连续级配集料分形理论的误差分析及求解示例  

Error Analysis and Solution Example of Fractal Theory of Continuous Grading Aggregate

作　　者：王璜琪 薄艾 王栋民[3] 张双成 吕南 WANG Huangqi;BO Ai;WANG Dongmin;ZHANG Shuangcheng;LYU Nan(School of Chemical and Environmental Engineering,China University of Mining and Technology-Beijing,Beijing,100083,China;Liaoning Yilifang Shaye,Co.,Ltd.,Benxi,117000,China)

机构地区：[1]中国矿业大学(北京)化学与环境工程学院,北京100083 [2]辽宁壹立方砂业有限公司,本溪117000 [3]中国矿业大学(北京)化学与环境工程学院混凝土与环境材料研究所,北京100083

出　　处：《材料导报》2021年第S02期254-258,共5页Materials Reports

基　　金：国家重点研发计划(2019YFC1907201)。

摘　　要：分形理论是当前新兴且活跃的理论,利用分形理论描述连续级配骨料的相关推导早已实现,但在实际求解分形维数的过程中常利用其近似方程进行计算,而并未对其实用性进行必要分析,该误差可能导致对骨料的描述失真。通过数学推导求得相关的绝对误差和相对误差,并分析了产生误差的系统因素和主要的实验因素。随后利用分形理论的性质,给出了基于二分法的分形维数迭代求解方法。理论推导及数学实验结果表明,采用常用的近似方法产生的误差大小与级配骨料粒径范围有关,最小粒径越小,产生的误差越大,且在砂子所属范围内将产生显著误差。利用本工作中所述的回归方法对具有分形特征的连续级配骨料进行拟合,可获得较好的拟合结果。Fractal theory is currently a new and active theory. The related derivation of using fractal theory to describe continuous graded aggregates has long been realized, but in the process of actually solving fractal dimensions, its approximate equations are often used to calculate, but its practicality is not carried out. It is necessary to analyze the error may lead to the distortion of the description of the aggregate. This article obtains the relative absolute error and relative error through mathematical derivation, and analyzes the system factors and main experimental factors that produce the error. Then, using the properties of fractal theory, an iterative solution method of fractal dimension based on dichotomy is given.Theoretical derivation and mathematical experiment results show that the size of the error produced by the commonly used approximation method is related to the range of the gradation aggregate particle size. The smaller the minimum particle size, the greater the error, and significant errors will occur within the range of the sand. Using the regression method described in this article to fit the continuous graded aggregate with fractal characteristics, a better fitting result can be obtained.

关 键 词：误差分析 分形理论 连续级配集料 二分法 

分 类 号：U414[交通运输工程—道路与铁道工程]