一种新的频响函数无偏估计方法

A New Unbiased Frequency Response Funcition Estimator in Experimental Modal Analysis

在对几种典型的频响函数估计进行分析的基础上 ,利用不相关信号的互功率谱多次平均趋于零的性质 ,提出了一种新的频响函数无偏估计方法。该估计方法不需要测试第 3个信号即可达到无偏估计的目的 ,避免了测试系统过于复杂 ,减小了测试工作量和因过多环节的引入而降低估计精度的可能性。测试 n组数据 ,可以进行 n(n-1) / 2次平均 ,平均次数是其他方法的 (n- 1) / 2倍 ,提高了频响函数估计的精度。

Based on the analysis of some typical FRF estimators and the feature of the mean of the CSD (Cross Spectral Density) of uncorrelated signals tending to zero, a new unbiased frequency response function (FRF) estimator is proposed. The proposed method can get the unbiased FRF estimation without a third signal. It can not only decrease the complexity of the measuring system, but also reduce the testing work and the probability of producing extra errors due to excessive processing. According to the method, for the n sets of tested signals, the number of average times is n(n-1)/2 , which is (n-1)/2 times as against other methods, resulting in the improvement of the accuracy of the FRF estimation.