﻿ 基于IABC优化LSSVR的变形预测研究
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 大地测量与地球动力学  2019, Vol. 39 Issue (1): 98-102  DOI: 10.14075/j.jgg.2019.01.019

### 引用本文

FENG Tengfei, LIU Xiaosheng, ZHONG Yu, et al. Research on Deformation Prediction Based on LSSVR Optimized by IABC[J]. Journal of Geodesy and Geodynamics, 2019, 39(1): 98-102.

### 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

FENG Tengfei, postgraduate, majors in deformation monitoring and data processing, E-mail:814479344@qq.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

1 基本理论介绍 1.1 最小二乘支持向量回归机

LSSVR的基本思想是利用已知的样本数据得出一个最佳拟合函数，根据这个函数再输入新的样本数据，从而计算出对应的输出值。其具体步骤[5-6]如下。

 $T = \left\{ {\left( {{x_1},{y_1}} \right), \cdots ,\left( {{x_l},{y_l}} \right)} \right\} \in {\left( {{R^n} \times Y} \right)^l}$ (1)

 $y\left( x \right) = {\mathit{\boldsymbol{\omega }}^{\rm{T}}}\mathit{\boldsymbol{\varphi }}\left( x \right) + b$ (2)

 $\begin{array}{*{20}{c}} {\mathop {\min }\limits_{\omega ,b,\xi } R = \frac{1}{2}{{\left\| \mathit{\boldsymbol{\omega }} \right\|}^2} + \frac{c}{2}\sum\limits_{i = 1}^l {{\xi ^2}} }\\ {{\rm{s}}.\;{\rm{t}}.\;\;\;{y_i} = {\mathit{\boldsymbol{\omega }}^{\rm{T}}}\mathit{\boldsymbol{\varphi }}\left( {{x_i}} \right) + b + {\xi _i}} \end{array}$ (3)

 $y\left( x \right) = \sum\limits_{i = 1}^l {{a_i}K\left( {x,{x_i}} \right)} + b$ (4)

 $K\left( {x,{x_i}} \right) = \exp \left( { - \frac{{\left\| {x - {x_i}} \right\|_2^2}}{{2{\sigma ^2}}}} \right)$ (5)
1.2 标准ABC

1) 随机产生蜜源的初始位置：

 ${x_{id}} = {L_d} + {\rm{rand}}\left( {0,1} \right)\left( {{U_d} - {L_d}} \right)$ (6)

2) 在初始蜜源的周围搜索，产生一个新的蜜源：

 ${v_{id}} = {x_{id}} + \varphi \left( {{x_{id}} - {x_{jd}}} \right)$ (7)

3) 评价2个蜜源的适应度，根据贪婪算法确定保留xivi

 ${\rm{fit}} = \left\{ \begin{array}{l} 1/\left( {1 + {f_i}} \right),{f_i} \ge 0\\ 1 + {\rm{abs}}\left( {{f_i}} \right),其他 \end{array} \right.$ (8)

4) 计算引领蜂找到的蜜源被跟随的概率：

 ${P_i} = {\rm{fi}}{{\rm{t}}_i}/\sum\limits_{i = 1}^{{\rm{NP}}} {{\rm{fi}}{{\rm{t}}_i}}$ (9)

5) 跟随蜂采用轮盘赌的方式选择引领蜂，即在[0, 1]内产生均匀分布的随机数r，当Pi>r，则跟随蜂在蜜源i周围产生一个新蜜源，利用贪婪算法确定保留的蜜源。判断蜜源是否满足被放弃的条件为：经t次迭代到达阈值limit仍没找到更好的蜜源，则放弃。

 $x_i^{t + 1} = \left\{ \begin{array}{l} {L_d} + {\rm{rand}}\left( {0,1} \right)\left( {{U_d} - {L_d}} \right),t \ge {\rm{limit}}\\ x_i^t,t < {\rm{limit}} \end{array} \right.$ (10)

2 改进的人工蜂群算法

2.1 种群构造的改进

Haupt等[9]认为，对群体智能优化算法而言，初始种群的好坏影响着算法的全局收敛速度和解的质量，多样性较好的初始种群对提高算法的寻优性能很有帮助。在标准ABC中，种群的初始化是随机的，无法保证其多样性。考虑到ABC对初始种群的构造方法较为敏感，本文提出一种正反双种群交叉寻优策略来构造种群。

1) 初始化一个种群A，并设其中一个解为a=(x1x2，…xd)，xi∈(mini)，则其反向解为b=(x'1x'2，…x'd)，其中x'i=mi+nixi，以此构造出种群A的反向种群B。

2) 对种群A和种群B分别进行一次寻优，得到当前最优值p1p2

3) 对双种群进行信息交换：

 $\begin{array}{*{20}{c}} {{{p'}_1} = {p_1} + {\rm{rand}}\left( {0,1} \right)\left( {{p_1} - {p_2}} \right)}\\ {{{p'}_2} = {p_2} + {\rm{rand}}\left( {0,1} \right)\left( {{p_2} - {p_1}} \right)} \end{array}$ (11)

4) 根据贪婪算法选择p1p'1作为种群A的当前最优值，选择p2p'2作为种群B的当前最优值。

5) 达到最大迭代次数T，根据贪婪算法确定整个种群的最优值。

2.2 搜索策略的改进

 ${v_{id}} = {x_{id}} + {\varphi _1}\left( {{x_{id}} - {x_{jd}}} \right) + {\varphi _2}\left( {{y_d} - {x_{id}}} \right)$ (12)

 $\begin{array}{l} {v_{id}} = {x_{id}} + {w_1}{\varphi _1}\left( {{x_{id}} - {x_{jd}}} \right) + {w_2}{\varphi _2}\left( {{y_d} - {x_{id}}} \right)\\ \;\;\;\;\;\;\;{\omega _1} = {\omega _{\min }} + \left( {{\omega _{\max }} - {\omega _{\min }}} \right)\left( {1 - \frac{t}{T}} \right)\\ \;\;\;\;\;\;\;{\omega _2} = {\omega _{\max }} - \left( {{\omega _{\max }} - {\omega _{\min }}} \right)\left( {1 - \frac{t}{T}} \right) \end{array}$ (13)

2.3 蜜源选择概率的改进

 $\begin{array}{l} {P_i} = \frac{{{\rm{fit}}_i^\lambda }}{{\sum\limits_{i = 1}^{{\rm{NP}}} {{\rm{fit}}_i^\lambda } }}\\ \lambda = {{\rm{e}}^{\frac{t}{T}\ln 2}} - 1 \end{array}$ (14)

 图 1 IABC算法流程 Fig. 1 Flowchart of IABC
3 基于IABC优化LSSVR的变形预测模型构建

LSSVR中存在2个待优化的参数——惩罚参数c和核函数参数σ。以LSSVR的预测准确率为目标函数，将IABC与LSSVR相结合，用于变形预测模型的构建。具体实现步骤如下。

1) 数据预处理。归一化(mapminmax)到(0, 1)区间：

 $y = \frac{{\left( {{y_{\max }} - {y_{\min }}} \right)\left( {x - {x_{\min }}} \right)}}{{{x_{\max }} - {x_{\min }}}} + {y_{\min }}$ (15)

2) 设置IABC的控制参数。包括蜂群数量NP，蜜源最大搜索次数limit，算法最大迭代次数T，自适应函数ω取值范围ωmaxωmin，蜜源的维度即待优化参数的个数D及各参数的取值范围。

3) 设置适应度函数。变形预测的目的即为获取最小误差的预测值，故本文采用均方根误差函数作为目标函数，并将目标函数转化为适用于IABC的适应度函数。目标函数为：

 $\min f\left( {c,\sigma } \right) = \sqrt {\frac{1}{l}\sum\limits_{i = 1}^l {{{\left[ {{y_i} - g\left( {{x_i},c,\sigma } \right)} \right]}^2}} }$

 ${\rm{fi}}{{\rm{t}}_i} = \frac{1}{{1 + {f_i}}}$

4) 构造双种群。根据待优化参数的取值范围随机生成种群A，根据反向学习策略计算出对应的反向种群B，以此构造出双种群。

5) 根据IABC算法对双种群分别进行蜜源搜索、适应度计算以及信息交换等操作。

6) 达到最大迭代次数T，得到最优参数组合解。

7) 滚动预测。首先输入m期训练样本，预测出第m+1期变形数据，然后将已预测出的第m+1期数据加入训练样本，组成新的训练样本(同时保持训练样本期数不变)预测出第m+2期数据。以此类推，直到得出所有待预测样本。

4 工程实例

 图 2 IABC-LSSVR与ABC-LSSVR预测进化图 Fig. 2 Predictive evolutionary graph of IABC-LSSVR and ABC-LSSVR

 图 3 各模型预测结果 Fig. 3 The prediction results of each model

5 结语

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Research on Deformation Prediction Based on LSSVR Optimized by IABC
FENG Tengfei1     LIU Xiaosheng1     ZHONG Yu1     YU Liang1
1. School of Architectural and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, 86 Hongqi Road, Ganzhou 341000, China
Abstract: It is difficult to determine the penalty parameter and kernel function parameter of least square support vector regression(LSSVR). Additionally, artificial bee colony(ABC) is easy to fall into local optimum and its convergence speed is slow. So, we propose an improved artificial bee colony(IABC) to optimize the parameters of LSSVR and do research on deformation prediction. First, IABC generates positive and negative populations to increase the diversity of the initial group using the reverse learning strategy. After one iteration, information is exchanged between the optimal food sources of two populations to achieve optimal selection. Furthermore, we design an adaptive weight function and adaptive selection function to balance the exploration and development capacity of ABC. Second, we consider the predictive accuracy of LSSVR as the objective function, and transform it into the fitness function of IABC, thereby building a prediction model based on IABC optimization LSSVR. Then, taking the monitoring data of foundation pit as an example, we compare the prediction effect of the LSSVR model optimized by IABC, the LSSVR model optimized by ABC, and the combination model based on PSO. The results show that IABC increases the diversity of the population and improves the convergence accuracy. The prediction trend based on the IABC optimized LSSVR model is more practical and the prediction accuracy is higher than the contrast model.
Key words: IABC; reverse learning strategy; adaptive weight function; adaptive selection function