利用小波算法建立棉纤维表面分形数学模型分析研究棉纤维的含糖量

【作者】 邢海英；

【导师】 钟宏杰；

【作者基本信息】 天津工业大学 ， 纺织工程， 2003， 硕士

【摘要】 本文介绍了用分形理论解析棉纤维表面，表明其表面具有统计自相似的分形特征。并利用小波算法建立棉纤维表面的分形数学模型来研究棉纤维的含糖量。结果表明，棉纤维表面分维数与含糖量间存在定量关系。 课题解决了现有几种棉纤维含糖量测试方法难以有效反应棉纤维含糖量规律和粘着性问题。 棉纤维含糖份，使其具有粘着性，这使纺纱生产中出现绕皮辊、绕罗拉、绕皮圈的“三绕”现象，影响生产的顺利进行。因此，需要通过含糖量测试，对含糖量高的原棉做预处理。实际生产中，要求这种测试实验条件严格，有些棉纺厂难以做到。而采用小波算法建立棉纤维表面分形数学模型，计算各种棉样的表面分维数，利用其与原棉含糖量间存在的定量关系，制成样本。生产中，计算原棉表面分维数，将其与样本作比较，获取原棉含糖量信息，再做预处理。这样，不但可以有效反应原棉含糖量规律，且更省时、省力，避免繁琐的实验过程。在实际生产过程中，可以提高生产率，降低生产成本。 文章在概述分形理论和小波理论的基础上，重点阐述了分形与小波的密切关系，表明小波算法最适合分形对象的研究。同时，通过分形布朗运动曲面与Weierstrass-Mandelbrot(W-M)函数模拟的分形表面的计算实例，证明由小波算法建立数学模型求取分形维数，能更好的接近理论值，同时具有良好的抗干扰能力。 课题中是利用Matlab实现小波算法建模的，结果表明采用Matlab编程在计算维数的准确性、有效性及简便性方面都有所提高。 课题创新点在于，运用分形理论解析棉纤维表面结构特征，建立其表面分维与含糖量间的关系。更多还原

【Abstract】 In this thesis, the theory of fractal has been applied to experimental studies of cotton fiber surface. It is evident that there are statistical self-similarity characteristic on the cotton fiber surface. To research the sugar content of cotton fiber with the help of wavelet algorithm, the fractal mathematics model is set up. As result, quantitative relations between the fractal dimension of cotton fiber surface and its sugar content can be made.The issue is resolved, that the regularity of sugar content and sticking can not be efficiently responded by traditional measurement.In the process of spinning from cotton to yarn, there are some phenomena of lapping top rollers lapping bottom roller and lapping apron, due to unsuitable sugar content of cotton fiber. So it is necessary to measure the sugar content of cotton fiber and prepare to handle high content before spinning for solving above problems. The strict conditions, which are required in measurement, can not be afforded by many cotton mills. Applying the fractal mathematics model, we can estimate the dimension of various kinds of cotton fiber surface, then, make the sample consulting the quantitative relation. In practice, the dimension of raw cotton being estimated can contrast with sample and obtain the information of cotton sugar content. Not only can this method respond the regulation of sugar content, but also it can save more time and more labor, avoid the tedious experiment process. It is more important that the method can increase the rate of production and decrease the production cost.Based on the clarification of fractal and wavelet theories, the thesis discuss the close relation between them and explain that the wavelet is the most applicable way to studying fractal. In addition to, two calculating example, that Fractal Brown and W-M Function model, illustrate wavelet algorithm to be more accurate and its ability of good anti-interference.Making use of MATLAB to set up model, accuracy efficiency and convenient have been improvedThe innovation of the thesis is analyzing the cotton fiber surface in application of fractal theory to analyzing the cotton fiber surface更多还原