| 非等间隔GM(1,1)幂模型及应用 |
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| 引用本文： | 李军亮,肖新平,廖锐全.非等间隔GM(1,1)幂模型及应用[J].系统工程理论与实践,2010,30(3):490-495. |
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| 作者姓名： | 李军亮 肖新平 廖锐全 |
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| 作者单位： | 1. 长江大学石油工程学院,荆州,434023
2. 武汉理工大学理学院,武汉,430063 |
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| 摘 要： | GM(1,1)幂模型是灰色Verhulst模型的推广.在灰色Verhulst模型和等间隔GM(1,1)幂模型基础上提出了非等间隔GM(1,1)幂模型,并对模型进行求解.同时讨论了GM(1,1)幂模型曲线形状和幂指数以及发展系数之间的关系,研究了非等间隔GM(1,1)幂模型的参数空间.将平均相对误差看成幂指数的函数,根据序列形状判断幂指数的范围,利用粒子群算法求解幂指数,克服了灰色Verhulst模型的缺陷.最后实例表明:GM(1,1)幂模型建模精度高于灰色Verhulst模型,该方法具有重要的理论意义.
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| 关 键 词： | 灰色Verhulst模型 非等间隔GM(1:1)幂模型 粒子群算法 |
Non-Equidistance GM(1,1) power and its application |
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| LI Jun-liang,XIAO Xin-ping,LIAO Rui-quan.Non-Equidistance GM(1,1) power and its application[J].Systems Engineering —Theory & Practice,2010,30(3):490-495. |
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| Authors: | LI Jun-liang XIAO Xin-ping LIAO Rui-quan |
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| Institution: | LI Jun-liang~1,XIAO Xin-ping~2,LIAO Rui-quan~1 (1.Petroleum Engineering College,Yangtze University,Jingzhou 434023,China,2.School of Science,Wuhan University of Technology,Wuhan 430063,China) |
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| Abstract: | GM(1,1) power model generalizes the grey Verhulst model.Based on the grey Verhulst model and the equidistance GM(1,1) power model,this paper puts forward the non-equidistance GM(1,1) power model and solves the model.In this paper,the relations of the model's curve and power's exponent, development coefficient are analyzed.At the same time the paper studies the non-equidistance GM(1, 1) power model's parameter space.The average relative error is seen as a function of power's exponent. The numeric area of pow... |
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| Keywords: | grey Verhulst model non-equidistance GM(1 1)power model particle Swarm optimization |
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