最优非负变权灰色非线性模型及桥梁变形预测
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摘要
针对灰色预测模型GM(1,1)拟合精度低的情况,创新性的提出GM(1,1)模型同正弦函数、余弦函数、指数函数和同常数相结合的灰色非线性模型,并给出模型解算和精度评定方法。在此基础上,根据变权原理又提出了最优非负变权灰色非线性模型解算思路。并用某桥梁变形监测工程实例进行验证。通过比较分析各模型精度发现:最优非负变权灰色非线性模型预测精度较GM(1,1)模型、灰色非线性模型得到一定程度的提高,可以应用于桥梁变形预测中。
The GM( 1,1) model fitting precision in some case is low,so this paper put forward the grey nonlinear model which combined GM( 1,1) with sine function,cosine function,exponential function and constant. the accuracy evaluation method also given by this paper. On this basis,the optimal non-negative variable weight combination model and it's calculating way have been proposed according to the principle of variable weight. The project of bridge deformation monitoring is used to verify the feasibility of the model. By comparing the precision,we found that the optimal non-negative variable weight combination forecasting accuracy is higher than GM( 1,1) model and the grey nonlinear model.Therefore,we can apply the optimal non-negative variable weight combination model to the bridge deformation prediction.
The GM( 1,1) model fitting precision in some case is low,so this paper put forward the grey nonlinear model which combined GM( 1,1) with sine function,cosine function,exponential function and constant. the accuracy evaluation method also given by this paper. On this basis,the optimal non-negative variable weight combination model and it's calculating way have been proposed according to the principle of variable weight. The project of bridge deformation monitoring is used to verify the feasibility of the model. By comparing the precision,we found that the optimal non-negative variable weight combination forecasting accuracy is higher than GM( 1,1) model and the grey nonlinear model.Therefore,we can apply the optimal non-negative variable weight combination model to the bridge deformation prediction.
引文
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[2]岳建平,田林亚.变形监测技术与应用[M].北京:国防工业出版社,2014:164~175.
[3]栾元重,栾亨宣,马德鹏等.桥梁变形数据小波去噪与混沌预测[J].大地测量与地球动力学,2013,35(5):133~135,139.
[4]Liu C,Shu T,Chen S,et al.An improved grey neural network model for predicting transportation disruptions[J].Expert Systems with Applications,2015,45(C):331~340.
[5]王昕,张巍,王振雷.基于多模型混合最小方差控制的时变扰动控制系统性能评估[J].自动化学报,2014,9(40),2037~2044.
[6]周吕,韩亚坤,陈冠宇等.动态GM(1,1)在建筑物沉降变形分析中的应用研究[J].城市勘测,2013(5):119~121.
[7]周吕,文鸿雁,胡纪元等.改进GM(1,1)在高铁隧道沉降变形预测中的对比应用[J].施工技术,2014,43(18):66~68.
[8]姚志立,郑国荣,李尚贤.GM(1,1)模型在长沙绕城高速公路软土地基沉降值预测中的应用[J].公路工程,2014,39(1):221~223,228.
[9]甘勤涛,聂永川,王微.Matlab2012数学计算与工程分析从入门到精通[M].北京:机械工业出版社,2012:1~277.
[10]任超,梁月吉,庞光锋等.最优非负变权组合模型在大坝变形中的应用[J].大地测量与地球动力学,2014,34(6):162~166.