基于数学形态学的分形维数计算及在轴承故障诊断中的应用

滚动轴承故障信号是一种典型的非线性信号，分形几何为描述轴承故障信号的特性提供了一个有力的分析工具。基于数学形态学的分形维数是在Minkowski-Boulingand维数基础上拓展的一种采用形态学操作计算分形维数的新方法。本文较详细的阐述了基于数学形态学的分维数计算方法，对比分析了与传统计盒维数方法的区别与联系，并对实际的滚动轴承正常、滚动体故障、内圈故障和外圈故障信号进行了分析，结果表明，基于数学形态学的分维数计算方法具有计算速度快，估计准确稳定的特点，为准确判断滚动轴承故障状态提供了一种快速有效的新方法。

Mathematic morphology-based fractal dimension calculation and its application in fault diagnosis of roller bearings

The vibration signal generated from defected roller bearing demonstrates a typical nonlinearity. The fractal theory provides an effective approach to analysis the characteristic of the roller bearing fault signal. As an extension of the traditional Minkowski-Boulingand fractal dimension, mathematical morphology based fractal dimension is calculated via the morphological operation. This new fractal estimation method was detailed in this study. A comparison between the new fractal dimension and the most used box dimension has also been studied by applying to the real vibration signal acquired from four different states of roller bearing, i.e. normal, roller element defect, inner race defect and outer race defect. The results reveal that the mathematical morphology based fractal dimension yields higher accuracy as well as less calculation cost and demonstrates as an effective tool for fault diagnosis of roller bearing.