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Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time–frequency domain with the STFT, which describes the local characteristic of the signal from the time–frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the traditional density-based spatial clustering of applications with noise (DBSCAN) algorithm in the mixing matrix estimation algorithm needs to artificially set the neighborhood radius and the number of core points, a double constrained particle swarm optimization (DCPSO) algorithm is proposed. The neighborhood radius parameters of the DBSCAN algorithm are optimized, and the obtained optimal parameters are used as the parameter input of the DBSCAN algorithm, and then the clustering center is calculated to complete the mixing matrix estimation. Aiming at the problem that the source signal number estimation algorithm based on distance sorting relies on the selection of empirical parameters and does not have the ability to eliminate noise points, a maximum distance sorting algorithm is proposed. The experimental results show that the improved algorithm is improved. The accuracy of source signal number estimation is nearly 40% higher than that of the original algorithm. The error of mixing matrix estimation is more than 3 dB higher than that of the comparison algorithm. Moreover, the proposed algorithm has a better convergence speed than the original algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a dual-channel speech separation method based on spatial estimation via sparse Bayesian inference (SBI) and nonnegative matrix factorization (NMF). The spatial information estimated by traditional compressed sensing (CS) models is insufficient when two microphones receive limited columns of mixed signals. Considering the sparsity of peak values in the cross-correlation spectrum between two received signals, the proposed method builds a new CS model based on cross-correlation spectrum and applies SBI algorithm to solve this model to improve the estimation accuracy of spatial information. Combined the spatial information with the spectral features decomposed by NMF, NMF coefficient matrix masks belonging to individual source are generated for pre-separation. To mitigate retained potential interference components, a post-separation processing stage is designed using an expectation maximization (EM) algorithm based on a Gaussian mixture model (GMM). The estimated spatial information and binary time–frequency masks are used for parameter initialization of the EM algorithm. The experimental results using real-world speech data show that the proposed method can achieve better separation performance compared to various existing methods. [ABSTRACT FROM AUTHOR]

This paper explores the important role of blind source separation (BSS) techniques in separating M mixtures including N sources using a dual-sensor array, i.e., M = 2 , and proposes an efficient two-stage underdetermined BSS (UBSS) algorithm to estimate the mixing matrix and achieve source recovery by exploiting time–frequency (TF) sparsity. First, we design a mixing matrix estimation method by precisely identifying high clustering property single-source TF points (HCP-SSPs) with a spatial vector dictionary based on the principle of matching pursuit (MP). Second, the problem of source recovery in the TF domain is reformulated as an equivalent sparse recovery model with a relaxed sparse condition, i.e., enabling the number of active sources at each auto-source TF point (ASP) to be larger than M. This sparse recovery model relies on the sparsity of an ASP matrix formed by stacking a set of predefined spatial TF vectors; current sparse recovery tools could be utilized to reconstruct N > 2 sources. Experimental results are provided to demonstrate the effectiveness of the proposed UBSS algorithm with an easily configured two-sensor array. [ABSTRACT FROM AUTHOR]

Underdetermined blind source separation (UBSS) is a critical technique in the field of intelligent mechanical operation and maintenance that allows for the disentanglement of source signals from their mixtures without the need for prior knowledge or extensive sensor information. The accuracy of source signal recovery depends on the estimation of the mixing matrix. To promote sparsity in source signals, we employed methods such as sparse representation and sparse component analysis. Traditional approaches, such as the Short-Time Fourier Transform (STFT), often suffer from limited time-frequency resolution, motivating the adoption of the Synchronous Extraction Transformation (SET) algorithm, which closely approximates the ideal time-frequency transform. SET significantly enhances the sparsity of the signals, thus facilitating the separation of the mixed signals. In the context of sparse component analysis, we introduce an improved density peaks clustering (DPC) method that successfully resolves source number estimation issues and robustly eliminates outliers. This improvement leads to a more accurate mixing matrix estimation. To determine the cluster centers, we employed K-means clustering, further refining our source separation process. In summary, our study presents an innovative approach that combines the Synchronous Extraction Transformation (SET) with ‘an improved density peaks clustering (DPC)’ method and K-means for mixing matrix estimation. Source signal recovery was achieved using the shortest-path algorithm. Extensive simulations and experiments validate the effectiveness of the method, outperforming the traditional techniques. When applied to rolling bearing fault diagnosis, the proposed approach effectively separates complex signals and accurately identifies the fault characteristic frequencies.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time–frequency domain with the STFT, which describes the local characteristic of the signal from the time–frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Recovering M sources from N mixtures in underdetermined cases, i.e., M > N, is a great challenge, especially for insufficiently sparse sources in noisy cases. To solve this problem, an improved underdetermined blind source separation (UBSS) method is proposed based on single source points (SSPs) identification and l0-norm. Firstly, we present a mixing matrix estimation method based on SSPs that is identified by directly searching the identical normalized time–frequency (TF) vectors of mixed signals. This method considers the linear representation relations among these TF vectors and therefore could achieve more accurate SSPs identification even in noisy cases. Then, we prove that a non-SSP will be misjudged as SSP with probability zero under some assumptions, which guarantees the stability and effectiveness of the proposed method. Secondly, SSPs are only searched in some optimal frequency bins so that all SSPs in these frequency bins can be identified at one time. Then, the mixing matrix is estimated using hierarchical clustering technique. Thirdly, to recover source signals with real number of active sources, a l0-norm-based source recovery method is proposed which would be transformed to find the submatrix with the least column of the mixing matrix that can linearly represent TF vectors of mixed signals. Therefore, source signals can be recovered with the real number of active sources, which improves the estimation accuracy of source signals. Some experiments are carried out to show the effectiveness of the proposed method. The present research could improve the estimation accuracy of sources for insufficiently sparse sources with noise in underdetermined cases. [ABSTRACT FROM AUTHOR]

Copyright of Information & Control is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The performance of the existing underdetermined blind source separation methods is very sensitive to the initial parameters, meanwhile, the existing setting or selection methods of initial parameters need to be improved. Consequently, an effective underdetermined blind source separation method is proposed in this paper to solve the above engineering problems. Based on the Archimedes optimization algorithm and quantum computing theory, this paper proposes a novel intelligent algorithm named quantum Archimedes optimization algorithm, which solves the objective functions for engineering problems. Then the optimal solution obtained through the quantum Archimedes optimization algorithm is used as the initial clustering centers of the K-means clustering algorithm to achieve mixing matrix estimation. In addition, the original initial estimation signal setting of the source recovery based on radial basis function network is converted into an initial solution in population for quantum Archimedes optimization algorithm. The optimal solution obtained through the quantum Archimedes optimization algorithm is used as the new initial estimation signal setting to achieve source recovery. The simulation results show that the proposed underdetermined blind source separation method has higher accuracy than previous methods. The proposed method that is more robust and applicable makes the setting and selection of initial parameters more reasonable so that the performance is no longer limited to the initial parameters. [ABSTRACT FROM AUTHOR]

Underdetermined blind source separation is a signal processing technique that is more suitable for practical applications and aims to separate the source signals from the mixed signals. The mixing matrix estimation is a major step in the underdetermined blind source separation. Since the current methods for estimating the mixing matrix have the disadvantages of insufficient accuracy or weak noise immunity, a two-stage single-source point screening that combines the cosine angle algorithm and the L1-norm optimization algorithm is proposed. During the first stage, the first-stage single-source points are extracted from the original mixed signals using the cosine angle algorithm. During the second stage, based on the L1-norm optimization algorithm, the reference single-source points are extracted from the original mixed signals. The reference single-source points are then clustered to obtain the clustering center, which is defined as the reference center. In combination with the reference center, the deviation and interference points in the first-stage single-source points are eliminated by the cosine distance. The remaining signal points are considered as the second-stage single-source points, which are clustered to obtain the mixing matrix estimation. Experiments on simulated and speech signals show that the proposed method can obtain more accurate and robust mixing matrix estimation, leading to better separation of the source signals. [ABSTRACT FROM AUTHOR]

The timely discovery of low-frequency oscillations in power systems and accurate identification of their modal parameters is critical in numerous applications. Therefore, we investigated the feasibility of using multi-channel signals and established a relative theory. An algorithm based on the underdetermined blind source separation (UBSS) algorithm was proposed using this theory. First, the energy ratio function was used to determine the fault occurrence time. Then, the Bayesian information criterion was used to estimate the number of fault sources, and the boundary conditions were set to determine the number of fault sources. Next, the UBSS algorithm was used to analyze raw data, extract individual components that characterize faults, and subsequently measure low-frequency oscillation modal parameters through the Hilbert transform. Finally, the fast independent component analysis (FastICA) algorithm was used to separate noise signal from raw data. This separation considerably reduced noise disturbance and ensured the stability of the proposed method. Model simulation was conducted in MATLAB and experimental measurement revealed that the proposed method effectively reduced noise disturbance and could be applied to conditions with considerable disturbance. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Underdetermined blind source separation has received increasing attention in recent years as an effective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed sensing approach, which is a two-step approach, is proposed herein to improve the accuracy of underdetermined blind source separation. The approach features the following two aspects: (1) A mixing matrix estimation method based on self-organizing mapping and density peak clustering, which can intuitively determine the number of source signals, remove outliers, and determine the column vector of the mixing matrix based on local density; (2) a compressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowledge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Blind source separation (BSS) recovers source signals from observations without knowing the mixing process or source signals. Underdetermined blind source separation (UBSS) occurs when there are fewer mixes than source signals. Sparse component analysis (SCA) is a general UBSS solution that benefits from sparse source signals which consists of (1) mixing matrix estimation and (2) source recovery estimation. The first stage of SCA is crucial, as it will have an impact on the recovery of the source. Single-source points (SSPs) were detected and clustered during the process of mixing matrix estimation. Adaptive time–frequency thresholding (ATFT) was introduced to increase the accuracy of the mixing matrix estimations. ATFT only used significant TF coefficients to detect the SSPs. After identifying the SSPs, hierarchical clustering approximates the mixing matrix. The second stage of SCA estimated the source recovery using least squares methods. The mixing matrix and source recovery estimations were evaluated using the error rate and mean squared error (MSE) metrics. The experimental results on four bioacoustics signals using ATFT demonstrated that the proposed technique outperformed the baseline method, Zhen's method, and three state-of-the-art methods over a wide range of signal-to-noise ratio (SNR) ranges while consuming less time. [ABSTRACT FROM AUTHOR]

It is essential to accurately estimate the mixing matrix and determine the number of source signals in the problem of underdetermined blind source separation. The problem is solved in this paper via sparse subspace clustering, which can be used to found low-dimensional data structures in observed data. To enhance the linear clustering characteristics of time-frequency points, the high energy points are reserved first, and the angle difference of real and imaginary portions is employed to screen single source points. After that, the time-frequency points are clustered using sparse subspace clustering, and the number of source signals is identified. Finally, the local density of eigenvectors is used to determine the mixing matrix. The proposed algorithm is capable of accurately estimating the mixing matrix. It has strong robustness and adaptable to a wide range of mixing circumstances. The proposed method's effectiveness is demonstrated by theoretical analysis and experimental data. [ABSTRACT FROM AUTHOR]

Underdetermined blind source separation (UBSS) has garnered significant attention in recent years due to its ability to separate source signals without prior knowledge, even when sensors are limited. To accurately estimate the mixed matrix, various clustering algorithms are typically employed to enhance the sparsity of the mixed matrix. Traditional clustering methods require prior knowledge of the number of direct signal sources, while modern artificial intelligence optimization algorithms are sensitive to outliers, which can affect accuracy. To address these challenges, we propose a novel approach called the Genetic Simulated Annealing Optimization (GASA) method with Adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering as initialization, named the CYYM method. This approach incorporates two key components: an Adaptive DBSCAN to discard noise points and identify the number of source signals and GASA optimization for automatic cluster center determination. GASA combines the global spatial search capabilities of a genetic algorithm (GA) with the local search abilities of a simulated annealing algorithm (SA). Signal simulations and experimental analysis of compressor fault signals demonstrate that the CYYM method can accurately calculate the mixing matrix, facilitating successful source signal recovery. Subsequently, we analyze the recovered signals using the Refined Composite Multiscale Fuzzy Entropy (RCMFE), which, in turn, enables effective compressor connecting rod fault diagnosis. This research provides a promising approach for underdetermined source separation and offers practical applications in fault diagnosis and other fields.

The existing methods for multi-point harmonic contribution evaluation usually require some preconditions, such as the node harmonic current is equivalent to the harmonic emission current and the number of measurements is not less than the number of sources. However, these requirements may not be satisfied in practice. In this context, this paper proposes an improved sparse component analysis (SCA) method to solve the underdetermined blind source separation model, which is used to describe the harmonic state under incomplete measurements. The improved SCA adopts a new two-stage technique. First, the mixing matrix containing harmonic transfer impedances is estimated through the synchrosqueezing S-transform. Then, the source signal vector containing harmonic emission currents is reconstructed through the modified subspace projection. By matching the harmonic impedances and currents, the multi-point harmonic contribution evaluation is further achieved. The efficiency of the proposed method is verified by simulations and field case studies. The results demonstrate that the proposed method outperforms the existing methods in terms of accurately estimating the harmonic emission currents and quantifying the harmonic contributions under incomplete measurements. [ABSTRACT FROM AUTHOR]

In this paper, we propose a noble algorithm for mixing matrix estimation in Underdetermined blind source separation. A concept of confidence measure and that of being able to be single source points at all the points in time frequency plane are introduced in the proposed algorithm. At first, we can detect the single source points from real parts and imaginary parts of time frequency coefficients of mixture signals and calculate principal vectors and its confidence measures through principal component analysis at the single source points using this algorithm. Finally, mixing matrix is obtained by clustering principal vectors according to its confidence measure. Experimental results show that the proposed algorithm is very suitable for actual situation of UBSS. [ABSTRACT FROM AUTHOR]

Industry 5.0 advocates for a sustainable industry, particularly in terms of energy. One of the most fundamental elements of comprehension is knowing when the systems are operated, as this is key to locating energy intensive subsystems and operations. Such knowledge is often lacking in practice. Activation statuses can be recovered from sensor data though. Some non-intrusive sensors (accelerometers, current sensors, etc.) acquire mixed signals containing information about multiple actuators at once. This paper considers different industrial settings in which the identification of binary sub-system activation sequences is sought. In this context, source signals are assumed to be quasi-stationary and they may be correlated. Existing methods either restrict these assumptions, e.g. , by imposing orthogonality or noise characteristics, or lift them using additional assumptions, typically using nonlinear transforms. This paper addresses these limitations, and introduces the unsupervised complex semi-binary matrix factorization (ℂ SBMF) as its main contribution. In particular, we show that the exact recovery of source activation sequences from non-intrusive sensor data is intrinsically tied to the presence of problematic phase shifts, the causes of which are detailed. A greedy algorithm is proposed, iteratively resynchronizing sources to converge towards the maximum decomposition of each operation despite these phase shifts. The ℂ SBMF is verified and compared to existing techniques on synthetic use cases, then validated on experimental data with signals of different nature. To that occasion, the CAFFEINE dataset for unsupervised time series multi-label classification is introduced. [ABSTRACT FROM AUTHOR]

The timely discovery of low-frequency oscillations in power systems and accurate identification of their modal parameters is critical in numerous applications. Therefore, we investigated the feasibility of using multi-channel signals and established a relative theory. An algorithm based on the underdetermined blind source separation (UBSS) algorithm was proposed using this theory. First, the energy ratio function was used to determine the fault occurrence time. Then, the Bayesian information criterion was used to estimate the number of fault sources, and the boundary conditions were set to determine the number of fault sources. Next, the UBSS algorithm was used to analyze raw data, extract individual components that characterize faults, and subsequently measure low-frequency oscillation modal parameters through the Hilbert transform. Finally, the fast independent component analysis (FastICA) algorithm was used to separate noise signal from raw data. This separation considerably reduced noise disturbance and ensured the stability of the proposed method. Model simulation was conducted in MATLAB and experimental measurement revealed that the proposed method effectively reduced noise disturbance and could be applied to conditions with considerable disturbance.

One challenge of bearing fault diagnosis is that the vibration signals are often a nonlinear mixture of unknown source signals. In addition, the practical installation position also limits the number of observed signals. Hence, bearing fault diagnosis is a nonlinear underdetermined blind source separation (UBSS) problem. In this paper, a novel nonlinear UBSS solution based on source number estimation and improved sparse component analysis (SCA) is proposed. Firstly, the ensemble empirical mode decomposition (EEMD), correlation coefficient (CC), and adaptive threshold singular value decomposition (ATSVD) joint approach is proposed to estimate the source number. Then, the observed signals are transformed into the time−frequency domain by short−time Fourier transform (STFT) to meet the sparsity requirement of SCA. The frequency energy is adopted to increase the accuracy of fuzzy C−means (FCM) clustering, so as to ensure the accuracy estimation of the mixing matrix. The L1−norm minimization is utilized to recover the source signals. Simulation results prove that the proposed UBSS solution can exactly estimate the source number and effectively separate the simulated signals in both linear and nonlinear mixed cases. Finally, bearing fault testbed experiments are conducted to verify the validity of the proposed approach in bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

An original algorithm for underdetermined mixing matrix estimation is proposed in this paper, which can estimate the mixing matrix effectively when the number of source signals is unknown. Firstly, a new single source point (SSP) detection algorithm based on transform matrix is proposed, which can effectively detect single source time-frequency (TF) points by using the characteristics of complex ratio and improve the sparsity of source signals. In view of the fact that the number of source signals is unknown, a novel estimation algorithm based on element sorting is proposed, which can significantly improve the estimation accuracy of the number of source signals. Finally, the mixing matrix is estimated by using the cluster center obtained by agglomerative hierarchical clustering (AHC) algorithm. The simulation results show that the proposed algorithm can improve the estimation accuracy of the number of source signals and underdetermined mixing matrix obviously, and the algorithm has higher robustness compared with other algorithms.

The underdetermined blind source separation (UBSS) has been considered to be a novel signal processing technique, which can separate the fault source signals from their mixtures. The mixing matrix estimation is a major step in the UBSS, this paper focuses on boosting the accuracy level of the estimated mixing matrix in the underdetermined case. Since the traditional clustering algorithms may not capture the signal characteristics well and secure a satisfactory estimation of the mixing matrix, an effective two-stage clustering algorithm is proposed to estimate the mixing matrix through a combination of hierarchical clustering and K-means. More specifically, first, the sum of frequency points energy in the time-frequency (TF) domain is calculated to estimate the number of source signals before clustering, and the initial clustering centers are obtained with a hierarchical clustering algorithm. Second, after eliminating outliers deviating from the initial clustering centers with the cosine distance, the new clustering centers are obtained by recalculating the mean value of each sub-cluster. Finally, the new clustering centers are set as the initial clustering centers of the K-means algorithm to estimate the mixing matrix. Extensive simulations and experiments show that the proposed method can effectively separate the source signals and ensure an estimate of the mixing matrix that is substantially more accurate than the K-means algorithm alone.

Blind source separation (BSS) recovers source signals from observations without knowing the mixing process or source signals. Underdetermined blind source separation (UBSS) occurs when there are fewer mixes than source signals. Sparse component analysis (SCA) is a general UBSS solution that benefits from sparse source signals which consists of (1) mixing matrix estimation and (2) source recovery estimation. The first stage of SCA is crucial, as it will have an impact on the recovery of the source. Single-source points (SSPs) were detected and clustered during the process of mixing matrix estimation. Adaptive time–frequency thresholding (ATFT) was introduced to increase the accuracy of the mixing matrix estimations. ATFT only used significant TF coefficients to detect the SSPs. After identifying the SSPs, hierarchical clustering approximates the mixing matrix. The second stage of SCA estimated the source recovery using least squares methods. The mixing matrix and source recovery estimations were evaluated using the error rate and mean squared error (MSE) metrics. The experimental results on four bioacoustics signals using ATFT demonstrated that the proposed technique outperformed the baseline method, Zhen’s method, and three state-of-the-art methods over a wide range of signal-to-noise ratio (SNR) ranges while consuming less time.

Aiming at the problem of insufficient separation accuracy of aliased signals in space Internet satellite ground communication scene, a stacked time domain convolutional network (Stacked-TCN) separation method based on deep learning is proposed. Firstly, the coding feature representation is extracted from the mixed signal. Then, the deep feature mask of the source signal is trained through the time-domain convolution network. The mask of each signal source and the coding feature of the mixed signal are multiplied by Hadamard to obtain the coding feature representation of the source signal. Finally, 1-D convolution is used to decode the characteristics of the source signal to obtain the original waveform. In the experiment, the negative scale invariant source to noise ratio is used as the loss function of network training, that is, the evaluation index of single channel blind source separation performance. The results show that the Stacked-TCN method has better separation accuracy and noise robustness than the other four algorithms. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Since roller bearing is one of the most vulnerable components, bearing faults usually occur in an unprepared situation with multiple faults, and the quantity of sensors is limited in the real-time working environment, resulting in an underdetermined blind source separation (UBSS) problem to extract the fault features. Because the collected signals are usually not independent and not sparse enough, traditional methods of separating signals cannot perform well. In this paper, an optimized intrinsic characteristic-scale decomposition (OICD) method is proposed to solve the underdetermined problem. Meanwhile, the constraint error factor is introduced to overcome the drawback that the ideal ending condition of ICD is not proper for the vibration signal of bearing. In addition, given that non-negative matrix factorization (NMF) is not limited by the source signal independence and sparsity, an improved UBSS model is constructed, and the PCs are used as the input matrix of local NMF to obtain the separation signal. Ultimately, envelope analysis is utilized to detect the source signal feature. Both simulated and experimental vibration signals are used to verify the effectiveness of the proposed approach. Besides, the traditional method is juxtaposed with the suggested method. The results indicate that the proposed method is effective in dealing with the compound faults separation of the rotating machinery.

Underdetermined blind source separation (UBSS) is a hot and challenging problem in signal processing. In the traditional UBSS algorithm, the number of source signals is often assumed to be known, which is very inconvenient in practice. In addition, it is more difficult to obtain the accurate estimation of mixing matrix in the underdetermined case. However, this information has a great influence on the source separation results, which can easily lead to poor separation performance. In this paper, a novel UBSS algorithm is presented to carry out a combined source signal number estimation and source signal separation task. First, in the proposed algorithm, we design a gap-based detection method to detect the number of source signals by eigenvalue decomposition. Then, the estimation of the mixing matrix is processed using a higher-order cumulant-based method so that the uniqueness of the estimated mixing matrix is guaranteed. Furthermore, an improved l1 -norm minimization algorithm is proposed to estimate the source signals. Meanwhile, the pre-conditioned conjugate gradient technology is employed to accelerate the convergence rate such that the computational load is reduced. Finally, a series of simulation experiments with synthetic heart sound data and image reconstruction results demonstrate that the proposed algorithm achieves better separating property than the state-of-the-art algorithms.

This paper presents a novel mixing matrix estimation method based on a frame cluster analysis for application to the dynamic system of radar signals under an underdetermined blind source separation. The received signals are first processed using an adaptive denoising method. They are then divided into different appropriate length frames. Next, the frame type is determined and each frame is processed in accordance with its type. Short-time Fourier transform is used to transform the mixed signals from time domain to time–frequency domain. A transformation matrix is introduced to resolve the issue of the traditional clustering algorithm not being applicable within the complex field. After introducing the transformation matrix, an innovative single-source point detection algorithm and an estimation algorithm for the number of source signals are proposed. Finally, the mixing matrix is estimated via a fuzzy c-means clustering algorithm based on the characteristics of complex numbers. The simulation results show that the proposed algorithm improves the estimation accuracy of the mixing matrix considerably. Further, it has evident advantages for blind estimation of the mixing matrix for time-varying radar signals in the dynamic system. [ABSTRACT FROM AUTHOR]

Given that the mixing matrix of underdetermined blind source separation (UBSS) changes with the recording environment, offline UBSS methods encounter difficulty in satisfying the time-varying estimation demand. Therefore, in this work, an online tensor algorithm has been proposed to estimate the time-varying mixing matrix for separating an instantaneous linear underdetermined mixture. First, we construct a canonical polyadic tensor model by assuming individually correlated sources. Second, an online tensor algorithm is applied to decompose the canonical polyadic tensor model to ensure the accuracy of the time-varying mixing matrix. Finally, two types of data, including speech and biomedical signals, have been used to substantiate the effectiveness of the proposed algorithm in estimating the time-varying mixing matrix for UBSS. The results show that the developed online tensor algorithm is significantly superior to the conventional offline UBSS methods in terms of time consumption and accuracy. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A sparse adaptive subspace pursuit based on the optimal support (OS-SASP) algorithm was proposed to deal with the problem of underdetermined blind source separation based on sparse component analysis. By introducing the idea of self-adaptation， the dependence of the traditional subspace pursuit(SP)algorithm on sparsity was overcome. At the same time， the size of the minimum support set was determined by the energy concentration characteristic of discrete cosine transform before the start of iteration. Further， the optimal support set was obtained by calculating the union of the minimum support sets. And the combination of the optimal support set and the candidate set in the joint iteration was used to locate the best atom， so as to improve the source signal′s restore accuracy. The simulation results showed that the OS-SASP algorithm can achieve promising performance in the underdetermined blind source recovery of the one-dimensional sparse signals and speech signals. [ABSTRACT FROM AUTHOR]

One challenge of bearing fault diagnosis is that the vibration signals are often a nonlinear mixture of unknown source signals. In addition, the practical installation position also limits the number of observed signals. Hence, bearing fault diagnosis is a nonlinear underdetermined blind source separation (UBSS) problem. In this paper, a novel nonlinear UBSS solution based on source number estimation and improved sparse component analysis (SCA) is proposed. Firstly, the ensemble empirical mode decomposition (EEMD), correlation coefficient (CC), and adaptive threshold singular value decomposition (ATSVD) joint approach is proposed to estimate the source number. Then, the observed signals are transformed into the time−frequency domain by short−time Fourier transform (STFT) to meet the sparsity requirement of SCA. The frequency energy is adopted to increase the accuracy of fuzzy C−means (FCM) clustering, so as to ensure the accuracy estimation of the mixing matrix. The L1−norm minimization is utilized to recover the source signals. Simulation results prove that the proposed UBSS solution can exactly estimate the source number and effectively separate the simulated signals in both linear and nonlinear mixed cases. Finally, bearing fault testbed experiments are conducted to verify the validity of the proposed approach in bearing fault diagnosis.

In order to improve the performance of network sorting under underdetermined conditions, this paper proposes a blind sorting method for multiple frequency hopping (FH) signals in synchronous networking based on the blind source separation. Firstly, the short-time Fourier transform is performed on the multiple FH signals received by the L-shaped antenna array, and the time-frequency map is denoised by using the adaptive threshold of the SNR. Then the time-frequency single-source-point (SSP) detection algorithm is used to get effective time-frequency SSP. The FH signal is segmented on the time-frequency diagram to detect the frequency hopping time. In a certain hopping time, carrier frequency and its corresponding mixing matrix is estimated. Finally, the DOA information of the FH signal is calculated according to the carrier frequency information and the estimated mixing matrix, and the multiple FH signals are sorted according to the DOA information. Theoretical research shows that multiple FH signals can be separated by only three receiving antennas, and simulation results verify the effectiveness of the proposed algorithm.

In order to improve the estimation accuracy of the mixing matrix in the underdetermined blind source separation, an adaptive density-based spatial clustering of applications with noise (A-DBSCAN) algorithm is proposed, which is based on the DBSCAN algorithm. To solve the problem that the neighborhood radius (Eps) and the number of neighborhood points (MinPts) of the DBSCAN algorithm are determined, First, the curve fitting method is used to obtain Eps, then MinPts is determined by analyzing the relationship between the number of cluster output categories and the number of noise points. The proposed algorithm is combined with the mixing matrix estimation model, and finally the source signal recovery is achieved by the shortest path algorithm. Experimental results show that compared with the comparison algorithm, the proposed algorithm has significantly improved the performance of mixing matrix estimation and source signal recovery. [ABSTRACT FROM AUTHOR]

This study proposes a new approach to determine harmonic contributions in distribution networks. The approach effectively combines underdetermined blind source separation (UBSS) and form similarity distance (FSD), and it aims to minimise the negative impacts of harmonic source coupling and background harmonic fluctuations. Considering the underdetermined measurement, UBSS is introduced to estimate the harmonic emission current in the light of the sparsity of source signals. Through analysing the form variation features of harmonic time series, FSD is applied to identify the relatively stable background harmonics for utility equivalent harmonic impedance calculation. Furthermore, a complete procedure of harmonic contribution assessment is presented. To verify the high performance of the proposed approach, the simulation study and field test are both conducted, and a detailed comparative analysis of different approaches is carried out. The results show that the proposed approach is able to more accurately determine harmonic contributions than the existing methods, and has better robustness against significant harmonic source coupling and drastic background harmonic fluctuations. [ABSTRACT FROM AUTHOR]

Due to the lack of sufficient prior information, how to estimate the mixing matrix in multiple underdetermined blind source separation (UBSS) models is a difficult problem. This study proposes an algorithm, which is used for the estimation of mixing matrix in instantaneous UBSS. Firstly, we propose an efficient single-source-points detection criterion with the transformation for the mixed signal vector, which is used as the basis for the clustering process. There are some shortcomings in the classical clustering algorithms, including the dependence on input parameters, restrictions on the data dimension, the requirement of the prior knowledge of the source signals and high complexity. To overcome these drawbacks, the modified density peaks clustering algorithm is used for the estimation of the initial clustering centers to adapt to different circumstances. Based on the idea of mean clustering, the single source points near each initial cluster center are processed, respectively, and the final estimation results of the mixing matrix are obtained. A variety of simulation experiments demonstrate the universality and validity of the proposed algorithm. The proposed method also has excellent performance even under the circumstance of low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Blind source separation (BSS) has been demonstrated to be a promising method for operational modal analysis (OMA). However, the conventional BSS-based modal identification methods can only handle the determined or overdetermined identification where the number of sensors must equal or exceed that of active modes, limiting their wider application. Furthermore, the existing methods for underdetermined BSS require sparsity assumption of sources, optimization of model parameters, or structural prior information, undermining the non-parametric and "blind" properties of BSS. This paper proposes a novel method for underdetermined OMA. Firstly, the bandlimited source separation using sinc-dictionaries is performed to efficiently transform the underdetermined problem into several determined or overdetermined ones. An improved second-order blind identification (SOBI) involving Hilbert transform and random time-lagged covariances is then applied for each bandlimited signal to recover modal responses and mode shapes. To attenuate noise, an adaptive singular spectrum analysis (SSA) can be optionally applied to the recovered modal responses for the highly noisy systems. Finally, the natural frequencies and damping ratios are estimated by the single-degree-of-freedom (SDOF) fitting technique. Several numerical examples, an experimental frame case, and a field test of a pedestrian bridge are studied to verify the effectiveness of the proposed strategy. • Bandlimited source separation using the sinc function is proposed. • Transforming the underdetermined problem to determined or overdetermined ones. • Adapting the second-order blind identification to underdetermined modal analysis. • Hilbert transform, random covariances, and adaptive singular spectrum analysis improve performance. • Numerical examples and real-life cases verify the effectiveness. [ABSTRACT FROM AUTHOR]

In practical engineering applications, the vibration signals collected by sensors often contain outliers, resulting in the separation accuracy of source signals from the observed signals being seriously affected. The mixing matrix estimation is crucial to the underdetermined blind source separation (UBSS), determining the accuracy level of the source signals recovery. Therefore, a two-stage clustering method is proposed by combining hierarchical clustering and K-means to improve the reliability of the estimated mixing matrix in this paper. The proposed method is used to solve the two major problems in the K-means algorithm: the random selection of initial cluster centers and the sensitivity of the algorithm to outliers. Firstly, the observed signals are clustered by hierarchical clustering to get the cluster centers. Secondly, the cosine distance is used to eliminate the outliers deviating from cluster centers. Then, the initial cluster centers are obtained by calculating the mean value of each remaining cluster. Finally, the mixing matrix is estimated with the improved K-means, and the sources are recovered using the least square method. Simulation and the reciprocating compressor fault experiments demonstrate the effectiveness of the proposed method.

In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.