中文摘要：

机械振动信号一般具有非线性、非平稳特性,多重分形特征是表示振动信号几何结构特征的一种重要手段。传统的多重分形特征计算方法计算量大,限制了多重分形特征的应用。小波leaders多重分形分析方法具有坚实的数学基础,且计算简便。针对齿轮正常状态和点蚀故障状态,提出基于小波leaders的多重分形振动信号特征提取及表示方法,提出基于bootstrap技术的最优块长求解算法,并建立振动信号小波leaders多重分形特征的统计性能分析方法。研究结果表明,小波leaders多重分形特征能够很好反映振动信号的几何结构特征,基于块bootstrap方法能有效分析多重分形特征统计性能,为机械设备状态监控和故障诊断提供了一种有效的选择。

英文摘要：

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.