﻿ 基于局部均值分解和相关向量机的变形预测
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 大地测量与地球动力学  2018, Vol. 38 Issue (11): 1128-1132  DOI: 10.14075/j.jgg.2018.11.006

### 引用本文

LUO Yiyong, XU Zhikuan, ZHANG Liting, et al. Deformation Prediction Based on Local Mean Decomposition and Relevance Vector Machine[J]. Journal of Geodesy and Geodynamics, 2018, 38(11): 1128-1132.

### Foundation support

National Natural Science Foundation of China, No.41861058;Key Laboratory for Digital Land and Resources of Jiangxi Province, East China University of Technology, No. DLLJ201612; Science and Technology Project of the Education Department of Jiangxi Province, No. GJJ150592.

### About the first author

LUO Yiyong, PhD candidate, associate professor, majors in deformation data processing method, E-mail:luoyiyong@whu.edu.cn.

### 文章历史

1. 东华理工大学测绘工程学院，南昌市广兰大道418号，330013;
2. 武汉大学测绘学院，武汉市珞喻路129号，430079;
3. 东华理工大学江西省数字国土重点实验室，南昌市广兰大道418号，330013

1 LMD和RVM算法的改进 1.1 LMD算法的改进 1.1.1 LMD基本原理

 $\left\{ \begin{array}{l} {u_1}\left( t \right) = x\left( t \right) - {\rm{P}}{{\rm{F}}_1}\left( t \right)\\ {u_2}\left( t \right) = {u_1}\left( t \right) - {\rm{P}}{{\rm{F}}_2}\left( t \right)\\ \;\;\;\;\;\;\;\;\;\;\;\;\; \vdots \\ {u_k}\left( t \right) = {u_{k - 1}}\left( t \right) - {\rm{P}}{{\rm{F}}_q}\left( t \right) \end{array} \right.$ (1)

 $x\left( t \right) = \mathop \sum \limits_{q = 1}^k {\rm{P}}{{\rm{F}}_q}\left( t \right) + {u_k}\left( t \right)$ (2)
1.1.2 LMD算法的改进

1.2 RVM算法的改进 1.2.1 RVM基本原理

 $\alpha _i^{{\rm{opt}}} = \frac{{1 - {\alpha _i}{S_{i, i}}}}{{F_i^2}}$ (3)
 ${({\sigma ^2})^{{\rm{opt}}}} = \frac{{{{\left| {\left| {t - \mathit{\Phi }F} \right|} \right|}^2}}}{{N - \mathop \sum \limits_{i = 0}^N (1 - {\alpha _i}{S_{i, i}})}}$ (4)

1.2.2 RVM算法的改进

 $\begin{array}{l} K = \mu \exp \left( { - \frac{{||{x_i} - {x_j}|{|^2}}}{{{\psi ^2}}}} \right) + \\ \;\;\;\;\;\left( {1 - \mu } \right){\left[ {{x_i}{{\left( {\frac{{{x_j}}}{{{\chi ^2}}}} \right)}^{\rm{T}}} + 1} \right]^2} \end{array}$ (5)

1.3 模型建立结构

 图 1 改进LMD-RVM预测模型结构图 Fig. 1 Sketch of improved LMD-RVM's prediction model

2 基于改进LMD-RVM模型的大坝变形预测

2.1 LMD处理大坝监测数据及小波阈值去噪

 图 2 改进LMD分解后变形分量 Fig. 2 Deformation components of improved LMD

2.2 RVM模型预测结果

 图 3 各变形分量预测结果 Fig. 3 The prediction results of each deformation component

3 精度分析

 图 4 各方法预测曲线图和实际变形量 Fig. 4 The curves of each method predict and actual deformation

 图 5 各方法预测值绝对误差 Fig. 5 The absolute error of each method predict value

4 结语

1) 通过改进LMD自适应分解非平稳信号获得多个具有一定物理特征的变形分量，能有效处理干扰因素对数据的影响，能适当减少模型结构的复杂程度且对挖掘数据内部规律有一定提升。

2) 建立RVM预测模型在处理小样本、贫信息及复杂非线性问题等方面具有很大优势，同时该方法求得的多项精度指标值均优于BP神经网络方法和RVM方法的预测结果，证实该方法具有较好的鲁棒性和较强的泛化能力，是一种预测精度较高的方法。

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Deformation Prediction Based on Local Mean Decomposition and Relevance Vector Machine
LUO Yiyong1,2,3     XU Zhikuan1     ZHANG Liting1     HUANG Xiaolang1     MIAO Yuzhou1
1. Faculty of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China;
2. School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China;
3. Key Laboratory for Digital Land and Resources of Jiangxi Province, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China
Abstract: A new multi-scale deformation prediction method is proposed based on improved local mean decomposition (LMD) and weighted kernel function relevance vector machine algorithm (RVM). The deformation data is decomposed into several physical deformation components by LMD, and each deformation component is predicted by RVM optimized by genetic algorithm. Finally, a multi-scale deformation prediction method is established and applied to dam deformation prediction by adding the prediction results of each deformation component. The experimental results show that the improved LMD-RVM method is superior to the BP neural network method, RVM method and the improved EMD-RVM method in many precision indexes, which proves the effectiveness and reliability of the new method.
Key words: local mean decomposition; relevance vector machine; deformation prediction