SAM
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http://hdl.handle.net/10985/10241
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control
LEYGUE, Adrien; BORDEU, Felipe; AGUADO, Jose Vicente; CUETO, Elias; GONZALEZ, David; HUERTA, Antonio; ALFARO, Icíar; AMMAR, Amine; CHINESTA SORIA, Francisco
In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102412013-01-01T00:00:00ZLEYGUE, AdrienBORDEU, FelipeAGUADO, Jose VicenteCUETO, EliasGONZALEZ, DavidHUERTA, AntonioALFARO, IcíarAMMAR, AmineCHINESTA SORIA, FranciscoIn this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.Reduced order modeling for physically-based augmented reality
http://hdl.handle.net/10985/13809
Reduced order modeling for physically-based augmented reality
BADIAS, Alberto; GONZALEZ, David; CUETO, Elias; ALFARO, Icíar; CHINESTA SORIA, Francisco
In this work we explore the possibilities of reduced order modeling for augmented reality applications. We consider parametric reduced order models based upon separate (affine) parametric dependence so as to speedup the associated data assimilation problems, which involve in a natural manner the minimization of a distance functional. The employ of reduced order methods allows for an important reduction in computational cost, thus allowing to comply with the stringent real time constraints of video streams, i.e., around 30 Hz. Examples are included that show the potential of the proposed technique in different situations.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/138092018-01-01T00:00:00ZBADIAS, AlbertoGONZALEZ, DavidCUETO, EliasALFARO, IcíarCHINESTA SORIA, FranciscoIn this work we explore the possibilities of reduced order modeling for augmented reality applications. We consider parametric reduced order models based upon separate (affine) parametric dependence so as to speedup the associated data assimilation problems, which involve in a natural manner the minimization of a distance functional. The employ of reduced order methods allows for an important reduction in computational cost, thus allowing to comply with the stringent real time constraints of video streams, i.e., around 30 Hz. Examples are included that show the potential of the proposed technique in different situations.Learning data-driven reduced elastic and inelastic models of spot-welded patches
http://hdl.handle.net/10985/20416
Learning data-driven reduced elastic and inelastic models of spot-welded patches
REILLE, Agathe; CHAMPANEY, Victor; DAIM, Fatima; TOURBIER, Yves; HASCOET, Nicolas; GONZALEZ, David; CUETO, Elias; DUVAL, Jean Louis; CHINESTA SORIA, Francisco
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.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/204162021-01-01T00:00:00ZREILLE, AgatheCHAMPANEY, VictorDAIM, FatimaTOURBIER, YvesHASCOET, NicolasGONZALEZ, DavidCUETO, EliasDUVAL, Jean LouisCHINESTA SORIA, FranciscoSolving 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.Parametric solutions involving geometry: A step towards efficient shape optimization
http://hdl.handle.net/10985/10244
Parametric solutions involving geometry: A step towards efficient shape optimization
HUERTA, Antonio; CUETO, Elias; LEYGUE, Adrien; AMMAR, Amine; CHINESTA SORIA, Francisco
Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102442014-01-01T00:00:00ZHUERTA, AntonioCUETO, EliasLEYGUE, AdrienAMMAR, AmineCHINESTA SORIA, FranciscoOptimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.On the effective conductivity and the apparent viscosity of a thin rough polymer interface using PGD‐based separated representations
http://hdl.handle.net/10985/19486
On the effective conductivity and the apparent viscosity of a thin rough polymer interface using PGD‐based separated representations
GHNATIOS, Chady; DELPLACE, Frank; BARASINSKI, Anais; DUVAL, Jean-Louis; CUETO, Elias; AMMAR, Amine; CHINESTA SORIA, Francisco
Composite manufacturing processes usually proceed from preimpregnated preforms that are consolidated by simultaneously applying heat and pressure, so as to ensure a perfect contact compulsory for making molecular diffusion possible. However, in practice, the contact is rarely perfect. This results in a rough interface where air could remain entrapped, thus affecting the effective thermal conductivity. Moreover, the interfacial melted polymer is squeezed flowing in the rough gap created by the fibers located on the prepreg surfaces. Because of the typical dimensions of a composite prepreg, with thickness orders of magnitude smaller than its other in-plane dimensions, and its surface roughness having a characteristic size orders of magnitude smaller than the prepreg thickness, high-fidelity numerical simulations for elucidating the impact of surface and interface roughness remain today, despite the impressive advances in computational availabilities, unattainable. This work aims at elucidating roughness impact on heat conduction and the effective viscosity of the interfacial polymer squeeze flow by using an advanced numerical strategy able to reach resolutions never attained until now, a sort of numerical microscope able to attain the scale of the smallest geometrical detail.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/194862020-01-01T00:00:00ZGHNATIOS, ChadyDELPLACE, FrankBARASINSKI, AnaisDUVAL, Jean-LouisCUETO, EliasAMMAR, AmineCHINESTA SORIA, FranciscoComposite manufacturing processes usually proceed from preimpregnated preforms that are consolidated by simultaneously applying heat and pressure, so as to ensure a perfect contact compulsory for making molecular diffusion possible. However, in practice, the contact is rarely perfect. This results in a rough interface where air could remain entrapped, thus affecting the effective thermal conductivity. Moreover, the interfacial melted polymer is squeezed flowing in the rough gap created by the fibers located on the prepreg surfaces. Because of the typical dimensions of a composite prepreg, with thickness orders of magnitude smaller than its other in-plane dimensions, and its surface roughness having a characteristic size orders of magnitude smaller than the prepreg thickness, high-fidelity numerical simulations for elucidating the impact of surface and interface roughness remain today, despite the impressive advances in computational availabilities, unattainable. This work aims at elucidating roughness impact on heat conduction and the effective viscosity of the interfacial polymer squeeze flow by using an advanced numerical strategy able to reach resolutions never attained until now, a sort of numerical microscope able to attain the scale of the smallest geometrical detail.Foreword
http://hdl.handle.net/10985/18796
Foreword
CUETO, Elias; BREITKOPF, Piotr; CHINESTA SORIA, Francisco
The range of topics covers a vivid scope of recent research subjects, on the frontier between applied mathematics and computational mechanics. The contributions range from the fundamentals of solid mechanics, and PDE revisited, through the physical interpretation of numerical models, mathematical foundations of reduced-order modeling up to methodological developments in time and parametric domains.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/187962018-01-01T00:00:00ZCUETO, EliasBREITKOPF, PiotrCHINESTA SORIA, FranciscoThe range of topics covers a vivid scope of recent research subjects, on the frontier between applied mathematics and computational mechanics. The contributions range from the fundamentals of solid mechanics, and PDE revisited, through the physical interpretation of numerical models, mathematical foundations of reduced-order modeling up to methodological developments in time and parametric domains.MORPH-DSLAM: Model Order Reduction for Physics-Based Deformable SLAM
http://hdl.handle.net/10985/23641
MORPH-DSLAM: Model Order Reduction for Physics-Based Deformable SLAM
BADIAS, Alberto; GONZALEZ, David; CUETO, Elias; ALFARO, Icíar; CHINESTA SORIA, Francisco
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.
Tue, 01 Nov 2022 00:00:00 GMThttp://hdl.handle.net/10985/236412022-11-01T00:00:00ZBADIAS, AlbertoGONZALEZ, DavidCUETO, EliasALFARO, IcíarCHINESTA SORIA, FranciscoWe 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.Wavelet-based multiscale proper generalized decomposition
http://hdl.handle.net/10985/13282
Wavelet-based multiscale proper generalized decomposition
ANGEL, Leon; BARASINSKI, Anais; CUETO, Elias; ABISSET-CHAVANNE, Emmanuelle; CHINESTA SORIA, Francisco
Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132822018-01-01T00:00:00ZANGEL, LeonBARASINSKI, AnaisCUETO, EliasABISSET-CHAVANNE, EmmanuelleCHINESTA SORIA, FranciscoSeparated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.Towards a high-resolution numerical strategy based on separated representations
http://hdl.handle.net/10985/6522
Towards a high-resolution numerical strategy based on separated representations
CUETO, Elias; GONZALEZ, David; AMMAR, Amine; CHINESTA SORIA, Francisco
Many models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/65222008-01-01T00:00:00ZCUETO, EliasGONZALEZ, DavidAMMAR, AmineCHINESTA SORIA, FranciscoMany models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.A novel sparse reduced order formulation for modeling electromagnetic forces in electric motors
http://hdl.handle.net/10985/19961
A novel sparse reduced order formulation for modeling electromagnetic forces in electric motors
SANCARLOS, Abel; CUETO, Elias; DUVAL, Jean-Louis; CHINESTA SORIA, Francisco
A novel model order reduction (MOR) technique is presented to achieve fast and real-time predictions as well as high-dimensional parametric solutions for the electromagnetic force which will help the design, analysis of performance and implementation of electric machines concerning industrial applications such as the noise, vibration, and harshness in electric motors. The approach allows to avoid the long-time simulations needed to analyze the electric machine at different operation points. In addition, it facilitates the computation and coupling of the motor model in other physical subsystems. Specifically, we propose a novel formulation of the sparse proper generalized decomposition procedure, combining it with a reduced basis approach, which is used to fit correctly the reduced order model with the numerical simulations as well as to obtain a further data compression. This technique can be applied to construct a regression model from high-dimensional data. These data can come, for example, from finite element simulations. As will be shown, an excellent agreement between the results of the proposed approach and the finite element method models are observed.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199612021-01-01T00:00:00ZSANCARLOS, AbelCUETO, EliasDUVAL, Jean-LouisCHINESTA SORIA, FranciscoA novel model order reduction (MOR) technique is presented to achieve fast and real-time predictions as well as high-dimensional parametric solutions for the electromagnetic force which will help the design, analysis of performance and implementation of electric machines concerning industrial applications such as the noise, vibration, and harshness in electric motors. The approach allows to avoid the long-time simulations needed to analyze the electric machine at different operation points. In addition, it facilitates the computation and coupling of the motor model in other physical subsystems. Specifically, we propose a novel formulation of the sparse proper generalized decomposition procedure, combining it with a reduced basis approach, which is used to fit correctly the reduced order model with the numerical simulations as well as to obtain a further data compression. This technique can be applied to construct a regression model from high-dimensional data. These data can come, for example, from finite element simulations. As will be shown, an excellent agreement between the results of the proposed approach and the finite element method models are observed.