基于局部基本解法的声学反问题模拟及Matlab实现  

Numerical Simulation and Matlab Implementation of Acoustic Inverse Problem Based on Localized Method of Fundamental Solutions

作　　者：蓝立源 王发杰 陈增涛 程隋福 LAN Liyuan;WANG Fajie;CHEN Zengtao;CHENG Suifu(College of Mechanical and Electrical Engineering,Qingdao University,Qingdao 266071,China;Institute of Multifunctional Materials and Structures Mechanics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学机电工程学院,山东青岛266071 [2]青岛大学多功能材料与结构力学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2023年第3期39-47,共9页Journal of Qingdao University(Engineering & Technology Edition)

摘　　要：针对柯西声学反问题,即部分边界信息未知的声学问题,本文采用局部基本解法,对基于局部基本解法的声学反问题模拟及Matlab实现进行研究。采用新型半解析无网格配点法,将中心节点处的声压表示成局部支撑域内支撑节点处声压的线性组合,再通过可测边界节点的已知物理量,使内部节点和不可测边界节点的声压值满足控制方程,建立一个大型稀疏线性方程,获得不可测边界的声压值。同时,给出局部基本解法的计算模型及其数值离散格式,并以Matlab为软件平台,设计了声学反问题仿真计算程序,开发了图形用户界面(graphics user interface,GUI)。仿真结果表明,该方法计算精度高,数值稳定,对含有噪声的边界数据可得到较好的反演结果。该研究为声学反问题的数值模拟提供了一种新的思路。For Cauchy acoustic inverse problem,which is acoustic problem with unknown boundary information,numerical simulation is carried out by using localized method of fundamental solutions in this paper.Adopted by the new semi-analytical meshless collocation method,the sound pressure at the center node is expressed as a linear combination of the sound pressure at the supporting node in the localized support domain.Then,through the known physical quantity of the measurable boundary nodes,the sound pressure of the inner nodes and the unmeasurable boundary nodes satisfy the governing equation,and a large sparse linear equation is established to obtain the unmeasurable boundary sound pressure.In this paper,the calculation model of localized method of fundamental solutions of acoustic inverse problem and its numerical discrete format are given.Based on this,a computational program of acoustic inverse problem simulation is designed according to Matlab as software platform,and a GUI user interface is developed.The simulation results show that this method has high precision and stable numerical value,and can still get good inversion results for boundary data with noise.The work in this paper provides a new idea for the numerical simulation of acoustic inverse problem.

关 键 词：局部基本解法 声学反问题 HELMHOLTZ方程 MATLAB工具箱 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] TB115[自动化与计算机技术—计算机科学与技术]