-
摘要: 在对气象数据进行插值的过程中, 如果只考虑数据的空间信息而忽视数据在时间上的关联, 必然影响插值的精度.针对具有时空特性的气象数据, 提出一种将时空Kriging方法与弹性网方法相结合的新方法.该方法主要利用弹性网算法解决时空Kriging算法中的时空变异函数矩阵为病态矩阵而无法求逆的问题, 通过弹性网算法获得变异函数矩阵方程的稀疏解, 从而提高时空插值的精度.在实际观测的气温数据和AQI数据上的仿真实验验证了该方法对气象时空数据插值的准确性.Abstract: In the process of interpolating meteorological data, if we only consider the spatial information of data and ignore the correlation of data in time, it will inevitably affect the accuracy of interpolation. For the meteorological data with time and space characteristics, this paper combines the spatial-temporal Kriging method with elastic net algorithm. This method uses the elastic net algorithm to solve the problems that the spatial-temporal variational function matrix in the spatial-temporal Kriging algorithm is ill-posed and we can not find its pseudoinverse. The elastic net algorithm is used to obtain the sparse solution of the variational function equation to improve the accuracy of spatial temporal interpolation. The simulation experiments on the observed temperature data and AQI data verify the high accuracy of the proposed method for spatial and temporal data interpolation.
-
Key words:
- Spatial-temporal data /
- spatial-temporal Kriging /
- interpolation /
- elastic net algorithm
-
图 4 STKriging对射阳市气温数据插值效果
Fig. 4 Interpolation curves of STKriging on temperature data of Sheyang City
图 8 STKriging对青岛市AQI数据插值效果
Fig. 8 Interpolation curves of STKriging on AQI data of Qingdao City
-
[1] 胡寿松, 张正道.基于神经网络的非线性时间序列故障预报.自动化学报, 2007, 33(7): 744-748 doi: 10.1360/aas-007-0744Hu Shou-Song, Zhang Zheng-Dao. Fault prediction for nonlinear time series based on neural network. Acta Automatica Sinica, 2007, 33(7): 744-748 doi: 10.1360/aas-007-0744 [2] 伦淑娴, 胡海峰.基于罚函数内点法的泄露积分型回声状态网的参数优化.自动化学报, 2017, 43(7): 1160-1168 doi: 10.16383/j.aas.2017.c160541Lun Shu-Xian, Hu Hai-Feng. Parameter optimization of leaky integrator echo state network with internal-point penalty function method. Acta Automatica Sinica, 2017, 43(7): 1160-1168 doi: 10.16383/j.aas.2017.c160541 [3] 苏本跃, 蒋京, 汤庆丰, 盛敏.基于函数型数据分析方法的人体动态行为识别.自动化学报, 2017, 43(5): 866-876 doi: 10.16383/j.aas.2017.c160120Su Ben-Yue, Jiang Jing, Tang Qing-Feng, Sheng Min. Human dynamic action recognition based on functional data analysis. Acta Automatica Sinica, 2017, 43(5): 866-876 doi: 10.16383/j.aas.2017.c160120 [4] 宋贺达, 周平, 王宏, 柴天佑.高炉炼铁过程多元铁水质量非线性子空间建模及应用.自动化学报, 2016, 42(11): 1664-1679 doi: 10.16383/j.aas.2016.c150819Song He-Da, Zhou Ping, Wang Hong, Chai Tian-You. Nonlinear subspace modeling of multivariate molten iron quality in blast furnace ironmaking and its application. Acta Automatica Sinica, 2016, 42(11): 1664-1679 doi: 10.16383/j.aas.2016.c150819 [5] Di Piazza A, Lo Conti F, Noto L V, Viola F, La Loggia G. Comparative analysis of different techniques for spatial interpolation of rainfall data to create a serially complete monthly time series of precipitation for Sicily, Italy. International Journal of Applied Earth Observation and Geoinformation, 2011, 13(3): 396-408 doi: 10.1016/j.jag.2011.01.005 [6] Ly S, Charles C, Degré A. Geostatistical interpolation of daily rainfall at catchment scale: The use of several variogram models in the Ourthe and Ambleve catchments, Belgium. Hydrology and Earth System Sciences, 2011, 15(7): 2259-2274 doi: 10.5194/hess-15-2259-2011 [7] 周登文, 申晓留.边导向的双三次彩色图像插值.自动化学报, 2012, 38(4): 525-530 doi: 10.3724/SP.J.1004.2012.00525Zhou Deng-Wen, Shen Xiao-Liu. Edge-directed bicubic color image interpolation. Acta Automatica Sinica, 2012, 38(4): 525-530 doi: 10.3724/SP.J.1004.2012.00525 [8] Wang Y, Akeju O V, Zhao T Y. Interpolation of spatially varying but sparsely measured geo-data: A comparative study. Engineering Geology, 2017, 231: 200-217 doi: 10.1016/j.enggeo.2017.10.019 [9] Jeffrey S J, Carter J O, Moodie K B, Beswick A R. Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environmental Modelling & Software, 2001, 16(4): 309-330 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ccce6481f2b1c81e50171ca87c1defb5 [10] Xiao M Y, Zhang G H, Breitkopf P, Villon P, Zhang W H. Extended co-Kriging interpolation method based on multi-fidelity data. Applied Mathematics and Computation, 2018, 323: 120-131 doi: 10.1016/j.amc.2017.10.055 [11] Li L X, Revesz P. Interpolation methods for spatio-temporal geographic data. Computers, Environment and Urban Systems, 2004, 28(3): 201-227 doi: 10.1016/S0198-9715(03)00018-8 [12] Antonić O, Križan J, Marki A, Bukovec D. Spatio-temporal interpolation of climatic variables over large region of complex terrain using neural networks. Ecological Modelling, 2001, 138(1-3): 255-263 doi: 10.1016/S0304-3800(00)00406-3 [13] 徐爱萍, 胡力, 舒红.空间克里金插值的时空扩展与实现.计算机应用, 2011, 31(1): 273-276 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jsjyy201101074Xu Ai-Ping, Hu Li, Shu Hong. Extension and implementation from spatial-only to spatiotemporal Kriging interpolation. Journal of Computer Applications, 2011, 31(1): 273-276 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jsjyy201101074 [14] Myers D E. Anisotropic radial basis functions. International Journal of Pure and Applied Mathematics, 2008, 42(2): 197-203 [15] De Cesare L, Myers D E, Posa D. Estimating and modeling space-time correlation structures. Statistics & Probability Letters, 2001, 51(1): 9-14 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=6f7474ad57568e5108834d108c0752a5 [16] De Iaco S, Myers D E, Posa D. Space-time analysis using a general product — Sum model. Statistics & Probability Letters, 2001, 52(1): 21-28 https://www.sciencedirect.com/science/article/pii/S0167715200002005 [17] De Iaco S, Myers D E, Posa D. On strict positive definiteness of product and product — Sum covariance models. Journal of Statistical Planning and Inference, 2011, 141(3): 1132-1140 doi: 10.1016/j.jspi.2010.09.014 [18] De Cesare L, Myers D E, Posa D. Product-sum covariance for space-time modeling: An environmental application. Environmetrics, 2001, 12(1): 11-23 doi: 10.1002/1099-095X(200102)12:1<11::AID-ENV426>3.0.CO;2-P [19] Bogaert P. Comparison of Kriging techniques in a space-time context. Mathematical Geology, 1996, 28(1): 73-86 doi: 10.1007/BF02273524 [20] Zeng Z C, Lei L P, Hou S S, Ru F, Guan X H, Zhang B. A regional gap-filling method based on spatiotemporal variogram model of CO$_2$ columns. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52(6): 3594-3603 doi: 10.1109/TGRS.2013.2273807 [21] McDaniel M D, Simpson R G, Malone B P, McBratney A B, Minasny B, Adams M A. Quantifying and predicting spatio-temporal variability of soil CH$_4$ and N$_2$O fluxes from a seemingly homogeneous Australian agricultural field. Agriculture, Ecosystems & Environment, 2017, 240: 182-193 [22] 李莎, 舒红, 徐正全.东北三省月降水量的时空克里金插值研究.水文, 2011, 31(3): 31-35 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=sw201103007Li Sha, Shu Hong, Xu Zheng-Quan. Study on spatial-temporal Kriging interpolation of monthly precipitation in three provinces of northeast China. Journal of China Hydrology, 2011, 31(3): 31-35 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=sw201103007 [23] 杜宇健, 萧德云. Kriging和Kalman技术在时空统计上的应用.见: 2004中国控制与决策学术年会论文集, 2004. 197-200, 205Du Yu-Jian, Xiao De-Yun. Application of Kriging and Kalman filter in spatial temporal statistics. In: Proceeding of the 2004 Chinese Control and Decision Conference, 2004. 197-200, 205 [24] 张桂梅, 孙晓旭, 刘建新, 储珺.基于分数阶微分的TV-$L^1$光流模型的图像配准方法研究.自动化学报, 2017, 43(12): 2213-2224Zhang Gui-Mei, Sun Xiao-Xu, Liu Jian-Xin, Chu Jun. Research on TV-$L^1$ optical flow model for image registration based on fractional-order differentiation. Acta Automatica Sinica, 2017, 43(12): 2213-2224 [25] 张文林, 张连海, 牛铜, 屈丹, 李弼程.基于正则化的本征音说话人自适应方法.自动化学报, 2012, 38(12): 1950-1957 doi: 10.3724/SP.J.1004.2012.01950Zhang Wen-Lin, Zhang Lian-Hai, Niu Tong, Qu Dan, Li Bi-Cheng. Regularization based eigenvoice speaker adaptation method. Acta Automatica Sinica, 2012, 38(12): 1950-1957 doi: 10.3724/SP.J.1004.2012.01950 [26] Liu Q S, Sun Y B, Wang C T, Liu T L, Tao D C. Elastic net hypergraph learning for image clustering and semi-supervised classification. IEEE Transactions on Image Processing, 2017, 26(1): 452-463 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f4419e755c4bb0d167e2cc8b4990b033 [27] You C, Li C G, Robinson D P, Vidal R. Oracle based active set algorithm for scalable elastic net subspace clustering. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition. Las Vegas, NV, USA: IEEE, 2016. 3928-3937 [28] Zhang Z, Lai Z H, Xu Y, Shao L, Wu J, Xie G S. Discriminative elastic-net regularized linear regression. IEEE Transactions on Image Processing, 2017, 26(3): 1466-1481 doi: 10.1109/TIP.2017.2651396 [29] Pavlyuk D. Short-term traffic forecasting using multivariate autoregressive models. Procedia Engineering, 2017, 178: 57-66 doi: 10.1016/j.proeng.2017.01.062 [30] Chatzis S P, Demiris Y. Echo state Gaussian process. IEEE Transactions on Neural Networks, 2011, 22(9): 1435-1445 doi: 10.1109/TNN.2011.2162109 -
下载:
图(8) / 表(2)
计量
- 文章访问数: 1332
- HTML全文浏览量: 228
- PDF下载量: 216
- 被引次数: 0
