基于新息优先分数阶累加的改进型灰色Verhulst模型  

Improved grey Verhulst model based on new information priority fractional order accumulation

作　　者：沈琴琴 党耀国[2] 曹阳 朱镕琦[3] SHEN Qinqin;DANG Yaoguo;CAO Yang;ZHU Rongqi(School of Transportation and Civil Engineering,Nantong University,Nantong 226019,China;College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;School of Information Science and Technology,Nantong University,Nantong 226019,China)

机构地区：[1]南通大学交通与土木工程学院,南通226019 [2]南京航空航天大学经济与管理学院,南京211106 [3]南通大学信息科学技术学院,南通226019

出　　处：《系统工程理论与实践》2025年第2期539-553,共15页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(61771265);江苏省“333工程”科研项目(2022044);江苏高校“青蓝工程”项目;南通市“226工程”科研项目。

摘　　要：为了更好地突出分数阶累加算子的新息优先性以及提升波动型数据的预测精度,提出一种新息优先分数阶累加的改进型灰色Verhulst模型.首先,基于Toeplitz矩阵理论详细研究了新息优先分数阶累加算子的性质,导出了该算子满足新息优先性的条件.其次,给出了改进型灰色Verhulst模型的建模过程,并用遗传算法寻求新息优先分数阶累加算子中的最优参数.最后,将改进型灰色Verhulst模型用于两个具有波动型数据特征的实际案例.数值结果验证了新息优先的重要性以及本文的理论结果,且新模型的拟合和预测精度均高于传统的灰色Verhulst模型、分数阶累加灰色Verhulst模型和新息优先灰色Verhulst模型.In order to better highlight the new information priority of the fractional order accumulation operator and improve the prediction accuracy of fluctuating data,an improved grey Verhulst model based on new information priority fractional order accumulation is proposed.Firstly,based on the Toeplitz matrix theory,some properties of the new information priority fractional order accumulation operator are studied in detail,and the conditions to satisfy the new information priority are derived.Secondly,the modeling process of the improved grey Verhulst model is presented,and genetic algorithm is adopted to search for the optimal parameters in the new information priority fractional order accumulation operator.Finally,the improved grey Verhulst model is applied to two practical cases with fluctuating data characteristics.Numerical results validate the importance of new information priority and the theoretical results of this article,and the fitting and prediction accuracy of the new model is higher than that of the traditional grey Verhulst model,the fractional order accumulation grey Verhulst model and the new information priority accumulation grey Verhulst model.

关 键 词：灰色VERHULST模型 分数阶累加算子 新息优先性 Toeplitz矩阵理论 

分 类 号：N941.5[自然科学总论—系统科学]