Error Analysis and Solution Example of Fractal Theory of Continuous Grading Aggregate
WANG Huangqi1,2, BO Ai1, WANG Dongmin1, ZHANG Shuangcheng2, LYU Nan2
1 School of Chemical and Environmental Engineering, China University of Mining and Technology-Beijing, Beijing, 100083, China 2 Liaoning Yilifang Shaye, Co., Ltd., Benxi, 117000, China
Abstract: 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.
王璜琪, 薄艾, 王栋民, 张双成, 吕南. 连续级配集料分形理论的误差分析及求解示例[J]. 材料导报, 2021, 35(z2): 254-258.
WANG Huangqi, BO Ai, WANG Dongmin, ZHANG Shuangcheng, LYU Nan. Error Analysis and Solution Example of Fractal Theory of Continuous Grading Aggregate. Materials Reports, 2021, 35(z2): 254-258.
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2021, Vol. 35 
