A complex eigenvector is a result of nonproportional damping present in a structural system. However, it is difficult to identify the accurate damping matrix considering the modal sparsity and coordinate sparsity. A nonproportional viscous damping parameter identification is formulated as an unconstrained optimization problem in the present study. The damping coefficient of each element is considered as the design variable for the optimization problem. The objective function is defined using the incomplete complex eigenvectors, which are generated because of the presence of external damping devices in the structure. This objective function is then minimized using standard particle swarm optimization to identify the damping coefficient of the damping matrix. The accuracy and efficiency of the particle swarm optimization are investigated by solving a few numerical problems with simulated measured data. The proposed method works well with the incomplete measured modal data. The current methodology performs satisfactorily with and without noisy data. A comparison study is performed with the existing gradient-based method, and the results show that the proposed method performs better than the existing gradient-based method for the present problem with and without noisy measurement data.

复本征向量是结构系统中存在非比例阻尼的结果。但是，考虑模态稀疏度和坐标稀疏度，很难确定准确的阻尼矩阵。在本研究中，非比例粘性阻尼参数辨识被公式化为无约束优化问题。每个元素的阻尼系数被认为是优化问题的设计变量。使用不完整的复特征向量定义目标函数，由于结构中存在外部阻尼装置，因此生成了不完整的复特征向量。然后使用标准粒子群优化来最小化该目标函数，以识别阻尼矩阵的阻尼系数。通过用模拟测量数据解决一些数值问题，研究了粒子群优化算法的准确性和效率。所提出的方法适用于不完整的测量模态数据。当前的方法在有噪声数据和无噪声数据的情况下都能令人满意地执行。与现有的基于梯度的方法进行了比较研究，结果表明，该方法在存在和不存在嘈杂的测量数据的情况下，都比现有的基于梯度的方法表现更好。