Search Results (28)

In complex and diverse practical application scenarios, the challenge of blind source separation under underdetermined and nonlinear conditions is often encountered. To address this challenge, this paper proposes an innovative underdetermined nonlinear bounded component analysis method. This method first employs Multivariate Nonlinear Chirp Mode Decomposition (MNCMD) to process and reconstruct the observed signals, transforming the original underdetermined problem into a positive definite problem. Subsequently, Gaussianization techniques are introduced as a means of nonlinear compensation, successfully converting the nonlinear model into an analyzable linear model, laying a solid foundation for subsequent signal separation. Finally, the signal is separated by the bounded component analysis method, which does not require the source signals to be independent of each other. To validate the effectiveness and superiority of the proposed algorithm, detailed simulation experiments were designed and implemented. The experimental results demonstrate that compared to traditional underdetermined blind source separation algorithms, the algorithm presented in this paper exhibits significant advantages in terms of universality, convergence speed, separation accuracy, and robustness. Furthermore, this paper successfully applies the algorithm to the blind extraction of fetal electrocardiogram (FECG) signals from real datasets. The experimental results show that the algorithm can rapidly and effectively extract clearer and more accurate FECG signals, demonstrating its great potential and value in practical applications. Full article

In order to solve the problem of difficult separation of audio signals collected in pig environments, this study proposes an underdetermined blind source separation (UBSS) method based on sparsification theory. The audio signals obtained by mixing the audio signals of pigs in different states with different coefficients are taken as observation signals, and the mixing matrix is first estimated from the observation signals using the improved AP clustering method based on the “two-step method” of sparse component analysis (SCA), and then the audio signals of pigs are reconstructed by L1-paradigm separation. Five different types of pig audio are selected for experiments to explore the effects of duration and mixing matrix on the blind source separation algorithm by controlling the audio duration and mixing matrix, respectively. With three source signals and two observed signals, the reconstructed signal metrics corresponding to different durations and different mixing matrices perform well. The similarity coefficient is above 0.8, the average recovered signal-to-noise ratio is above 8 dB, and the normalized mean square error is below 0.02. The experimental results show that different audio durations and different mixing matrices have certain effects on the UBSS algorithm, so the recording duration and the spatial location of the recording device need to be considered in practical applications. Compared with the classical UBSS algorithm, the proposed algorithm outperforms the classical blind source separation algorithm in estimating the mixing matrix and separating the mixed audio, which improves the reconstruction quality. Full article

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. Full article

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. Full article

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. Full article

With radio frequency identification (RFID) becoming a popular wireless technology, more and more relevant applications are emerging. Therefore, anti-collision algorithms, which determine the time to tag identification and the accuracy of identification, have become very important in RFID systems. This paper presents the algorithms of ALOHA for randomness, the binary tree algorithm for determinism, and a hybrid anti-collision algorithm that combines these two algorithms. To compensate for the low throughput of traditional algorithms, RFID anti-collision algorithms based on blind source separation (BSS) are described, as the tag signals of RFID systems conform to the basic assumptions of the independent component analysis (ICA) algorithm. In the determined case, the ICA algorithm-based RFID anti-collision method is described. In the under-determined case, a combination of tag grouping with a blind separation algorithm and constrained non-negative matrix factorization (NMF) is used to separate the multi-tag mixing problem. Since the estimation of tag or frame length is the main step to solve the RFID anti-collision problem, this paper introduces an anti-collision algorithm based on machine learning to estimate the number of tags. Full article

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. Full article

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. Full article

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. Full article

The estimation accuracy of the mixed matrix is very important to the performance of the underdetermined blind source separation (UBSS) system. To improve the estimation accuracy of the mixed matrix, the sparsity of the mixed signal is required. The novel fractional domain time–frequency plane is obtained by rotating the time–frequency plane after the short-time Fourier transform. This plane represents the fine characteristics of the mixed signal in the time domain and the frequency domain. The rotation angle is determined by global searching for the minimum L1 norm to make the mixed signal sufficiently sparse. The obtained time–frequency points do not need single source point detection, reducing the calculation amount of the original algorithm, and the insensitivity to noise in the fractional domain improves the robustness of the algorithm in the noise environment. The simulation results show that the sparsity of the mixed signal and the estimation accuracy of the mixed matrix are improved. Compared with the existing mixed matrix estimation algorithms, the proposed method is effective. Full article

As a promising alternative to conventional contact sensors, vision-based technologies for a structural dynamic response measurement and health monitoring have attracted much attention from the research community. Among these technologies, Eulerian video magnification has a unique capability of analyzing modal responses and visualizing modal shapes. To reduce the noise interference and improve the quality and stability of the modal shape visualization, this study proposes a hybrid motion magnification framework that combines linear and phase-based motion processing. Based on the assumption that temporal variations can represent spatial motions, the linear motion processing extracts and manipulates the temporal intensity variations related to modal responses through matrix decomposition and underdetermined blind source separation (BSS) techniques. Meanwhile, the theory of Fourier transform profilometry (FTP) is utilized to reduce spatial high-frequency noise. As all spatial motions in a video are linearly controllable, the subsequent phase-based motion processing highlights the motions and visualizes the modal shapes with a higher quality. The proposed method is validated by two laboratory experiments and a field test on a large-scale truss bridge. The quantitative evaluation results with high-speed cameras demonstrate that the hybrid method performs better than the single-step phase-based motion magnification method in visualizing sound-induced subtle motions. In the field test, the vibration characteristics of the truss bridge when a train is driving across the bridge are studied with a commercial camera over 400 m away from the bridge. Moreover, four full-field modal shapes of the bridge are successfully observed. Full article

In the acoustics-based power transformer fault diagnosis, a transformer acoustic signal collected by an acoustic sensor is generally mixed with a large number of interference signals. In order to separate transformer acoustic signals from mixed acoustic signals obtained by a small number of sensors, a blind source separation (BSS) method of transformer acoustic signal based on sparse component analysis (SCA) is proposed in this paper. Firstly, the mixed acoustic signals are transformed from time domain to time–frequency (TF) domain, and single source points (SSPs) in the TF plane are extracted by identifying the phase angle differences of the TF points. Then, the mixing matrix is estimated by clustering SSPs with a density clustering algorithm. Finally, the transformer acoustic signal is separated from the mixed acoustic signals based on the compressed sensing theory. The results of the simulation and experiment show that the proposed method can separate the transformer acoustic signal from the mixed acoustic signals in the case of underdetermination. Compared with the existing denoising methods of the transformer acoustic signal, the denoising results of the proposed method have less error and distortion. It will provide important data support for the acoustics-based power transformer fault diagnosis. Full article

It has been challenging to separate the time–frequency (TF) overlapped wireless communication signals with unknown source numbers in underdetermined cases. In order to address this issue, a novel blind separation strategy based on a TF soft mask is proposed in this paper. Based on the clustering property of the signals in the sparse domain, the angular probability density distribution is obtained by the kernel density estimation (KDE) algorithm, and then the number of source signals is identified by detecting the peak points of the distribution. Afterward, the contribution degree function is designed according to the cosine distance to calculate the contribution degrees of the source signals in the mixed signals. The separation of the TF overlapped signals is achieved by constructing a soft mask matrix based on the contribution degrees. The simulations are performed with digital signals of the same modulation and different modulation, respectively. The results show that the proposed algorithm has better anti-aliasing and anti-noise performance than the comparison algorithms. Full article

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. Full article

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. Full article