PSO-GM(1,1,N,p,ξ)模型在变形预测中的应用
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摘要
通过对传统GM(1,1)缺陷分析和改进的基于权的PGM(1,1)建模机理描述,顾及PGM(1,1)中背景值构造时取相同的参数不能充分降低模型的预测误差,对不同的时刻引入不同的参数来改进GM(1,1)背景值序列的计算公式,将这种背景值构造方法和灰元N引入GM(1,1)建立了新的白化方程。在建立的新的白化方程基础上,用龙格-库塔法以修正的初始值计算累加值的模拟序列。针对引入的参数较多问题,采用粒子群算法寻找满足相对误差均值最优的参数,从而建立了基于粒子群优化算法和加权灰色组合的PSO-GM模型。工程实例应用表明,新模型的拟合精度高,预测效果好,相对其他两种原有模型预测精度有明显提高。
Through defect analysis on traditional GM(1,1)and the mechanism description of improved base on the weight of PGM(1,1),we consider that if the same parameters are taken in GM(1,1)when constructing background values,then the prediction error of the model cannot be sufficiently reduced.Different parameters are applied at different times to improve the GM(1,1)background value sequence formula.This kind of background value construction method and grey element Nare applied to the GM(1,1)to build a new albino equation.On the basis of the establishment of the new albino equation,the modified initial value through the Runge-Kutta method is applied to calculate the accumulated value of the simulation sequence.To resolve the introduction of many parameters,the particle swarm optimization algorithm is used to find optimal parameters which satisfy the relative error,so the PSD-GM model based on the particle swarm optimization algorithm and the weighted grey combination is established.The application of an engineering example shows that fitting precision of the new model is high,the predictive effect is good,and the predictive accuracy of the new model is improved significantly compared with the other two models.
Through defect analysis on traditional GM(1,1)and the mechanism description of improved base on the weight of PGM(1,1),we consider that if the same parameters are taken in GM(1,1)when constructing background values,then the prediction error of the model cannot be sufficiently reduced.Different parameters are applied at different times to improve the GM(1,1)background value sequence formula.This kind of background value construction method and grey element Nare applied to the GM(1,1)to build a new albino equation.On the basis of the establishment of the new albino equation,the modified initial value through the Runge-Kutta method is applied to calculate the accumulated value of the simulation sequence.To resolve the introduction of many parameters,the particle swarm optimization algorithm is used to find optimal parameters which satisfy the relative error,so the PSD-GM model based on the particle swarm optimization algorithm and the weighted grey combination is established.The application of an engineering example shows that fitting precision of the new model is high,the predictive effect is good,and the predictive accuracy of the new model is improved significantly compared with the other two models.
引文
[1]周世健,赖志坤,臧德彦,等.加权灰色预测模型及其计算实现[J].武汉大学学报:信息科学版,2002,27(5):451-455(Zhou Shijian,Lai Zhikun,Zang Deyan,et al.Weighted Grey Prediction Model and Implement of Its Compution[J].Geomatics and Imformation Science of Wuhan University,2002,27(5):451-455)
[2]李大军,孙旭红,汤拥军.PGM(1,1)灰色预测模型及其应用[J].华东地质学院学报,2002,25(1):40-43(Li Dajun,Sun Xuhong,Tang Yongjun.PGM(1,1)Grey Prediction Model and Its Application[J].Journal of East China Geological Institute,2002,25(1):40-43)
[3]牛东晓,赵磊,张博,等.粒子群优化灰色模型在负荷预测中的应用[J].中国管理科学,2007,15(1):69-73(Niu Dongxiao,Zhao Lei,Zhang Bo,et al.The Application of Particle Swarm Optimization Based Grey Model to Power Load Forecasting[J].Chinese Journal of Managenment Science,2007,15(1):69-73)
[4]王忠桃.灰色预测模型相关技术研究[D].成都:西南交通大学,2008(Wang Zhongtao.Research on Technique of Grey Prediction Model[D].Chengdu:Southeast Jiaotong University,2008)
[5]王宝强,崔伟杰,温毓繁,等.PSO-GM模型在拱坝变形预报中的应用[J].三峡大学学报:自然科学版,2014,36(5):23-27(Wang Baoqiang,Cui Weijie,Wen Yufan,et al.Application of PSO-GM Model to Prediction of Arch Dam Deformation[J].Journal of China Three Gorge University:Nature Science,2014,36(5):23-27)
[6]李克昭,李志伟,孟福军,等.基于综合优化GM(1,1)的形变预测模型[J].大地测量与地球动力学,2016,36(2):120-123(Li Kezhao,Li Zhiwei,Meng Fujun,et al.Deformation Forecasting Model Based on Synthetic and Optimized GM(1,1)[J].Journal of Geodesy and Geodynamics,2016,36(2):120-123)
[7]王奉伟,周世健,周清,等.三重加权变形监测预测模型及应用[J].测绘科学,2016,41(4):10-14(Wang Fengwei,Zhou Shijian,Zhou Qing,et al.Application of Development Weighted Treble in TPGM(1,1)Model[J].Science of Surveying and Mapping,2016,41(4):10-14)
[8]郭文杰.基于灰色系统理论的深基坑边坡稳定性研究[D].武汉:华中科技大学,2006(Guo Wenjie.Study on Slope Stability of Deep Foundation Excavation Based on the Gray System Theory[D].Wuhan:Huazhong University of Science and Thchnology,2006
[9]王大鹏,汪秉文.基于变权缓冲灰色模型的中长期负荷预测[J].电网技术,2013,37(1):167-171(Wang Dapeng,Wang Bingwen.Medium and Long-Term Load Forecasting Based on Variable Weights Buffer Grey Model[J].Power System Technology,2013,37(1):167-171)
[10]赖志坤,王新洲,朱欣焰.PGM(1,1)预测模型及其参数估计[J].测绘通报,2003(11):14-16(Lai Zhikun,Wang Xinzhou,Zhu Xinyan.PGM(1,1)Forecasting Model and Its Parameter Estimate[J].Bulletin of Surveying and Mapping,2003(11):14-16)
[11]李夏云,陈传淼.用龙格-库塔法求解非线性方程组[J].数学理论与应用,2008(2):62-65(Li Xiayun,Chen Chuanmiao.Solving Nonliner Equations by Using Runge-Kutta Method[J].Mathematical Theory and Applications,2008(2):62-65)
[2]李大军,孙旭红,汤拥军.PGM(1,1)灰色预测模型及其应用[J].华东地质学院学报,2002,25(1):40-43(Li Dajun,Sun Xuhong,Tang Yongjun.PGM(1,1)Grey Prediction Model and Its Application[J].Journal of East China Geological Institute,2002,25(1):40-43)
[3]牛东晓,赵磊,张博,等.粒子群优化灰色模型在负荷预测中的应用[J].中国管理科学,2007,15(1):69-73(Niu Dongxiao,Zhao Lei,Zhang Bo,et al.The Application of Particle Swarm Optimization Based Grey Model to Power Load Forecasting[J].Chinese Journal of Managenment Science,2007,15(1):69-73)
[4]王忠桃.灰色预测模型相关技术研究[D].成都:西南交通大学,2008(Wang Zhongtao.Research on Technique of Grey Prediction Model[D].Chengdu:Southeast Jiaotong University,2008)
[5]王宝强,崔伟杰,温毓繁,等.PSO-GM模型在拱坝变形预报中的应用[J].三峡大学学报:自然科学版,2014,36(5):23-27(Wang Baoqiang,Cui Weijie,Wen Yufan,et al.Application of PSO-GM Model to Prediction of Arch Dam Deformation[J].Journal of China Three Gorge University:Nature Science,2014,36(5):23-27)
[6]李克昭,李志伟,孟福军,等.基于综合优化GM(1,1)的形变预测模型[J].大地测量与地球动力学,2016,36(2):120-123(Li Kezhao,Li Zhiwei,Meng Fujun,et al.Deformation Forecasting Model Based on Synthetic and Optimized GM(1,1)[J].Journal of Geodesy and Geodynamics,2016,36(2):120-123)
[7]王奉伟,周世健,周清,等.三重加权变形监测预测模型及应用[J].测绘科学,2016,41(4):10-14(Wang Fengwei,Zhou Shijian,Zhou Qing,et al.Application of Development Weighted Treble in TPGM(1,1)Model[J].Science of Surveying and Mapping,2016,41(4):10-14)
[8]郭文杰.基于灰色系统理论的深基坑边坡稳定性研究[D].武汉:华中科技大学,2006(Guo Wenjie.Study on Slope Stability of Deep Foundation Excavation Based on the Gray System Theory[D].Wuhan:Huazhong University of Science and Thchnology,2006
[9]王大鹏,汪秉文.基于变权缓冲灰色模型的中长期负荷预测[J].电网技术,2013,37(1):167-171(Wang Dapeng,Wang Bingwen.Medium and Long-Term Load Forecasting Based on Variable Weights Buffer Grey Model[J].Power System Technology,2013,37(1):167-171)
[10]赖志坤,王新洲,朱欣焰.PGM(1,1)预测模型及其参数估计[J].测绘通报,2003(11):14-16(Lai Zhikun,Wang Xinzhou,Zhu Xinyan.PGM(1,1)Forecasting Model and Its Parameter Estimate[J].Bulletin of Surveying and Mapping,2003(11):14-16)
[11]李夏云,陈传淼.用龙格-库塔法求解非线性方程组[J].数学理论与应用,2008(2):62-65(Li Xiayun,Chen Chuanmiao.Solving Nonliner Equations by Using Runge-Kutta Method[J].Mathematical Theory and Applications,2008(2):62-65)