Optimal filtering of angle-time cyclostationary signals: Application to vibrations recorded under nonstationary regimes

Abstract

Mechanical signals are often a mixture of multiple components produced by different sources. The separation of these components is beneficial for differential diagnosis, fault severity assessment and prognosis. An optimal way to accomplish this task is to apply a linear periodically time-variant filter, also known as the cyclic Wiener filter (CWF), assuming the signal to be cyclostationary and assuming that the source periodicity is a priori known. For the first assumption to be valid, the machine must operate under a stationary regime which is generally a restrictive condition. This paper addresses this issue by proposing a formal extension of the CWF to the nonstationary regime case within the angle-time cyclostationary framework. This framework was specifically designed to describe and process machine signals recorded under variable speed conditions. In addition to the theoretical formalisation of the so-called angle-time CWF, a simple and fast algorithm based on the Welch estimator is proposed. The efficiency of the new filter is demonstrated, and compared to the classical one, on synthetic and real vibration signals.