基于遗传算法的快速多极基本解法的源点分布优化分析

doi:10.3901/JME.2016.07.196

机械工程学报 ›› 2016, Vol. 52 ›› Issue (7): 196-204.doi: 10.3901/JME.2016.07.196

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基于遗传算法的快速多极基本解法的源点分布优化分析

陈长征¹, 张士伟¹, 周勃²

1. 沈阳工业大学机械工程学院沈阳 110870;
2. 沈阳工业大学建筑工程学院沈阳 110870

出版日期:2016-04-05 发布日期:2016-04-05
作者简介:陈长征,男,1964年出生,博士,教授,博士研究生导师。主要研究方向为振动噪声分析与控制、故障诊断。E-mail: chencz6699@sina.com;张士伟(通信作者),男,1983年出生,博士研究生。主要研究方向为振动噪声控制。E-mail：zsw1260320@126.com
基金资助:
中国博士后科学基金(2014M560220)和国家科学支撑计划(2013BAF07B04)资助项目

The Optimization of the Distribution of Source Points for the Fast Multipole Method of Fundamental Solutions Based on Genetic Algorithms

CHEN Changzheng¹, ZHANG Shiwei¹, ZHOU Bo²

1. School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870;
2. Architectural and Engineering Institute, Shenyang University of Technology, Shenyang 110870

Online:2016-04-05 Published:2016-04-05

摘要/Abstract

摘要： 快速多极基本解法的计算精度主要由源点数和源点分布决定,针对源点的布置具有一定盲目性的问题,提出了基于遗传算法的快速多极基本解法。给出了基于遗传算法的快速多极基本解法的理论公式,并用于预测发动机表面辐射声场。结果表明,利用遗传算法优化后的源点分布,在保证计算精度的基础上,可实现减少源点数和配置点数的目的,从而提高计算效率。源点和配置点之间的距离过小时,计算误差变大;反之,计算误差变小,同时会导致源点分布越来越密集,使矩阵呈现病态。基于遗传算法的快速多极基本解法用于发动机表面辐射声场的预测,计算结果与试验值吻合较好,表明该方法的可行性和正确性,同时也为该方法在工程中进一步应用提供了借鉴。

关键词: 快速多极基本解法, 声场预测, 遗传算法, 源点分布

Abstract: The computational precision of fast multipole method of fundamental solutions mainly depends on the number and distribution of source points. In order to overcome the difficulty of determining the distribution of source points, GA-based FMMFS is proposed. The theoretical formula of this method is given, and it is used to predict the acoustic radiation field of engine surface. The results show that with the optimized distribution of source points, the number of source points and collocation points can be reduced and meanwhile the computational precision is maintained. The distance between the source points and collocation points is too less and computational errors are increased. Conversely, computational errors become small, meanwhile this enables source points become denser and induce the matrix’s ill-condition. GA-based FMMFS is applied for the prediction of the acoustic radiation field of engine surface and experimental results are in good agreement with computational results. It shows that GA-based FMMFS is validated and it may also allow its application to the practical engineering problems.

Key words: acoustic field prediction, distribution of source points, fast multipole method of fundamental solutions, genetic algorithms(GA)

中图分类号:

TB532

陈长征, 张士伟, 周勃. 基于遗传算法的快速多极基本解法的源点分布优化分析[J]. 机械工程学报, 2016, 52(7): 196-204.

CHEN Changzheng, ZHANG Shiwei, ZHOU Bo. The Optimization of the Distribution of Source Points for the Fast Multipole Method of Fundamental Solutions Based on Genetic Algorithms[J]. Journal of Mechanical Engineering, 2016, 52(7): 196-204.

参考文献

[1] KUPRADZE V,ALEKSIDZE M. The method of functional equations for the approximate solution of certain boundary value problems[J]. Computational Mathematics and Mathematical Physics,1964,4(4)：82-126.
[2] JIANG Xinrong,CHEN Wen. A fast method of fundamental solutions for solving helmholtz-type equations[J]. International Journal of Computational Method,2013,10(2)：1-20.
[3] 张炳荣,陈剑,陈立涛,等. 二维场预测的快速多极基本解法[J]. 声学学报,2014,39(3)：347- 352.
ZHANG Bingrong,CHEN Jian,CHEN Litao,et al. A fast multipole method of fundamental solutions for two dimensional acoustic radiation problems[J]. Chinese Journal of Acoustics,2014,39(3)：347-352.
[4] 陈长征,张士伟,周勃,等. 基于区域分解的快速多极基本法预测发动机表面辐射声场[J]. 振动与冲击,2015,34(16)：31-37.
CHEN Changzheng,ZHANG Shiwei,ZHOU Bo,et al. Prediction of acoustic radiation field of engine surface by domain decomposition-based fast multipole method of fundamental solution[J]. Journal of Vibration and Shock,2015,34(16)：31-37.
[5] GORZELANCZYK P,KOLODZIEJ J. Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods[J]. Engineering Analysis with Boundary Elements,2008,32(1)：64-75.
[6] 李加庆,陈进,杨超,等. 波叠加声场重构精度的影响因素分析[J]. 物理学报,2008,57(7)：4258-4264.
LI Jiaqing,CHEN Jin,YANG Chao,et al. Analysis of the impact factors on the accuracy of sound field reconstruction based on wave superposition[J]. Chinese Journal of Physics,2008,57(7)：4258-4264.
[7] 吴绍维,向阳,李胜杨. 体积速度匹配分布源边界点法的特解源位置优化方法研究[J]. 声学学报,2015,40(3)：381-390.
WU Shaowei,XIANG Yang,LI Shengyang. Research on position optimization of particular solution sources for distributed source boundary point method by velocity-matching [J]. Chinese Journal of Acoustics,2015,40(3)：381-390.
[8] HUBERT J,KOLODZIEJ J. Application of genetic algorithms for optimal positions of source points in method of fundamental solutions[J]. Computer Assisted Mechanics and Engineering Sciences,2008,15(4)： 215-224.
[9] CISILINO A,SENSALE B. Application of a simulated annealing algorithm in the optimal placement of the source points in the method of the fundamental solutions[J]. Computational Mechanics,2002,28(2)： 129-136.
[10] 李兵,杨殿阁,郑四发,等. 基于遗传算法的动态优化波叠加噪声源识别方法[J]. 机械工程学报,2010,46(12)：99-106.
LI Bing,YANG Diange,ZHENG Sifa,et al. Sound source identification method with dynamic optimal wave superposition algorithm based on genetic algorithm[J]. Journal of Mechanical Engineering,2010,46(12)：99-106.
[11] FAIRWEATHER G,KARAGEOGHIS A,MARTIN P. The method of fundamental solutions for scattering and radiation problems[J]. Engineering Analysis with Boundary Elements,2003,27(7)：759-769.
[12] HOLLAND J. Adaptation in natural and artificial systems[M]. Ann Arbor：University of Michigan Press,1975.
[13] GOUNOT Y,MUSAFIR R. Genetic algorithms：A global search tool to find optimal equivalent source sets[J]. Journal of Sound and Vibration,2009,322：280-296.

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基于遗传算法的快速多极基本解法的源点分布优化分析

The Optimization of the Distribution of Source Points for the Fast Multipole Method of Fundamental Solutions Based on Genetic Algorithms

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