﻿ 基于PSR-WSVM模型的边坡位移预测
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 大地测量与地球动力学  2020, Vol. 40 Issue (6): 577-580  DOI: 10.14075/j.jgg.2020.06.006

### 引用本文

LI Jianxin, LIU Xiaosheng, XIAO Gang, et al. Slope Displacement Prediction Based on PSR-WSVM Model[J]. Journal of Geodesy and Geodynamics, 2020, 40(6): 577-580.

### Foundation support

National Natural Science Foundation of China, No. 41561091.

### Corresponding author

LIU Xiaosheng, PhD, professor, PhD supervisor, majors in geodesy and survey engineering, E-mail:lxs9103@163.com.

### 第一作者简介

LI Jianxin, postgraduate, majors in deformation monitoring and forecasting, E-mail:ljx1995@126.com.

### 文章历史

1. 江西理工大学建筑与测绘工程学院，江西省赣州市红旗大道86号，341000;
2. 河海大学地球科学与工程学院，南京市佛城西路8号，211100

1 PSR-WSVM模型 1.1 相空间重构理论(PSR)

 $\begin{array}{l} X\left\{ {{X_i}\left| {{Xi} = \left[ {{x_i}, {x_{i + \tau }} \cdots , {x_{i + \left( {m - 1} \right)\tau }}} \right]} \right.} \right., \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left. {i = 1, 2, \cdots M} \right\} \end{array}$ (1)

1.2 支持向量机

 $f\left( x \right) = \mathit{\boldsymbol{w}} \cdot \phi \left( x \right) + b$ (2)

 $f\left( x \right) = \sum\limits_{i = 1}^n {\left( {{\alpha _i} - {\alpha _i}^*} \right)} K\left( {{x_i}, x} \right) + b$ (3)

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} K\left( {{x_i}, x} \right) = \\ \prod\limits_{i = 1}^d {\cos } \left( {\frac{{1.75\left( {{x_i} - x} \right)}}{\sigma }} \right)\exp \left( { - \frac{{{{\left( {{x_i} - x} \right)}^2}}}{{2{\sigma ^2}}}} \right) \end{array}$ (4)
1.3 PSR-WSVM模型构建

 图 1 PSR-WSVM模型流程 Fig. 1 PSR-WSVM model flow chart
2 工程实例

 图 2 监测点累积沉降变化曲线 Fig. 2 Cumulative settlement curve of monitoring point

C-C算法可以同时确定时间延迟τ和嵌入维数m的原因在于tw=(m-1)t, tw为时间窗口，也就意味着只要确定了时间延迟τ和时间窗口tw，嵌入维数m也随之确定。算法运行过程中计算3个统计量(ΔS(t)、S(t)和Scor(t))随时间的变化情况，具体计算过程见文献[14]。通常选择ΔS(t)的第1个局部极小值点和S(t)的第1个零点中的较小值作为时间延迟τScor(t)的全局最小值作为时间窗口tw。本文C-C算法统计量计算结果见图 3，由图可知，时间延迟τ取14较为合适，时间窗口tw取23，根据三者的关系可确定嵌入维数m取3较为合适。

 图 3 C-C算法统计量计算结果 Fig. 3 Statistical calculation results of C-C algorithm

3 结语

1) 将相空间重构理论应用于边坡位移时间序列，通过C-C算法确定时间延迟τ和嵌入维数m，将一维数据形式转换为高维形式，能够充分挖掘出边坡位移时间序列的隐藏信息，为边坡位移预测奠定基础。

2) 构造小波核函数作为支持向量机的核函数，通过工程实例验证了小波核函数具有较高的函数逼近能力，能够提高支持向量机模型的泛化能力和预测精度。

3) 工程实例测试结果显示，PSR-WSVM模型的预测精度优于SVM模型、WSVM模型和PSR-SVM模型，因此PSR-WSVM模型在边坡预测领域具有一定的应用前景，能够为边坡位移预测提供参考。

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Slope Displacement Prediction Based on PSR-WSVM Model
LI Jianxin1     LIU Xiaosheng1     XIAO Gang2     ZHOU Wen2     LIU Renzhi2
1. School of Architecture and Surveying and Mapping Engineering, Jiangxi University of Science and Technology, 86 Hongqi Road, Ganzhou 341000, China;
2. School of Earth Sciences and Engineering, Hohai University, 8 West-Focheng Road, Nanjing 211100, China
Abstract: In order to establish a high-precision slope displacement prediction model, we use phase space reconstruction(PSR) to transform the slope displacement time series data into multi-dimensional data. The wavelet kernel function is constructed to improve the support vector machine model and to establish the PSR-WSVM model. The model is applied to slope displacement prediction. The PSR-WSVM model prediction results are compared with the traditional support vector machine model(SVM), wavelet support vector machine model(WSVM) and phase space reconstruction-based support vector machine model(PSR-SVM) prediction results. The average absolute error is passed. Mean absolute error percentage(MAPE) and root mean square error(RMSE) accuracy evaluation indicators verify the feasibility of the PSR-WSVM model. The results of engineering examples show that the three precision evaluation indexes of PSR-WSVM model prediction result are better than the other three models, and the accuracy of slope displacement prediction has obvious improvement.
Key words: phase space reconstruction; wavelet kernel function; support vector machine; slope displacement prediction