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Modal parameter identification by an iterative approach and by the state space model

机译：通过迭代方法和状态空间模型识别模态参数

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The problem of estimating a spectral representation of exponentially decaying signals from a set of sampled data is of considerable interest in several applications such as in vibration analysis of mechanical systems. In this paper we present a nonparametric and a parametric method for modal parameter identification of vibrating systems when only output data is available. The nonparametric method uses an iterative adaptive algorithm based in the formation of a two dimensional grid mesh, both in frequency and damping domains. We formulate the identification problem as an optimization problem where the signal energy is obtained from each frequency grid point and damping grid point. The modal parameters are then obtained by minimizing the signal energy from all grid points other than the grid point which contains the modal parameters of the system. The parametric approach uses the state space model and properties of the controllability matrix to obtain the state tran-sition matrix which contains all modal information. We discuss and illustrate the benefits of the proposed algorithms using a numerical and two experimental tests and we conclude that the nonparametric approach is very time consuming when a large number of samples is considered and does not outperform the parametric approach.
机译：从一组采样数据中估计指数衰减信号的频谱表示的问题在诸如机械系统的振动分析之类的几种应用中引起了极大的兴趣。在本文中，我们提出了仅输出数据可用时用于振动系统模态参数识别的非参数方法和参数方法。非参数方法使用迭代自适应算法，该算法基于在频域和阻尼域中二维网格的形成。我们将识别问题公式化为优化问题，从每个频率网格点和阻尼网格点获得信号能量。然后，通过使来自除包含系统模态参数的网格点以外的所有网格点的信号能量最小化来获得模态参数。参数化方法使用状态空间模型和可控性矩阵的属性来获取包含所有模态信息的状态转换矩阵。我们使用数值和两个实验测试来讨论和说明所提出算法的好处，并得出结论，当考虑大量样本并且非参数化方法不优于参数化方法时，非参数化方法非常耗时。

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