﻿ 一种QPSO的地下浅层震源定位方法
 计算机系统应用  2020, Vol. 29 Issue (1): 215-219 PDF

Shallow Seismic Source Localization Method Based on QPSO
HE Ming, SU Xin-Yan, LI Jian
Shanxi Provincial Key Laboratory of Information Detection and Processing, North University of China, Taiyuan 030051, China
Foundation item: Shanxi Provincial University Innovation Project (201802083)
Abstract: In some traditional source location algorithms, the requirement of the initial source solution is high, the dependence is large, the search range has a certain limitation, and the source location optimization is difficult to be carried out in the large area range where the group wave aliasing is serious and the spectral component is complex. In order to solve this problem, a method of underground shallow source location based on Quantum Particle Swarm Optimization (QPSO) algorithm is proposed. The algorithm is realized by simulation, and the advantages and disadvantages of the proposed algorithm and the traditional algorithm are evaluated. The experimental results show that in the range of –100 m×100 m×–40 m, the location algorithm’s positioning accuracy of the shallow single-target source based on QPSO is obviously higher than that of the traditional source location algorithm based on PSO, the positioning accuracy can reach 0.324 m, which is of great practical application value.
Key words: underground source     single objective     source location     beam cross-location     QPSO

DOA模型求解方法主要分为两类: 传统的解算方法和智能优化求解方法. 传统算法为(1)最小二乘+Taylor算法, 该算法首先用最小二乘法解出震源初始估计值, 再利用泰勒中值定理对定位方程展开, 然后只保留一次导数, 在初始位置的基础上, 在每一步迭代时, 都沿当前点函数值下降的方向进行, 但该算法对初始解的依赖性比较大, 定位精度会随初始值的多次迭代后误差累加, 从而使定位精度降低[1]; (2)基于几何约束加权被动定位算法, 该算法将震源位置与传感器节点的距离作为参数, 两两传感器在空间中进行交叉定位, 再计算空间中各个交叉点的权值, 该方法对定位参数精度的要求比较高, 否则会出现交叉点异面的情况, 在计算震源交叉点权值时, 受权值的归一化影响, 可能导致最终解偏离真实震源解, 使误差增大. 智能优化求解方法主要为PSO (Particle Swarm Optimization)粒子群定位算法, 因为在该算法中, 粒子运动状态受速度—位移影响, 限制了粒子的搜索范围, 使得粒子只能在特定的轨迹进行搜索, 不能脱离粒子群本身, 容易陷入局部最优, 缩小了搜索范围并使最终定位结果不准确.

1 基于DOA的震源定位模型构建

 图 1 三维空间中DOA定位示意图

 \left\{ {\begin{aligned} &{{\tan}{\theta _i} = \frac{{x - {x_i}}}{{y - {y_i}}}}\\ &{\tan {\varphi _i} = \frac{{z - {z_i}}}{{{r_i}}}}\\ &{{r_i} = \sqrt {{{(x - {x_i})}^2} + {{(y - {y_i})}^2}} } \end{aligned}} \right. (1)

 \left\{\begin{aligned} & x_i-y_i\tan \theta_i=x-y\tan \theta_i\\ & z=\sqrt {(x-x_i)^2+(y-y_i)^2} \tan \varphi_i+z_i \end{aligned}\right. (2)

2 基于量子粒子群算法的DOA震源定位模型的解算 2.1 量子粒子群(QPSO)算法原理

QPSO量子化系统的特点在于, 引入了波函数, 使得粒子的运动状态由波函数决定, 具有随机性和不确定性. 测量前, 粒子没有既定的轨道束缚, 会以一定的概率出现在任何位置, 能以一定的概率在空间范围内任意搜索, 随机程度高, 能够达到全局搜索的目的, 摆脱了粒子运动的局限性[3]. 另外, 速度信息和位置信息归于一个参数, 算法收敛精度高. QPSO粒子运动状态如图3所示.

 图 2 PSO粒子状态转换图

 图 3 QPSO粒子状态转换图

 ${P_{i,n}} = {{\left( {{\varphi _1} * {P_{ibest,n}} + {\varphi _2} * {G_{best}}} \right)} / {({\varphi _1} + {\varphi _2})}}$ (3)

 $mbest = \frac{1}{M}\sum\limits_{i = 1}^M {{P_i} = \left(\frac{1}{M}\sum\limits_{i = 1}^M {{P_{i,1,\cdots,}}\frac{1}{M}} \sum\limits_{i = 1}^M {{P_{i,n}}} \right)}$ (4)

 $L(t + 1) = 2*\beta *\left| {mbest - x(t)} \right|$ (5)

 \begin{aligned}[b] & x(t + 1) = p \pm \beta *\left| {mbest - x(t)} \right|*\ln ({1 / u})\\ & u ={\rm rand}(0,1) \end{aligned} (6)

 $\beta (t) = ({\beta _0} - {\beta _1}) * ({{({t_{\max }} - t)}/ {{t_{\max }}}}) + {\beta _1}$ (7)
2.2 基于QPSO的DOA算法的具体实现过程 2.2.1 目标函数的构建

 $f(x,y,z) = \sum\limits_{i = 1}^2 {(({x_i} - x + (y - {y_i})} \cdot\tan {\theta _i}{)^2} + {(z - {z_i} - {r_i}\tan {\varphi _i})^2})$ (8)

2.2.2 QPSO的粒子更新方式

2.2.3 基于QPSO的DOA定位算法具体实现过程

 图 4 QPSO算法执行流程

3 算法仿真

 图 5 传感器及炸点分布图

 图 6 3种方法适应度曲线图

 图 7 3种方法误差曲线图

4 结论

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