In this work, we introduce a novel method, namely Spectral Optimization-based Modal Identification (SOMI) for estimating the modal parameters of structures. SOMI is developed to estimate highly accurate modal damping ratios and mode shapes using the Frequency Domain Decomposition (FDD) principles. The FDD method (and most of the present modal identification techniques), encounters some problems such as modal complexity, lack of accuracy in the case of large damping ratios, and noticeable error in mode shape estimation. In the FDD formulation, the Singular Value Decomposition (SVD) estimation is precise only for lightly damped structures for obtaining the mode shapes and the Power Spectral Density (PSD) function of the modal coordinates. Moreover, the complexity of the mode shapes obtained from the FDD method is significantly biased and should not be used for physical interpretations. The main idea behind the proposed SOMI method is the elimination of the SVD estimation and obtaining the PSD function of the modal coordinates and the mode shapes with the least approximations. Moreover, the modal damping ratio is directly estimated in the frequency domain without any transformation into time domain using two equations derived in this paper. SOMI method uses optimization to make the PSD function of the modal coordinates follow the theoretical equations and estimates highly accurate mode shapes. In this work, the derivations are given for the displacement, velocity, and acceleration signals. The detailed formulation of the proposed method is presented, it is validated with some examples, and its competitive accuracy is compared with the FDD method. The accuracy and robustness of SOMI in noisy conditions are also assessed, with results indicating its effectiveness in handling noise and maintaining accuracy.

在这项工作中，我们介绍了一种新方法，即基于谱优化的模态识别 (SOMI)，用于估计结构的模态参数。SOMI 的开发是为了使用频域分解 (FDD) 原理估算高精度的模态阻尼比和振型。FDD方法（以及目前的大多数模态识别技术）遇到了一些问题，例如模态复杂，在大阻尼比的情况下缺乏准确性，以及模态估计中的明显误差。在 FDD 公式中，奇异值分解 (SVD) 估计仅适用于轻阻尼结构，用于获取振型和模态坐标的功率谱密度 (PSD) 函数。而且，从 FDD 方法获得的振型的复杂性存在明显偏差，不应用于物理解释。所提出的 SOMI 方法背后的主要思想是消除 SVD 估计并获得模态坐标的 PSD 函数和具有最小近似值的模态形状。此外，模态阻尼比是直接在频域中估计的，无需使用本文推导的两个方程转换到时域。SOMI方法使用优化使模态坐标的PSD函数遵循理论方程并估计高精度的振型。在这项工作中，给出了位移、速度和加速度信号的推导。提出了所提出方法的详细表述，并通过一些例子进行了验证，并将其具有竞争力的准确性与 FDD 方法进行了比较。还评估了 SOMI 在嘈杂条件下的准确性和稳健性，结果表明其在处理噪声和保持准确性方面的有效性。