| 基于小波变换的分形曲线维数计算方法的研究 |
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| 引用本文： | 杨大勇,刘莹,李小兵.基于小波变换的分形曲线维数计算方法的研究[J].润滑与密封,2007,32(1):40-42,134. |
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| 作者姓名： | 杨大勇 刘莹 李小兵 |
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| 作者单位： | 1. 南昌大学环境科学与工程学院,江西南昌,330029;南昌大学机电工程学院,江西南昌,330029
2. 南昌大学机电工程学院,江西南昌,330029 |
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| 基金项目： | 国家自然科学基金;南昌大学校科研和教改项目 |
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| 摘 要： | 研究了基于小波变换的分形曲线维数计算方法，具有算法简单和容易实现的优点；通过构造典型分形曲线并加以应用研究，提出并总结了小波分解尺度对维数计算精度的影响规律。根据影响规律，采用小波变换计算分形曲线维数，首先应该估计曲线的采样长度，根据曲线特征选择特定的小波函数，确定最佳的小波分解尺度，这样既提高了计算精度，又缩短了计算时间；其次，当分形曲线有限长度较短时，应该采用信号周期延拓的方法可以减少计算误差。
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| 关 键 词： | 小波变换 分形曲线 分形维数 分解尺度 |
| 文章编号： | 0254-0150（2007）1-040-3 |
| 修稿时间： | 2006-06-15 |
Study on Calculation Method of Dimension of Fractal Curve Based on Wavelet Transformation |
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| Yang Dayong,Liu Ying,Li Xiaobing.Study on Calculation Method of Dimension of Fractal Curve Based on Wavelet Transformation[J].Lubrication Engineering,2007,32(1):40-42,134. |
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| Authors: | Yang Dayong Liu Ying Li Xiaobing |
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| Abstract: | Calculation method of fractal dimension of fractal curve was studied based on wavelet transformation, which can be realized simply and easily in algorithm. Interrelations between wavelet decomposition scale and fractal dimension precision were found and summarized by constructing the typical fractal curve. Based on these interrelations, sample dimension of fractal curve should be estimated firstly, and then ensure the best wavelet decomposition scale, which can improve the presion of calculation dimension and shorten the computational time;secondly, sample signal should be extended periodically while sample length is finite so that the computational error can be reduced. |
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| Keywords: | wavelet transformation fractal curve fractal dimension decomposition scale |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
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