Applications of detrended-fluctuation analysis to gearbox fault diagnosis

Aiming at fault diagnosis, we study vibration signals obtained from gearboxes under various conditions. We consider normal gearboxes, gearboxes containing scratched gears, and gearboxes containing toothless gears, both unloaded and under load, with several rotation frequencies. By applying detrended-fluctuation analysis (DFA), a mathematical tool introduced to study fractal properties of time series, we are able to distinguish the signals with respect to their working conditions. For each signal, DFA involves performing a linear fit to the data inside intervals of a certain size, and evaluating the corresponding fluctuations detrended by the local fit. Repeating this procedure for many interval sizes yields a curve of the average fluctuation as a function of size. From the curves, we define vectors whose components correspond to the average fluctuation associated with suitably chosen interval sizes. We finally apply principal component analysis to the set of all vectors, obtaining very good clustering of the transformed vectors according to the different working conditions, with a performance comparable to that obtained from Fourier analysis, especially for gears working under load.