多种群遗传算法与截断奇异值分解法在开关电弧反演中的应用

doi:10.11985/2018.06.003

电气工程学报 ›› 2018, Vol. 13 ›› Issue (6): 14-19.doi: 10.11985/2018.06.003

多种群遗传算法与截断奇异值分解法在开关电弧反演中的应用

赵宏晨¹,王刚²,刘晓明³

^1. 沈阳工业大学电气工程学院沈阳 110870
^2. 贵州理工学院机械工程学院贵阳 550003
^3. 天津工业大学天津市电工电能新技术重点实验室天津 300387

收稿日期:2018-04-22 出版日期:2018-06-25 发布日期:2018-06-25
作者简介:赵宏晨男 1989年生,博士研究生,主要研究方向为电弧反演问题、智能优化算法。|王刚男 1989年生,博士,副教授,主要研究方向为矩阵分析、H_∞控制及正则化方法。
基金资助:
国家自然科学基金面上项目(51377106)

Application of Multi-Population Genetic Algorithm and Truncated Singular Value Decomposition in Switching Arc Inversion

Zhao Hongchen¹,Wang Gang²,Liu Xiaoming³

^1. Shenyang University of Technology Shenyang 110870 China
^2. Guizhou Institute of Technology Guiyang 550003 China
^3. Tianjin Polytechnic University Tianjin 300387 China

Received:2018-04-22 Online:2018-06-25 Published:2018-06-25

摘要/Abstract

摘要：

利用电流与空间磁场的对应关系,将电弧视为具有变弧径多条电流线集合。基于毕奥萨伐尔定律,通过正演分析获取组合电弧电流线在空间的磁场分布。为简化问题复杂度,考虑电弧未入栅片的阶段,利用多种群遗传算法优化目标函数求解电磁逆问题非线性方程组,以确定电弧空间位置。在上述基础上,为解决逆问题不适定性,采用截断奇异值分解法反演电弧电流分布,并通过GCV准则获取正则化参数。反演结果有助于理解开关电弧的物理特性。

关键词: 开关电弧反演, 不适定性, 多种群遗传算法, 截断奇异值分解, GCV准则

Abstract:

By using the corresponding relationship between the current and the space magnetic field, the arc is regarded as a set of multiple current lines with variable arc diameters. Based on Biot-Savart’s law, the magnetic field distribution of combined arc streamlines in space is obtained by forward analysis. To simplify the complexity of the problem, the research only considers the phase of the arc not entering the splitter plates, and the multi-population genetic algorithm(MPGA) is used to optimize the objective function for solving the nonlinear equations of the electromagnetic inverse problem to determine the space position of the arc. On the basis of the above, the truncated singular value decomposition(TSVD) method is used to inverse the arc current distribution, with the regularization parameters obtained by the GCV criterion. The inversion results will contribute to understand the physical characteristics of the switch arc.

Key words: Switching arc inverse problem, ill-posed, MPGA, TSVD, GCV criterion

中图分类号:

TM501

赵宏晨,王刚,刘晓明. 多种群遗传算法与截断奇异值分解法在开关电弧反演中的应用[J]. 电气工程学报, 2018, 13(6): 14-19.

Zhao Hongchen,Wang Gang,Liu Xiaoming. Application of Multi-Population Genetic Algorithm and Truncated Singular Value Decomposition in Switching Arc Inversion[J]. Journal of Electrical Engineering, 2018, 13(6): 14-19.

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电流线标号	最小二乘法(%)	截断奇异值分解法(%)
1	8.01	1.14
2	28.99	2.77
3	30.85	3.28
4	39.83	6.56
5	31.89	6.01

多种群遗传算法与截断奇异值分解法在开关电弧反演中的应用

Application of Multi-Population Genetic Algorithm and Truncated Singular Value Decomposition in Switching Arc Inversion

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