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

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。

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.