On the Combination of Random Matrix Theory With Measurements on a Single Structure
On the Combination of Random Matrix Theory With Measurements on a Single Structure
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随机矩阵理论与单一结构测量的结合
DOI：
10.1115/1.4054172
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发表时间：
2022
影响因子：
1.9
通讯作者：
Igea F
中科院分区：
文献类型：
--
作者：
Igea F
提出了一种方法，用于评估的概率密度函数（PDF）的模态参数的合奏名义上相同的结构时，只有一个单一的结构和色散参数是已知的。该方法结合了特征系统实现算法的动态数据集，一个显式的非参数概率方法。一个单一的结构，无论是数学模型或原型，用于获得模拟数据或测量，用于建立一个离散的时间状态空间模型描述。分散参数用于描述由于不同来源引起的不确定性，例如在总体中发现的变异性和在来自实验的噪声测量中发现的识别误差。该方法不需要通过系统的控制方程来传递不确定性，而是通过对状态空间模型中的矩阵进行随机化来获得整个系综的模态参数分布。通过两个自由度的质量弹簧阻尼系统和悬臂系统的分析表明该方法的适用性。结果表明，如果不确定性的来源是未知的，它是可能的，以指定一个整体水平的不确定性，通过访问一个单一的系统的测量，它是可能的，以评估所产生的PDF的模态参数。还发现，高值的色散参数可能会导致非物理的结果，如负阻尼比值。
An approach is proposed for the evaluation of the probability density functions (PDFs) of the modal parameters for an ensemble of nominally identical structures when there is only access to a single structure and the dispersion parameter is known. The approach combines the Eigensystem realization algorithm on sets of dynamic data, with an explicit nonparametric probabilistic method. A single structure, either a mathematical model or a prototype, is used to obtain simulated data or measurements that are employed to build a discrete time state-space model description. The dispersion parameter is used to describe the uncertainty due to different sources such as the variability found in the population and the identification errors found in the noisy measurements from the experiments. With this approach, instead of propagating the uncertainties through the governing equations of the system, the distribution of the modal parameters of the whole ensemble is obtained by randomizing the matrices in the state-space model with an efficient procedure. The applicability of the approach is shown through the analysis of a two degrees-of-freedom mass-spring-damper system and a cantilever system. The results show that if the source of uncertainty is unknown and it is possible to specify an overall level of uncertainty, by having access to a single system's measurements, it is possible to evaluate the resulting PDFs on the modal parameters. It was also found that high values of the dispersion parameter may lead to nonphysical results such as negative damping ratios values.