An Efficient Multi-scale-Based Multi-fractal Analysis Method to Extract Weak Signals for Gearbox Fault Diagnosis

Weak fault signals are always embedded in mass vibration noise in many gear systems, thus making difficulty in gear fault diagnosis. In order to extract weak fault signals, a new multi-scale-based multi-fractal analysis (MMA) method is introduced in this paper, which is based on classical multi-fractal detrended fluctuation analysis (MFDFA) framework. Firstly, the Hurst surface features are utilized to describe the characteristics with multifractal of the vibration signal, which have been proved to be sensitive to the dynamical responses of the various gear faults. Secondly, a moving fitting window is added to the MFDFA framework to sweep through all the range of the scales, and then obtain final multi-scale features, whose purpose is to magnify those features in some important scales and weaken the rest scales. In addition, other techniques, such as the distance-based feature selection and the random forest (RF) classifier, are also introduced into the gearbox fault diagnosis procedure to verify the effectiveness of extracted features for differentiating various gear states. Experiments using the Qianpeng testbed (QT) prove that the MMA method can effectively extract weak signals, and has higher diagnostic accuracy than other algorithms, such as empirical mode decomposition (EMD), wavelet transform (WT), and classical MFDFA.