用几何最小二乘法改进 ITD 法的阻尼识别精度

Improvement of damping factors of ITD identification using GLS

ＩＴＤ（ＩｂｒａｈｉｍＴｉｍｅＤｏｍａｉｎ）模态识别方法可不用输入系统的信息就识别系统的模态参数，但识别的模态参数常常很不精确，且阻尼比的识别精度很差。当激励信号不是独立白噪声信号时，不应该采用ＩＴＤ法进行模态识别。推导了ＩＴＤ法识别的模态频率和阻尼比的相对误差公式，由此分析了造成阻尼比识别结果很差的原因，并且引入了Ｉ－ｂｒａｈｉｍ提出的双最小二乘算法（ＤＬＳ），在此基础上，提出了几何最小二乘法（ＧＬＳ）。通过理论推导和算例验证得到：一般情况下，ＧＬＳ和ＤＬＳ算法均可提高阻尼比的识别精度，且前者的识别结果优于后者。

ITD (Ibrahim Time Domain) method can identify structural modal parameters without structural input information, but results of ITD identification are often inaccurate and damping factors of ITD identification are very bad. When input of system is not independent white noise, ITD identification method is not adopted. With relative error equations of modal frequencies and damping factors, reason of low accuracy of damping factors is known. Considering double least square (DLS) Ibrahim proposed, geometric least square (GLS) is presented. Theory and examples calculated show that GLS and DLS can enhance accuracy of damping factors and former results are better than the latter.