Inverse Gaussian mixtures models of bearing vibrations under local faults

• Re-occurrence of vibrational patterns is described as realisation of a point process.
• The governing point process has inverse Gaussian inter-event times.
• Mixture inverse Gaussian distribution can be used under variable rotational speed.
• The proposed model overcomes the deficiency of negative inter-event times.
• The corresponding point process is shown to be quasi-cyclostationary.

Repetitive impacts performed by damaged spot on a component of the rolling element bearing specific statistical properties, due to the constant angular distance between the roller elements. Under (almost) constant rotational speed the successive impacts are regarded as almost periodic with small random fluctuations due to slippage. Often these random components are modelled as normally distributed, which is unrealistic since physically impossible events, such as negative time between two consecutive impacts, become likely by the nature of the distribution. Motivated by this deficiency we propose a new model that describes the occurrence of repetitive vibrational patterns as realisation of a point process with the (mixture) inverse Gaussian distribution of the inter-event times. Such a model is applicable to both constant and variable rotational speeds. Additionally, the proposed model inherently describes the quasi-cyclostationarity of the impact times under almost constant rotational speed. The applicability of the model was evaluated using vibrational signals generated by bearings with localised surface fault.