波形长度分形维数在结构振动诊断中的应用

Application of length fractal dimension on waveform in structure vibration monitoring

在Hausdorff维数和分配维数的基础上 ,采用拓扑映射技术 ,提出了振动波形长度分形维数的定义和计算公式 ,并对其数学严密性进行了证明。结合工程实例探讨了基于振动波形长度分形维数计算的结构振动诊断技术 :模型增长法和滑动窗法。该技术对于波形异常检测表现出精度高、抗噪能力强及自动快捷等优势 ,构成了一条分形理论用于结构振动诊断的有效技术路线 ,具有良好的应用价值。

Based on Hausdorff dimension and Divider dimension,the definition and computing formula of Length fractal dimension(D_L) on vibration waveform are proposed using topology mapping. The formula's mathematical strictness is proved.Clear physical concept,simple computation and easy realization in program are D_L's properties.By D_L the methods of model growth and sliding window to structure vibration monitoring are studied and their advantages of high accuracy,strong immunity to noise,excellent automatization and swiftness are validated in detecting the singularities of waveform from practical engineering examples.So an effective technology routine is formed, and is of good application value.