基于Kalman滤波的灰色模型在沉降预测中的研究
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摘要
针对沉降观测数据存在各种扰动,以及GM(1,1)模型的不足,提出卡尔曼滤波GM(1,1)模型,通过卡尔曼滤波去噪后,再利用GM(1,1)模型进行预测。由实验数据可得,改进模型的后验误差比值、小误差概率以及精度等级分别为0.108 0、100%、一级,而原有的3种模型中只有3次指数平滑接近改进模型,但改进模型的后验误差比值更小;从残差看,改进模型的预测残差比原有模型都小,这表明改进模型提高了沉降预测的精度。
Based on various disturbance of Settlement Observation Data and the weaknesses of GM( 1,1),this paper presents the Kalman Filter GM( 1,1) Model,which will make predictions with it after denoising. From the experimental data,under the help of GM( 1,1),the Posterior error ratio,Small error probability and the Precision grade are 0. 108 0、100% and first optimum,while exponential smoothing approached the improved model's only three times based on the previous three models,and the Posterior error ratio of improved model is more smaller. In view of the residual error,the forecasting residual of advanced model is smaller than the previous model,which indicates that it improves the precise of the Settlement Prediction.
Based on various disturbance of Settlement Observation Data and the weaknesses of GM( 1,1),this paper presents the Kalman Filter GM( 1,1) Model,which will make predictions with it after denoising. From the experimental data,under the help of GM( 1,1),the Posterior error ratio,Small error probability and the Precision grade are 0. 108 0、100% and first optimum,while exponential smoothing approached the improved model's only three times based on the previous three models,and the Posterior error ratio of improved model is more smaller. In view of the residual error,the forecasting residual of advanced model is smaller than the previous model,which indicates that it improves the precise of the Settlement Prediction.
引文
[1]张正禄,黄全义,文鸿雁,等.工程的变形监测分析与预报[M].北京:测绘出版社,2007.
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[3]潘家宝.时空Kalman滤波及其在变形监测数据处理中的应用[D].长沙:中南大学,2014.
[4]何湘黔.基于kalman滤波的灰色BP神经网络方法的电力变压器运行状态评估[J].电子世界,2013(19):25-26.
[5]邓聚龙.灰色控制系统[M].武汉:华中理工大学出版社,1985.
[6]袁嘉祖.灰色系统理论及其应用[M].北京:科学出版社,1991.
[7]李秀珍,孔纪名,王成华.灰色GM(1,1)残差修正模型在滑坡预测中的对比应用[J].山地学报,2007(6):741-746.
[8]苏观南,郑东健,孙斌斌.卡尔曼滤波灰色模型在大坝变形预测中的应用[J].水电能源科学,2014(4):37-40.
[9]郑志萍,黄庆丰.电力负荷预测数学模型的统计检验[J].水利科技,2007(1):56-57.
[2]王利,李亚红,刘万林.卡尔曼滤波在大坝动态变形监测数据处理中的应用[J].西安科技大学学报,2006,26(3):353-357.
[3]潘家宝.时空Kalman滤波及其在变形监测数据处理中的应用[D].长沙:中南大学,2014.
[4]何湘黔.基于kalman滤波的灰色BP神经网络方法的电力变压器运行状态评估[J].电子世界,2013(19):25-26.
[5]邓聚龙.灰色控制系统[M].武汉:华中理工大学出版社,1985.
[6]袁嘉祖.灰色系统理论及其应用[M].北京:科学出版社,1991.
[7]李秀珍,孔纪名,王成华.灰色GM(1,1)残差修正模型在滑坡预测中的对比应用[J].山地学报,2007(6):741-746.
[8]苏观南,郑东健,孙斌斌.卡尔曼滤波灰色模型在大坝变形预测中的应用[J].水电能源科学,2014(4):37-40.
[9]郑志萍,黄庆丰.电力负荷预测数学模型的统计检验[J].水利科技,2007(1):56-57.