The signal acquisition process is limited by the installation position and number of sensors in particular types of equipment. Moreover, the observed signals are often compounded by all sources. In order to solve these problems, an underdetermined blind source separation (UBSS) approach with source number estimation and improved sparse component analysis (SCA) is studied. Firstly, the angular probability distribution of scatter as one of measures is obtained in time-frequency (TF) domain based on the sparsity of observations. Meanwhile, the energy sum of each frequency bin as another measure is calculated to eliminate the influence of poor sparsity or non-sparsity. Source number estimation can be obtained by selecting a small peak value between the above two measures. Then, the frequency bins corresponding to these peaks of the energy sum are clustered into two categories, whose first row in cluster center matrix is regarded as the corresponding column of estimated mixing matrix. Finally, the combinatorial algorithm of L1-norm is used to realize the estimation of source signals. Simulation results demonstrate that the proposed method can effectively separate the simulated vibration signals and is more accurate than traditional clustering and hyperplane space methods. Additionally, the natural frequency and damping ratio of modal response can be accurately identified in the test of measured cantilever beam hammering.

中文翻译：

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基于源数估计和改进稀疏分量分析的欠定盲源分离

在特定类型的设备中，信号采集过程受到安装位置和传感器数量的限制。此外，观察到的信号通常由所有来源混合而成。为了解决这些问题，研究了一种结合源数估计和改进稀疏分量分析（SCA）的欠定盲源分离（UBSS）方法。首先，基于观测的稀疏性，在时频（TF）域中获得散射角概率分布作为度量之一。同时，计算每个频率仓的能量总和作为另一种度量，以消除稀疏性或非稀疏性的影响。可以通过在上述两个度量之间选择一个小的峰值来获得源数量估计。然后，能量和的这些峰值对应的频点被聚类为两类，聚类中心矩阵中的第一行被视为估计混合矩阵的对应列。最后利用L1-范数的组合算法实现源信号的估计。仿真结果表明，该方法能够有效地分离模拟振动信号，并且比传统的聚类和超平面空间方法更准确。此外，在实测悬臂梁锤击试验中可以准确识别模态响应的固有频率和阻尼比。采用L1-范数的组合算法实现源信号的估计。仿真结果表明，该方法能够有效地分离模拟振动信号，并且比传统的聚类和超平面空间方法更准确。此外，在实测悬臂梁锤击试验中可以准确识别模态响应的固有频率和阻尼比。采用L1-范数的组合算法实现源信号的估计。仿真结果表明，该方法能够有效地分离模拟振动信号，并且比传统的聚类和超平面空间方法更准确。此外，在实测悬臂梁锤击试验中可以准确识别模态响应的固有频率和阻尼比。