采用多重分形改进算法提取往复压缩机振动信号的多重分形特征，得到了轴承故障的广义维数谱。
The multifractal features are extracted from the vibration signals of different spots on reciprocating compressor using the improving arithmetic, the general dimension spectrum of bearing.
最后，根据降秩技术中的交叉谱思想，提出了一种新的对信号子空间维数减少时的处理算法。
Finally, to deal with the situation that the dimension of the signal subspace decreases, a new algorithm is proposed based on the idea of the Cross Spectral Method.
首先通过计算原始图像和特征灰度图像的分形维数实现第一次的粗分类提取，然后采用多重分形奇异谱方法进一步完成了细分。
At first, the fractal dimension is extracted from the original image and special gray image for the rough classification, and then the multi-fractal dimension is used for further classification.
人们所熟知的常用以代替分形维数的各种度量将在分维谱意义下加以统一，最后讨论多重分形及其分维谱的应用。
The usual fractal dimensions familiar to all us will be united by the multifractal dimension spectrum. Finally, the applications of the multifractal and its dimension spectrum will be discussed.
研究结果表明：地震分布的多重分形维数谱和奇异性谱对于一些典型震区的强震发生具有中期预报价值。
The results show that the medium term symptoms of strong earthquakes in some regions can be proposed from the multi fractal dimension spectrum and singularity spectrum of earthquake distribution.
文章就在铁谱监测技术中应用分形理论，诸如磨粒识别、分形维数计算等方面进行了初步探讨。
This paper discusses the application of fractal geometry theory in ferrography monitoring technology like the identification of wear particles, the calculation of fractal dimension and so on.
确定谱的分形维数与物质相变、维晶状态以及结晶粒子线度的关系。
The relation among the matter phase-transition, crystalline degree, crystal site and spectrum fractal were discussed.
结果表明，尺度-小波能量谱和时间-小波能量谱相比有较好的分类效果和较低的特征维数。
The result shows that, compared with the time-wavelet power spectrum, the scale-wavelet power spectrum has a higher recognition accuracy and smaller dimension of feature vector.
阐述了分形与分形维数的定义，给出了铁谱磨粒分形维数和无标度区间的计算原理。
The definition of the fractal and fractal dimension were expatiated, the calculation principle of fractal dimension was set forth.
阐述了分形与分形维数的定义，给出了铁谱磨粒分形维数和无标度区间的计算原理。
The definition of the fractal and fractal dimension were expatiated, the calculation principle of fractal dimension was set forth.
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