Sparsity in array processing: methods and performances

International audienceIn the last few years, we witnessed to an extraordinary and still growing development of sparse signal recovery in a wide number of applicative contexts such as communications, biomedicine, radar, microwave imaging, source localization, astronomy, seismology... In many realistic array processing applications, the sparsity nature underlying various signals/arrays has to be exploit in recovery algorithms to enhance their performances. In this special session, most recent results in estimators based on sparsity-­‐promoting criteria is proposed

On Gevrey regularity of solutions for inhomogeneous nonlinear moment partial differential equations

In this article we investigate Gevrey regularity of formal power series solutions for a certain class of nonlinear moment partial differential equations, the inhomogeneity of which is $\sigma$-Gevrey with respect to the time variable $t$ for a fixed $\sigma\ge 0$. The results are achieved by analyzing the geometric structure of the Newton polygon associated with the equation and are a generalization of similar results obtained for standard nonlinear partial differential equations as well as linear moment differential equations

Fast multilinear Singular Values Decomposition for higher-order Hankel tensors

International audienceThe Higher-Order Singular Value Decomposition (HOSVD) is a possible generalization of the Singular Value Decomposition (SVD) to tensors, which have been successfully applied in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a Nth- order tensor involves the computation of the SVD of N matrices. Previous works have shown that it is possible to reduce the complexity of HOSVD for third-order structured tensors. These methods exploit the columns redundancy, which is present in the mode of structured tensors, especially in Hankel tensors. In this paper, we propose to extend these results to fourth order Hankel tensor. We propose two ways to extend Hankel structure to fourth order tensors. For these two types of tensors, a method to build a reordered mode is proposed, which highlights the column redundancy and we derive a fast algorithm to compute their HOSVD. Finally we show the benefit of our algorithms in terms of complexity

Impact of motion limits on sloped wave energy converter optimization

In a previous article [1] (subsequently referred to as the ‘original study’ and whose prior reading is recommended to make the most of what follows), the authors explored the concept of sloped power take-off (PTO) for a free-floating wave energy converter (WEC) using linear potential flow theory. Part of the study focused on the optimization of four parameters: the mass reference m2, its vertical position wG2r, the PTO angle θ0 and the magnitude of the linear damping α. It was decided for the optimization part of the original study to exclude configurations exhibiting normalized motion amplitude (NMA) maxima in surge, heave and pitch above a certain limit, or threshold. This method to keep results realistic within the context of linear potential flow theory was chosen over adding extra damping coefficients to the hydrodynamic model. The reasoning is that, as the PTO angle varies between configurations, the PTO provides more or less damping in pitch for the same α. Therefore, some configurations require less additional hydrodynamic damping (representing shape drag) than others to keep pitch normalized motion amplitudes within a realistic limit. Adding a fixed additional damping in pitch would dissipate energy, and therefore penalize some configurations more than others

Quantification of the influence of directional sea state parameters over the performances of wave energy converters

Accurate predictions of the annual energy yield from wave energy converters are essential to the development of the wave industry. The current method based on power matrices uses only a small part of the data available from sea state estimations and it is consequently prone to inaccuracies. The research presented in this work investigates the issue of energy yield prediction and questions the power matrix method. This is accomplished by quantifying the influence of several directional sea states parameters on the performances of wave energy converters. The approach taken was to test several wave energy converters in the Edinburgh Curved tank with a large set of sea states. The selected wave energy converters are a fix OWC, a set of two OWCs acting as a weak directional device and the desalination duck model. Uni-modal and bi-modal sea states were used. For the uni-modal sea states, parameters related to the wave system shape were considered. For the bi-modal sea states, the relative position of the wave system peaks was investigated and the uni-modality index was introduced to quantify the degree to which sea states could be considered bi-modal. For all sea states, the significant wave height was kept constant. The experimental work required good spectral estimates. The MLM and MMLM were adapted to deterministic waves to improve their stability and accuracy. A routine to isolate wave systems was also developed in order to estimate parameters with respect to each wave systems. For uni-modal spectra, parametric models of the observed performances of the devices could be devised. The frequency spreading and its interaction with the energy period proved to be as important as the energy period itself, which suggests that the frequency spreading should be used for energy production prediction. For bi-modal spectra, evidence of the duck sensitivity to directionality was found while the OWCs were not affected

Performance Analysis for Sparse Biased Estimator : Application to Line Spectra Analysis

International audienceDictionary based sparse estimators are based on the matching of continuous parameters of interest to a discretized sampling grid. Generally, the parameters of interest do not lie on this grid and there exists an estimator bias even at high Signal to Noise Ratio (SNR). This is the off-grid problem. In this work, we propose and study analytical expressions of the Bayesian Mean Square Error (BMSE) of dictionary based biased estimators at high SNR. We also show that this class of estimators is efficient and thus reaches the Bayesian Cramér-Rao Bound (BCRB) at high SNR. The proposed results are illustrated in the context of line spectra analysis and several popular sparse estimators are compared to our closed-form expressions of the BMSE

On the concept of sloped motion for free-floating wave energy converters

A free-floating wave energy converter (WEC) concept whose power take-off (PTO) system reacts against water inertia is investigated herein. The main focus is the impact of inclining the PTO direction on the system performance. The study is based on a numerical model whose formulation is first derived in detail. Hydrodynamics coefficients are obtained using the linear boundary element method package WAMIT. Verification of the model is provided prior to its use for a PTO parametric study and a multi-objective optimization based on a multi-linear regression method. It is found that inclining the direction of the PTO at around 50. to the vertical is highly beneficial for the WEC performance in that it provides a high capture width ratio over a broad region of the wave period range

Investigation into wave basin calibration based on a focused wave approach

The purpose of this paper is to present a detailed numerical investigation concerning the calibration of force controlled wave generation facilities. The methodology is presented for a 2-dimensional calibration; the findings being equally applicable to the calibration of 3-dimensional wave basins. State-of-the-art force controlled wavemaking facilities comprise sophisticated hardware, software and control systems, commonly incorporating active absorption mechanisms. Such facilities have the potential to reproduce ocean wave of exceptional quality, but poor understanding of accurate calibration processes often hinders full exploitation. A technique based upon the generation of focused wave events may oer a very accurate and time-efficient calibration. However, such a methodology may lead to erroneous results if not employed correctly. The theoretical and statistical analysis presented herein investigates the sensitivity of such method to a number of important parameters. The results obtained are directly applicable to a large number of hydrodynamic facilities