逆边界无网格法声源识别的理论与实验

Theoretical and experimental research on noise source identification with inverse boundary meshless method

针对逆向求解声源识别中的声辐射传输建模问题,采用无网格法将Kirchhoff-Helmholtz边界积分方程离散为受边界条件约束的有限维线性方程组,通过分块矩阵法对该约束方程组进行求解,得到了离散后声辐射传输模型的数值表达式。在此基础上,进一步研究了逆向求解声源识别问题的基本原理及其不适定性。为克服其不适定性,采用Tikhonov正则化和L曲线正则化参数选取方法,从而确立了有效的逆向求解方法。此外,还进行了扬声器阵列声源识别实验,实验结果验证了逆边界无网格声源识别理论和方法的可行性及可靠性。

The modelling of acoustic radiation and transfer by using inverse calculation for noise source identification（NSI） is the main content of this research.The Kirchhoff-Helmholtz boundary integral equations were discretized as a set of finite-dimension equations constrained by boundary conditions by use of the boundary meshless method（BMLM）.These discrete equations were solved by the matrix-division method to obtain the numeric expression of acoustic radiation and transfer model.On this basis,a further study was given to the basic principle and the unadaptability of NSI by using inverse acoustic calculation.A feasible method of solving this NSI problem was presented based on Tikhonov regulation strategy and ＂L＂ curve parameter selection method.Therefore the unadaptability of NSI could be eliminated by this new solving method.An experiment on the identification of the speaker array sources was carried out.The results proved that the theories and methods of inverse boundary meshless for NSI proposed are feasible and reliable.