Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures

In this paper we propose a novel approach for the diagnosis of gearboxes in presumably non-stationary and unknown operating conditions. The approach makes use of information indices based on the Rényi entropy derived from coefficients of the wavelet packet transform of measured vibration records. These indices quantify some statistical properties of instantaneous power of the generated vibration that are largely unaffected by changes in the operating conditions. The analysis is based on probability density of the envelope of a sum of sinusoidal signals with random amplitude and phase. Such an approach requires no a priori information about the operating conditions and no prior data describing physical characteristics of the monitored drive. The fault detection capabilities of the proposed feature set are demonstrated on a two-stage gearbox operating under different rotational speeds and loads with various seeded mechanical faults.

► Distribution of the vibration's envelope is sensitive to variations in load and speed.
► Faults alter the shape of the probability distribution of the signal's envelope.
► Wavelet packet coefficients preserve the shape of the distribution of the envelope.
► Rényi entropy and Jensen–Rényi divergence can be used to quantify alterations in the distribution.
► Fault detection is possible without information about the operating conditions.