整体正交多项式法识别模态参数的改进

Richardson正交多项式法识别动力学参数已得到广泛应用，但其识别结果不是最小方差估计，立算法运算量大。研究提出了通过引入误差权函数来降低估计方差，对分子和分母采用相同的正交多项式基函数来降低算法复杂性和运算量的一种新算法。无噪声算例的估计结果验证了该算法的可行性；有噪声算例的识别结果表明，引入误差权函数可显著提高识别精度；权函数可通过迭代确定，采用原点导纳的虚部可降低迭代次数，甚至无须迭代。

Improvements of identification modal parameters by orthogonal polynomial method

The modal parameters' identification by global orthogonal polynomial method proposed by Richardson, has been accepted widely. Nevertheless, it isn't the least variance estimation, the algorithm is very complicated, and the computation work is rather heavy. The improved method can reduce the estimation variance by including an extra error weighting function (EEWF), and the computation amount will be reduced with the base functions of denominator and numerator being chosen as identical series of orthogonal polynomials. The estimation results of the example without noise showed the validity of the new algorithm. For the example with noise, it is shown that the introducing of EEWF can improve the estimation precision efficiently, which can be obtained by iteration, and if the imaginary part absolute of the driving point compliance is adopted as the initial value of EEWF, the iteration times can be decreased down.