Acta Geodaetica et Cartographica Sinica >

2017 , Vol. 46 >Issue 4: 526 - 532

DOI: https://doi.org/10.11947/j.AGCS.2017.20160531

Method of Deformation Probability Prediction Considering the Influence of Uncertainty Factors

  • WEI Guanjun ,
  • DANG Yamin ,
  • ZHANG Chuanyin ,
  • YANG Weifang
Expand
  • 1. Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China;
    2. Chinese Academy of Surveying and Mapping, Beijing 100830, China

Received date: 2016-10-24

  Revised date: 2017-03-16

  Online published: 2017-05-05

Fold

Abstract

A probabilistic prediction method of deformation is proposed based on the MCMC algorithm and the Bayesian Prediction Theory.This method describes the uncertainty of deformation prediction using probability distributions and implement the recursive process of prediction by probability rules. The settlement data from the Nanjing-Hangzhou high-speed roadbed is used to quantitatively analyze the forecast values, reliability intervals and so on, and then the results are compared with those obtained by the least squares estimation and the immune algorithm, and it has shown that the proposed method is effective and feasible.

Key words： prediction uncertainty; measurement error; parameter uncertainty; Gibbs sampling; probability predication

Cite this article

WEI Guanjun , DANG Yamin , ZHANG Chuanyin , YANG Weifang . Method of Deformation Probability Prediction Considering the Influence of Uncertainty Factors[J]. Acta Geodaetica et Cartographica Sinica, 2017 , 46(4) : 526 -532 . DOI: 10.11947/j.AGCS.2017.20160531

References

[1] 黄声享, 尹晖, 蒋征. 变形监测数据处理[M]. 2版. 武汉: 武汉大学出版社, 2010. HUANG Shengxiang, YIN Hui, JIANG Zheng. Deformation Monitoring Data Processing[M]. 2nd ed. Wuhan: Wuhan University Press, 2010.
[2] 徐伟, 何金平. 基于多尺度小波分析的大坝变形自回归预测模型[J]. 武汉大学学报(工学版), 2012, 45(3): 285-289. XU Wei, HE Jinping. Forecast Model of Dam Deformation Based on Multi-scale Wavelet Analysis and Autoregressive Method[J]. Engineering Journal of Wuhan University, 2012, 45(3): 285-289.
[3] 潘国荣. 基于时间序列分析的动态变形预测模型研究[J]. 武汉大学学报(信息科学版), 2005, 30(6): 483-487. PAN Guorong. Forecast Model of Dynamic Deformation Based on Time Series Analysis[J]. Geomatics and Information Science of Wuhan University, 2005, 30(6): 483-487.
[4] 马攀, 孟令奎, 文鸿雁. 基于小波分析的Kalman滤波动态变形模型研究[J]. 武汉大学学报(信息科学版), 2004, 29(4): 349-353. MA Pan, MENG Lingkui, WEN Hongyan. Kalman Filtering Model of Dynamic Deformation Based on Wavelet Analysis[J]. Geomatics and Information Science of Wuhan University, 2004, 29(4): 349-353.
[5] 魏冠军, 党亚民, 章传银. 应用贝叶斯动态模型的地基沉降概率分析与预测[J]. 测绘科学, 2012, 37(2): 52-53, 90. WEI Guanjun, DANG Yamin, ZHANG Chuanyin. Foundation Settlement Probability Analysis and Prediction Based on Bayes Dynamic Linear Model[J]. Science of Surveying and Mapping, 2012, 37(2): 52-53, 90.
[6] 李广春, 戴吾蛟, 杨国祥, 等. 时空自回归模型在大坝变形分析中的应用[J]. 武汉大学学报(信息科学版), 2015, 40(7): 877-881. LI Guangchun, DAI Wujiao, YANG Guoxiang, et al. Application of Space-Time Auto-Regressive Model in Dam Deformation Analysis[J]. Geomatics and Information Science of Wuhan University, 2015, 40(7): 877-881.
[7] 尹晖, 周晓庆, 张晓鸣. 非等间距多点变形预测模型及其应用[J]. 测绘学报, 2016, 45(10): 1140-1147. DOI: 10.11947/j.AGCS.2016.20160005. YIN Hui, ZHOU Xiaoqing, ZHANG Xiaoming. Non-equidistant Multi-Point Deformation Prediction Model and Its Application[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(10): 1140-1147. DOI: 10.11947/j.AGCS.2016.20160005.
[8] 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. ZHANG Zhenglu, HUANG Quanyi, WEN Hongyan, et al. Deformation Monitoring Analysis and Prediction for Engineering Constructions[M]. Beijing: Surveying and Mapping Press, 2007.
[9] 刘维宁. 岩土工程反分析方法的信息论研究[J]. 岩石力学与工程学报, 1993, 12(3): 193-205. LIU Weining. Study of Back Analysis Methods in Rock and Soil Engineering by the Information Theory[J]. Chinese Journal of Rock Mechanics and Engineering, 1993, 12(3): 193-205.
[10] NEUMANN I, KUTTERER H. Congruence Tests and Outlier Detection in Deformation Analysis with Respect to Observation Imprecision[J]. Journal of Applied Geodesy, 2007, (1): 1-7. DOI: 10.1515/jag.2007.001.
[11] EICHHORN A. Tasks and Newest Trends in Geodetic Deformation Analysis: A Tutorial[C]//Proceedings of the 15th European Signal Processing Conference. Poznan: IEEE, 2007: 1156-1160.
[12] 刘宁, 郭志川, 罗伯明. 地基沉降的概率分析方法和可靠度计算[J]. 岩土工程学报, 2000, 22(2): 143-150. LIU Ning, GUO Zhichuan, LUO Boming. Probabilistic Analysis and Reliability Assessment for Foundation Settlement[J]. Chinese Journal of Geotechnical Engineering, 2000, 22(2): 143-150.
[13] 贺钢, 蒋楚生. 边坡岩土工程不确定性及对策分析[J]. 铁道工程学报, 2010, 27(4): 19-22. HE Gang, JIANG Chusheng. Analysis of Uncertainty of Slope Rock-Soil Engineering and Countermeasure[J]. Journal of Railway Engineering Society, 2010, 27(4): 19-22.
[14] 杨杰, 胡德秀, 吴中如. 大坝安全监控模型因子相关性及不确定性研究[J]. 水利学报, 2004, 35(12): 99-105. YANG Jie, HU Dexiu, WU Zhongru. Multiple Co-linearity and Uncertainty of Factors in Dam Safety Monitoring Model[J]. Journal of Hydraulic Engineering, 2004, 35(12): 99-105.
[15] NEUMANN I, KUTTERER H. Geodetic Deformation Analysis with Respect to Observation Imprecision[C]//XXⅢ FIG Congress. Munich, Germany: [s.n.], 2006.
[16] 杜钧, 邓国. 单一值预报向概率预报转变的价值: 谈谈概率预报的检验和应用[J]. 气象, 2010, 36(12): 10-18. DU Jun, DENG Guo. The Utility of the Transition from Deterministic to Probabilistic Weather Forecasts-Verification and Application of Probabilistic Forecasts[J]. Meteorological Monthly, 2010, 36(12): 10-18.
[17] KRZYSZTOFOWICZ R. Bayesian Theory of Probabilistic Forecasting via Deterministic Hydrologic Model[J]. Water Resources Research, 1999, 35(9): 2739-2750.
[18] 邢贞相, 芮孝芳, 崔海燕, 等. 基于AM-MCMC算法的贝叶斯概率洪水预报[J]. 水利学报, 2007, 38(12): 1500-1506. XING Zhenxiang, RUI Xiaofang, CUI Haiyan, et al. Bayesian Probabilistic Flood Forecasting Model Based on Adaptive Metropolis-MCMC Algorithm[J]. Journal of Hydraulic Engineering, 2007, 38(12): 1500-1506.
[19] PAPAIOANNOU I,BETZ W,ZWIRGLMAIER K,et al. MCMC Algorithms for Subset Simulation[J]. Probabilistic Engineering Mechanics, 2015, 41: 89-103.
[20] WEST M, HARRISON J. Bayesian Forecasting and Dynamic Models[M]. 2nd ed. New York: Springer-Verlag, 1997.
[21] 杨杰, 胡德秀, 吴中如. 基于最大熵原理的贝叶斯不确定性反分析方法[J]. 浙江大学学报(工学版), 2006, 40(5): 810-815, 835. YANG Jie, HU Dexiu, WU Zhongru. Bayesian Uncertainty Inverse Analysis Method Based on POME[J]. Journal of Zhejiang University (Engineering Science), 2006, 40(5): 810-815, 835.
[22] 陈斌, 刘宁, 卓家寿. 岩土工程反分析的扩展贝叶斯法[J]. 岩石力学与工程学报, 2004, 23(4): 555-560. CHEN Bin, LIU Ning, ZHUO Jiashou. Extended Bayesian Method of Inverse Analysis in Geoengineering[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(4): 555-560.
[23] YALÇINKAYA M,TANIR E.A Study on Using Bayesian Statistics in Geodetic Deformation Analysis[C]//Proceedings of the 11th FIG Symposium on Deformation Measurements. Santorini, Greece: [s.n.], 2003.
[24] KOCH K R. Bayesian Inference with Geodetic Applications[M]. Berlin Heidelberg, Germany: Springer-Verlag, 1990.
[25] NTZOUFRAS I. Bayesian Modeling Using WinBUGS[M]. New York: Wiley, 2009.
[26] GEMAN S, GEMAN D. Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(6): 721-741.
[27] GELFAND A E, SMITH A F M, LEE T M. Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling[J]. Journal of the American Statistical Association, 1992, 87(418): 523-532.
[28] GUO Jia, ZHENG Junjie, LIU Yong. Application of an Immune Algorithm to Settlement Prediction[J]. Journal of Zhejiang University-SCIENCE A, 2009, 10(1): 93-100.
[29] SMITH A F M, ROBERTS G O. Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods[J]. Journal of the Royal Statistical Society Series B: Methodological, 1993, 55(1): 3-23.
Options
Outlines

/

〈 〉