Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure

International audienceIn this paper we prove the existence of a solution of a coupled system involving a two phase incompressible flow in the ground and the mechanical deformation of the porous medium where the porosity is a function of the global pressure. The model is strongly coupled and involves a nonlinear degenerate parabolic equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Frechet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system

Parametric Electromagnetic Analysis of Radar-Based Advanced Driver Assistant Systems

Efficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems

Learning data-driven reduced elastic and inelastic models of spot-welded patches

Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors

Etude théorique et numérique de couplages entre écoulements et déformations mécaniques dans l'extraction d'hydrocarubres

Fraçois Alouges : Président, Olivier Goubet : Rapporteur, Florian De Vuyst : Rapporteur, Monique Madaune-Tort : Examinatrice, Hatem Zaag : Membre Invité)The purpose of this thesis is to study theoretical and numerical aspects of some coupled models between a flow in porous medium and the mechanical deformation of the ground. We consider two coupled models on the one hand (1) between a linear compressible flow and the mechanical deformation of the ground, and on the other hand (2) between a nonlinear two-phase flow and the mechanical deformation of the medium. For the first model (1), we show the existence and the uniqueness of the weak solution by means of the Galerkin method. The second model (2) is strongly coupled and involves a parabolic degenerate equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Fréchet-Kolmogorov theorem which yields the convergence of a subsequence to a weak solution of the parabolic system. The second part is devoted to the numerical study; we compare two coupling algorithms for the coupled models. The first one, which is used by engineers, is based upon computations by means of a fixed point method; the second one, which we propose, relies on a preconditionned conjugate gradient approach. We show that the second algorithm is more robust than the first one.L'objet de cette thèse est l'étude de modèles mathématiques pour les phénomènes de couplage entre l'écoulement de fluides et la déformation mécanique du sol lors de l'extraction d'hydrocarbures en milieu poreux. Dans la partie théorique, on considère deux modèles de couplage, d'une part (1) entre les déformations du sol et un écoulement linéaire compressible, et d'autre part (2) entre les déformations du sol et un écoulement diphasique non linéaire. Pour le modèle (1), on prouve l'existence et l'unicité d'une solution faible par la méthode de Galerkin. Le modèle (2) est fortement couplé et comporte une équation parabolique dégénérée; pour démontrer l'existence de solution, on considère une suite de problèmes uniformément paraboliques associés et on démontre qu'ils admettent une solution classique l'aide du théorème de point fixe de Schauder. On s'appuie ensuite sur le théorème de Fréchet-Kolmogorov pour prouver la compacité relative des suites de solutions et établir la convergence d'une sous-suite vers une solution faible du problème initial. Dans une seconde partie, on aborde l'étude numérique. On compare deux algorithmes pour les modèles de couplage. Le premier, utilisé par les ingénieurs du pétrole, est basé sur une méthode de point fixe; le second, que nous proposons et qui est plus robuste que le premier, s'appuie sur la méthode du gradient conjugué préconditionné

Sur la sensibilité paramétrique de l'Hyper-réduction en Dynamique des structures

International audienceDans cette communication, nous présentons un résultat mathématique sur la sensibilité paramétrique de la technique d'Hyper-réduction de modèles, par une base réduite obtenue grâce à la méthode de la décomposition orthogonale aux valeurs propres (POD) et un domaine d'intégration réduit (RID) associé à cette base. Nous nous intéressons plus particulièrement au cadre des équations hyperboliques de la dynamique des structures avec une loi de comportement visco-élastique. Nous présenterons au cours de la conférence une comparaison avec des simulations numériques pour la configuration d'un cas académique de dynamique d'une plaque d'acier

Data Augmentation for Regression Machine Learning Problems in High Dimensions

Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex, and depend on a high number of parameters. High-dimensional problems intrinsically involve the need for large amounts of data through the curse of dimensionality. That is why new approaches based on smart sampling techniques have been investigated to minimize the number of samples to be given to train the model, such as active learning methods. Here, we propose a technique based on a combination of the Fisher information matrix and sparse proper generalized decomposition that enables the definition of a new active learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy outperforms the usual ones

A parametric and non-intrusive reduced order model of car crash simulation

International audienceIndustrials have an intensive use of numerical simulations in order to avoid physical testing and to speed up the design stages of their products. The numerical testing is indeed quicker to set-up, less expensive, and supplies a lot of information about the system under study. Moreover, it can be much closer to the physical tests as the computation power increases. Despite the rise of this power, time consuming simulations remain challenging to be used in design process, especially in an optimization study. Crash simulations belong to this category. These rapid dynamic computations are used by RENAULT during the sizing of the vehicle structure in order to ensure that it meets specifications set up to reach safety criteria in case of accidents. They are completed using finite element software such as VPS (Virtual Performance Solver) developed by ESI group that will be used in this study. For car manufacturers, the goal of the optimization study is to minimize the mass of the vehicle (and thus its consumption) by modifying the thicknesses of some parts (from 20 to 100 variables). Industrials such as RENAULT currently perform optimization studies based on numerical design of experiments. The number of computations required by this technique is from 3 to 10 times the number of variables. This is too much in order to be intensively used in a design process.In order to decrease the time-to-market and to explore alternative technical solutions, we explore the potential of using a parametrized reduced order model in the optimization studies. The parametrized reduced order model gives an estimation of the high-fidelity result for a new set of parameters without using the solver, by analysing the existing results of previous computations with various sets of parameters. The developed reduced order model is called ReCUR. It is partly based on a CUR approach embedded in a regression analysis. The regression statistical model uses the data of a few calculations made with the solver. Other tools such as clustering and linear programming are used to get the regression analysis more efficient.It is hoped to drastically reduce the number of required simulations of a standard optimization study. In this paper, the construction of the reduced order model will be presented. Then, the relevancy of using the reduced order model into a design process will be exhibited through the treatment of two industrial test-cases. Some improvements of the method as well as several potential uses will then be outlined. The applications will highlights the promising power of the method to shorten design process using optimisation and long-run simulations

A parametric and non-intrusive reduced order model of car crash simulation

International audienceIndustrials have an intensive use of numerical simulations in order to avoid physical testing and to speed up the design stages of their products. The numerical testing is indeed quicker to set-up, less expensive, and supplies a lot of information about the system under study. Moreover, it can be much closer to the physical tests as the computation power increases. Despite the rise of this power, time consuming simulations remain challenging to be used in design process, especially in an optimization study. Crash simulations belong to this category. These rapid dynamic computations are used by RENAULT during the sizing of the vehicle structure in order to ensure that it meets specifications set up to reach safety criteria in case of accidents. They are completed using finite element software such as VPS (Virtual Performance Solver) developed by ESI group that will be used in this study. For car manufacturers, the goal of the optimization study is to minimize the mass of the vehicle (and thus its consumption) by modifying the thicknesses of some parts (from 20 to 100 variables). Industrials such as RENAULT currently perform optimization studies based on numerical design of experiments. The number of computations required by this technique is from 3 to 10 times the number of variables. This is too much in order to be intensively used in a design process.In order to decrease the time-to-market and to explore alternative technical solutions, we explore the potential of using a parametrized reduced order model in the optimization studies. The parametrized reduced order model gives an estimation of the high-fidelity result for a new set of parameters without using the solver, by analysing the existing results of previous computations with various sets of parameters. The developed reduced order model is called ReCUR. It is partly based on a CUR approach embedded in a regression analysis. The regression statistical model uses the data of a few calculations made with the solver. Other tools such as clustering and linear programming are used to get the regression analysis more efficient.It is hoped to drastically reduce the number of required simulations of a standard optimization study. In this paper, the construction of the reduced order model will be presented. Then, the relevancy of using the reduced order model into a design process will be exhibited through the treatment of two industrial test-cases. Some improvements of the method as well as several potential uses will then be outlined. The applications will highlights the promising power of the method to shorten design process using optimisation and long-run simulations

Advanced model order reduction and artificial intelligence techniques empowering advanced structural mechanics simulations: application to crash test analyses

International audienceThis paper proposes a general framework for expressing parametrically quantities of interest related to the solution of complex structural mechanics models, in particular the ones involved in crash analyses where strongly coupled nonlinear and dynamic behaviors coexist with space-time localized mechanisms. Advanced nonlinear regressions able to proceed in the low-data limit, enabling to accommodate heterogeneous parameters, will be proposed and their performances evaluated in the case of crash simulations. As soon as these parametric expressions will be determined, they can be used for generating large amounts of realizations of the quantity of interest for different choices of the parameters, for supporting data-analytics. On the other hand, such parametric representations allow the use advanced optimization techniques, evaluate sensitivities and propagate uncertainty all them under the stringent real-time constraint

Protective effects of thymoquinone against acrylamide-induced liver, kidney and brain oxidative damage in rats

International audienceAcrylamide (AA), an industrial monomer, may cause multi-organ toxicity through induction of oxidative stress and inflammation. The antioxidant properties of thymoquinone (TQ), an active constituent of Nigella sativa, have been established before. Theaim of the current study was to assess the protective effects of TQ against AA-induced toxicity in rats. Forty-eight male Wistarrats were divided into six groups each of eight rats. The first group acted as a negative control and received normal saline. GroupsII and III were administered TQ orally at doses of 10 and 20 mg/kg b.wt., respectively, for 21 days. The four group received AA(20 mg/kg b.wt.) for 14 days. The five and six groups were given TQ at either dose for 21 days, starting seven days before AAsupplementation (for 14 days). Acrylamide intoxication was associated with significant (p < 0.05) increases in serum levels ofliver injury biomarkers (alanine transferase, aspartate transferase, and alkaline phosphatase), renal function products (urea,creatinine), DNA oxidative damage biomarker (8-oxo-2′-deoxyguanosine), and pro-inflammatory biomarkers (interleukin-1β,interleukin-6, and tumor necrosis factor-α). Moreover, AA intoxication was associated with increased lipid peroxidation andnitric oxide levels, while reduced glutathione concentration and activities of glutathione peroxidase, superoxide dismutase, andcatalase in the liver, kidney, and brain. TQ administration normalized AA-induced changes in most serum parameters andenhanced the antioxidant capacity in the liver, kidney, and brain tissues in a dose-dependent manner. In conclusion, the currentexperiment showed that TQ exerted protective and antioxidant activities against AA-induced toxicity in mice