A novel blind source separation (BSS) method for time-delayed mixtures in underdetermined case is studied in this paper. The proposed method not only addresses the problem of source separation with limited sensors but also avoids the influence of propagation delay. Firstly, the sparse domain is converted by utilizing the spectrum of observed signals to perform modulus operation in time-frequency (TF) domain, which appears several clustering lines in the scatter plot. Secondly, based on the linear clustering features of observed signals in the sparse domain, the angular probability distribution of preprocessing scatter is calculated to estimate the source number. Thirdly, the frequency bin corresponding to the peak of distance between scatter and original point is selected to construct the binary TF mask according to the estimated source number, and then the spectrum of recovered source is obtained via mask. Finally, the estimated sources considering padding line are calculated to eliminate the boundary effect in time domain. Experimental results demonstrate that the proposed method can effectively recover the simulated vibration sources with time-delayed mixtures in underdetermined case. In addition, two experimental validations manifest that compared with state-of-the-art algorithms, the proposed method improves signal separation performance and identifies the natural frequency of monomodal response successfully.

研究了一种不确定情况下时延混合物的盲源分离（BSS）方法。所提出的方法不仅解决了传感器有限的源分离问题，而且避免了传播延迟的影响。首先，通过利用观测信号的频谱对时域（TF）域执行模运算来转换稀疏域，该域在散点图中出现了几条聚类线。其次，基于稀疏域中观测信号的线性聚类特征，计算预处理散射的角概率分布，以估计源数。第三，根据估计的源数，选择与散点到原始点之间的距离的峰值对应的频点，以构建二进制TF模板；然后通过掩模获得回收源的光谱。最后，计算考虑填充线的估计源，以消除时域中的边界效应。实验结果表明，该方法可以在不确定情况下有效地恢复时延混合后的振动源。此外，两个实验验证表明，与最新算法相比，该方法可提高信号分离性能并成功识别单峰响应的固有频率。实验结果表明，该方法可以在不确定情况下有效地恢复时延混合后的振动源。此外，两个实验验证表明，与最新算法相比，该方法可提高信号分离性能并成功识别单峰响应的固有频率。实验结果表明，该方法可以在不确定情况下有效地恢复时延混合后的振动源。此外，两个实验验证表明，与最新算法相比，该方法可提高信号分离性能并成功识别单峰响应的固有频率。