基于广义分形的旋转机械故障诊断识别与分类  

Application of multifactal theory to coupling fault diagnosis

作　　者：徐玉秀[1] 钟建军[2] 刘薇[1] 周晓梅[1] 

机构地区：[1]天津工业大学机械电子学院,天津300160 [2]中国军事交通学院汽车工程系,天津300161

出　　处：《辽宁工程技术大学学报（自然科学版）》2005年第4期591-594,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(50275024)

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。对故障样本进行功率谱分析、广义维数计算分析,找出用分形维数分析识别故障的依据。另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理论响应模拟、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的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 is got from general dimension. The power spectrum of the fault sample is analyzed, the general dimension of it is calculated. And the relationship between spectrum energy 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, which obtains good results to diagnose, identify and classify the measuring 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.

关 键 词：多重分形理论 广义维数 耦合故障诊断 分形诊断分类 

分 类 号：O321[理学—一般力学与力学基础]