Abstract: Mechanical vibration signal is a typical non-linear，nonstationary signal, and multifractal features are powerful tool to express the geometry features of such signals. The traditional multifractal features extraction methods require complex computation, which limit their application. Wavelet leaders-based multifractal analysis has solid supports of mathematical theories and can be calculate easily. A multifractal features extraction method is presented based on wavelet leaders, which is applied to the gears vibration signals under normal and pitting conditions. An optimization algorithm is given to conform the block length of bootstrap technology , and then a validity testing method is presented to test the characteristic variables obtained from vibration signals with wavelet leaders-based multifractal features extraction. The result shows that the geometry features of vibration signal can be reflected with wavelet leaders multifractal features, and the block bootstrap method can be used to analyze the statistical performance of multifractal features, which provides an effective approach for condition monitoring and fault diagnosis of mechanical equipment.

Key words: Block bootstrap, Fault diagnosis, Multifractal features, Performance analysis, Wavelet leaders