Retour Accueil / Recherche / Publications sur H.A.L.

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process. Reference: Koml\'os, J., Major, P. and Tusn\'ady, G. (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 111-131.

Sergio Alvarez-Andrade, Salim Bouzebda, Aimé Lachal

In this paper, we address the issue of conducting a sensitivity analysis of complex models with both static and dynamic uncertain inputs. While several approaches have been proposed to compute the sensitivity indices of the static inputs (i.e. parameters), the one of the dynamic inputs (i.e. stochastic fields) have been rarely addressed. For this purpose, we first treat each dynamic as a Gaussian process. Then, the truncated Karhunen–Loève expansion of each dynamic input is performed. Such an expansion allows to generate independent Gaussian processes from a finite number of independent random variables. Given that a dynamic input is represented by a finite number of random variables, its variance-based sensitivity index is defined by the sensitivity index of this group of variables. Besides, an efficient sampling-based strategy is described to estimate the first-order indices of all the input factors by only using two input samples. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties (static inputs) and the weather data (dynamic inputs) on the energy performance of a real low energy consumption house.

Floriane Anstett-Collin, Jeanne Goffart, Thierry Mara, Lilianne Denis-Vidal

The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß Newton method and show numerical experiments in the special case of star-shaped obstacles.

Frédérique Le Louër

This paper deals with parameter and state estimation in a bounded-error context for uncertain dynamical aerospace models when the input is considered optimized or not. In a bounded-error context, perturbations are assumed bounded but otherwise unknown. The parameters to be estimated are also considered bounded. The tools of the presented work are based on a guaranteed numerical set integration solver of ordinary differential equations combined with adapted set inversion computation. The main contribution of this work consists in developing procedures for parameter estimation whose performance is highly related with the input of system. In this paper, a comparison with a classical non-optimized input is proposed.

Qiaochu Li, Carine Jauberthie, Lilianne Denis-Vidal, Zohra Cherfi

This study aims to understand the mechanisms of nitrite appearance during wastewater denitrification by biofilters, focusing on the role of the carbon source. Experiments were carried out at lab-scale (batch tests) and full-scale plant (Parisian plant, capacities of 240,000 m3 day−1). Results showed that the nature of the carbon source affects nitrite accumulation rates. This accumulation is low, 0.05 to 0.10 g N-NO2 − per g N-NO3 − eliminated, for alcohols such as methanol, ethanol, or glycerol. The utilization of glycerol leads to fungal development causing clogging of the biofilters. This fungal growth and consequent clogging exclude this carbon source, with little nitrite accumulation, as carbon source for denitrification. Whatever the carbon source, the C/N ratio in the biofilter plays a major role in the appearance of residual nitrite; an optimal C/N ratio from 3.0 to 3.2 allows a complete denitrification without any nitrite accumulation.

Vincent Rocher, Anniet M Laverman, Johnny Gasperi, Sam Azimi, Sabrina Guérin

[...]

V. Rocher, Anniet M. Laverman, C. Paffoni, A. Goncalves, S. Guerin

Dans cet article, nous nous intéressons à la modélisation de l'écoulement d'un fluide monophasique dans un milieu poreux faillé en utilisant les méhodes de décomposition de domaine. Le problème à résoudre est un problème d'interface non standard qui prend en compte l'écoulement dans les fractures. Dans l'approche proposée, la fracture est considée comme une interface active, les conditions de transmission et les échanges entre la roche et la fracture font intervenir les propriétés de l'écoulement dans la fracture.

Laila Amir, Michel Kern, Jean E. Roberts, Vincent Martin

In this communication, we perform the sensitivity analysis of a building energy model. The aim is to assess the impact of the weather data on the performance of a model of a passive house, in order to better control it. The weather data are uncertain dynamic inputs to the model. To evaluate their impact, the problem of generating coherent weather data arises. To solve it, we carry out the Karhunen-Loève decomposition of the uncertain dynamic inputs. We then propose an approach for the sensitivity analysis of this kind of models. The originality for sensitivity analysis purpose is to separate the random variable of the dynamic inputs, propagated to the model response, from the deterministic spatio/temporal function. This analysis highlights the role of the solar gain on a high-insulated passive building, during winter time.

Floriane Anstett-Collin, Thierry Mara, Jeanne Goffart, Lilianne Denis-Vidal

In this paper, we address the issue of performing sensitivity analysis of complex models presenting uncertain static and dynamic inputs. The dynamic inputs are viewed as random processes which can be represented by a linear combination of the deterministic functions depending on time whose coefficients are uncorrelated random variables. To achieve this, the Karhunen-Loève decomposition of the dynamic inputs is performed. For sensitivity analysis purposes, the influence of the dynamic inputs onto the model response is then given by the one of the uncorrelated random coefficients of the Karhunen-Loève decomposition, which is the originality here. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties and the weather data on the energy performance of a real low energy consumption house.

Floriane Anstett-Collin, Jeanne Goffart, Thierry Mara, Lilianne Denis-Vidal

Blood flow in high static magnetic fields induces elevated voltages that disrupt the ECG signal recorded simultaneously during MRI scans for synchronization purposes. This is known as the magnetohydrodynamic (MHD) effect, it increases the amplitude of the T wave, thus hindering correct R peak detection. In this paper, we present an algorithm for extracting an efficient reference signal from an ECG contaminated by the Nuclear Magnetic Resonance (NMR) environment, that performs a good separation of the R-wave and the MHD artifacts. The proposed signal processing method is based on sub-band decomposition using the wavelet transform, and has been tested on human and small rodents ECG signals acquired during MRI scans in various magnetic field intensities. The results showed an almost flawless trigger generation in fields up to 4.7 Tesla during the three tested imaging sequences (GE, FSE and IRSE)

D Abi-Abdallah, A Drochon, V Robin, P Poulet, O Fokapu

A real time algorithm for cardiac and respiratory gating, which only requires an ECG sensor, is proposed here. Three ECG electrodes are placed in such a manner that the modulation of the recorded ECG by the respiratory signal would be maximal; hence, given only one signal we can achieve both cardiac and respiratory MRI gating. First, an off-line learning phase based on wavelet decomposition is run to compute an optimal QRS filter. Afterwards, on one hand the QRS filter is used to accomplish R peak detection, and on the other, a low pass filtering process allows the retrieval of the respiration cycle so that the image acquisition sequences would be triggered by the R peaks only during the expiration phase.

D Abi-Abdallah, A Drochon, V Robin, O Fokapu

Blood flow in high static magnetic fields induces elevated voltages that contaminate the ECG signal which is recorded simultaneously during MRI scans for synchronization purposes. This is known as the magnetohydrodynamic (MHD) effect, it increases the amplitude of the T wave, thus hindering correct R peak detection. In this paper, we inspect the MHD induced alterations of human ECG signals recorded in a 1.5 Tesla steady magnetic field and establish a primary characterization of the induced changes using time and frequency domain analysis. We also reexamine our previously developed real time algorithm for MRI cardiac gating and determine that, with a minor modification, this algorithm is capable of achieving perfect detection even in the presence of strong MHD artifacts.

Dima Abi Abdallah, Vincent Robin, Agnès Drochon, Odette Fokapu

Cardiac Magnetic Resonance Imaging (MRI) requires synchronization to overcome motion related artifacts caused by the heart’s contractions and the chest wall movements during respiration. Achieving good image quality necessitates combining cardiac and respiratory gating to produce, in real time, a trigger signal that sets off the consecutive image acquisitions. This guarantees that the data collection always starts at the same point of the cardiac cycle during the exhalation phase. In this paper, we present a real time algorithm for extracting a cardiac-respiratory trigger signal using only one, adequately placed, ECG sensor. First, an off-line calculation phase, based on wavelet decomposition, is run to compute an optimal QRS filter. This filter is used, afterwards, to accomplish R peak detection, while a low pass filtering process allows the retrieval of the respiration cycle. The algorithm’s synchronization capabilities were assessed during mice cardiac MRI sessions employing three different imaging sequences, and three specific wavelet functions. The prominent image enhancement gave a good proof of correct triggering. QRS detection was almost flawless for all signals. As for the respiration cycle retrieval it was evaluated on contaminated simulated signals, which were artificially modulated to imitate respiration. The results were quite satisfactory.

Dima Abi-Abdallah, Agnès Drochon, Vincent Robin, Odette Fokapu

This paper investigates the influence of static magnetic field exposure on blood flow. We mainly focus on steady flows in a rigid vessel and review the existing theoretical solutions, each based on some simplifying hypothesis. The results are developed, examined and compared, showing how the magnetohy-drodynamic interactions reduce the flow rate and generate electric voltages across the vessel walls. These effects are found to be moderate for magnetic fields such as those used in magnetic resonance imaging. In this case, a very simplified solution, formulated by neglecting the walls conductivity as well as the induced magnetic fields, is proven suitable.

Dima Abi Abdallah, Agnès Drochon, Vincent Robin, Odette Fokapu

Blood flow in a steady magnetic field has been of great interest over the past years.Many researchers have examined the effects of magnetic fields on velocity profiles and arterial pressure, and major studies focused on steady or sinusoidal flows. In this paper we present a solution for pulsed magnetohydrodynamic blood flow with a somewhat realistic physiological pressure wave obtained using a windkessel lumped model. A pressure gradient is derived along a rigid vessel placed at the output of a compliant module which receives the ventricle outflow. Then, velocity profile and flow rate expressions are derived in the rigid vessel in the presence of a steady transverse magnetic field. As expected, results showed flow retardation and flattening. The adaptability of our solution approach allowed a comparison with previously addressed flow cases and calculations presented a good coherence with those well established solutions.

Dima Abi Abdallah, Agnès Drochon, Vincent Robin, Odette Fokapu

In this paper we describe a high order spectral algorithm for solving the time-harmonic Navier equations in the exterior of a bounded obstacle in three space dimensions, with Dirichlet or Neumann boundary conditions. Our approach is based on combined-field boundary integral equation (CFIE) reformulations of the Navier equations. We extend the spectral method developped by Ganesh and Hawkins - for solving second kind boundary integral equations in electromagnetism - to linear elasticity for solving CFIEs that commonly involve integral operators with a strongly singular or hypersingular kernel. The numerical scheme applies to boundaries which are globally parameterised by spherical coordinates. The algorithm has the interesting feature that it leads to solve linear systems with substantially fewer unknowns than with other existing fast methods. The computational performances of the proposed spectral algorithm are demonstrated on numerical examples for a variety of three-dimensional convex and non-convex smooth obstacles.

Frédérique Le Louër

We consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell-Laplace operator of a domain $\Omega$, involving only geometrical informations. We provide such an upper bound, by generalizing Brock's inequality concerning Steklov eigenvalues, and we conjecture that balls maximize the Wentzell eigenvalue, in a suitable class of domains, which would improve our bound. To support this conjecture, we prove that balls are critical domains for the Wentzell eigenvalue, in any dimension, and that they are local maximizers in dimension 2 and 3, using an order two sensitivity analysis. We also provide some numerical evidence.

Marc Dambrine, Djalil Kateb, Jimmy Lamboley

Karhunen-Loève's decompositions (KLD) or the proper orthogonal decompositions (POD) of bivariate functions are revisited in this work. We investigate the truncation error first for regular functions and try to improve and sharpen bounds found in the literature. However it happens that (KL)-series expansions are in fact more sensitive to the liability of fields to approximate to be well represented by a small sum of products of separated variables functions. We consider this very issue for some interesting fields solutions of partial differential equations such as the transient heat problem and Poisson's equation. The main tool to state approximation bounds is linear algebra. We show how the singular value decomposition underlying the (KL)-expansion is connected to the spectrum of some Gram matrices. Deriving estimates on the truncation error is thus strongly tied to the spectral properties of these Gram matrices which are structured matrices with low displacement ranks.

Mejdi Azaïez, Faker Ben Belgacem

Ill-posedness and/or Ill-conditioning are features users have to deal with appropriately in the controllability of diffusion problems for secure and reliable outputs. We investigate those issues in the case of a boundary Dirichlet control, in an attempt to underline the origin of the troubles arising in the numerical computations and to shed some light on the difficulties to obtain good quality simulations. The exact controllability is severely ill-posed while, in spite of its well-posedness, the null-controllability turns out to be very badly ill-conditioned. Theoretical and numerical results are stated on the heat equation in one dimension to illustrate the specific instabilities of each problem. The main tools used here are first a characterization of the subspace where the HUM control lies and the study of the spectrum of some structured matrices, of Pick and Löwner type, obtained from the Fourier calculations on the state and adjoint equations.

Faker Ben Belgacem, Sidi-Mahmoud Kaber

Observability Gramians of diffusion equations have been recently connected to infinite Pick and Cauchy matrices. In fact, inverse or observability inequalities can be obtained after estimating the extreme eigenvalues of these structured matrices, with respect to the diffusion semi-group matrix. The purpose is hence to conduct a spectral study of a subclass of symmetric Cauchy matrices and present an algebraic way to show the desired observability results. We revisit observability inequalities for three different observation problems of the diffusion equation and show how they can be (re)stated through simple proofs.

Faker Ben Belgacem, Sidi-Mahmoud Kaber