摘要
运用多重分形理论,提出广义维数最小二乘法的计算公式,对实测的时域信号进行了广义维数计算,得到 广义维数序列值,并从广义维数中获取盒维数、信息维数、关联维数以及敏感维数,对故障样本进行广义维数计 算分析,找出用分形维数分析识别故障的依据。此外,运用广义维数序列和数学方法相结合提出分形诊断分类方 法,用广义维数最大相关系数和广义维数序列单值优化逼近原理方法,对待检信号的耦合故障分别进行了试验数 据与动态振型数据的诊断、识别分类,收到了良好的一致效果。通过对转子系统故障诊断的实例说明从广义维数 中提取的各分形维数都能较好地对故障状态进行诊断、识别,且耦合故障的分形诊断分类方法具有较好的实效性。
The multi-fractals theory is applied for proposing the calculation formula of general dimension least square method. The general dimension of measured time domain signal is calculated, the sequence value of general dimension is obtained, and the box dimension, the information dimension, the correlation dimension and the sensitive dimension are got from general dimension. The general dimension of the fault sample is calculated. And the relationship between fault and fractal is found out. These provide the basis of analyzing the fault strength by fractal dimension. In addition, combined general dimension sequence value and mathematics method, the fractal diagnosis classification is proposed. It achieves good results to diagnose, identify and classify the measuring and modal coupling fault signal by the utilizing theorem of the general dimension maximum correlation coefficient and the general dimension sequence signal value. Through the example of the rotor system fault diagnosis, it explains that the fractal dimensions abstracted from the general dimension can better diagnose, identify the fault and its degree. The method of fractal diagnosis and classification has better actual effective property.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2005年第12期186-189,共4页
Journal of Mechanical Engineering
基金
国家自然科学基金资助项目(50275024)。
关键词
多重分形理论
故障敏感维数
振型分形特征
耦合故障诊断
分形诊断分类
Multi-fractal theory Fault sensitive dimension Modal fractal characteristic Coupling fault diagnosis Fractal diagnosis and classify
