﻿ 基于DE−GRNN算法的布里渊散射谱拟合
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 应用科技  2019, Vol. 46 Issue (3): 46-50  DOI: 10.11991/yykj.201809003 0

### 引用本文

KANG Weixin, LI Hui, HAN Yue. A fitting method based on DE-GRNN for Brillouin scattering spectrum[J]. Applied Science and Technology, 2019, 46(3), 46-50. DOI: 10.11991/yykj.201809003.

### 文章历史

A fitting method based on DE-GRNN for Brillouin scattering spectrum
KANG Weixin , LI Hui , HAN Yue
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: In order to improve the feature extraction accuracy of Brillouin scattering spectrum based on Brillouin optical time domain analysis (BOTDA) distributed optical fiber sensor technology, a curve fitting algorithm based on differential evolution algorithm (DE) is proposed to optimize general regression neural network (GRNN). The DE algorithm is used to automatically optimize the smoothing factor of GRNN and reduce the complexity of human testing. Simulation results show that the hybrid optimization algorithm has good fitting performance for Brillouin scattering spectrum under different signal-noise-ratio and linewidth. The optimum fitting degree can be above 0.99, the minimum root mean square error is 0.0120, and the fitting performance is better than the traditional Brillouin scattering algorithms.
Keywords: fiber optics    Brillouin scattering spectrum    differential evolution (DE)    general regression neural network (GRNN)    curve fitting    fault detection    feature exctraction    fitting precision

1 基本原理 1.1 布里渊散射谱模型

 ${g_B}\left( v \right) = {g_0}\frac{{{{\left( {\Delta {v_B}/2} \right)}^2}}}{{{{\left( {v - {v_B}} \right)}^2} + {{\left( {\Delta {v_B}/2} \right)}^2}}}$

 $\begin{array}{l} {f_B}\left( v \right) = k\displaystyle\frac{{{{\left( {\Delta {v_{{B_1}}}/2} \right)}^2}}}{{{{\left( {v - {v_B}} \right)}^2} + {{\left( {\Delta {v_{{B_1}}}/2} \right)}^2}}} + \\ \qquad\quad \left( {1 - k} \right)\exp [ - 2.773{\left( {\Delta {v_{{B_2}}}^{ - 2}\left( {v - {v_B}} \right)} \right)^2}] \\ \end{array}$ (1)

1.2 广义回归神经网络

 $E[y|x] =\frac{{ \displaystyle\int_{ - \infty }^\infty {yg(x,y){\rm{d}}y} }}{{ \displaystyle\int_{ - \infty }^\infty {g(x,y){\rm{d}}y} }}$ (2)
 $\begin{array}{l} g(x,y) = \displaystyle\frac{1}{{{{(2{\rm{{\text{π}} }})}^{\frac{{(m + 1)}}{2}}}{\sigma ^{(m + 1)}}}} \cdot \displaystyle\frac{1}{n}\sum\limits_{i = 1}^n {\exp \left[ - \displaystyle\frac{{{{({{x}} - {x_i})}^{\rm{T}}}({{x}} - {x_i})}}{{2{\sigma ^2}}}\right]} \cdot \\ \qquad \qquad \exp \left[ - \displaystyle\frac{{{{({{y}} - {y_i})}^2}}}{{2{\sigma ^2}}}\right] \end{array}$ (3)

 $\hat y(x) = \displaystyle\frac{{\displaystyle\sum\limits_{i = 1}^n {{y_i}\exp \left( { - \displaystyle\frac{{{{({{x}} - {x_i})}^{\rm{T}}}({{x}} - {x_i})}}{{2{\sigma ^2}}}} \right)} }}{{\displaystyle\sum\limits_{i = 1}^n {\exp \left( - \displaystyle\frac{{{{({{x}} - {x_i})}^{\rm{T}}}({{x}} - {x_i})}}{{2{\sigma ^2}}}\right)} }}$

GRNN结构模型相似于RBF网络结构，由4层组成，分别是输入层、模式层、求和层、输出层，如图1所示。输入层的元素是简单的线性神经元，每个神经元对应输入的参数 $x$ ；模式层也叫隐含回归层，每个神经元对应一个训练样本；求和层有2个神经元，一个计算模式层的线性权重和，另一个计算模式层实际目标值的权重和，估计值 $\hat y$ 等于2部分和之商。

1.3 DE-GRNN混合优化算法

DE−GRNN算法中，利用DE搜索GRNN的最优扩展常数。DE随机产生初始扩展常数种群，进行迭代寻优直至达到最大迭代次数，将获得的最优扩展常数代入GRNN中进行曲线拟合。拟合值和真实值之间欧几里得距离的倒数用于评价差分进化操作得到的最优个体的性能，即适应度函数。当欧几里得距离越来越小，则拟合值越来越大，意味着拟合曲线趋近于真实值，有更好的拟合精度，适应度函数为：

 $f(m) =\displaystyle \frac{1}{{\sqrt {\displaystyle\sum\limits_{i = 1}^n {{{({m_i} - {M_i})}^2}} } }}$

2 仿真分析

3 结论

1）该混合优化算法可以实现不同信噪比和不同线宽情况下布里渊散射谱的曲线拟合，最优拟合度达0.998 3，最小均方根误差为0.012 0，最小平均绝对误差为0.010 1；

2）相较于传统PSO、QPSO、GAPSO、LM-PSO和GA-QPSO，布里渊散射谱拟合算法，具有更高的拟合度；

3）同时，该算法不依赖初值，避免了传统算法易陷入局部极值的弊端，对于BOTDA型分布式光纤传感系统的布里渊散射谱拟合，提高分布式光纤传感器故障点检测精度具有重要实际意义。

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