应用实正交多项式的多模态辨识迭代算法

Iterative algorithm for identifying multi-modes using real orthogonal polynomials

针对在实验模态分析中系统多模态整体参数辨识的系数方程易病态问题,对传统正交多项式频域模态参数辨识方法进行了改进.应用部分分式实正交多项式构建频响函数幅值平方的分析模型,规避了原有复正交多项式的复杂计算.应用模态隔离方法将原多模态整体参数辨识的过程拆分为由分步单模态参数辨识实现,减轻了系数方程的病态,并且放宽了对所辨识模态数量的限制.经多次的迭代提高分步单模态参数辨识的精度.数值结果表明,该算法的参数辨识精度高且结果收敛迅速.

In the experimental modal analysis, the system of equations to determine orthogonal polynomial coefficients is vulnerable to be ill-condition when the number of modes for identification exceeds a certain threshold. To avoiding the drawback, the normal frequency domain orthogonal polynomial method for identifying modal parameters was improved. The complex frequency response function was replaced by a real function, namely the square of amplitude of frequency response function, by using real orthogonal polynomial partial fraction, thus evading the complex calculation. A single modal identification method with modal isolation was used to identify modal parameters step by step. Iterative algorithm was used to improve the precision of modal parameters. Numerical results show that the iterative algorithm converges fast and the precise results of modal parameters can be obtained.