[1]于芳星,姬波,CHENG Quanrun,等.双腔光反馈干涉激光系统中Lang-Kobayashi方程的六阶龙格-库塔算法[J].郑州大学学报(工学版),2021,42(5):37-43.[doi:10.13705/j.issn.1671-6833.2021.05.021]
　Yu Fangxing,Ji Bo,Cheng Quanrun,et al.Sixth-order Longe-Kuta algorithm for the Lang-Kobayashi equation in a two-cavity optical feedback interferometric laser system[J].Journal of Zhengzhou University (Engineering Science),2021,42(5):37-43.[doi:10.13705/j.issn.1671-6833.2021.05.021]
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双腔光反馈干涉激光系统中Lang-Kobayashi方程的六阶龙格-库塔算法()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
42
期数:
2021年5期
页码:
37-43
栏目:
出版日期:
2021-09-10

文章信息/Info

Title:
Sixth-order Longe-Kuta algorithm for the Lang-Kobayashi equation in a two-cavity optical feedback interferometric laser system
作者:
于芳星1,姬波1,CHENG Quanrun2,卢红星1,柳宏川1
1．郑州大学 信息工程学院，河南 郑州 450001; 2．伍伦贡大学 电子计算机与通信工程学院，澳大利亚新南威尔士州 伍伦贡市 2522
Author(s):
Yu Fangxing1; Ji Bo1; Cheng Quanrun2; Lu Hongxing1; Liu Hongchuan1;
1．School of Information Engineering，Zhengzhou University，Zhengzhou 450001，China; 2．School of Electrical Computer and Telecommunications Engineering，University of Wollongong，Wollongong 2522，Australia
关键词:
Keywords:
dual-cavity OFI system;  Lang-Kobayashi equation;  sixth-order Runge-Kutta algorithm;  simulation software
DOI:
10.13705/j.issn.1671-6833.2021.05.021
文献标志码:
A
摘要:
双腔光反馈干涉( OFI) 系统常用于移动物体的高灵敏度感测，其动态行为可通过求解 LangKobayashi( L-K) 方程进行描述，而求解精度会对系统准确性产生决定性影响。为了提高双腔 OFI 系统对移动物体的测量精度，提出一种求解 L-K 方程的六阶龙格-库塔算法。通过分析微分方程数值解法的原理，在四阶龙格-库塔算法的基础上选取更多区间点计算积分曲线的斜率平均值，使其更接近于真实值以进一步提高求解精度。同时，设计并实现了基于光电信号双腔 OFI 系统的移动物体运动检测仿真软件并进行仿真实验，将六阶龙格-库塔算法分别与欧拉法、四阶龙格-库塔算法的仿真结果进行对比分析。实验结果表明: 该算法与欧拉法相比，求解精度平均提高了约 22%; 与四阶龙格-库塔算法相比，求解精度平均提高了约 6%。六阶龙格-库塔算法可以提高 L-K 方程的求解精度，从而生成更精确的仿真结果，提高双腔 OFI 系统的感测灵敏度。
Abstract:
The dual-cavity optical feedback interference system is often used for high-sensitivity sensing of moving objects. Its dynamic behavior can be solved by the Lang-Kobayashi (L-K) equation, and the accuracy of the solution will have a decisive influence on the measurement accuracy. In order to improve the measurement accuracy of the dual-cavity OFI system for moving objects, a sixth-order Runge-Kutta algorithm to solve the L-K equation is proposed. By analyzing the principle of the numerical solution method of differential equations, more interval points are selected to calculate the average slope of the integral curve on the basis of the fourth-order Runge-Kutta algorithm, so as to make it closer to the real value and further improve the solution accuracy. At the same time, the simulation software of moving object motion detection is designed and implemented based on the optoelectronic signal dual-cavity OFI system for simulation experiments, and the simulation results of the sixth-order Runge-Kutta algorithm is compared with the Euler method and the fourth-order Runge-Kutta algorithm. Experimental results show that compared with Euler′s method, the solution accuracy is improved by about 22% on average; Compared with the fourth-order Runge-Kutta algorithm, the solution accuracy is improved by about 6% on average. The sixth-order Runge-Kutta algorithm can improve the solving accuracy of L-K equation, thus generating more accurate simulation results and improving the sensing sensitivity of the dual-cavity OFI system.

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更新日期/Last Update: 2021-10-11