小波多重分形及其在振动信号分析中应用的研究

不同于许多基于FFT的信号分析方法，多重分形谱分析的是信号的几何结构特征。以前，多重分形谱的计算方法都有其固有的缺点，使多重分形谱的应用受到限制。而小波局部极大模方法因其简单性和有效性，近来在多重分形谱计算方面受到了广泛的关注。较系统地阐述了多重分形的概念和多重分形谱的小波局部极大模计算方法，讨论了多重分形谱在故障诊断领域的应用途径，并用多重分形谱对不平衡、油膜涡动、联轴器不对中和碰摩等旋转机械的4种典型故障的振动信号进行了事例研究。研究结果表明，多重分形谱能够很好的反映振动信号的几何结构特征，为机械设备故障诊断提供了又一种有效的方法。

WAVELET MULTIFRACTAL SPECTRUM: APPLICATION TO ANALYSIS VIBRATION SIGNALS

Different from the FFT-based methods, the objects of the multifractal spectrum treaded with are the signals' geometry features. Before, the inherent limitations of the algorithm for the multifractal spectrum limited its application. Now, the wavelet local maxima modulus based method is received more attentions because it can calculate the multifractal spectrum effectively and simply. The concept of multifractal spectrum is presented systematically and the wavelet local maxima modulus based method is introduced detailedly. The way of applying the multifractal spectrum for fault diagnosis is discussed. The vibration signals of four kinds of typical faults: unbalance, oil whirl, coupling misalignment and rub-impact are then studied. The result shows that the geometry features of vibration signals can be reflected through multifractal spectrum, which provides an effective way for fault diagnosis.