地球科学进展

地球科学进展 ›› 2018, Vol. 33 ›› Issue (8): 874 -883. doi: 10.11867/j.issn.1001-8166.2018.08.0874

研究简报 上一篇    

一种新的耦合模糊控制局地化的同化方法
常明恒( ), 摆玉龙 *( ), 马小艳, 孟若玉, 王丽丽   
  1. 西北师范大学物理与电子工程学院,甘肃 兰州 730070
  • 收稿日期:2018-04-28 修回日期:2018-06-04 出版日期:2018-08-10
  • 通讯作者: 摆玉龙 E-mail:changmingheng@126.com;yulongbai@gmail.com
  • 基金资助:
    国家自然科学基金项目“进化计算类智能算法在数据同化误差处理中的应用研究”(编号:41461078);西北师范大学科研能力提升团队项目“智能计算理论及应用”(编号:NWNU-LKQN-1706)资助.

Localization Analysis of Data Assimilation Methods Coupled with Fuzzy Control Algorithms

Mingheng Chang( ), Yulong Bai *( ), Xiaoyan Ma, Ruoyu Meng, Lili Wang   

  1. College of Physics and Electrical Engineering, Northwest Normal University, Lanzhou 730070, China
  • Received:2018-04-28 Revised:2018-06-04 Online:2018-08-10 Published:2018-09-14
  • Contact: Yulong Bai E-mail:changmingheng@126.com;yulongbai@gmail.com
  • About author:

    First author:Chang Mingheng(1992-), male ,Qin'an County, Gansu Province, Master student. Research areas include data assimilation observation error. E-mail: changmingheng@126.com

  • Supported by:
    Project supported by the National Natural Science Foundation of China “The application of intelligent algorithms with evolutionary computing in data assimilation about error processing”(No.41461078);The Northwest Normal University Scientific Research Improvement Team Foundation “Intelligent computing theory and application”(No.NWNU-LKQN-1706).
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由于在数据同化过程中远距离的观测与同化状态之间存在着虚假相关,局地化方法受到广泛关注。同时,在集合数目较少的同化情况下,观测数据难以得到有效利用,使得同化效果欠佳。因此,提出了一种新的模糊控制局地化同化方法,通过模糊控制算法判断观测点与状态更新点之间的距离,构造观测位置模糊权重。利用非线性Lorenz-96模型,比较分析模糊控制局地化同化(FLETKF)算法与模糊控制同化(FETKF)方法、局地化分析同化(LETKF)算法和集合转换卡尔曼滤波(ETKF)算法在非线性强迫参数变化时的性能,同时探讨了4种算法在不同强度下的优劣。研究结果表明,新方法能够获得更有效的观测权重,避免了远距离观测与状态变量之间的虚假相关,减小由于观测数据难以得到有效利用而带来的误差,在不同观测误差协方差情况下,随着集合数的增加,4种算法中FLETKF能够保持较好的鲁棒性,在观测误差协方差较大时,FLETKF方法的均方根误差(RMSE)相对FETKF方法的RMSE值减小98.2%,提高了同化精度,但在同化所需时间上,由于模糊控制局地化同化方法在判断观测点与状态更新点之间的距离,构造观测位置等价权重需要较长的额外时间,因此,并行计算的性能需进一步研究。

关键词: 模糊控制局地化同化(FLETKF), 模糊控制, 局地化方法, 集合转换卡尔曼滤波(ETKF)

Due to the fake correlation between distance-observations and assimilation-states during data assimilation, more attention has been paid to the localization method. Meanwhile, in the case of assimilation with a small number of sets, the observation data is difficult to be used effectively, which makes the assimilation effect not good enough. Therefore, a new fuzzy control was proposed to analyze the local method. The fuzzy control algorithm was used to judge the distance between the observation point and the status update point and to construct the fuzzy weight of the observation position. The study aimed to make use of the nonlinear Lorenz-96 model to compare the Fuzzy control combine Local Analysis algorithm (FLETKF) and Fuzzy control combine Ensemble Transform Kalman Filter method (FETKF), local Ensemble Transform Kalman Fliter (LETKF) and Ensemble Transform Kalman Filter algorithm (ETKF) when the nonlinear forced parameter changed. In addition, the strengths and weaknesses of four algorithms were discussed by different intensities. The results show that the new method can obtain more effective observation weights, avoiding the false correlation between long-distance observations and state variables, reducing the errors caused by the observation data which is difficult to be used effectively. Under different assimilation strength, FLETKF can maintain good robustness. However, in terms of assimilation time, the construction of the equivalent weight of the observation position requires additional time because the localization assimilation method of fuzzy control determines the distance between the observation point and the status update point. Parallel computing performance needs further study.

Key words: FLETKF, Fuzzy Control, Localization methods, ETKF

中图分类号: 

图1 耦合模糊控制的同化系统原理图
Fig.1 Schematic diagram of assimilation system coupled with the fuzzy control
图1 耦合模糊控制的同化系统原理图
Fig.1 Schematic diagram of assimilation system coupled with the fuzzy control
图2 观测位置与状态之间模糊控制同化示意图 [ 22 ]
Fig.2 Diagram of assimilation system coupled with the fuzzy control between observation position and status [ 22 ]
图2 观测位置与状态之间模糊控制同化示意图 [ 22 ]
Fig.2 Diagram of assimilation system coupled with the fuzzy control between observation position and status [ 22 ]
表1 模糊控制规则表
Table 1 The rule table of fuzzy control
disti
coeffsi
Vi		 NB NM NS ZO PS PM PB
NB PB PB PM PM PS PS ZO
NM PB PM PM PS PS ZO NS
NS PM PM PS PS ZO NS NS
ZO PM PS PS ZO NS NS NM
PS PS PS ZO NS NS NM NM
PM PS ZO NS NS NM NM NB
PB ZO NS NS NM NM NB NB
表1 模糊控制规则表
Table 1 The rule table of fuzzy control
disti
coeffsi
Vi		 NB NM NS ZO PS PM PB
NB PB PB PM PM PS PS ZO
NM PB PM PM PS PS ZO NS
NS PM PM PS PS ZO NS NS
ZO PM PS PS ZO NS NS NM
PS PS PS ZO NS NS NM NM
PM PS ZO NS NS NM NM NB
PB ZO NS NS NM NM NB NB
图3 三角形隶属度函数图
Fig.3 The graph of triangle membership function
图3 三角形隶属度函数图
Fig.3 The graph of triangle membership function
表2 FLETKF的模糊控制响应表
Table 2 The fuzzy control response table of FLETKF
△dist 0~2.3 0~3.2 1.1~1.4 1.5~5.2 1.6~5.6 … 15.25~20
△coeffs 1~0.975 0.975~0.95 0.95~0.925 0.925~0.95 0.9~0.875 … 0.025~0
表2 FLETKF的模糊控制响应表
Table 2 The fuzzy control response table of FLETKF
△dist 0~2.3 0~3.2 1.1~1.4 1.5~5.2 1.6~5.6 … 15.25~20
△coeffs 1~0.975 0.975~0.95 0.95~0.925 0.925~0.95 0.9~0.875 … 0.025~0
表3 FETKF的模糊控制响应表
Table 3 The fuzzy control response table of FETKF
dist 0~2.5 0~3.5 1.5~2 2.5~4.5 3~5.5 … 17.35~20
g 1~0.95 0.925~0.9 0.9~0.875 0.875~0.85 0.85~0.825 … 0.025~0
表3 FETKF的模糊控制响应表
Table 3 The fuzzy control response table of FETKF
dist 0~2.5 0~3.5 1.5~2 2.5~4.5 3~5.5 … 17.35~20
g 1~0.95 0.925~0.9 0.9~0.875 0.875~0.85 0.85~0.825 … 0.025~0
图4 强迫参数 F对同化结果的影响
Fig.4 The influence of forcing parameters F for assimilation results
图4 强迫参数 F对同化结果的影响
Fig.4 The influence of forcing parameters F for assimilation results
图5 随强迫参数 F变化的RMSE变化趋势
Fig.5 The variable trend of RMSE with forcing parameters F
图5 随强迫参数 F变化的RMSE变化趋势
Fig.5 The variable trend of RMSE with forcing parameters F
图6 同化强度为 R=0.001时,4种算法随集合数的变化
Fig.6 The four algorithms vary with the Ensemble number when assimilation intensity R is 0.001
图6 同化强度为 R=0.001时,4种算法随集合数的变化
Fig.6 The four algorithms vary with the Ensemble number when assimilation intensity R is 0.001
图7 同化强度为 R=1时,4种算法随集合数的变化
Fig.7 The four algorithms vary with the Ensemble number when assimilation intensity R is 1
图7 同化强度为 R=1时,4种算法随集合数的变化
Fig.7 The four algorithms vary with the Ensemble number when assimilation intensity R is 1
图8 同化强度为 R=10时,4种算法随集合数的变化
Fig.8 The four algorithms vary with the Ensemble number when assimilation intensity R is 10
图8 同化强度为 R=10时,4种算法随集合数的变化
Fig.8 The four algorithms vary with the Ensemble number when assimilation intensity R is 10
表4 4种算法在不同同化强度下的性能比较
Table 4 Comparison of performance of four algorithms at different assimilation strengths
内容
同化强度		 方法 同化时间/s RMSE
R=0.001 ETKF 0.012 3.735
LETKF 0.279 3.621
FETKF 6.913 3.527
FLETKF 7.82 3.237
R=1 ETKF 0.012 4.397
LETKF 0.275 4.03
FETKF 7.012 3.971
FLETKF 13 2.983
R=10 ETKF 0.012 4.616
LETKF 0.269 4.021
FETKF 8.723 3.985
FLETKF 12.5 3.912
表4 4种算法在不同同化强度下的性能比较
Table 4 Comparison of performance of four algorithms at different assimilation strengths
内容
同化强度		 方法 同化时间/s RMSE
R=0.001 ETKF 0.012 3.735
LETKF 0.279 3.621
FETKF 6.913 3.527
FLETKF 7.82 3.237
R=1 ETKF 0.012 4.397
LETKF 0.275 4.03
FETKF 7.012 3.971
FLETKF 13 2.983
R=10 ETKF 0.012 4.616
LETKF 0.269 4.021
FETKF 8.723 3.985
FLETKF 12.5 3.912
表5 2种算法的RMSE减小百分比
Table 5 The percentage reduction of RMSE of two algorithms
R=0.001 R=1 R=10
FLETKF 3.237 2.983 3.912
FETKF 3.527 3.971 3.985
减小百分比/% 91.8 75.1 98.2
表5 2种算法的RMSE减小百分比
Table 5 The percentage reduction of RMSE of two algorithms
R=0.001 R=1 R=10
FLETKF 3.237 2.983 3.912
FETKF 3.527 3.971 3.985
减小百分比/% 91.8 75.1 98.2
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