奇异值分解(SVD)和Tikhonov正则化方法在振速重建中的应用

Vibrating Velocity Reconstruction Using Singular Value Decomposition and Tikhonov Regularization Method

基于辐射声压重建结构表面的振动速度存在着解的离散病态问题 ,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果对附加噪声的高度灵敏性的影响 ,对传递矩阵进行奇异值分解 ,并用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 .

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.