| 分数阶反向累加Verhulst模型 |
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| 引用本文： | 王建宏,朱彤,张楠,余若楠.分数阶反向累加Verhulst模型[J].系统工程理论与实践,2019,39(12):3262-3268. |
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| 作者姓名： | 王建宏 朱彤 张楠 余若楠 |
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| 作者单位： | 南通大学 理学院, 南通 226019 |
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| 基金项目： | 教育部产学合作协同育人计划项目（201801235001，201802151037）；南通大学博士启动项目（17B05） |
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| 摘 要： | 本文提出采用反向累加的方式对原始数据进行处理,并在整数阶的基础上将其推广到分数阶领域,以分数阶反向累加生成算子和分数阶反向累减生成算子为基础,建立分数阶反向累加Verhulst模型,并应用实例与分数阶反向累加GM(1,1)模型作对比,检验模型模拟误差.相关结果显示,相较于传统Verhulst模型与分数阶反向累加GM(1,1)模型,分数阶反向累加Verhulst模型的数据拟合精度较高.
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| 关 键 词： | 分数阶 反向累加 Verhulst模型 拟合精度 |
| 收稿时间： | 2017-09-26 |
Fractional order reverse accumulative Verhulst model |
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| WANG Jianhong,ZHU Tong,ZHANG Nan,YU Ruonan.Fractional order reverse accumulative Verhulst model[J].Systems Engineering —Theory & Practice,2019,39(12):3262-3268. |
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| Authors: | WANG Jianhong ZHU Tong ZHANG Nan YU Ruonan |
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| Institution: | School of Sciences, Nantong University, Nantong 226019, China |
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| Abstract: | This paper proposes to process the original data in a reverse-accumulation manner, and generalizes it to the fractional domain on an integer-order basis, based on fractional-order inverse-accumulation-generating operators and fractional-order inverse-reduction-generating operators. A fractional-order inverse cumulative Verhulst model was established, and the application examples were compared with fractional order inverse cumulative GM(1,1) model to test the model simulation error. The correlation results showed that compared with the traditional Verhulst model and fractional order inverse cumulative GM(1,1) model, the accuracy of the data fitting of the fractional-order inverse cumulative Verhulst model is high. |
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| Keywords: | fractional order reverse accumulation Verhulst model fitting accuracy |
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