signal (cyclic pulse train) with an impulse response of the system. The impulse response corresponds to a transmission path through which the informative signal propagates. The informative signal is a signal that contains information about a local damage. The classical method that estimates the impulse response of the system is called minimum entropy deconvolution (MED) and it aims to maximize kurtosis of the deconvolved signal, i.e. kurtosis of the informative signal estimate. Recently, skewness-based deconvolution (equalization) has been proposed as an alternative method for damage detection in rotating machines. In this paper we incorporate an alternative criterion which combines advantages of both of the previously used deconvolution criteria. Kurtosis is a widely-used tool for impulsiveness detection even if they are hidden in the signal, although favouring single-spike signals is a disadvantage of kurtosis. On the other hand, skewness is more robust, since it incorporates statistical moment one order lower than kurtosis. However, signals related to local damage are not always asymmetric, thus skewness is not a suitable criterion for their extraction. Thus, it is worth to combine both kurtosis and skewness in a single deconvolution criterion. We compare properties of two previously used criteria (kurtosis and skewness) with the novel one which is based on the Jarque–Bera statistic using a simulation study. An experimental validation on a real vibration signal (two-stage gearbox from an open-pit mine) is performed as well.