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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。
The ITD (IbrahimTimeDomain) modal identification method can identify the system modal parameters without inputting the system information, but the modal parameters identified are often inaccurate and the recognition accuracy of the damping ratio is poor. When the excitation signal is not an independent white noise signal, ITD method should not be used for modal identification. The formula of relative error of modal frequency and damping ratio identified by ITD method is deduced. The reason for the poor recognition result of damping ratio is analyzed, and the double least squares algorithm (DLS) proposed by I-brahim is introduced. Based on the proposed geometric least squares (GLS). The theoretical derivation and example verification show that, under normal circumstances, both the GLS and DLS algorithms can improve the recognition accuracy of the damping ratio, and the former has better recognition results than the latter.