Réduction de dimension pour la Séparation Aveugle de Sources

National audienceIn this article, we consider the dimension reduction problem in the context of blind source separation. We propose (1) a new model based on approximate joint block diagonalization, which allows to find the sources along with their subspace simultaneously, and (2), a Riemannian optimization approach to solve it, original in this context. Our model recovers sources that are independant from the noise and less sensible to the à priori estimation of the number of sources. The efficiency of our model as compared to the state of the art is illustrated through the source separation of an electroencephalographic recording.Dans cet article, nous considérons le problème de la réduction de dimension dans le cadre de la séparation aveugle de sources. Nous proposons (1) un nouveau modèle basé sur la diagonalisation par blocs conjointe qui permet de retrouver simultanément les sources et leur sous-espace et (2), une approche par optimisation Riemannienne pour le résoudre, originale dans ce contexte. Notre modèle produit des sources indépendantes du bruit et moins sensibles à l'estimation à priori du nombre de sources. L'efficacité de notre modèle par rapport à l'état de l'art est illustré sur la séparation de sources d'un enregistrement électroencéphalographique

Une nouvelle approche fréquentielle pour la séparation aveugle de signaux non-stationnaires et autocorrélés

Nous avons récemment développé une nouvelle méthode pour la séparation aveugle de sources non-stationnaires en mélanges linéaires instantanés, appelée méthode à décorrélation spectrale. Contrairement aux méthodes classiques exploitant la non-stationnarité des signaux sources, notre méthode ne nécessite pas la stationnarité par morceaux et traite les mélanges dans le domaine fréquentiel. Cependant, elle suppose que les signaux sources sont temporellement non-corrélés, ce qui n'est pas le cas de la plupart des signaux réels. C'est pourquoi nous proposons dans cet article une extension de cette approche également applicable au cas de signaux non-stationnaires autocorrélés. Les résultats de tests avec ce type de signaux (parole, musique, images) montrent que notre méthode conduit à de meilleures performances que les méthodes classiques de séparation de sources

Newton-Type Methods For Simultaneous Matrix Diagonalization

This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equations associated to this problem, we construct a sequence that converges quadratically towards the solution. This construction is not based on the resolution of a linear system as is the case in the classical Newton method. Moreover, we provide a theoretical analysis of this construction and exhibit a condition to get a quadratic convergence. We also propose numerical experiments, which illustrate the theoretical results.Comment: Calcolo, Springer Verlag, 202

Estimation efficace des paramètres de signaux d'usagers radio-mobile par traitement avec antenne-réseau

Cette thèse aborde le problème d’estimation des paramètres de signaux d’usagers radio-mobile par traitement avec antenne-réseau. On adopte une approche de traitement théorique rigoureuse au problème en tentant de pallier aux limitations et désavantages des méthodes d’estimation existantes en ce domaine. Les chapitres principaux ont été rédigés en couvrant uniquement les aspects théoriques en lien aux contributions principales, tout en présentant une revue de littérature adéquate sur les sujets concernés. La thèse présente essentiellement trois volets distincts en lien à chacune des contributions en question. Suite à une revue des notions de base, on montre d’abord comment une méthode d’estimation exploitant des statistiques d’ordre supérieur a pu être développée à partir de l’amélioration d’un algorithme existant en ce domaine. On présente ensuite le cheminement qui a conduit à l’élaboration d’une technique d’estimation non linéaire exploitant les propriétés statistiques spécifiques des enveloppes complexes reçues, et ne possédant pas les limitations des algorithmes du second et quatrième ordre. Finalement, on présente le développement relatif à un algorithme d’estimation exploitant le caractère cyclostationnaire intrinsèque des signaux de communication dans un environnement asynchrone naturel. On montre comment un tel algorithme parvient à estimer la matrice de canal des signaux incidents indépendamment du caractère de corrélation spatiotemporel du bruit, et permettant de ce fait même une pleine exploitation du degré de liberté du réseau. La procédure d’estimation consiste en la résolution d’un problème de diagonalisation conjointe impliquant des matrices cibles issues d’une opération différentielle entre des matrices d’autocorrélation obtenues uniquement à partir de statistiques d’ordre deux. Pour chacune des contributions, des résultats de simulations sont présentés afin de confirmer l’efficacité des méthodes proposées.This thesis addresses the problem of parameter estimation of radio signals from mobile users using an antenna array. A rigorous theoretical approach to the problem is adopted in an attempt to overcome the limitations and disadvantages of existing estimation methods in this field. The main chapters have been written covering only the theoretical aspects related to the main contributions of the thesis, while at the same time providing an appropriate literature review on the considered topics. The thesis is divided into three main parts related to the aforesaid contributions. Following a review of the basics concepts in antenna array processing techniques for signal parameter estimation, we first present an improved version of an existing estimation algorithm expoiting higher-order statistics of the received signals. Subsequently, we show how a nonlinear estimation technique exploiting the specific statistical distributions of the received complex envelopes at the array can be developed in order to overcome the limitations of second and fourth-order algorithms. Finally, we present the development of an estimation algorithm exploiting the cyclostationary nature of communication signals in a natural asynchronous environment. We show how such an algorithm is able to estimate the channel matrix of the received signals independently of the spatial or temporal correlation structure of the noise, thereby enabling a full exploitation of the array’s degree of freedom. The estimation process is carried out by solving a joint diagonalization problem involving target matrices computed by a differential operation between autocorrelation matrices obtained by the sole use of second-order statistics. Various simulation experiments are presented for each contribution as a means of supporting and evidencing the effectiveness of the proposed methods

Theoretical and Experimental Study of Damage Identification of Beams and Plates

Structural characteristic deflection shapes (CDS’s) such as mode shapes and operational deflection shapes which contain spatial information of structures are highly sensitive for damage detection and localisation in beam- or plate- type structures. Despite substantial advances in this kind of methods, several issues must be addressed to boost their efficiency and practical applications, including the following: (1) The estimation of CDS’s involves substantial inaccuracies and is mainly affected by operational, environmental, measurement and computational uncertainties. (2) The curvature estimation of CDS’s is much more sensitive to measurement noise. (3) The extraction of damage-caused singularities from CDS’s or their curvatures is difficult when the baseline data of healthy structures is not available. (4) Damage index for multi-damage identification is challenging due to the different damage location sensitivities of each CDS. These problems have been investigated and the objective of this study is to enhance the accuracy and noise robustness of baseline-free damage detection and localisation. The original contributions of this study have been made in several aspects. Firstly, common principal component analysis is proposed to enhance accuracy of mode shape estimation in operational modal analysis, which statistically evaluates the common subspace bases of a set of covariance or power spectral density matrices as the mode shapes. Secondly, without the baseline data of healthy structures, polynomial fitting approaches and low-rank models are investigated for damage localisation, which extract the damage-induced local shape singularities by using only mode shapes or mode shape curvatures of damaged structures. Thirdly, in order to fairly incorporate damage information of several modes, two robust damage indexes are proposed for beam-type structures and plate-type structures, respectively. The above studies focus on linear damage such as open cracks in beam or plate structures without nonsmooth mass and stiffness distribution. Apart from these, the identification of fatigue cracks in stepped beam-type structures is investigated as well. In the theoretical aspect, the relationship between damage and structural characteristic deflection shapes is explained. Then, the finite element models of beams and plates are coded in MATLAB, which are validated by comparing corresponding results with the commercial software ABAQUS. Moreover, the numerical models of beams and plates with multiple damage are used to verify the feasibility and efficiency of the proposed methods in damage identification. Here, the damage is introduced by reducing the depth of beams or thickness of plates. In the experimental aspect, beams and plates with multiple damage are tested to demonstrate the proposed damage detection and localisation methods. In order to acquire the data of a large number of measurement points, the advanced scanning laser Vibrometer is used. It is found that the proposed mode shape estimation approaches are demonstrated to be more accurate and noise robust than the traditional frequency domain decomposition and time domain decomposition methods. Additionally, the noise effects on spatial domain features such as mode shape and mode shape curvatures can be significantly reduced by the polynomial fitting or multi-scale approaches. Furthermore, the developed robust multi-damage indexes for beams and plates are validated to be effective by using numerical simulations and experimental results. Finally, the proposed breathing crack identification approaches are effective in localising the breathing cracks but insensitive to the steps of the beams

The University Defence Research Collaboration In Signal Processing

This chapter describes the development of algorithms for automatic detection of anomalies from multi-dimensional, undersampled and incomplete datasets. The challenge in this work is to identify and classify behaviours as normal or abnormal, safe or threatening, from an irregular and often heterogeneous sensor network. Many defence and civilian applications can be modelled as complex networks of interconnected nodes with unknown or uncertain spatio-temporal relations. The behavior of such heterogeneous networks can exhibit dynamic properties, reflecting evolution in both network structure (new nodes appearing and existing nodes disappearing), as well as inter-node relations. The UDRC work has addressed not only the detection of anomalies, but also the identification of their nature and their statistical characteristics. Normal patterns and changes in behavior have been incorporated to provide an acceptable balance between true positive rate, false positive rate, performance and computational cost. Data quality measures have been used to ensure the models of normality are not corrupted by unreliable and ambiguous data. The context for the activity of each node in complex networks offers an even more efficient anomaly detection mechanism. This has allowed the development of efficient approaches which not only detect anomalies but which also go on to classify their behaviour

Source separation and beamforming

As part of the last day of the UDRC 2021 summer school, this presentation provides an overview over polynomial matrix methods. The use of polynomial matrices is motivated through a number of broadband multichannel problems, involving space-time covariance matrices, filter banks, or wideband MIMO systems. We extend the utility of EVD from narrowband to broadband solutions via a number of factorisation algorithms belonging to the second order sequential rotation or sequential matrix diagonalisation families of algorithms. In a second part of this presentation, a number of application areas are explored, ranging from precoder and equaliser design for broadband MIMO communications systems, to broadband angle of arrival estimation, broadband beamforming, and the problem of identifying source-sensor transfer paths from the second order statistics of the sensor signals

Latent variable regression and applications to planetary seismic instrumentation

The work presented in this thesis is framed by the concept of latent variables, a modern data analytics approach. A latent variable represents an extracted component from a dataset which is not directly measured. The concept is first applied to combat the problem of ill-posed regression through the promising method of partial least squares (PLS). In this context the latent variables within a data matrix are extracted through an iterative algorithm based on cross-covariance as an optimisation criterion. This work first extends the PLS algorithm, using adaptive and recursive techniques, for online, non-stationary data applications. The standard PLS algorithm is further generalised for complex-, quaternion- and tensor-valued data. In doing so it is shown that the multidimensional algebras facilitate physically meaningful representations, demonstrated through smart-grid frequency estimation and image-classification tasks. The second part of the thesis uses this knowledge to inform a performance analysis of the MEMS microseismometer implemented for the InSight mission to Mars. This is given in terms of the sensor's intrinsic self-noise, the estimation of which is achieved from experimental data with a colocated instrument. The standard coherence and proposed delta noise estimators are analysed with respect to practical issues. The implementation of algorithms for the alignment, calibration and post-processing of the data then enabled a definitive self-noise estimate, validated from data acquired in ultra-quiet, deep-space environment. A method for the decorrelation of the microseismometer's output from its thermal response is proposed. To do so a novel sensor fusion approach based on the Kalman filter is developed for a full-band transfer-function correction, in contrast to the traditional ill-posed frequency division method. This algorithm was applied to experimental data which determined the thermal model coefficients while validating the sensor's performance at tidal frequencies 1E-5Hz and in extreme environments at -65C. This thesis, therefore, provides a definitive view of the latent variables perspective. This is achieved through the general algorithms developed for regression with multidimensional data and the bespoke application to seismic instrumentation.Open Acces