Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain

International audienceThis paper considers the blind separation of non-stationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e. there is at most one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved thanks to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources, one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

A novel underdetermined source recovery algorithm based on k-sparse component analysis

Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation in array signal processing applications. We are motivated by problems that arise in the applications where the sources are densely sparse (i.e. the number of active sources is high and very close to the number of sensors). The separation performance of current underdetermined source recovery (USR) solutions, including the relaxation and greedy families, reduces with decreasing the mixing system dimension and increasing the sparsity level (k). In this paper, we present a k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems. Assuming the sources is at most (m−1) sparse where m is the number of mixtures; the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection framework. Simulation results show that the proposed algorithm achieves better separation performance in k-SCA conditions compared to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1, smoothed L0, focal underdetermined system solver and orthogonal matching pursuit

Precoder design for space-time coded systems over correlated Rayleigh fading channels using convex optimization

A class of computationally efficient linear precoders for space-time block coded multiple-input multiple-output wireless systems is derived based on the minimization of the exact symbol error rate (SER) and its upper bound. Both correlations at the transmitter and receiver are assumed to be present, and only statistical channel state information in the form of the transmit and receive correlation matrices is assumed to be available at the transmitter. The convexity of the design based on SER minimization is established and exploited. The advantage of the developed technique is its low complexity. We also find various relationships of the proposed designs to the existing precoding techniques, and derive very simple closed-form precoders for special cases such as two or three receive antennas and constant receive correlation. The numerical simulations illustrate the excellent SER performance of the proposed precoders

Bridge Operational Modal Identification Using Sparse Blind Source Separation

© 2020, Springer Nature Singapore Pte Ltd. The bridge infrastructures are subjected to continuous degradation due to ageing, environmental and excess loading. Monitoring of these structures is a key part of any maintenance strategy as it can give early warning if a bridge is becoming unsafe. Most of the current approaches are using direct measurements that the sensors are installed at different specific locations on the bridge to capture the dynamic characteristics of the structure under random input, such as wind loads, traffic loads and ground motions. Based on the assumption on the white noise characteristics of the random input, structural properties of the bridge could be extracted from the vibration responses only. However, the bridge is subjected to non-stationary traffic loads, and the frequency characteristics of vibrations are varied. Especially for short-span bridges, the non-stationary traffic excitation is significant and most of the existing output-only structural identification methods could not be used to assess the bridge condition. This study proposes a blind source separation (BSS) method using short time Fourier transform (STFT) for the analysis of non-stationary measurements in time frequency (TF) domain. The proposed method is capable of source component separation from response measurement for underdetermined problems when the number of independent measurements (sensors) is less than that of source component. The proposed method is applied to a cable-stayed bridge in the field for the operational modal identification under different traffic conditions

Single-Channel Signal Separation Using Spectral Basis Correlation with Sparse Nonnegative Tensor Factorization

A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model. The mixing mixture is an analogy of a stereo signal concept given by one real and the other virtual microphones. An “imitated-stereo” mixture model is thus developed by weighting and time-shifting the original single-channel mixture. This leads to an artificial mixing system of dual channels which gives rise to a new form of spectral basis correlation diversity of the sources. Underlying all factorization algorithms is the principal difficulty in estimating the adequate number of latent components for each signal. This paper addresses these issues by developing a framework for pruning unnecessary components and incorporating a modified multivariate rectified Gaussian prior information into the spectral basis features. The parameters of the imitated-stereo model are estimated via the proposed sparse nonnegative tensor factorization with Itakura–Saito divergence. In addition, the separability conditions of the proposed mixture model are derived and demonstrated that the proposed method can separate real-time captured mixtures. Experimental testing on real audio sources has been conducted to verify the capability of the proposed method

Underdetermined blind separation by combining sparsity and independence of sources

In this paper, we address underdetermined blind separation of N sources from their M instantaneous mixtures, where N>M , by combining the sparsity and independence of sources. First, we propose an effective scheme to search some sample segments with the local sparsity, which means that in these sample segments, only Q(Q < M) sources are active. By grouping these sample segments into different sets such that each set has the same Q active sources, the original underdetermined BSS problem can be transformed into a series of locally overdetermined BSS problems. Thus, the blind channel identification task can be achieved by solving these overdetermined problems in each set by exploiting the independence of sources. In the second stage, we will achieve source recovery by exploiting a mild sparsity constraint, which is proven to be a sufficient and necessary condition to guarantee recovery of source signals. Compared with some sparsity-based UBSS approaches, this paper relaxes the sparsity restriction about sources to some extent by assuming that different source signals are mutually independent. At the same time, the proposed UBSS approach does not impose any richness constraint on sources. Theoretical analysis and simulation results illustrate the effectiveness of our approach

Temperature-Driven Anomaly Detection Methods for Structural Health Monitoring

Reported in this thesis is a data-driven anomaly detection method for structural health monitoring which is based on the utilization of temperature-induced variations. Structural anomaly detection should be able to identify meaningful changes in measurements which are due to structural abnormal behaviour. Because, the temperature-induced variations and structural abnormalities may produce significant misinterpretations, the development of solutions to identify a structural anomaly, accounting for temperature influence, from measurements, is a critical procedure to support structural maintenance. A temperature-driven anomaly detection method is proposed, that introduces the idea of blind source separation for extracting thermal response and for further anomaly detection. Two thermal feature extraction methods are employed corresponding to the classification of underdetermined and overdetermined methods. The underdetermined method has the three phases of: (a) mode decomposition by utilising Empirical Mode Decomposition or Ensemble Empirical Mode Decomposition; (b) data reduction by performing Principal Component Analysis (PCA); (c) blind separation by applying Independent Component Analysis (ICA). The overdetermined method has the two stages of the pre-indication according to PCA and the blind separation by the devotion of ICA. Based on the extracted thermal response, the temperature-driven anomaly detection method is later developed in combination with the four methodologies of: Moving Principal Component Analysis (MPCA); Robust Regression Analysis (RRA); One-Class Support Vector Machine (OCSVM); Artificial Neural Network (ANN). Therefore, the proposed temperature-driven anomaly detection methods are designed as Td-MPCA, Td-RRA, Td-OCSVM, and Td-ANN. The proposed thermal feature extraction methods and temperature-driven anomaly detection methods have been investigated in the context of three case studies. The first case is a numerical truss bridge with simulated material stiffness reduction to create levels of damage. The second case is a purpose constructed truss bridge in the Structures Lab at the University of Warwick. The third case study is Ricciolo curved viaduct in Switzerland. Two primary findings can be confirmed from the evaluation results of these three case studies. Firstly, temperature-induced variations can conceal damage information in measurements. Secondly, the detection abilities of temperature-driven methods, which are Td-MPCA, Td-RRA, Td-OCSVM, and Td-ANN, for disclosing slight anomalies in time are more efficient when compared with the current anomaly detection method, which are MPCA, RRA, OCSVM, and ANN. The unique features of the author’s proposed temperature-driven anomaly detection method can be highlighted as follows: (a) it is a data-driven method for extracting features from an unknown structural system. In another word, the prior knowledge of the structural in-service conditions and physical models are not necessary; (b) it is the first time that blind source separation approaches and relative algorithms have been successfully employed for extracting temperature-induced responses; (c) it is a new approach to reliably assess the capability of using temperature-induced responses for anomaly detection

Audio-based signal extraction techniques for stamping tool condition monitoring

This thesis developed blind signal separation techniques to extract wear related information from the signal mixtures. Extracted signal analysis demonstrated that there is a significant qualitative association between the emitted audio and the wear progression of sheet metal stamping tools and this is the first study that identifies such correlation.<br /

Méthodes de séparation aveugle de sources pour le démélange d'images de télédétection

Nous proposons dans le cadre de cette thèse, de nouvelles méthodes de séparation aveugle de mélanges linéaires instantanés pour des applications de télédétection. La première contribution est fondée sur la combinaison de deux grandes classes de méthodes de Séparation Aveugle de Sources (SAS) : l'Analyse en Composantes Indépendantes (ACI), et la Factorisation en Matrices Non-négatives (NMF). Nous montrons comment les contraintes physiques de notre problème peuvent être utilisées pour éliminer une partie des indéterminations liées à l'ACI et fournir une première approximation des spectres de endmembers et des fractions d'abondance associées. Ces approximations sont ensuite utilisées pour initialiser un algorithme de NMF, avec pour objectif de les améliorer. Les résultats obtenus avec notre méthode sont satisfaisants en comparaison avec les méthodes de la littérature utilisées dans les tests réalisés. La deuxième méthode proposée est fondée sur la parcimonie ainsi que sur des propriétés géométriques. Nous commençons par mettre en avant quelques propriétés facilitant la présentation des hypothèses considérées dans cette méthode, puis nous mettons en lumière les grandes lignes de cette dernière qui est basée sur la détermination des zones bi-sources contenues dans une image de télédétection, ceci à l'aide d'un critère de corrélation. A partir des intersections des droites générées par ces zones bi-sources, nous détaillons le moyen d'obtention des colonnes de la matrice de mélange et enfin des sources recherchées. Les résultats obtenus, en comparaison avec plusieurs méthodes de la littérature sont très encourageants puisque nous avons obtenu les meilleures performances.Within this thesis, we propose new blind source separation (BSS) methods intended for instantaneous linear mixtures, aimed at remote sensing applications. The first contribution is based on the combination of two broad classes of BSS methods : Independent Component Analysis (ICA), and Non-negative Matrix Factorization (NMF). We show how the physical constraints of our problem can be used to eliminate some of the indeterminacies related to ICA and provide a first approximation of endmembers spectra and associated sources. These approximations are then used to initialize an NMF algorithm with the goal of improving them. The results we reached are satisfactory as compared with the classical methods used in our undertaken tests. The second proposed method is based on sparsity as well as on geometrical properties. We begin by highlighting some properties facilitating the presentation of the hypotheses considered 153 in the method. We then provide the broad lines of this approach which is based on the determination of the two-source zones that are contained in a remote sensing image, with the help of a correlation criterion. From the intersections of the lines generated by these two-source zones, we detail how to obtain the columns of the mixing matrix and the sought sources. The obtained results are quite attractive as compared with those reached by several methods from literature