基于优化G-P算法求解关联维数  

Calculation of Correlation Dimension Based on Optimized G-P Algorithm

作　　者：方若望 何越磊[1] 李再帏[1] 路宏遥 赵彦旭 FANG Ruowang;HE Yueei;LI Zaiwei;LU Hongyao;ZHAO Yanxu(School of Urban Rail Transportation,Shanghai University of Engineering Science,Shanghai 201620;China Railway 21st Bureau Group Co.,Ltd.,Lanzhou 730070)

机构地区：[1]上海工程技术大学城市轨道交通学院,上海201620 [2]中铁二十一局集团有限公司,兰州730070

出　　处：《计算机与数字工程》2024年第5期1270-1274,共5页Computer & Digital Engineering

基　　金：国家自然科学基金项目(编号:51978393);甘肃省科技计划项目(编号:19ZD2FA001);中国铁建科技研发计划项目(编号:2019-B08)资助。

摘　　要：为了解决研究混沌关联维数主流算法G-P算法存在的问题,包括相空间和距离矩阵的循环构造,相关参量选取不当影响结论,Heaviside阶跃函数判断冗余等,提出改进的G-P算法。该算法在原理和重复计算上作出优化,在原矩阵的基础上操作形成后续矩阵及对距离矩阵进行排序,避免了循环判断,大大缩减了计算周期;对相关参量取值做出决策,使结论更严谨;对双对数图像的无标度区间采用Taylor级数法确定,使其更加直观。后续以Lorenz系统数据进行实例分析,仿真的结果也证明了改进算法的准确性。In order to solve problems in the study of the mainstream algorithm G-P algorithm of chaotic associated dimension,including the cycle structure of the phase space and distance matrix,the relevant parameter selection is not properly affected,and the Heaviside step function determines redundant,etc.,an improved G-P algorithm is proposed.The algorithm is optimized in prin-ciple and repetition calculation,and operates a subsequent matrix on the basis of the original matrix and sorts the distance matrix to avoid cyclic judgment,which greatly reduces the calculation cycle.It makes decisions to the related parameters,and makes the con-clusion strictly.The non-scaling section of the double logarithmic image is determined by the Taylor grade method,making it more intuitive.Subsequently,the system data is used for case analysis,the results of simulation also prove the accuracy of the improved algorithm.

关 键 词：混沌 相空间重构 关联维数 算法优化 G-P算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] TP391[自动化与计算机技术—计算机科学与技术]