基于复化Simpson公式优化背景值的GM(1,1)模型及应用
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摘要
文中针对传统GM(1,1)模型背景值求解存在误差,模型预测精度低的问题,通过分析误差来源,根据已有复化Simpson公式优化背景值的方法,利用积分函数分区间积分求解逼近的思想,构建动态序列预测模型,并结合实例分析进一步验证了该方法的有效性,能够减弱背景值影响误差,提高模型的拟合预测精度,对工程实际应用具有适用性。
Aiming at the problem that the traditional GM( 1,1) model had errors in solving the background value and low prediction precision,in this paper,the error sources were analyzed,dynamic sequence prediction model was constructed according to the method of optimizing background value by complex Simpson formula by using the idea of integral function interzonal integration to solve approximation,and the effectiveness of the method was further verified by an example analysis. The influence error of background value could be reduced and the fitting and prediction accuracy of the model was improved,which was applicable to the practical engineering applications.
Aiming at the problem that the traditional GM( 1,1) model had errors in solving the background value and low prediction precision,in this paper,the error sources were analyzed,dynamic sequence prediction model was constructed according to the method of optimizing background value by complex Simpson formula by using the idea of integral function interzonal integration to solve approximation,and the effectiveness of the method was further verified by an example analysis. The influence error of background value could be reduced and the fitting and prediction accuracy of the model was improved,which was applicable to the practical engineering applications.
引文
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[2]欧阳经富,谢新宇,李江浪. GM(1,1)模型在边坡变形监测中的应用研究[J].勘察科学技,2018,(1):50-53.
[3]李志伟,李克昭.基于Markov理论的加权非等距GM(1,1)预测优化模型[J].测绘工程,2016,25(12):38-43.
[4]王露. GM(1,1)模型在凤山隧道变形预测中的应用[J].建筑技术,2017,48(9):990-992.
[5]王景环,豆红磊,刘龙飞,等.基于优化GM(1,1)模型在基坑变形预测中的应用研究[J].矿山测量,2018,46(1):18-21.
[6]林飞,甄龙,张胜,等. GM(1,1)模型在高铁软土路基沉降监测中的作用[J].地理空间信息,2016,14(3):97-101.
[7]祖培福,赵文英,谢威,等.基于背景值优化的GM(1,1)模型在牡丹江GDP预测中的应用[J].数学的实践与认识,2018,48(1):1-7.
[8]李庆杨,王能超,易大义.数值分析[M].北京:清华大学出版社,2008.
[9]蒋诗泉,刘思峰,周兴才.基于复化梯形公式的GM(1,1)模型背景值的优化[J].控制与决策,2014,29(12):2221-2225.
[10]肖文,范志平,蔡仁澜,等.灰色系统GM(1,1)模型在建筑物变形监测中的应用[J].地理空间信息,2010,8(2):148-150.