Search

Nowadays data is acquiring an indisputable importance in every field including engineering. In the past, experimental data was used to calibrate state-of-the art models. Once the model was optimally calibrated, numerical simulations were run. However, data can offer much more, playing a more important role than calibration or statistical analysis in the modeling/simulation process. Indeed, today data is gathered and used to train models able to replace complex engineering systems. The more and better the training data, the more accurate the model is. However, in engineering experimental data use to be the best data but also the most expensive in time and computing effort. Therefore, numerical simulations, cheaper and faster, are used instead but, even if they are closed to reality, they always present an error related to the ignorance of the engineer over the complex real system. It seems thus coherent to take advantage of each approach. This leads to the “hybrid twin” rationale. On the one hand, numerical simulations are computed as primary data source, assuming their inherent error. On the other hand, some experimental data is gathered to train a machine learning correction model which fills the prediction-measurement gap. However, learning this ignorance gap becomes difficult in some fields such as fluids dynamics, where a regression over the localized solutions can lead to non physical interpolated solutions. Therefore, the “hybrid twin” methodology proposed in this article relies on Optimal Transport theory, which provides a mathematical framework to measure distances between general objects and a completely different interpolation approach between functions.

Code verification is an intricate and crucial part of code developed. Due to the nature of the partial differential equations being solved, an analytical solution might not exit. To prove that the code is solving the correct equations, the method of manufactured solutions (MMS) is the go to approach. In this method we create a forcing term to drive the solution to a predetermined function. By performing a mesh refinement study, we can verify if the code is solving correctly the governing equations. In this work, we present the procedure of MMS as well as a tool developed in an open-source software for symbolic computation of the forcing term, appropriate boundary conditions and error norm computation withing the OpenFOAM® framework.

International audience; Recently published research indicated that, in additive manufacturing fields, single fiber reinforcements often increased some mechanical properties of composites, but at the same time decreased other mechanical behaviors, leading to a limited application of single fiber filled composites in the industry. Therefore, 3D printed hybrid composites made from a combination of short/short fibers, short/continuous fibers, or continuous/continuous fibers have received significant attention from researchers, owing to the comprehensive performance improvements and tailored mechanical behaviors. This paper reviewed the state-of-the-art 3D printed hybrid composites and elaborated on their mechanical behaviors, application limitations, potential improvements and future perspectives. The review started with a detailed discussion of different existing hybrid composite printing methods. Then, the mechanical performance, deformation and failure behaviors of hybrid composites were discussed. Finally, this review explored the limitations of printed hybrid composites and looked forward to printing hybrid composite with improved performance.

This paper aims at introducing the main building blocks of a digital twin, embracing physics-based and data-driven functionalities, both enriching mutually. Both should proceed in almost real-time, and the last being able to proceed in the scarce data limit. When applied to materials and processes, model order reduction technologies enable the construction of the so-called “computational vademecum”, whereas data-driven modelling, based in advanced regressions, must be informed by the physics to encompass rapidity and accuracy, in the low data limit. Despite of the recent advances, a lot of functionalities are needed and are under progress, some of them representing real scientific challenges. A number of them, the ones that we estimate being the most crucial, will be discussed in the present work.

The description of a physical problem through a model necessarily involves the introduction of parameters. Hence, one wishes to have a solution of the problem that is a function of all these parameters: a parametric solution. However, the construction of such parametric solutions exhibiting localization in space is only ensured by costly and time-consuming tests, which can be both numerical or experimental. Numerical methodologies used classically imply enormous computational efforts for exploring the design space. Therefore, parametric solutions obtained using advanced nonlinear regressions are an essential tool to address this challenge. However, classical regression techniques, even the most advanced ones, can lead to non physical interpolation in some fields such as fluid dynamics, where the solution localizes in different regions depending on the problem parameters choice. In this context, Optimal Transport (OT) offers a mathematical approach to measure distances and interpolate between general objects in a, sometimes, more physical way than the classical interpolation approach. Thus, OT has become fundamental in some fields such as statistics or computer vision, and it is being increasingly used in fields such as computational mechanics. However, the OT problem is usually computationally costly to solve and not adapted to be accessed in an online manner. Therefore, the aim of this paper is combining advanced nonlinear regressions with Optimal Transport in order to implement a parametric real-time model based on OT. To this purpose, a parametric model is built offline relying on Model Order Reduction and OT, leading to a real-time interpolation tool following Optimal Transport theory. Such a tool is of major interest in design processes, but also within the digital twin rationale.

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique., 9 pages, 5 figures

The interpretation of earthquakes produced by very large glaciers in Greenland and Antarctica (so-called icequakes) due to iceberg calving at the glacier terminus, crevasse opening, and/or sliding of the glacier over the bedrock, requires an accurate knowledge of the seismic response of polar ices. On the other hand, the polar ice microstructure plays an important role in glacier dynamics and may be recovered from seismic investigation. Quantification of the effective elastic properties of polycrystalline ice and associated seismic response, possibly anisotropic, and of their strong dependency on the ice microstructure is therefore a key issue. For polar ices, important microstructural features include (i) the strongly pronounced crystallographic texture (LPO) with grains c-axes typically oriented towards the in-situ vertical direction or aligned with the vertical plane, (ii) the open porosity in the firn (down to ~100m depth), (iii) the air bubble (closed porosity) down to ~1000m depth, (iv) melt pockets in temperate ices, and (v) the inclusion of sand/rocks coming from the bedrock erosion in the ~100m bottom layer. All these microstructures are associated with a large mechanical contrast in the material. To estimate the seismic response of such ices, we make use of a mean-field homogenization model (elastic self-consistent model) that allows estimating the effective elastic properties of polar ices with respect to the microstructural parameters, and the interplay between these parameters. Associated anisotropic seismic response will be discussed and compared with observations. We then propose a reduced-order modeling of the seismic response based on a sparse Proper Generalized Decomposition.

In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.

This paper presents a data-driven structural health monitoring (SHM) method by the use of so-called reduced-order models relying on an offline training/online use for unidirectional fiber and matrix failure detection in a 3D woven composite plate. During the offline phase (or learning) a dataset of possible damage localization, fiber and matrix failure ratios is generated through high-fidelity simulations (ABAQUS software). Then, a reduced model in a lower-dimensional approximation subspace based on the so-called sparse proper generalized decomposition (sPGD) is constructed. The parametrized approach of the sPGD method reduces the computational burden associated with a high-fidelity solver and allows a faster evaluation of all possible failure configurations. However, during the testing phase, it turns out that classical sPGD fails to capture the influence of the damage localization on the solution. To alleviate the just-referred difficulties, the present work proposes an adaptive sPGD. First, a change of variable is carried out to place all the damage areas on the same reference region, where an adapted interpolation can be done. During the online use, an optimization algorithm is employed with numerical experiments to evaluate the damage localization and damage ratio which allow us to define the health state of the structure.

This paper explores numerical methods dedicated to 3D elastic waves simulations in spatially separable domains such as plates. The objective is to reduce the computation time and the memory requirements associated to these large simulations involving fine space and time discretizations. The 3D problem is decomposed into a sequence of lower dimensional problems with the Proper Generalized Decomposition. The spatial discretization is performed with the Spectral Element Method to provide more compact separated representations compared to the ones obtained with a finite element discretization. Following previous works on space separation in elastodynamics, we explore hybrid explicit/implicit time marching schemes to improve the solution through one direction as needed, without decreasing the time step due to stability constraints. Large 3D numerical problems with several millions of degrees of freedom are efficiently solved with memory requirements characteristic of 2D problems.

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding multi-parametric solutions can be viewed as a sort of computational vademecum that, once computed offline, can be then used in a variety of real-time engineering applications including optimization, inverse analysis, uncertainty propagation or simulation based control. Sometimes, these multi-parametric problems can be solved by using advanced model order reduction—MOR-techniques. However, solving these multi-parametric problems can be very costly. In that case, one possibility consists in solving the problem for a sample of the parametric values and creating a regression from all the computed solutions. The solution for any choice of the parameters is then inferred from the prediction of the regression model. However, addressing high-dimensionality at the low data limit, ensuring accuracy and avoiding overfitting constitutes a difficult challenge. The present paper aims at proposing and discussing different advanced regressions based on the proper generalized decomposition (PGD) enabling the just referred features. In particular, new PGD strategies are developed adding different regularizations to the s-PGD method. In addition, the ANOVA-based PGD is proposed to ally them.

In industrial settings, engineering products are often divided into separate components for detailed conception. They often require iterative corrections between different designers/teams to optimize the final product with all components assembled into a system. This article proposes a surrogate modeling approach with functional descriptions of parts in the model and aims to accelerate the design and optimization phase in real projects. The approach is applied to a vibration problem of a two-component plate structure, where the model estimates the dynamic behavior of the assembled system when only the properties of each individual part are available. A database is built using high-fidelity numerical simulations, and neural-network-based regressions provide reliable predictions on unseen data.

We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.

Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic functions involving the different space coordinates. In the case of complex shapes, more sophisticated geometrical transformations are needed to map the complex physical domain into a regular one where computations are performed. This paper aims at proposing a very efficient route for accomplishing such space separation. A NURBS-based geometry representation, usual in computer aided design—CAD—, is retained and combined with a fully separated representation for allying efficiency (ensured by the fully separated representations) and generality (by addressing complex geometries). Some numerical examples are considered to prove the potential of the proposed methodology.

In many contexts of scientific computing and engineering science, phenomena are monitored over time and data are collected as time-series. Plenty of algorithms have been proposed in the field of time-series data mining, many of them based on deep learning techniques. High-fidelity simulations of complex scenarios are truly computationally expensive and a real-time monitoring and control could be efficiently achieved by the use of artificial intelligence. In this work we build accurate data-driven models of a two-phase transient flow in a heated channel, as usually encountered in heat exchangers. The proposed methods combine several artificial neural networks architectures, involving standard and transposed deep convolutions. In particular, a very accurate real-time integrator of the system has been developed.

International audience; 3D-printed continuous ramie fiber reinforced polypropylene composites (CRFRPP) are expected to ensure good mechanical properties while meeting the requirements of environmental friendliness and sustainability. To promote the wide industrial application of CRFRPP, this work investigated the effects of printing parameters (extrusion flow rate, printing temperature, layer thickness and printing speed) on the interfacial properties of CRFRPP. The interlayer and intralayer interfacial properties of CRFRPP with different printing parameters were studied using the design of experiment approach. Machine learning methods and response surface methodology prediction were also carried out based on the experimental results to bridge the printing parameters and interfacial properties. According to the prediction results, the printing parameters were optimized to improve the production efficiency while ensuring the desired interfacial performance. At last, the bending tests were conducted to investigate how the difference in interfacial properties can be translated to the mechanical performance. The results found that printed specimens with weak interfacial strength suffered interlaminar delamination failure when subjected to bending loads, greatly weakening the mechanical properties of the composites.

Inverse problems can be challenging and interesting to study in the context of metallurgical processes. This work aims to carry out a method for inverse modeling for simultaneous double-frequency induction hardening process. In this investigation, the experimental measured hardness profiles were considered as input data, while the output data were the process parameters. For this purpose experiments were carried out on C45 steel spur-gear. The method is based on machine learning algorithms and data treatment for dealing with inverse approach issues. In addition to the inverse modeling, a forward problem-based verification completes the study. It was found that according to promising results that this method is suitable and applicable for inverse problem of hardness modeling.

International audience; 3D printing using continuous fiber reinforcement provides a new technical method for preparing complex components with high mechanical behaviors. However, these printed composites have great differences in interfacial behaviors, affecting overall performance. This study aimed to investigate the tensile behaviors of 3D printed continuous fiber filled composites. The structural evolutions and failure features of the composites induced by strain were analyzed with the consideration of interfaces, influenced by the reinforcement fibers, stacking sequences as well as raster orientations. A roller peeling test was conducted to quantify the interfacial strength of different materials. An analytical approach was proposed to predict the stiffness behavior of the printed composites by introducing an interfacial strengthening coefficient into the volume average stiffness model. The predictions of stiffness, for the 3D printed continuous fiber filled composites with different fibers, stacking sequences and raster orientations, were in good agreement with experimental results.

Ti-6Al-4V titanium is considered a difficult-to-cut material used in critical applications in the aerospace industry requiring high reliability levels. An appropriate selection of cutting conditions can improve the machinability of this alloy and the surface integrity of the machined surface, including the generation of compressive residual stresses. In this paper, orthogonal cutting tests of Ti-6Al-4V titanium were performed using coated and uncoated tungsten carbide tools. Suitable design of experiments (DOE) was used to investigate the influence of the cutting conditions (cutting speed Vc, uncut chip thickness h, tool rake angle γn, and the cutting edge radius rn) on the forces, chip compression ratio, and residual stresses. Due to the time consumed and the high cost of the residual stress measurements, they were only measured for selected cutting conditions of the DOE. Then, the machine learning method based on mathematical regression analysis was applied to predict the residual stresses for other cutting conditions of the DOE. Finally, the optimal cutting conditions that minimize the machining outcomes were determined. The results showed that when increasing the compressive residual stresses at the machined surface by 40%, the rake angle should be increased from negative (−6°) to positive (5°), the cutting edge radius should be doubled (from 16 µm to 30 µm), and the cutting speed should be reduced by 67% (from 60 to 20 m/min).

Data-driven modeling approach constitutes an appealing alternative to the finite element method for optimizing complex multiphysics parametrized problems. In this context, this paper aims at proposing a parametric solution for the temperature-time evolution during the multiphysics induction heating process by using a data-driven non-intrusive modeling approach. To achieve this goal, firstly, a set of synthetic solutions was collected, at some sparse sensors in the space domain and for properly selected process parameters, by solving the full-order finite element models using FORGE® software. Then, the gappy proper orthogonal decomposition method was used to complete the missing data. Next, the proper orthogonal decomposition method coupled with the nonlinear sparse proper generalized decomposition regression method was applied to find a low-dimensional space onto which the original solutions were projected and a model for the low-dimensional representations was, therefore, created. Hence, a real-time prediction of the temperature-time evolution and for any new process parameters could be efficiently computed at the predefined positions (sensors) in the space domain. Finally, spatial interpolation was carried out to extend the solutions everywhere in the spatial domain by applying a strategy based on the nonlinear dimensionality reduction by locally linear embedding method and the proper orthogonal decomposition method with radial basis functions interpolation. It was shown that the results are promising and the applied approaches provide good approximations in the low-data limit case. This research was carried out as part of a project TRANS-FUGE sponsored by the french institute of research and technology in materials, metallurgy and processes (IRT-M2P), France. The project benefited from funding from a consortium of industrial partners and the French PIA (Plan d’Investissement d’Avenir) granted the French National Agency for Research (ANR).

International audience; Non-intrusive approaches for the construction of computational vademecums face different challenges, especially when a parameter variation affects the physics of the problem considerably. In these situations, classical interpolation becomes inaccurate. Therefore, classical approaches for the construction of an offline computational vademecum, typically by using model reduction techniques, are no longer valid. Such problems are faced in different physical simulations, for example welding path problems, resin transfer molding, or sheet compression molding, among others. In such situations, the interpolation of precomputed solutions at prescribed parameter values (built using either intrusive or non intrusive techniques) generates spurious numerical artifacts. In this work, we propose an alternative interpolation and simulation strategy by using physically-based morphing of spaces. The morphing will transform the uncompatibe physical domains of the problem’s solution into a compatible one, where an interpolation free of artifacts can be performed. Later on, an inverse transformation can be used to push-back the solution. Different relevant examples are illustrated in this work to motivate the use of the proposed method

Several defects might affect a casting part and degrade its quality and the process efficiency. Porosity formation is one of the major defects that can appear in the resulting product. Thus, several research studies aimed at investigating methods that minimize this anomaly. In the present work, a porosity prediction procedure is proposed to assist users at optimizing porosity distribution according to their application. This method is based on a supervised learning approach to predict shrinkage porosity from thermal history. Learning data are generated by a casting simulation software operating for different process parameters. Machine learning was coupled with a modal representation to interpolate thermal history time series for new parameters combinations. By comparing the predicted values of local porosity to the simulated results, it was demonstrated that the proposed model is efficient and can open perspectives in the casting process optimization.

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and analysis (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (grey box) modeling but also in the correction for real physics adaptation in low data regimes and partial observations of the dynamics. The method presented is extensible to other domains such as the development of cognitive digital twins, able to learn from observation of phenomena for which they have not been trained explicitly., 15 pages, 8 figures

A domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS allow a compact and powerful domain mapping into a fully separated reference geometry, while the PGD allows recovering an affine structure of the problem in the reference domain, facilitating the use of the standard PGD solver for computing the parametric solution in each subdomain first, and then by enforcing the interface transmission conditions, in the whole domain.

Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, . . . ). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis—TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes.

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions in mixed reality using deep learning. The graph-based architecture of the method ensures the thermodynamic consistency of the predictions, whereas the visualization pipeline allows a natural and realistic user experience. Two examples of virtual solids interacting with virtual or physical solids in mixed reality scenarios are provided to prove the performance of the method., Comment: 11 pages, 7 figures

International audience; Fused deposition modeling (FDM) is a promising additive manufacturing technique for fabrication of continuous fiber-reinforced thermoplastic composites. For composite applications, the balance of material properties, including rigidity and toughness, needs to be considered. To overcome the drawbacks induced by single continuous fiber reinforcement, this study focused on the design and characterization of hybrid continuous fiber (continuous carbon and Kevlar fibers)-reinforced polyamide (PA)-based composites, prepared by 3D printing, to achieve comprehensive performance improvements and designable mechanical properties. The deformation and failure behaviors with the effects of hybrid conception, stacking sequences, and raster orientations of composites were investigated. A hybrid effect model was introduced to evaluate the hybrid effect of 3D printed continuous fiber-filled composites. Besides, compared to composites fabricated via conventional methods, a major difference in 3D printed hybrid composites is the performance of interfacial bonding. A roller peeling test was therefore conducted to investigate the interfacial strength of different materials. An analytical approach was developed to predict the tensile modulus of the printed hybrid composites by introducing an interfacial strengthening coefficient into the volume average stiffness model. The combined experimental and predicted results showed that hybrid composite specimens with separated distribution sequence showed a higher tensile modulus compared to hybrid composites with concentrated distribution. The higher tensile properties of the printed hybrid composites with separated continuous fiber-reinforced layers were attributed to the strong interfacial bonding, which delayed crack initiation and propagation.

Modeling systems from collected data faces two main difficulties: the first one concerns the choice of measurable variables that will define the learnt model features, which should be the ones concerned by the addressed physics, optimally neither more nor less than the essential ones. The second one is linked to accessibility to data since, generally, only limited parts of the system are accessible to perform measurements. This work revisits some aspects related to the observation, description, and modeling of systems that are only partially accessible and shows that a model can be defined when the loading in unresolved degrees of freedom remains unaltered in the different experiments.

Simulation-based engineering has been a major protagonist of the technology of the last century. However, models based on well established physics fail sometimes to describe the observed reality. They often exhibit noticeable differences between physics-based model predictions and measurements. This difference is due to several reasons: practical (uncertainty and variability of the parameters involved in the models) and epistemic (the models themselves are in many cases a crude approximation of a rich reality). On the other side, approaching the reality from experimental data represents a valuable approach because of its generality. However, this approach embraces many difficulties: model and experimental variability; the need of a large number of measurements to accurately represent rich solutions (extremely nonlinear or fluctuating), the associate cost and technical difficulties to perform them; and finally, the difficulty to explain and certify, both constituting key aspects in most engineering applications. This work overviews some of the most remarkable progress in the field in recent years.

Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://www.frontiersin.org/articles/10.3389/frai.2021.761123/full Este artículo pertenece a la sección "AI in Business". The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Most of existing methodologies enabling efficient diagnosis are based on the data analysis, and in particular on some statistical quantities derived from the data. The present work explores the use of an original approach that instead of analyzing quantities derived from the data, analyzes the “shape” of the data, that is, the time series topology based on the homology persistence. We will prove that this procedure is able to extract valuable patterns able to discriminate the trajectories that the robot follows depending on the particular patch in which it operates, as well as to differentiate the robot behavior before and after undergoing a maintenance operation. Even if it is a preliminary work, and it does not pretend to compare its performances with respect to other existing technologies, this work opens new perspectives in considering quite natural and simple descriptors based on the intrinsic information that data contains, with the aim of performing efficient diagnosis and prognosis.

International audience; Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.; Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

El objetivo de este trabajo es utilizar inteligencia artificial para aprender las leyes físicas que gobiernan un sistema arbitrario y predecir así su evolución en el tiempo. Para ello se utilizan varios sesgos inductivos, que aseguran la correcta estructura matemática del problema y mejoran su capacidad de generalización.

Two main problems are studied in this article. The first one is the use of the extrusion process for controlled thermo-mechanical degradation of polyethylene for recycling applications. The second is the data-based modelling of such reactive extrusion processes. Polyethylenes (high density polyethylene (HDPE) and ultra-high molecular weight polyethylene (UHMWPE)) were extruded in a corotating twin-screw extruder under high temperatures (350 °C < T < 420 °C) for various process conditions (flow rate and screw rotation speed). These process conditions involved a decrease in the molecular weight due to degradation reactions. A numerical method based on the Carreau-Yasuda model was developed to predict the rheological behaviour (variation of the viscosity versus shear rate) from the in-line measurement of the die pressure. The results were successfully compared to the viscosity measured from offline measurement assuming the Cox-Merz law. Weight average molecular weights were estimated from the resulting zero-shear rate viscosity. Furthermore, the linear viscoelastic behaviours (Frequency dependence of the complex shear modulus) were also used to predict the molecular weight distributions of final products by an inverse rheological method. Size exclusion chromatography (SEC) was performed on five samples, and the resulting molecular weight distributions were compared to the values obtained with the two aforementioned techniques. The values of weight average molecular weights were similar for the three techniques. The complete molecular weight distributions obtained by inverse rheology were similar to the SEC ones for extruded HDPE samples, but some inaccuracies were observed for extruded UHMWPE samples. The Ludovic® (SC-Consultants, Saint-Etienne, France) corotating twin-screw extrusion simulation software was used as a classical process simulation. However, as the rheo-kinetic laws of this process were unknown, the software could not predict all the flow characteristics successfully. Finally, machine learning techniques, able to operate in the low-data limit, were tested to build predicting models of the process outputs and material characteristics. Support Vector Machine Regression (SVR) and sparsed Proper Generalized Decomposition (sPGD) techniques were chosen to predict the process outputs successfully. These methods were also applied to material characteristics data, and both were found to be effective in predicting molecular weights. More precisely, the sPGD gave better results than the SVR for the zero-shear viscosity prediction. Stochastic methods were also tested on some of the data and showed promising results.

The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.

In the automotive industry, building parametric surrogate models is a fundamental tool to evaluate, in real time, the performance of newly designed car components. Such models allow to compute any Quantity of Interest -QoI-, such as a specific safety protocol index, for any choice of material and/or geometrical parameters characterizing the component, within the stringent real time constraint. For instance, they can be exploited to guarantee safer designs (e.g., maximizing energy absorption by the crash boxes) or to reduce manufacturing costs (e.g., minimizing the mass of a specific structure under some safety protocol constraints). In general, these parametric simulation tools allow a significant gain in terms of manufacturing costs and time delays during the investigation phase. In this study, we focus on the vehicle frontal structure system considering its performance in a full-frontal crash scenario. In the front structure system we parameterize the crash boxes (left and right) and the inner/outer side front members (left and right, front and rear) with respect to the part thickness and the material parameters characterizing the Krupkowski plasticity curve. Moreover, Strain Rate Effect is also taken into account via Neural Network based regressions, whose training dataset comes from experimental data. The parametric metamodel is built via Non-Intrusive PGD -NI-PGD- strategies, relying on a sparse sampling of the parametric space, and allowing a quite reduced number of High Fidelity -HiFi- simulations. A novel strategy based on clustering and classification, known as Multi-PGD, is also applied and numerically verified.

International audience; The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the flow induced orientation, on the fibers’ geometrical center trajectory. The number of interactions as well as the interaction intensity will depend on the fiber volume fraction and the applied shear, which should affect the stochastic trajectory. Topological data analysis (TDA) will be applied on the geometrical center trajectories of the simulated fiber to prove that a characteristic pattern can be extracted depending on the flow conditions (concentration and shear rate). This work proves that TDA allows capturing and extracting from the so-called persistence image, a pattern that characterizes the dependence of the fiber trajectory on the flow kinematics and the suspension concentration. Such a pattern could be used for classification and modeling purposes, in rheology or during processing monitoring.

Third millennium engineering is addressing new challenges in materials sciencesand engineering. In particular, the advances in materials engineering, combined with the advances in data acquisition, processing and mining as well as artificial intelligence, allow new ways of thinking in designing new materials and products. Additionally, this gives rise to new paradigms in bridging raw material data and processing to the induced properties and performance. On the one hand, the linkage can be done purely on a data-driven basis, i.e., models are created from scratch based on the obtained experimental data alone, forinstance with statistical methods or advanced methods of machine learning. Particularly obvious advantages of such kinds of models are that no simplification or assumptions need to be incorporated a priori, and that it allows real-time prediction, leading to a so-called digital twin of the specific material/process. However, such approaches typically face somegeneral challenges, such as the necessity of (maybe unnecessarily) large and comprehensive datasets, because they rely only on the data themselves and allow prediction only within the investigated/trained dataspace. Another way of addressing the challenge of predicting the complex processing–structure–property relationships in materials is the enhancement of already existing physics-based models via data and machine learning tools, i.e., combininga physics-based model (often called virtual twin) and a data-based model, leading to a so-called hybrid twin [1]. In this regard, possible deviations of the physics-based model, which rely on a number of simplifications and assumptions, can be healed by correcting the model based on a data-driven approach, i.e., combining the advantages of both models.

Numerical simulations have long been used in many engineering process industries for the virtual evaluation of responses from an accurate solution of the physics/mathematical models describing it. However, in most industrial cases, these simulations tend to be time-consuming, especially in studies involving parameter optimization studies/inverse analysis where a multitude of direct computations are necessary. Non-intrusive Model Order Reduction techniques (SSL-PGD, s-PGD) enable the construction of parametric solution spaces to ensure almost instantaneous responses to changes in input parameters. These parametrized solutions are built from snapshots generated from simulations using commercially available software, but the process parameters and re-meshing rules add a condition that the different snapshots be suitably parametrized for being able to compute and represent the parametric solutions using the MOR techniques. The snapshots generated in the case of sheet-metal forming simulations are 3D surfaces. Even though surface parametrization is a fairly easy process in the case of planar surfaces, the problem ceases to be trivial in the case of 3D surfaces. In this work, we present a conformal mapping procedure based on the Riemannian surface parametrization using the Yamabe-flow for the parametrization of 3D surfaces into planar 2D surfaces. These parametrized surfaces can then be interpolated to create parametric solution configurations for the full range of input parameters and hence allows the application of non-intrusive model order reduction techniques to simulations which include adaptive mesh refinement.

International audience; The present work aims at performing a molecular dynamics modeling of suspensions composed of flexible linear molecules. Molecules are represented by a series of connected beads, whose dynamics is governed by three potentials: the extension potential affecting the elongation of segments connecting consecutive beads, the one governing the molecule bending and finally the Lennard-Jones describing the interaction of non-consecutive beads. A population of non-interacting molecules is simulated in elongation and shear flows for different flow and molecule parameters. The flow-induced conformation is analyzed in the different considered situations. Finally a model for predicting the evolution of the population conformation will be obtained by using deep-learning.

International audience; This work aims at proposing a new procedure for parametric problems whose separated representation has been considered difficult, or whose SVD compression impacted the results in terms of performance and accuracy. The proposed technique achieves a fully separated representation for layered domains with interfaces exhibiting waviness or – more generally – deviating from planar surfaces, parallel to the coordinate plane. This will make possible a simple separated representation, equivalent to others, already analyzed in some of our former works. To prove the potentialities of the proposed approach, two benchmarks will be addressed, one of them involving an efficient space–time separated representation achieved by considering the same rationale.

International audience; In this work we develop a void filling and void motion dynamics model using volatile pressure and squeeze flow during tape placement process. The void motion and filling are simulated using a non-local model where their presence is reflected in the global macroscale behavior. Local pressure gradients during compression do play a critical role in void dynamics, and hence the need for a non-local model. Deriving a non-local model accounting for all the void motion and dynamics entails a prohibitive number of degrees of freedom, leading to unrealistic computation times with classical solution techniques. Hence, Proper Generalized Decomposition – PGD – is used to solve the aforementioned model. In fact, PGD circumvents the curse of dimensionality by using separated representation of the space coordinates. For example, a 2D problem can be solved as a sequence of 1D problems to find the 2D solution. The non-local model solution sheds light on the fundamental of the void dynamics including their pressure variation, motion and closure mechanisms. Finally, a post treatment of the transient compression of the voids is used to derive conclusions regarding the physics of the void dynamics.

Nowadays, the use of simulation in industrial applications is a routine practice. However, the need of considering high fidelity models and their associated solutions is demanding for more efficient solvers. Despite the remarkable progress accomplished in hardware and software in the last decades, the ability to simulate high fidelity 3D models, taking into consideration all their richness is still challenging. For example, if we wish to simulate a 3D problem including 10 parameters, each of them taking 10 different values we should solve 1010 3D problems. This issue is known as the curse of dimensionality, and compromises the solution of models defined in high dimensional spaces.