数学形态学分形维数广义估算方法及其应用

Generalized estimation method of fractal dimension based on mathematical morphology and its application in bearing degradation status identification

预测特征提取是设备故障预测中的关键问题,它直接关系到故障预测的可信性。滚动轴承故障信号具有典型的非线性特征,利用分形维数可以定量描述其复杂性和不规则度。首先对分形维数的形态学计算方法进行介绍,然后对形态学覆盖的定义进行扩展,提出了三种形态学分形维数广义估算方法,对其精确性和计算效率进行了对比分析。最后,提出基于形态学分形维数的和灰色关联分析的性能退化状态识别方法,采用轴承实测数据验证了该方法的有效性。

Feature extraction is the key problem of,because the credibility of fault prognosis depends on feature extraction.Rolling bearing fault signal has a character of non-linear and fractal dimension,and by which the complexity and irregularity of the signal can be described in quantity.The calculating method of fractal dimension based on mathematical morphology is introduced first in the paper.Then the definition of mathematical cover was expanded and three kinds of generalized estimation method for mathematical morphological fractal dimension were proposed.The accuracy and efficiency were contrasted and analyzed by means of emulation.In the last,a kind of degenerate status recognition process based on mathematical morphological fractal dimension and grey relational analysis was proposed,its effectiveness was verified via rolling bearing experiment data.