基于等间距化的非等间距灰色GM(1,1)模型及优化
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摘要
针对现有非等间距GM(1,1)模型存在的不足,借鉴分段线性插值将非等间距序列等间距化的思想,以非等间距的方法建立了一种新的非等间距GM(1,1)模型,模型不需计算插值数据,可直接利用原始数据建模.然后通过赋予原始数据下标序列变换系数,利用平均模拟相对误差最小的原则确定各参数,建立优化后的非等间距GM(1,1)模型.最后通过算例测试和应用实例表明提出模型的有效性和可行性.
Aiming at the limitations of the existing non-equidistant GM(1,1) model and using the ideas of equal spacing to non-equidistant sequence by piecewise linear interpolation,a new non-equidistant GM(1,1) model is established with non-equidistant method.The model doesn' t need to calculate the interpolation data and can directly use the original data modeling.With transforming the original data subscript sequence and determining the parameters by the principle of the minimum average relative error,the optimized non-equidistant GM(1,1) model is established.Finally,taking a numerical example and an application example to show the effectiveness and feasibility of the proposed model.
Aiming at the limitations of the existing non-equidistant GM(1,1) model and using the ideas of equal spacing to non-equidistant sequence by piecewise linear interpolation,a new non-equidistant GM(1,1) model is established with non-equidistant method.The model doesn' t need to calculate the interpolation data and can directly use the original data modeling.With transforming the original data subscript sequence and determining the parameters by the principle of the minimum average relative error,the optimized non-equidistant GM(1,1) model is established.Finally,taking a numerical example and an application example to show the effectiveness and feasibility of the proposed model.
引文
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[3]马符讯,沈大伟,艾斯卡尔·阿不力米提.非等间距灰色优化模型及其在基坑沉降预测中的应用[J].黑龙江工程学院学报:自然科学版,2014,28(1):27-29.
[4]王作雷,蔡国粱.非等间距序列建模过程中存在的问题及改进[J].大学数学,2003,19(2):46-50.
[5]王钟羡,吴春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践与认识,2003,33(10):16-20.
[6]王正新,党耀国,刘思峰.非等间距GM(1,1)幂模型及其工程应用[J].中国工程科学,2012,14(7):98-102.
[7]熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1,1)建模方法[J].控制与决策,2015,30(11):2097-2102.
[8]江艺羡,张岐山.非等间距GM(1,1)模型背景值的改进及其应用[J].福州大学学报,2016,44(3):306-310.
[9]杨跃东,冯倩妮.非等间距GM(1,1)模型背景值的构造及其应用[J].陕西科技大学学报:自然科学版,2014,32(5):165-168.
[2]傅立著.灰色系统理论及其应用[M].北京:科技文献出版社,1992.
[3]马符讯,沈大伟,艾斯卡尔·阿不力米提.非等间距灰色优化模型及其在基坑沉降预测中的应用[J].黑龙江工程学院学报:自然科学版,2014,28(1):27-29.
[4]王作雷,蔡国粱.非等间距序列建模过程中存在的问题及改进[J].大学数学,2003,19(2):46-50.
[5]王钟羡,吴春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践与认识,2003,33(10):16-20.
[6]王正新,党耀国,刘思峰.非等间距GM(1,1)幂模型及其工程应用[J].中国工程科学,2012,14(7):98-102.
[7]熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1,1)建模方法[J].控制与决策,2015,30(11):2097-2102.
[8]江艺羡,张岐山.非等间距GM(1,1)模型背景值的改进及其应用[J].福州大学学报,2016,44(3):306-310.
[9]杨跃东,冯倩妮.非等间距GM(1,1)模型背景值的构造及其应用[J].陕西科技大学学报:自然科学版,2014,32(5):165-168.