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从Helmholtz积分方程出发,利用奇异值分解技术和统计计算方法,导出了任意形振动源表面振速重建公式.文中首先利用边界元方法对Helmholtz积分方程进行离散化,其中采用了线性插值的平面三角形单元和四边形单元,每个单元上的表面积分采用二维高斯积分.为了消除或减小各种附加噪声对重建结果的影响,对最小二乘解的残量进行了方差估计,并在给定的约束条件下,确定合适的阻尼因子来修正奇异值,从而改善了最小二乘解.数值结果表明,本文的方法是可行的、有效的.
Starting from the Helmholtz integral equation, using the singular value decomposition technique and the statistical calculation method, the reconstruction formula of the surface vibration velocity of an arbitrary vibration source is deduced. Firstly, the Helmholtz integral equation is discretized using the boundary element method, and the linear interpolation plane triangles Units and quadrilateral elements, and the surface integrals of each element are two-dimensional Gaussian integrals.In order to eliminate or reduce the influence of various additional noises on the reconstruction results, the residuals of the least square solutions are estimated by variance, , The optimal damping factor is determined to correct the singular value and the least squares solution is improved. Numerical results show that the proposed method is feasible and effective.