Comparison of the cyclostationary and the bilinear approaches: theoretical aspects and applications to industrial signals

The aim of our study is to compare two a priori different approaches: bilinearity and cyclostationarity. Indeed, we underline that cyclostationary and bilinear tools make it possible to determine both nonlinear and nonstationary links. These results are based on calculations, simulations for synthetic signals and finally applications to industrial signals. Then, we introduce different applications of these approaches to industrial vibrations. These methods enable us to obtain much more interesting results than classical methods such as Fourier, spectrum, time-frequency studies etc. Finally we conclude on the interest and the reliability of such approaches and we introduce a method to determine if a link between two frequencies is rather cyclostationary than bilinear. This method is based on the use of higher-order cyclic statistics.