奇异值分解(SVD)和Tikhonov正则化方法在振速重建中的应用

基于辐射声奔放理建结构表面的振动速度存在解的离散病态问题，从间接边界元法（IBEM）的双层势表达式出发，建立了外部场压和结构表面振动速度之间关系的传递矩阵，为消除病态问题引起的重建结构对附加噪声的高度灵敏性的影响，对传递短阵进行奇异值分解，关用Tikhonov正则化方法对重建结果处理，且采用L－曲线标准选择出最佳的正则化参数，数值计算结果表明，重建结果与真实振源比较接近，该方法可进一步用于重建任意复杂结构面上的振速。

Vibrating Velocity Reconstruction Using Singular Value Decomposition and Tikhonov Regularization Method

To start with, the indirect boundary element formulations are established for analysis of exterior acoustic problems and the transfer matrix relating the pressure at every field point to the normal component of surface velocity is formed. To circumvent this undesirable badly conditioned transfer matrix, the solution techniques are based on the singular value decomposition(SVD) of the transfer matrix and Tikhonov regularization. Furthermore, how to estimate the optimal parameters in this regularization process is considered. It turned out numerically that the reconstructed velocity is a good approximation to the real source. The methods are practical and feasible to reconstruct the surface velocity for arbitrary odd\|shaped objects.