Schuhmacher Andreas, Hald Jørgen, Rasmussen Karsten Bo, Hansen Per Christian
Brüel & Kjaer A/S, Skodsborgvej 307, DK-2850 Naerum, Denmark.
J Acoust Soc Am. 2003 Jan;113(1):114-27. doi: 10.1121/1.1529668.
Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.
标准边界元计算聚焦于从振动结构计算辐射声场的正向问题，而本工作的目的是逆转这个过程，即根据声场数据确定振动。这个逆问题被转化为适合用逆边界元方法求解的形式。由于逆源重建的数值处理会导致离散不适定问题，因此要进行正则化以避免由误差主导的不稳定解。在本工作中，重点是蒂霍诺夫正则化和不需要误差范数估计来选择合适正则化量的参数选择方法。最近已经提出了几种参数选择策略，但这些策略在处理带有实际测量数据的工业应用时效果如何仍有待观察。在本工作中证明了，L曲线准则在实际测量情况下对误差具有鲁棒性。特别是，对于当前的轮胎噪声研究，表明L曲线准则优于更传统的广义交叉验证（GCV）方法。
