陶叶青, 王坚, 刘超. 附不等式约束的地表沉降时间序列自回归EIV模型[J]. 武汉大学学报 ( 信息科学版), 2020, 45(9): 1455-1460. DOI: 10.13203/j.whugis20180268
引用本文: 陶叶青, 王坚, 刘超. 附不等式约束的地表沉降时间序列自回归EIV模型[J]. 武汉大学学报 ( 信息科学版), 2020, 45(9): 1455-1460. DOI: 10.13203/j.whugis20180268
TAO Yeqing, WANG Jian, LIU Chao. A Solution for Ground Subsidence Prediction of Time Series Based on Autoregression EIV Model with Inequality Constraints[J]. Geomatics and Information Science of Wuhan University, 2020, 45(9): 1455-1460. DOI: 10.13203/j.whugis20180268
Citation: TAO Yeqing, WANG Jian, LIU Chao. A Solution for Ground Subsidence Prediction of Time Series Based on Autoregression EIV Model with Inequality Constraints[J]. Geomatics and Information Science of Wuhan University, 2020, 45(9): 1455-1460. DOI: 10.13203/j.whugis20180268

附不等式约束的地表沉降时间序列自回归EIV模型

A Solution for Ground Subsidence Prediction of Time Series Based on Autoregression EIV Model with Inequality Constraints

  • 摘要: 地表沉降监测是预防地质灾害发生的有效方法, 时间序列模型是进行地表沉降预测的主要模型。传统AR(autoregression)模型参数估计算法没有顾及模型系数矩阵中的元素含有观测误差的情况。为同时顾及模型观测向量与系数矩阵中的元素均含有观测误差的情况, 应用变量中含有误差(errors-in-variables, EIV)的参数估计模型改进基于时间序列的地表沉降预测模型。为提高AR模型参数解的收敛速度与精度, 应用先验信息构建具有不等式约束的EIV模型, 将建立的附有不等式约束EIV模型参数估计问题转化为非线性模型的二次规划问题, 结合中位函数建立参数估计迭代算法。为论证所建立算法的有效性与可行性, 通过实验分别对AR模型参数估计的最小二乘算法、EIV模型参数估计算法与该算法进行比较。实验证明, 所建立算法具有较高的精度和效率, 是一种可行的方法。

     

    Abstract: Ground subsidence monitoring is an effective method to forecast geological hazard, and time series model is the main model for ground subsidence prediction. To take into account both the observation errors existing in coefficient matrix and observation vector, in this contribution, the time series model of ground subsidence is developed to improve errors-in-variables (EIV) model, while the traditional model only takes into account the observation error existing in observation error. Besides, to improve efficiency and accuracy of computation model parameters, prior information is utilized to establish EIV model with inequality constraints, and the inequality constraints model for ground subsidence prediction is converted into quadratic programming of nonlinear model. And the iterative algorithm which is combined with median function is proposed. The efficiency and feasibility of the presented algorithm are verified through the instances, which are compared with the traditional least squares estimation algorithm and current algorithm for EIV model.

     

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