谱值对定常线性系统的参数估计

Parameter Estimation of Definite Linear System from Spectral Data

本文主要讨论振动系统中的逆特征值问题,参照了 Jacobi 矩阵性质,并运用了Lanczos 算法和正交多项式的三项递推关系来估计振动参数,即惯量(质量)与刚度。文章引证了共振频率处的留数可以作为正交多项式的计权系数。实验结果表明:参数估计的误差小于±15%。它取决于共振频率和反共振频率的测量精度。

The inverse eigenvalue problem in vibration of the definite linear sy- stem is concerned in this paper.According to the property of Jacobi ma- trix,the Lanczos algorithm and three-term recurence relation of the or- thogonal polynomials will be utilized to reconstruct uniquely the vibra- tion parameter;i.e,inertia(mass)and stiffness.In particular,the residues at resonant frequency has to be verified for the weights of the orthogonal polynomials.From the theoretical analysis and the experments give after, the accuracy of parameter estimation is less than±15%,and it depends upon the measurement of the resonant and anti-resonant frequencys.