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International audience; The direct parametrisation method for invariant manifolds (DPIM) is applied to rotating structures. Reduced- order models of arbitrary order expansion can be derived for non-autonomous systems of nonlinear differential equations stemming from finite element models of continuous structures. The method is applied to a rotating simplified fan blade with comparisons to full order model simulations.

In this thesis, I examine filtering based stabilization methods to design new regularized reduced order models (ROMs) for under-resolved simulations of unsteady, nonlinear, convection-dominated systems. The new ROMs proposed are variable delta filtering applied to the evolve-filter-relax ROM (V-EFR ROM), variable delta filtering applied to the Leray ROM, and approximate deconvolution Leray ROM (ADL-ROM). They are tested in the numerical setting of Burgers equation, a nonlinear, time dependent problem with one spatial dimension. Regularization is considered for the low viscosity, convection dominated setting. Master of Science Numerical solutions of partial differential equations may not be able to be efficiently computed in a way that fully captures the true behavior of the underlying model or differential equation, especially if significant changes in the solution to the differential equation occur over a very small spatial area. In this case, non-physical numerical artifacts may appear in the computed solution. We discuss methods of treating these calculations with a goal of improving the fidelity of numerical solutions with respect to the original model.

Major concerns of carbon dioxide (CO2) sequestration in subsurface formations are knowledge of the well injectivity and gas storage capacity of the formation, the CO2 pressure and saturation plume extensions during and after injection, and the risks associated with CO2 leakage and fault reactivation. Saline reservoirs are considered as one of the target formations for CO2 sequestration through structural, residual, dissolution, and mineral trapping mechanisms. The boundary condition of the saline reservoir dictates the pressure and saturation plume extension of the injected supercritical CO2 that could expand over large distances. This can lead to sources of risk, e.g., leakage and/or fault reactivation due to presence of wells, thief zones, and geological discontinuities. Therefore, there is a critical need to develop a model that describes how risk-related performance metrics (i.e., the CO2 saturation plume size, the pressure differential plume area, and the pressure differential at specific locations) vary as a function of the size of injection, time following injection, injection operations, and geologic environment. In this study, a systematic reservoir modeling studies of anthropogenic CO2 sequestration in Citronelle dome, Alabama, was performed where all relevant scenarios and conditions to address the questions of the saturation and pressure plume size in the area of review (AoR) and post-injection site care (PISC) are considered. The objective for this study was firstly to systematically simulate CO2 sequestration, i.e., saturation dynamics, and pressure behavior over a range of operational and geological conditions and to derive conclusions about the factors influencing saturation and pressure plume size, post-injection behavior, and the risk associated with them, by developing third-generation reduced order models (ROMs) for reservoir behavior. Finally, to assess the uncertainty associated with our studies, Latin Hypercube Sampling (LHS) together with an experimental design technique, i.e., Plackett–Burman design, was used. Application of Pareto charts and respond surfaces enabled us to determine the most important parameters impacting saturation and pressure plume sizes and to quantify the auto- and cross-correlation among different parameters in both history-matched and upscaled models.

This paper describes a new efficient method for the construction of an approximately balanced aerodynamic Reduced Order Model (ROM) via the frequency domain using Computational Fluid Dynamics data. Time domain ROM construction requires CFD data, which is obtained from the DLR TAU RANS or Euler Linearised Frequency Domain (LFD) solver. The ROMs produced with this approach, using a small number of frequency simulations, are shown to exhibit a strong ability to reconstruct the system response for inviscid flow about the NLR7301 aerofoil and the FFAST wing; and viscous flow about the NASA Common Research Model. The latter demonstrates that the reduced order model approach can reconstruct the full order frequency response of a viscous aircraft configuration with excellent accuracy using a strip wise approach. The time domain models are built using the frequency domain, but also give promising results when applied to reconstruct non-periodic motions. Results are compared to time domain simulations, showing good agreement even with small ROM sizes, but with a substantial reduction in calculation time. The main advantage of the current model order reduction approach is that the method does not require the formation and storage of large matrices, such as in POD approaches.

This paper presents a new approach for reduction of commensurate fractional-order single-input-single-output systems. The minimization in the frequency response error of the reduced order model (ROM) relative to the original system is carried out in the F-plane. A constrained optimization technique is introduced to satisfy the angle criteria for F-domain stability of the proposed ROM. Significant improvements in both the time- and frequency-responses over the recently published literature are illustrated using several numerical examples.

In dieser Arbeit untersuchen wir Autodecoder-Netzwerke und deren Anwendung in Daten-getriebenen reduzierten Modellen von Strömungssimulationen. Als Autodecoder wird ein Feedforward Neural Network bezeichnet, das als generatives Modell verwendet werden kann. Um Lösungen von Fluidströmungen zu erzeugen, bildet das Netzwerk Koordinaten einer Referenzdomäne und einen Zeitschritt auf entsprechende Strömungsgeschwindigkeiten ab. Als zusätzlichen Netzwerk-Input wird eine latente Kodierung verwendet, die einer bestimmter Fluidströmung entspricht. Außerdem kann das Netzwerk verwendet werden, um die Fluidgeschwindigkeiten für beliebige Koordinaten und Zeitschritte zu erzeugen.Wir verwenden dieses Netzwerk als reduziertes Modell für drei verschiedene Arten von Fluidströmungen. Wir untersuchen die Auswirkungen der Netzwerkbreite, der Größe der Latent-Kodierung and zwei Datennormalisierungsmethoden auf die Genuigkeit des reduzierten Modells. Wir stellen fest, dass für alle simulierten Strömungstypen die Netzwerkbreite die Genauigkeit am stärksten beeinflusst. Im Gegensatz dazu zeigen die anderen zwei Faktoren fallweise unterschiedliche Resultate.Schließlich untersuchen wir die Eignung von Autodecodern als reduzierte Modelle, indem wir den gelernten Latentraum betrachten. Die Latentkodierungen von ähnlichen Fluidströmungen sind im Latentraum klar gegliedert, was Interpolation im Latentraum ermöglicht. Dadurch kann der Autodecoder verwendet werden, um Lösungen von ungesehenen Parameterkonfigurationen zu erzeugen., Here we investigate the application of an autodecoder network for data-driven reduced modeling of fluid flows. An autodecoder is a feedforward neural network which can be used as generative model. For generating fluid flow solutions, it maps coordinates of a reference domain and a timestep to corresponding fluid velocities. Additionally, the network takes a latent code as input which corresponds to a certain type of fluid flow. Thus, only one network is needed to yield solutions of a family of similar flows. Furthermore, the network can be queried to yield the flow velocities for arbitrary coordinates and timesteps.We apply this network as a reduced model for three different types of fluid flows. We investigate the effects of the network width, the latent code size and two data normalization methods on the accuracy of the reduced model. We observe that for all simulated cases the network width has the highest impact on the accuracy of the network while the other two factors show case-dependent results.Finally, we investigate the suitability of the autodecoder as a reduced model by exploring the learned latent spaces. For similar flows, their corresponding latent codes are well-structured in the latent space, indicating that interpolation in the latent space can be applied. This can be leveraged to yield solutions of unseen parameter configurations.

International audience; In this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that the data-driven ROM closure studied here (i.e., the data-driven variational multiscale ROM) is verifiable. Finally, we investigate the verifiability of the data-driven variational multiscale ROM in the numerical simulation of the one-dimensional Burgers equation and a two-dimensional flow past a circular cylinder at Reynolds numbers Re=100 and Re=1000.

This is the peer reviewed version of the following article: Cavaliere, F. [et al.]. Nonintrusive reduced order model for parametric solutions of inertia relief problems. "International journal for numerical methods in engineering", 30 Agost 2021, vol. 122, núm. 16, p. 4270-4291., which has been published in final form at DOI:10.1002/nme.6702. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the IR method is formulated in a parametric setting for both material and geometric parameters. A reduced order model using the encapsulated PGD suite is then developed to solve the parametric IR problem, circumventing the so-called curse of dimensionality. With just one offline computation, the proposed PGD-IR scheme provides a computational vademecum that contains all the possible solutions for a predefined range of the parameters. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. The applicability and potential of the developed technique is shown using a three-dimensional test case and a more complex industrial test case. The first example is used to highlight the numerical properties of the scheme, whereas the second example demonstrates the potential in a more complex setting and it shows the possibility to integrate the proposed framework within a commercial FE package. In addition, the last example shows the possibility to use the generalized solution in a multi-objective optimization setting. This project is part of the Marie Sk lodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with grant number 764636. The work of Fabiola Cavaliere, Sergio Zlotnik and Pedro D´ıez is partially supported by the Spanish Ministry of Economy and Competitiveness, Spain (Grant number: DPI2017-85139- C2-2-R) and by the Generalitat de Catalunya, Spain (Grant number: 2017-SGR-1278). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant number: EP/P033997/1).

Based on Recursive Radial Basis Function (RRBF) neural network, the Reduced Order Model (ROM) of compressor cascade was established to meet the urgent demand of highly efficient prediction of unsteady aerodynamics performance of turbomachinery. One novel ROM called ASA-RRBF model based on Adaptive Simulated Annealing (ASA) algorithm was developed to enhance the generalization ability of the unsteady ROM. The ROM was verified by predicting the unsteady aerodynamics performance of a highly-loaded compressor cascade. The results show that the RRBF model has higher accuracy in identification of the dimensionless total pressure and dimensionless static pressure of compressor cascade under nonlinear and unsteady conditions, and the model behaves higher stability and computational efficiency. However, for the strong nonlinear characteristics of aerodynamic parameters, the RRBF model presents lower accuracy. Additionally, the RRBF model predicts with a large error in the identification of aerodynamic parameters under linear and unsteady conditions. For ASA-RRBF, by introducing a small-amplitude and high-frequency sinusoidal signal as validation sample, the width of the basis function of the RRBF model is optimized to improve the generalization ability of the ROM under linear unsteady conditions. Besides, this model improves the predicting accuracy of dimensionless static pressure which has strong nonlinear characteristics. The ASA-RRBF model has higher prediction accuracy than RRBF model without significantly increasing the total time consumption. This novel model can predict the linear hysteresis of dimensionless static pressure happened in the harmonic condition, but it cannot accurately predict the beat frequency of dimensionless total pressure.

Carbon sequestration in deep saline aquifers has been proposed for long-term storage of CO₂ as an alternative to the release of CO₂ into the atmosphere. In this article, we present a computationally efficient numerical model based on a sequentially coupled Finite Element Method (FEM) and Streamline Upwind Finite Element Method (SU-FEM)-Finite Difference Method (FDM). An adaptive timestep strategy is implemented which allows computationally efficient and stable solutions as time progresses. The computational efficiency of the formulation is demonstrated by four examples that consider nonuniform permeability, multiple injection wells, an upsloping aquifer, and a dome-shaped aquifer. The adaptive timesteps reduce the computational cost by 75-82% compared to constant timesteps in the four examples considered. The proposed formulation is compared against a benchmark study where eleven different simulators were used to determine the arrival time of the CO₂ plume at a leaky well. The original benchmark study did not include an FEM-based discretization of the reduced order equations. To the authors’ best knowledge, the current work is the first FEM based implementation of reduced order (vertically averaged) multiphase flow equations evaluated against this benchmark. The proposed formulation is in good general agreement with the results from the various simulators studied in the benchmark, and excellent agreement with an FDM discretization of the vertically averaged governing equations.

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry., Published online: 25 Jan 2021

The dynamic stall at high angle of attack is an important aerodynamic problem faced by aircraft, and it has always been a hotspot of aerodynamic research. The traditional reduced order model (ROM) methods needs to establish an accurate model, and has a high demand for experience. In this paper, a novel nonlinear aerodynamic identification method based on recurrent neural networks (RNNs) is proposed. The computational fluid dynamics (CFD) method is used to calculate the unsteady aerodynamic parameters of the NACA0012 airfoil. A group of sinusoidal chirp signals with variable amplitude and frequency are adopted as the excitation signals, and the obtained data are used to train the recurrent neural networks, and the ROM of the nonlinear aerodynamic model of high angle of attack dynamic stall is obtained. Finally, the aerodynamic parameters of a group of composite sinusoidal motion signals different from the training signals are predicted by the trained neural networks model and compared with the CFD results.

Accurate prediction of the mechanical failure of structural components plays an important role in the design of engineering structures. However, the fracture process is challenging to model numerically due to the existence of an elastic singularity at the crack tip. The phase field model (PFM) is one promising approach for modeling brittle fracture using an auxiliary field variable to regularize discontinuities associated with sharp cracks. Unfortunately, it is generally computationally expensive due to the need to solve a fourth-order partial differential equation. In order to reduce the computational burden for parameterized problems, different reduced order modeling approaches such as proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM), have been proposed. However, these frameworks are model-based and intrusive approaches and need in-depth efforts in modifying existing complex simulation codes. In this work, a tensor train (TT) approach is proposed in combination with Gaussian process regression (GPR) for modeling and predicting the dynamics of fracture in composite materials. As opposed to POD and DEIM, the TT-GPR approach is a fully data-driven and non-intrusive approach. In this work, we study the fracture of a brittle elastic 2D rectangular slab with a pre-existing crack under Mode I (crack opening) loading conditions. The high dimensional training data for the TT model was generated using PFM with the finite difference method. The predictions by the TT-GPR model are compared with the results from the finite difference method. The TT-GPR is robust enough to predict the catastrophic evolution of the crack growth trend with an accuracy of up to 95% with computational load reduced by two orders of magnitude.

Background: Atrial fibrillation is a prevalent cardiac arrhythmia and may reduce cerebral blood perfusion augmenting the risk of dementia. We hypothesize that geometric variations in the cerebral arterial structure called the Circle of Willis (CoW) play an important role in influencing cerebral perfusion. The objective of this work was to develop a novel cardio-cerebral lumped parameter hemodynamic model to investigate the role of CoW variants on cerebral blood flow dynamics under atrial fibrillation conditions. Methods: A computational blood flow model was developed by coupling whole-body and detailed cerebral circulation descriptions, modified to represent six common variations of the CoW. Cerebral blood flow dynamics were simulated in common CoW variants, under control and imposed atrial fibrillation conditions. Risk was assessed based on the frequency of beat-wise hypoperfusion events, and sensitivity analysis was performed with respect to this model output. Results: It was found that the geometry of the CoW influenced the frequency of hypoperfusion events at different heart rates, with the variant missing a P1 segment having the highest risk. Sensitivity analysis revealed that intrinsic heart rate is most associated with the considered outcome. Conclusions: Our results suggest that CoW geometry plays an important role in influencing cerebral hemodynamics during atrial fibrillation. The presented study may assist in guiding our future clinical-imaging research.

Background: Micro-texturing is an increasingly used technique that aims at improving the functional behaviour of components during their useful life, and it is applied in different industrial manufacturing processes for different purposes, such as reducing friction on dynamic rubber seals for pneumatic equipment, among others. Micro-texturing is produced on polymer components by transfer from the mould and might critically increase the adhesion and friction between the moulded rubber part with the mould, provoking issues during demoulding, both on the mould itself and on the rubber part. The mould design, the coating release agent applied to the mould surface, and the operational parameters of the moulding/demoulding process, are fundamental aspects to avoid problems and guarantee a correct texture transfer during the demoulding process. Methods: In this work, the lack of knowledge about demoulding processes was addressed with an in-house test rig and a robust experimental procedure to measure demoulding forces (DFs) as well as the final quality of the moulded part, between thermoset polymers and moulds. After the characterization of several Sol-Gel coating formulations (inorganic; hybrid) the influence of several parameters was analysed experimentally, i.e.: Sol-Gel efficiency, texture effects, pattern geometry, roughness and material compound. Results: The results obtained from the experimental studies revealed that texture depth is the most critical geometrical parameter, showing high scatter among the selected compounds. Finally, the experimental results were used to compute a model through reduced order modelling (ROM) technique for the prediction of DFs. Conclusions: The characterization of DFs in a laboratory, with a specific device operated by a universal testing machine (UTM), provided valuable information that allows a fast and optimized introduction of texturing in rubber components. Selection of a novel Sol-Gel coating and the use of the ROM technique contributed to speed up implementation for mass production.

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the vortex merger benchmark. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization., 19 pages, 18 figures

Dynamics of pantographic sheets presents exotic aspects that deserve investigation. In this paper, we focus the attention on some possible modalities of non-linear wave propagation in planar pantographic sheets. We use a smaller length-scale lattice model, in which the beams and pivots constituting the sheet are described by constrained Euler- Bernoulli beams together with a meso-reduced-order model which belongs to the class of second-gradient elastic materials and with a macro multi-field 1D continuum model, whose displacement is augmented by a specific class of cross-section deformations. Such a three-step reduction process is developed to allow for fast computational analysis of symmetric wave propagation patterns with respect to the longitudinal axis of the sheet. It is conceived by using suitable kinematical hypotheses for the 1D continuum descriptors referring to pantographic sheet sections which are inspired by the numerical evidence obtained performing simulations based on the smaller scale lattice model. The deformation energy of the pantographic sheet, successfully postulated in dell'Isola et al. (2016) for a meso-reduced-order second gradient model, is pivotal in the whole model reduction process: It allows for the determination of generalized 1D deformation energy in terms of the mechanical properties of the micro-lattice model. Performed numerical simulations prove that several waveforms propagate in planar pantographic sheets with low dispersion and motivate further investigations in the subject.(c) 2022 Elsevier B.V. All rights reserved.

The maritime industry is actively exploring alternative fuels and drive train technology to reduce the emissions of hazardous air pollutants and greenhouse gases. High temperature solid oxide fuel cells (SOFCs) represent a promising technology to generate electric power on ships from a variety of renewable fuels with high efficiencies and no hazardous emissions. However, application in ships is still impeded by a number of challenges, such as low power density and high capital cost. A slow response to load transients is another challenges, which is typically a result of the conservative thermal management strategies used to ensure that excessive thermal stresses in the stack are avoided. Therefore, a reduced order SOFC stack model is developed in this work for model-based control. The model is subsequently verified with a high fidelity model developed in previous work. In addition, a preliminary framework for its use for model predictive SOFC control is provided. The reduced order model and control framework will be used in future work to optimise thermal management of SOFC stacks for improved transient response while respecting physical and operational constraints.

The maritime industry is actively exploring alternative fuels and drive train technology to reduce the emissions of hazardous air pollutants and greenhouse gases. High temperature solid oxide fuel cells (SOFCs) represent a promising technology to generate electric power on ships from a variety of renewable fuels with high efficiencies and no hazardous emissions. However, application in ships is still impeded by a number of challenges, such as low power density and high capital cost. A slow response to load transients is another challenges, which is typically a result of the conservative thermal management strategies used to ensure that excessive thermal stresses in the stack are avoided. Therefore, a reduced order SOFC stack model is developed in this work for model-based control. The model is subsequently verified with a high fidelity model developed in previous work. In addition, a preliminary framework for its use for model predictive SOFC control is provided. The reduced order model and control framework will be used in future work to optimise thermal management of SOFC stacks for improved transient response while respecting physical and operational constraints.

This paper serves to address a current limitation in moderator characterization in criticality safety applications. The standard practice evaluates only the concentration of hydrogen assuming the contributions of secondary elements to be negligible. This paper quantifies the relationship between selected secondary moderating elements added to a hydrogenous moderating medium and their impact on criticality safety calculations and safety limits. A regression model is developed based on three parameters in a common safety basis calculation: quantity of moderator (in atoms/barn-cm), quantity of fissile material (in grams ²³⁵U), and various reflective environments. Results show that a simple equation, linear with respect to moderator density and quadratic with respect to mass of ²³⁵U, may be generated for a given reflector environment to accurately predict the effective multiplication factor to within 2.5% for moderating materials that are predominately (>50%) hydrogenous in composition.

To successfully monitor and actively control hydrodynamic and aerodynamic systems (e.g., wind turbine blade, wind farm, hydrofoil, aircraft wings), it can be critical to estimate and predict the unsteady flow around them in real-time. We propose to introduce a new algorithm to couple onboard measurements with fluid dynamics simulations and data in real-time without the need to rely on an extensive computational infrastructure. This coupling is achieved by combining a Proper Orthogonal Decomposition Galerkin method, a model under location uncertainty stochastic closure, and a particle filtering scheme. We focus our numerical tests on a two-and a three-dimensional wake flows at low and moderate Reynolds numbers, respectively. Using a single measurement point, we obtain almost optimal flow estimations for up to 14 vortex shedding cycles after the learning time window.

This Habilitation thesis (Habilitation à Diriger des Recherches - HDR) manuscript focuses on my research work carried out within the Fuel Studies Department (DEC) of the the French Alternative Energies and Atomic Energy Commission (CEA) since 2009. The first of my two main lines of research focuses on efficiency and precision of multiphysics couplings. In this context, I worked around the formalism of convergence acceleration of vector fixed point series, the reduced order modeling for the contact mechanics, but also around advanced multiphysics modeling and simulation for understanding the mechanism of pellet-cladding gap closure in fast neutron reactors.My second major area of research concerns the implementation of multiscale couplings for solid mechanics and for different scale ratios. I thus contributed to develop adaptive local multigrid mesh refinement techniques for nonlinear mechanics and I also worked around the industrial implementation of full field numerical homogenization methods based on the finite element square approach.; Ce manuscrit d'Habilitation à Diriger des Recherches (HDR) se focalise sur mes travaux de recherche menés au sein du Département d'Études des Combustibles (DEC) du Commissariat à l'Énergie Atomique et aux Énergies Alternatives (CEA) depuis 2009. Le premier de mes deux grands axes de recherche s'articule autour del'efficacité et de la précision des couplages multiphysiques. Dans ce cadre, j'ai travaillé autour du formalisme d'accélération de convergence des suites vectorielles de point fixe, de la réduction d'ordre de modèle pour la mécanique du contact, mais également autour de la modélisation et simulation multiphysiques avancées pour lacompréhension du mécanisme de rattrapage du jeu pastille-gaine dans les réacteurs à neutrons rapides.Mon deuxième grand axe de recherche concerne la mise en oeuvre de couplages multiéchelles pour la mécanique des solides et ce pour différents rapports d'échelles. J'ai ainsi contribué à développer des techniques de raffinement adaptatif de maillage de type multigrille local pour la mécanique non linéaire et j'ai également travaillé autour de la mise en oeuvre industrielle de méthodes d'homogénéisation numérique par champs complets de type éléments finis au carré.

Background: In patients with aortic stenosis, computed tomography (CT) provides important information about cardiovascular anatomy for treatment planning but is limited in determining relevant hemodynamic parameters such as the transvalvular pressure gradient (TPG).Purpose: In the present study, we aimed to validate a reduced-order model method for assessing TPG in aortic stenosis using CT data.Methods: TPGCT was calculated using a reduced-order model requiring the patient-specific peak-systolic aortic flow rate (Q) and the aortic valve area (AVA). AVA was determined by segmentation of the aortic valve leaflets, whereas Q was quantified based on volumetric assessment of the left ventricle. For validation, invasively measured TPGcatheter was calculated from pressure measurements in the left ventricle and the ascending aorta. Altogether, 84 data sets of patients with aortic stenosis were used to compare TPGCT against TPGcatheter.Results: TPGcatheter and TPGCT were 50.6 ± 28.0 and 48.0 ± 26 mmHg, respectively (p = 0.56). A Bland–Altman analysis revealed good agreement between both methods with a mean difference in TPG of 2.6 mmHg and a standard deviation of 19.3 mmHg. Both methods showed good correlation with r = 0.72 (p < 0.001).Conclusions: The presented CT-based method allows assessment of TPG in patients with aortic stenosis, extending the current capabilities of cardiac CT for diagnosis and treatment planning.

Background: In patients with aortic stenosis, computed tomography (CT) provides important information about cardiovascular anatomy for treatment planning but is limited in determining relevant hemodynamic parameters such as the transvalvular pressure gradient (TPG). Purpose: In the present study, we aimed to validate a reduced-order model method for assessing TPG in aortic stenosis using CT data. Methods: TPG(CT) was calculated using a reduced-order model requiring the patient-specific peak-systolic aortic flow rate (Q) and the aortic valve area (AVA). AVA was determined by segmentation of the aortic valve leaflets, whereas Q was quantified based on volumetric assessment of the left ventricle. For validation, invasively measured TPG(catheter) was calculated from pressure measurements in the left ventricle and the ascending aorta. Altogether, 84 data sets of patients with aortic stenosis were used to compare TPG(CT) against TPG(catheter). Results: TPG(catheter) and TPG(CT) were 50.6 �� 28.0 and 48.0 �� 26 mmHg, respectively (p = 0.56). A Bland-Altman analysis revealed good agreement between both methods with a mean difference in TPG of 2.6 mmHg and a standard deviation of 19.3 mmHg. Both methods showed good correlation with r = 0.72 (p < 0.001). Conclusions: The presented CT-based method allows assessment of TPG in patients with aortic stenosis, extending the current capabilities of cardiac CT for diagnosis and treatment planning.

IF=3.633; International audience; This paper presents a new method to efficiently approximate both linear buckling loads and associated mode shapes of finite element structures subject to perturbations. To achieve this, a coupling between a Reduced Order Model (ROM) based on the Homotopy Perturbation Method (HPM) and a Kriging model is presented here. The ROM maintains the link between eigenvalues, related eigenvectors and the dependencies between each eigenvector components, leading to a high precision level. The computational time is greatly reduced by the surrogate model which avoids the computation of modified finite element matrices for each prediction. Next, the capabilities of the method allow to efficiently handle the prediction, sensitivity and optimization steps of an uncertain propagation problem using fuzzy formalism. Additive Manufacturing is a powerful and impressive process but many factors can be responsible for relatively large discrepancies in the mechanical and geometrical characteristics of the manufactured structure. Lastly, a study shows how the proposed fuzzy strategy allows the prediction of the buckling variability of a set of lattice structures.

In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We manage to tackle the instability issues of such methods whenever strong nonlinearities appear and to utilize their flexibility of the fixed background geometry -- and mesh -- characteristic, through which, one can avoid e.g. in parametrized geometries the remeshing on the full order level, as well as, transformations to reference geometries on the reduced level. As a final goal, we manage to find an efficient global, concerning the geometrical manifold, and independent of geometrical changes, reduced order basis. The POD-Galerkin approach exhibits its strength even with pseudo-random discontinuous initial data verified by numerical experiments.

In this paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the role played by difference quotients (DQs) in obtaining reducedorder model (ROM) error bounds that are optimal with respect to both the time discretizationerror and the ROM discretization error. When the DQs are not used, we prove that both the PODprojection error and the ROM error are suboptimal. When the DQs are used, we prove that both thePOD projection error and the ROM error are optimal. The numerical results for the heat equationsupport the theoretical results.

International audience; This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.; Dans cet article, une méthode de réduction récemment développée est utilisée pour étudier les interactions en contact d'une aube industrielle soumise à de grands déplacements. La méthode de réduction consiste à projeter le problème dynamique sur une base de réduction composée de modes de Craig-Bampton et d'une sélection de leurs dérivées modales. Les forces internes non linéaires causées par les grands déplacements de la structure sont évaluées avec la méthode dite `stiffness evaluation procedure' et le contact est traité numériquement à l'aide de multiplicateurs de Lagrange. La stratégie numérique est appliquée à un modèle ouvert d'aube de compresseur industriel (l'aube rotor 37 de la NASA) afin de permettre la reproductibilité des résultats. Deux scénarios de contact sont étudiés, respectivement avec contact direct entre l'aube et le carter et avec un matériau abradable déposé sur le carter. L'influence des non-linéarités géométriques est évaluée dans les deux cas. En particulier, des cartes d'interaction et des cartes d'usure sont utilisées pour identifier les interactions en contact les plus dangereuses pour l'intégrité du moteur.

International audience; Noise reduction for passengers comfort in transport industry, or more generally in an acoustic cavity, is now an important constraint to be taken into account during the design process. The optimization of internal structures positioned according to acoustic of the cavity can lead to the study of several configurations and thus may become prohibitive in terms of computational time. The aim of this work is to be able to efficiently optimize the position of structures in an acoustic cavity. The first idea is to use XFEM in order to take into account the embedded structures, such as seats in a plane cabin [Legay 2013]. These structures are immersed arbitrarily within the acoustic mesh allowing to always use the same acoustic mesh, the acoustic pressure is enriched by a Heaviside function. This makes the parametric study easier since it does not involve a meshing process anymore. The second idea of the proposed approach is to use a surrogate-based optimization in order to furthermore reduce the computational time of the whole optimization process. It is based on the Efficient Global Optimization [Jones 1998]. At least, the use of the XFEM approach enables to easily compute the gradient of the pressure field with respect to the design variables which governed the position of the structure in the cavity. Moreover, a reduced basis [Legay 2015] is used to compute the solution as well as the gradient. Many operators remain indeed independent of the design variables and the main effort consists only of building gradients of the XFEM enrichment operators. These gradients enable to build a more accurate surrogate model [Laurent 2019]. This strategy enable to divide the CPU time by a factor from 2 to 10, depending of the problem complexity. The whole strategy is applied on some 2D and 3D cavities on which the position of a wall is determined in order to minimize the mean quadratic pressure in a control volume. - A. Legay. An extended finite element method approach for structural-acoustic problems involving immersed structures at arbitrary positions. International Journal for Numerical Methods in Engineering, 93(4):376-399. 2013 - A. Legay. The extended finite element method combined with a modal synthesis approach for vibro-acoustic problems. International Journal for Numerical Methods in Engineering, 101(5):329-350. 2015 - L. Laurent, R. Le Riche, B. Soulier and P.-A. Boucard. An Overview of Gradient-Enhanced Metamodels with Applications. Archives of Computational Methods in Engineering, 26(1):61-106. 2019

International audience; This paper investigates the use of different model reduction methods accounting for geometric nonlinearities. These methods are adapted to retain physical degrees-of-freedom in the reduced space in order to ease contact treatment. These reduction methods are applied to a 3D finite element model of an industrial compressor blade (NASA rotor 37). In order to compare the different reduction methods, a scalar indicator is defined. This performance indicator allows to quantify the accuracy of the predicted displacement both locally (at the blade tip) and globally. The robustness of each method with respect to variations of the external excitation is also assessed. The performances of the reduction methods are then compared in the case of frictional contact between the blade tip and the surrounding casing. This work brings evidence that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.; Cet article étudie l'utilisation de différentes méthodes de réduction de modèles tenant compte des non-linéarités géométriques. Ces méthodes sont adaptées afin de conserver des degrés de liberté physiques dans l'espace réduit et ainsi de faciliter le traitement du contact. Les méthodes de réduction sont appliquéesà un modèle éléments finis 3D d'une aube de compresseur industriel (l'aube rotor 37 de la NASA). Afin de comparer les différentes méthodes de réduction, un indicateur scalaire est défini. Cet indicateur de performance permet de quantifier la précision du déplacement prédit aussi bien localement (en bout d'aube) que globalement (dans toute l'aube). La robustesse de chaque méthode par rapport aux variations de l'excitation appliquée est aussiévaluée. Les performances des méthodes de réduction sont ensuite comparées dans le cas de contact avec frottement entre le bout d'aube et le carter. Ce travail montre que les modèles réduits sont des alternatives numériquement efficaces aux modèle séléments finis complets pour la prédiction précise de la réponse temporelle de structures mécaniques en présence de non-linéarités distribuées et localisées.

Tighter specifications in synchrotron instrumentation development force the design engineers more and more often to choose a mechatronics design approach. This includes actively controlled systems that need to be properly designed. The new Nano Active Stabilization System (NASS) for the ESRF beamline ID31 was designed with such an approach. We chose a multi-body design modelling approach for the development of the NASS end-station. Significance of such models depend strongly on its input and consideration of the right stiffness of the system���s components and subsystems. For that matter, we considered sub-components in the multi-body model as reduced order flexible bodies representing the component���s modal behaviour with reduced mass and stiffness matrices obtained from finite element analysis (FEA) models. These matrices were created from FEA models via modal reduction techniques, more specifically the component mode synthesis (CMS). This makes this design approach a combined multibody-FEA technique. We validated the technique with a test bench that confirmed the good modelling capabilities using reduced order flexible body models obtained from FEA for an amplified piezoelectric actuator (APA)., Proceedings of the 11th Mechanical Engineering Design of Synchrotron Radiation Equipment and Instrumentation, MEDSI2020, Chicago, IL, USA

This paper presents an effective procedure for model order reduction of discrete time control system. The exact model derived from complex dynamic systems proves to be very complicated for analysis, control and design. This necessity brings about using a tool known as model order reduction technique or model simplification. A novel mixed method has been implemented in this paper for reducing the order of the large scale dynamic discrete system. Dominant pole based pole clustering method has been used to derive the coefficients of denominator polynomial while Padé approximation has been applied to obtain the coefficients of numerator polynomial of the reduced order model. The proposed method is quite simple and able to generate a stable reduced order model from high order stable discrete systems. The dominancy of poles has been decided by values of the ratio of residue to its pole. The pole is considered dominant which have larger ratio value. An illustrative example has been considered to show the various reduction steps. The result obtained confirms the effectiveness of the approach.

In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynamical system was improved using a calibration method based on a least-square optimization process. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least- square procedure is a combination of POD method and the solution of an optimization problem. The obtained model can predict accurate time variations of flow field with high speed. For long time periods, the calibration term can be computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has recently been proposed by the authors. The results obtained from the calibrated reduced order model show close agreements to the benchmark DNS data, proving high accuracy of our model.

Computational Mechanics' problems are often solved using the Finite Element Method (FEM). The resulting systems of equations may lead to large data and therefore, the solution requires high memory and time to be computed. This situation can be surpassed by applying Reduced Order Modeling (ROM) techniques, allowing the user to capture the system's dominant effects to build a high-fidelity reduced model that gives the possibility to predict and analyze the behaviour of a complex model using low computational resources within a micro time-step. This paper aims to enrich the already implemented Kratos' Rom Application with a reconstruction of the reaction and 2nd Piola Kirkchhoff stress fields. The applied methodology is a projection-based strategy using the Proper Orthogonal Decomposition together with a Gappy Data reconstruction technique. The gappy data comes from building a hyper-reduced order model (HROM). A surrogate model application using static condensation and HROM techniques is proposed to show the possibility of solving multibody systems interfacing Kratos' ROM framework with Mathworks control capabilities in a fast and accurate way. The validation of the applied methodology is given by 3D complex models.

Energy storage devices are key components to enable stable, more efficient, and controllable energy flow in systems. Furthermore, they are facilitators for maximizing the use of renewable primary energy sources, which often do not meet immediate supply-demand needs. Thermal batteries can be configured as tube and flat fin heat exchangers using water as working fluid inside the tubes and surrounded by a Phase-Change Material (PCM) on the external surface. These components typically require transient high-order modeling physics to simulate their behavior that are generally computationally intensive. This paper presents a low computational cost tool for design optimization of the heat exchangers for these batteries during discharge, i.e., solidification of the PCM. The approach consists of evaluating the heat transfer rate for an average PCM mass fraction of 50% and assuming a quasi-steady-state condition. The PCM thermal resistance is predicted using metamodels derived from validated CFD simulations. Using experimental data, the solver prediction matched the heat transfer rate during phase change from 2.3% to 22.9% for the same battery at different water inlet temperatures. The proposed solver is more than four orders of magnitude faster than the full transient model for a single design. This allows for using optimization such as Multi-Objective Genetic Algorithms (MOGA) to explore novel designs in only a few minutes. Finally, the optimization study suggested that for a particular battery, there is a trade-off where one may save more than 22% in material cost for the same performance or increase more than 6% in thermal performance for the same cost. Two distinct points in a Pareto front were selected and evaluated with the full transient model; the results provided good evidence that the proposed solver is sufficiently robust in predicting battery thermal performance and degradation.

This dissertation contains work that addresses both theoretical and numerical aspects of reduced order models (ROMs). In an under-resolved regime, the classical Galerkin reduced order model (G-ROM) fails to yield accurate approximations. Thus, we propose a new ROM, the data-driven variational multiscale ROM (DD-VMS-ROM) built by adding a closure term to the G-ROM, aiming to increase the numerical accuracy of the ROM approximation without decreasing the computational efficiency. The closure term is constructed based on the variational multiscale framework. To model the closure term, we use data-driven modeling. In other words, by using the available data, we find ROM operators that approximate the closure term. To present the closure term's effect on the ROMs, we numerically compare the DD-VMS-ROM with other standard ROMs. In numerical experiments, we show that the DD-VMS-ROM is significantly more accurate than the standard ROMs. Furthermore, to understand the closure term's physical role, we present a theoretical and numerical investigation of the closure term's role in long-time integration. We theoretically prove and numerically show that there is energy exchange from the most energetic modes to the least energetic modes in closure terms in a long time averaging. One of the promising contributions of this dissertation is providing the numerical analysis of the data-driven closure model, which has not been studied before. At both the theoretical and the numerical levels, we investigate what conditions guarantee that the small difference between the data-driven closure model and the full order model (FOM) closure term implies that the approximated solution is close to the FOM solution. In other words, we perform theoretical and numerical investigations to show that the data-driven model is verifiable. Apart from studying the ROM closure problem, we also investigate the setting in which the G-ROM converges optimality. We explore the ROM error bounds' optimality by considering the difference quotients (DQs). We theoretically prove and numerically illustrate that both the ROM projection error and the ROM error are suboptimal without the DQs, and optimal if the DQs are used. Doctor of Philosophy In many realistic applications, obtaining an accurate approximation to a given problem can require a tremendous number of degrees of freedom. Solving these large systems of equations can take days or even weeks on standard computational platforms. Thus, lower-dimensional models, i.e., reduced order models (ROMs), are often used instead. The ROMs are computationally efficient and accurate when the underlying system has dominant and recurrent spatial structures. Our contribution to reduced order modeling is adding a data-driven correction term, which carries important information and yields better ROM approximations. This dissertation's theoretical and numerical results show that the new ROM equipped with a closure term yields more accurate approximations than the standard ROM.

In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to an in-phase relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Practical industrial application of a mitigation strategy requires early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically represent the relationship between heat release and acoustic perturbations. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predictive capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between OH* or CH* chemiluminescence to heat release. This is an ideal case; in reality, practical burners produce turbulent and partially premixed flames. Due to the additional straining of the flame caused by turbulence, the heat release is no longer proportional to chemiluminescence quantities. Also, partially premixed systems have spatially varying equivalence ratios and heat release rates, meaning analysis reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations is needed. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. This was the first time that a reduced order model was developed to study PIM effects on the thermoacoustic response. Model development used a linear FTF and can predict the system frequency and stability response. Through the frequency response, mode shapes can be constructed which show the axial variation in acoustic values, along with node and anti-node locations. Stability trends can be predicted, such as the independent effects of system parameter variation, to determine its stability response. The model was compared to canonical case studies as well as experimental data with reasonable agreement. With PIM addition, it was shown that a combustor would be under stable operation at more flow conditions than without PIM. The work also shows the stability sensitivity to different porous parameters and PIM locations within the combustor. The model has been used to aid in the design of other combustion systems developed at Virginia Tech's Advanced Propulsion and Power Laboratory. To better understand how PIM is affecting the system stability and demonstrate measurements for the improvement of a numerical FTF, experimental work to resolve the spatially varying equivalence ratio fluctuations was conducted in an atmospheric, swirl-stabilized combustor. The experimental studies worked to improve the fundamental understanding of PIM and its mitigation effects through spatially and temporally resolved equivalence ratios during a self-excited instability. The experimental combustor has an optically accessible flame region which allowed for high speed chemiluminescence to be captured during the instability. Equivalence ratio values were calculated from a relation involving OH*/CH* chemiluminescence ratio. The acoustic perturbations were studied to show how the equivalence ratio fluctuations were being generated and coupling with the acoustic waves. The fluctuation in equivalence ratio showed about 65% variation around its mean value during the period of an instability cycle. When porous media was added to the system, the fluctuation in equivalence ratio was mitigated and a reduction in peak frequency (sound pressure level) SPL of 38 dB was observed. Changes in the spatial distribution of equivalence ratio with PIM addition were shown to produce a more stable operation. Effects such as locally richer burning and changes to recirculation zones promoted more stable operation with PIM addition. Testing with forced acoustic input was also conducted to quantify the flame response. The results demonstrated that a flame in a system with PIM responds differently than without PIM, highlighting the need to develop FTF for systems with PIM. This experimental study was the first to study equivalence ratio in a turbulent, partially premixed combustor using PIM as a mitigation technique. A final experimental investigation was conducted to resolve the spatially defined heat release and its fluctuation during a thermoacoustic instability period. This was the first time that heat release had been investigated in a partially premixed, thermoacoustically unstable system, using PIM as a migration method. Heat release was quantified using equivalence ratio, strain rate, OH* intensity, and a correction factor determined from a chemical kinetic solver. The heat release analysis built upon the equivalence ratio study with additional flow field analysis using PIV. The velocity vectors showed prominent corner and central recirculation zones in the no PIM case which have been shown to be feedback mechanisms that support instability formation. With PIM addition, these flow features were reduced and decoupled from the combustor inlet reactants. The velocity results were decomposed using a spectral proper orthogonal decomposition (SPOD) method. The energy breakdown showed how PIM reduced and distributed the energy in the flow structures, creating a more stable flow field. Heat release results with velocity information demonstrated the significant coupling mechanisms in the flow field that were mitigated with the PIM addition. The no PIM case showed high heat release areas being directly influenced by the incoming flow fluctuations. The feedback mechanisms, both mean flow and acoustic, have a direct path to the incoming flow to the combustor. In the PIM case, there is significant mixing and burning taking place in locations where it is less likely that feedback can reach the incoming flow to couple to form an instability. The methodology to quantify heat release provides a framework for quantifying a non-linear FTF with PIM. The development and testing to determine a non-linear FTF with PIM are reserved for future work and discussed in the final chapter. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. Doctor of Philosophy In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to a relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Implementation of these mitigation strategies require early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically model the flame response. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predicative capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics with varying levels of success. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between flame light emission and heat release. This is an ideal case; in reality, practical burners produce complex turbulent flames. Due to complex turbulent flame, the heat release is no longer proportional to the flame light emission quantities. Also, partially premixed systems have spatially variant flame quantities, meaning analyses reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations are required. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. The model uses a simple relationship to model the flame response in an acoustic framework. To improve the model and understanding of PIM mitigation, experimental data such as the local heat release rates and equivalence ratios need to be quantified. An experimental technique was utilized on an optically accessible atmospheric, swirl-stabilized combustor, to resolve the spatially variant equivalence ratio and heat release rates. From these results, better understanding of how PIM is improving the stability in a combustion environment is shown. Quantities such as velocity, acoustic pressure, equivalence ratio, and heat release are all studied and used to explain the improved stability with PIM addition. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. Furthermore, the present work provides a framework for quantifying spatially varying heat release measurements, which can be used to develop FTF for use with thermoacoustic modeling approaches.

Pulse Width Modulation (PWM) control of electric motors induces torque oscillations over a wide frequency range and with large amplitudes. These excitations can lead to the rupture of rotating parts. The PWM control coupled with simplified mechanical models often leads to oversizing of complex rotors. The objective of this thesis is to provide confident models describing the dynamic behavior when excited by PWM strategies. The first methodological contribution consists in a reduced order modelling strategy of the mechanical model of the rotor based on a projection basis linking the DOFs of the complete model to the rotation DOFs of the reduced model. In addition, the computation of stresses in the rotating parts during a speed-up is obtained by expanding the solution obtained from the resolution of the problem in the reduced space. The second contribution focuses on the dynamic behavior of the laminated stack. An asymptotic non-linear homogenization methodology is proposed. The equivalent elasticity moduli of the laminated stack are estimated from a series of non-linear quasi-static computations and by the prediction of the assembly preload. The results of this method are compared to experimental tests on both academic and industrial cases.; Le pilotage par Modulation de Largeur d’Impulsion (MLI) des moteurs électriques induit des oscillations de couple au niveau du rotor sur une large plage de fréquence et avec des amplitudes importantes. Ces excitations peuvent conduire à la rupture des pièces tournantes. Ce pilotage couplé à des modèles mécaniques simplifiés rend le dimensionnement des rotors complexes, ce qui mène à un surdimensionnement. L’objectif de la thèse est de maîtriser les modélisations dynamiques des rotors et de définir une méthodologie de dimensionnement sous excitation MLI. Le premier apport méthodologique concerne une méthode de réduction du modèle mécanique du rotor s’appuyant sur une base de projection liant les DDLs du modèle complet aux DDLs en rotation du modèle réduit. De plus, l’estimation des contraintes dans les pièces tournantes sur une montée en vitesse, nécessaire au dimensionnement, est obtenue par opération inverse à partir de la résolution du problème dans l’espace réduit. Le second apport se focalise sur le comportement dynamique du paquet de tôles. Une méthodologie d’homogénéisation non-linéaire asymptotique est proposée. Les modules d’élasticité équivalents de l’empilement de tôles sont estimés à partir d’un ensemble de calculs quasi-statiques non-linéaires et par la prédiction de la précharge dans l’assemblage. Les résultats issus de cette méthode sont comparés à des essais expérimentaux sur deux cas, académique et industriel.

In this paper, we present a new method to quantify the uncertainty introduced by the drastic dimensionality reduction commonly practiced in the field of computational fluid dynamics, the ultimate goal being to simulate accurate priors for real-time data assimilation. Our key ingredient is a stochastic Navier--Stokes closure mechanism that arises by assuming random unresolved flow components. This decomposition is carried out through Galerkin projection with a proper orthogonal decomposition (POD-Galerkin) basis. The residual velocity fields, model structure, and evolution of coefficients of the reduced order's solutions are used to compute the resulting multiplicative and additive noise's correlations. The low computational cost of these consistent correlation estimators makes them applicable to the study of complex fluid flows. This stochastic POD-reduced order model (POD-ROM) is applied to 2-dimensional and 3-dimensional direct numerical simulations of wake flows at Reynolds 100 and 300, respectively, with uncertainty quantification and forecasting outside the learning interval being the main focus. The proposed stochastic POD-ROM approach is shown to stabilize the unstable temporal coefficients and to maintain their variability under control, while exhibiting an impressively accurate predictive capability.

Energy Performance Contracting (EPC), as a tool to enhance energy efficiency of buildings, can accelerate investment in cost-effective energy conservation measures (ECMs) for existing buildings. However, there are many risks and barriers that can slow down the uptake of EPC, such as the complexity of the process or uncertainty of building performance post-retrofit. The International Performance Measurement and Verification Protocol (IPMVP®), which was originally developed to help increase investment in energy and water efficiency, demand management and renewable energy projects, has the potential to reduce some of the EPC barriers. However, due to limited and uncertain information about existing buildings, the application of this Measurement and Verification (M&V) protocol in retrofitting projects is often complex and requires novel use of building simulation tools. In order to address the challenges of utilising M&V IPMVP® in building retrofitting projects, and to enhance the uptake of EPC, the research presented here developed a novel Reduced Order Model (ROM) technology framework that can be used for (i) systematic quantification of energy savings (avoided energy consumption) achieved through ECMs, and (ii) direct estimation of energy savings through the investigation of different envelope retrofit scenarios. The framework was demonstrated on pilot buildings in Sant Cugat, Spain. This research work was funded by the Irish Research Council (IRC) - R2M Solution S.r.l Enterprise Partnership Scheme Postgraduate Scholarship 2017 (project ID EPSPG/2017/359). This project was partially funded by the European Union under the Horizon 2020 GEOFIT project (Grant agreement No. 792210). peer-reviewed

In this paper we present an a posteriori error estimate for a reduced order model (ROM) for the incompressible Navier-Stokes equations that is based on the fact that the full order model is a finite element (FE) approximation. Both this FE approximation and the ROM are stabilized by means of a variational multi-scale (VMS) strategy, in which the unknowns are split into FE scales and sub-grid scales (SGS), the latter being modeled in terms of the former. The SGS, when properly scaled, provide directly the a posteriori error estimate, both for the ROM and for the FE approximation. R. Codina acknowledges the support received from the ICREA Acadèmia Research Program, from the Catalan Government. R. Reyes acknowledges the scholarship received from COLCIENCIAS, from the Colombian Government. J. Baiges acknowledges the support of the Spanish Government through the Ramón y Cajal grant RYC-2015-17367. This work was partially funded through the TOP-FSI: RTI2018-098276-B-I00 project of the Spanish Government.

This work presents new robust adaptive control strategies of adaptive robust controllers, in discrete time, applied to the grid-injected currents control of a voltage-fed three-phase three-wires static converter connected to the electrical grid with LCL filter. The application of adaptive controllers on grid-tied converters is justified due to the uncertainties and pa- rametric variations inherent to the grid impedance. However, typically, adaptive controllers based on a reference model implemented for this application are complexes, because the reference model need to has the same relative degree of modelled part of the plant, which is equal to three, in continuous time, or relative degree equal to two, if discretised consi- dering implementation delay. It implies on a complex control design and will require a high processing capacity from microcontroller to execute it. Thereby, initially an order reduction of LCL filter model is proposed, where is demonstrated mathematically that filter capacitor can be considered as an unmodelled dynamics of additive type, resulting in an first order model. With this, it is possible to design a robust adaptive controller with a first order re- ference model, since the relative degree of the modelled part of the plant is one. Next, two new robust adaptive controllers are proposed, entirely in discrete time. The first new strategy, PI-RMRAC, is a robust PI (Proportional-Integral) controller based on a reference model. This new control approach is a reformulation of the parameter vector, which, like the previous strategy, is based on a first-order reference model. The second proposed new controller, a robust adaptive PI controller, tracks straightforwardly the reference currents, consequently it does not require the reference model implementation, further simplifying the controller design. In this controller, the identification of adaptive gains is equivalent to estimate, indirectly, the closed-loop system gains. Furthermore, the stability and robustness proofs of controllers, in discrete time, are presented. In addition, to corroborate the propo- sed strategies performance, the experimental results are compared with a robust adaptive controller with a third-order reference model. Este trabalho apresenta novas estratégias de controle robustos adaptativos, em tempo dis- creto, aplicados ao controle da corrente injetada na rede através de um conversor estático trifásico a três fios alimentado em tensão conectado à rede elétrica por filtro LCL. A apli- cação de controladores adaptativos nos conversores conectados à rede se justifica devido as incertezas e variações paramétricas inerentes à impedância da rede. Entretanto, tipi- camente, os controladores adaptativos baseados em modelo de referência implementados para esta aplicação são complexos, pois o modelo de referência deve ter o mesmo grau re- lativo da parte modelada da planta, que é igual a três, em tempo contínuo, ou grau relativo igual a dois, se discretizado considerando o atraso de implementação. Isto implica em um projeto de controle complexo e exigirá uma elevada capacidade de processamento do mi- crocontrolador para executá-lo. Assim, inicialmente é proposta uma redução de ordem do modelo do filtro LCL, onde é demonstrado matematicamente que o capacitor do filtro pode ser considerado como uma dinâmica não modelada do tipo aditiva, resultando em um mo- delo de primeira ordem. Com isso, pode-se projetar um controlador robusto adaptativo com modelo de referência de primeira ordem, pois o grau relativo da parte modelada da planta é um. Em seguida, propõem-se dois novos controladores robustos adaptativos, de com- plexidade reduzida, totalmente em tempo discreto. A primeira nova estratégia, PI-RMRAC, é um controlador PI (Proporcional-Integral) robusto adaptativo baseado em modelo de re- ferência. Esta nova abordagem de controle é uma reformulação do vetor de parâmetros, que, assim como a estratégia anterior, baseia-se em um modelo de referência de primeira ordem. Já o segundo novo controlador proposto, um PI robusto adaptativo, rastreia dire- tamente a referência, ou seja, não requer a implementação de um modelo de referência, simplificando ainda mais o projeto do controlador. Neste controlador, a identificação dos ganhos adaptativos equivale a estimar, indiretamente, os ganhos do sistema em malha fe- chada. Ainda, as provas de estabilidade e robustez dos controladores, em tempo discreto, são apresentadas. Além disso, para corroborar o desempenho das estratégias propostas, os resultados experimentais são comparados com um controlador robusto adaptativo com modelo de referência de grau relativo igual a três.

This manuscript outlines the production of a flight mechanics and reduced order aerodynamics coupled model for stability analysis of tiltrotor aircraft. By including time history effects this improves on classical stability analysis where a truncated Taylor expansion is used. These effects are important to consider due to the high amount of interaction of the wake from the rotating proprotors with the airframe. The flight mechanics is based on the 12 degrees of freedom 3D rigid body equations and the aerodynamic system is evaluated using the unsteady vortex lattice method. The aerodynamic model is reduced by two methods, using the eigensystem realisation algorithm for a linear time invariant approximation and a periodic reduced order model for the full linear time periodic system. The methodology is applied to a Bell XV-15 type tiltrotor aircraft in hover and forward flight and comparisons are drawn to prior stability analysis found in literature to assess the capability of the methodology. The coupled system indicates more instability when compared to the classical analysis, which suggests that the low order Taylor series expansion removes important dynamics attributed to the time history. The two model order reduction methods are compared which shows close correlation near to the stability boundary however a greater difference in the more unstable eigenvalues. This indicates that the time averaged model is more applicable to only lightly unstable situations.

Controlling bipedal robotic walking is a challenging task. The dynamics is hybrid, nonlinear, high-dimensional, and typically underactuated. Complex physical constraints have to be satisfied in the walking generation. The stability in terms of not-falling is also hard to be encoded in the walking synthesis. Canonical approaches for enabling robotic walking typically rely on large-scale trajectory optimizations for generating optimal periodic behaviors on the full-dimensional model of the system; then the stabilities of the controlled behaviors are analyzed through the numerically derived Poincaré maps. This full-dimensional periodic behavior based synthesis, despite being theoretically rigorous, suffers from several disadvantages. The trajectory optimization problem is computationally challenging to solve. Non-trivial expert-tuning is required on the cost, constraints, and initial conditions to avoid infeasibilities and local optimality. It is cumbersome for realizing non-periodical behaviors, and the synthesized walking can be sensitive to model uncertainties. In this thesis, we propose an alternative approach of walking synthesis that is based on reduced order modeling and dynamics approximation. We formulate a discrete step-to-step (S2S) dynamics of walking, where the step size is treated as the control input to stabilize the pre-impact horizontal center of mass (COM) state of the robot. Stepping planning thus is converted into a feedback control problem. To effectively and efficiently solve this feedback stepping planning problem, an underactuated Hybrid Linear Inverted Pendulum (H-LIP) model is proposed to approximate the dynamics of underactuated bipedal walking; the linear S2S dynamics of the H-LIP then approximates the robot S2S dynamics. The H-LIP based stepping controller is hence utilized to plan the desired step sizes on the robot to control its pre-impact horizontal COM state. Stable walking behaviors are consequently generating by realizing the desired step size in the output construction and stabilizing the output via optimization-based controllers. We evaluate this approach successfully on several bipedal walking systems with an increase in the system complexity: a planar five-linkage walker AMBER, an actuated version of the Spring Loaded Inverted Pendulum (aSLIP) in both 2D and 3D, and finally the 3D underactuated robot Cassie. The generated dynamic walking behaviors on these systems are shown to be highly versatile and robust. Furthermore, we show that this approach can be effectively extended to realizing more complex walking tasks such as global trajectory tracking and walking on rough terrain.

At the dawn of Industry 4.0, it has become apparent that assessment of engineered systems should be informed from the state of the system “as-is”. To this end, data needs to be fused with adequate and efficient system models. Such system models should account for the underlying physics and the possibly nonlinear dynamic processes involved. This paper introduces a physics-based parametric formulation for nonlinear structural systems. A Reduced Order Model (ROM) of the high fidelity system is developed, retaining the dependencies on system properties and on temporal and spectral characteristics of the excitation. The ROM formulation relies on i) Proper Orthogonal Decomposition applied to snapshots of the nonlinear response, and ii) manifold interpolation of the resulting projection bases. Its performance is evaluated on a 3D earthquake-excited shear frame with nonlinear couplings. The developed ROM can be exploited for a number of tasks including monitoring, diagnostics and residual life estimation of critical components.

In this thesis, we propose a space-time Finite Element (FEM) / Finite Volume (FVM) scheme on moving Chimera grids for a general linear and nonlinear advection-diffusion problem. Special care is devoted to grid overlapping zones in order to devise a compact and accurate discretization stencil to exchange information between different mesh patches. Like in the ADER method, the equations are discretized on a space-time slab. Thus, instead of time-dependent spatial transmission conditions between relatively moving blocks, we define interpolation polynomials on arbitrarily intersecting space-time cells at the block boundaries. Through this scheme, a mesh-free FEM-predictor/FVM-corrector approach is employed for representing the solution. In this discretization framework, a new space-time Local Lax-Friedrichs (LLF) stabilization speed is defined by considering both the advective and diffusive nature of the equation. The numerical illustrations for linear and nonlinear systems show that background and foreground moving meshes do not introduce spurious perturbations to the solution, uniformly reaching second order of accuracy in space and time. It is shown that several foreground meshes, possibly overlapping and with independent displacements, can be employed thanks to this approach.The main application of the scheme is for the Navier-Stokes equations in order to simulate incompressible viscous flows in an evolving domain. In this case, the employed evolving space-time overset grids are able to take into account both possibly moving objects and the evolution of the domain. Since a classical fractional step method is adopted, a Poisson problem for the pressure needs to be numerically solved. For this reason, for the discretization of the gradient operator, a hybrid technique is defined which is able to automatically encode the particular local overlapping configuration at the interfaces of two blocks. This avoids a subsequent interpolation step at the interface to exchange information between different blocks. The resulting method is second order accurate for both velocity and pressure in space and time. The accuracy and efficiency of the method are tested through reference simulations.Finally, a reduced and hyper-reduced ADER scheme for general advection-diffusion equations on overset grids is presented. This scheme, based on the Proper Orthogonal Decomposition (POD) approach, allows to reduce the computational costs for both finding the numerical solution and for computing the integrals involved in the definition of the matrices of the algebraic counterpart. In an offline training stage it is built a proper reduced subspace onto which the reduced solution is later projected. Successively, in the online step, a numerical reduced solution is found with respect to a parameter defining the evolution of the domain. In order to enlighten the computational costs for performing the numerical integrals via quadrature rule, a further offline training stage is computed. It allows to define a largely small set of quadrature nodes for any admissible movement of the mesh. The approach is in a Domain Decomposition (DD) frame: consequently over the background mesh the reduced solution is recovered while in background the solution is high-fidelity. The performance of the proposed scheme is tested on both linear and nonlinear problem for different movement of the computational domain. Results show that the computational costs reduce to mathcal{O}(1) degrees of freedom by preserving the accuracy of the solution., Dans cette thèse, nous proposons un schéma éléments finis (FEM) / volumes finis (FVM) spatio-temporel sur des grilles Chimera mobiles pour un problème général d'advection-diffusion linéaire et non linéaire. Une attention particulière est accordée aux zones de superposition des grilles afin de concevoir un stencil de discrétisation compact et précis pour échanger des informations entre les différents patchs de maillage. Comme dans la méthode ADER, les équations sont discrétisées sur un maillage spatio-temporel. Ainsi, au lieu de conditions de transmission spatiale dépendant du temps entre des blocs en mouvement relatif, nous définissons des polynômes d'interpolation sur des cellules spatio-temporelles se croisant arbitrairement aux frontières des blocs. Grâce à ce schéma, une approche FEM-prédicteur/FVM-correcteur mesh-free est utilisée pour représenter la solution. Dans ce cadre de discrétisation, une nouvelle vitesse de stabilisation locale de Lax-Friedrichs (LLF) spatio-temporelle est définie en considérant à la fois la nature advective et diffusive de l'équation. Les illustrations numériques pour les systèmes linéaires et non linéaires montrent que les mailles mobiles de background et foreground n'introduisent pas de perturbations parasites dans la solution, atteignant uniformément le deuxième ordre de précision en espace et en temps. Il est démontré que plusieurs mailles du foreground, pouvant se superposer et ayant des déplacements indépendants, peuvent être utilisées grâce à cette approche.La principale application de ce schéma concerne les équations de Navier-Stokes afin de simuler des écoulements visqueux incompressibles dans un domaine évolutif. Dans ce cas, les grilles évolutives spatio-temporelles utilisées sont capables de prendre en compte à la fois les objets éventuellement en mouvement et l'évolution du domaine. Puisqu'une méthode classique à pas fractionnaire est adoptée, un problème de Poisson pour la pression doit être résolu numériquement. Ainsi, pour la discrétisation de l'opérateur de gradient, une technique hybride est définie afin d'encoder automatiquement la configuration locale particulière de superposition aux interfaces de deux blocs. Ceci évite une étape ultérieure d'interpolation à l'interface pour échanger des informations entre différents blocs. La méthode qui en résulte est précise au second ordre pour la vitesse et la pression en espace et en temps. La précision et l'efficacité de la méthode sont testées par des simulations de référence.Enfin, un schéma ADER réduit et hyper-réduit pour les équations d'advection-diffusion générales sur des grilles overset est présenté. Ce schéma, basé sur l'approche de la Décomposition Orthogonale Propre (POD), permet de réduire les coûts de calcul à la fois pour trouver la solution numérique et pour calculer les intégrales impliquées dans la définition des matrices au niveau discret. Dans une étape d'apprentissage offline, on construit un sous-espace réduit approprié sur lequel la solution réduite est ensuite projetée. Successivement, dans l'étape online, une solution réduite numérique est trouvée par rapport à un paramètre définissant l'évolution du domaine. Afin de réduire les coûts de calcul des intégrales numériques via la règle de quadrature, une étape supplémentaire d'apprentissage offline est effectuée. Elle permet de définir un ensemble largement réduit de nœuds de quadrature pour tout mouvement admissible du maillage. L'approche se situe dans un cadre de décomposition de domaine (DD) : par conséquent, sur le maillage de foreground, la solution réduite est récupérée alors que dans le maillage de background, la solution est haute-fidélité. La performance du schéma proposé est testée sur des problèmes linéaires et non linéaires pour différents mouvements du domaine de calcul. Les résultats montrent que les coûts de calcul sont réduits à mathcal{O}(1) degrés de liberté en préservant la précision de la solution.

Microcapsules are liquid droplets enclosed by a thin elastic membrane. Being suspended in an external fluid, they undergo large deformations when flowing. Their deformation can be solved numerically, but the resolution of the fluid–structure interactions (FSI) requires extremely long computation times. This is a major constraint for instance when identifying the membrane mechanical properties from experimentations of microcapsules flowing in a microfluidic channel of similar size (Hu et al. PFE 2013). We propose to apply Model Order Reduction (MOR) to predict in real time the steady-state capsule deformed shape, needed to determine the membrane elasticity. A database of the capsule deformed shapes was obtained numerically by solving the three-dimensional (3D) FSI through a finite element-boundary integral method coupling, and by varying systematically the two non-dimensionalized parameters of the problem: the capillary number, ratio of the viscous to the elastic forces, and the capsule-to-tube size ratio. Among the MOR techniques, we chose to apply Proper Orthogonal Decomposition (POD) onto the database, which provides a vector basis of principal components, defining a multi-dimensional vector space. The advantage is that, when all the capsule shapes of the database are mapped into this new vector space, they form a manifold (smooth hypersurface) that represents all the admissible solutions of the problem. We show that POD with a manifold walking technique can be successfully applied to 3D microcapsule data sets, whether they are Lagrangian (e.g. known position vector fields) or Eulerian (i.e. when data is acquired experimentally or numerically using methods like level sets). In both cases, the problem dimensionality is reduced, the predicted capsule shapes are obtained within computation times of milliseconds, and they accurately fit the full FSI simulations. This paves the way to real-time computations for capsules in flow, while retaining all the physical ingredients of the FSI problem.

In civil engineering, almost all structures are somehow in contact with soil - i.e., have foundations or support elements that either rest on or are embedded in soil. Thus, their seismic response is governed by the interaction between the structure, the non-structural components, the foundation, and the surrounding soil. Predicting such interaction becomes increasingly complex when uncertainties of soil and structural material, ground motion variability, and dissipation mechanisms are considered. The accuracy of numerical models to predict the linear or nonlinear responses of structures depends not only on how well the uncertainties in the material properties and input motion are estimated, but also on how well the various sources of energy dissipation and their interaction are modeled. Therefore, high-fidelity simulation of soil-structure interaction (SSI) problems require advanced models that can capture the nonlinear behavior of soils and structures, and parallel computing capabilities to optimize the cost associated with large scale problems. In spite of this fact, SSI in practice is widely accounted for using fixed-base building and reduced-order-models (ROM) which usually trade accurate solution for fast ones. Unfortunately, if SSI effects are neglected or poorly estimated, then critical response measures of a structure can be over- or under-estimated, which in turn can lead to unsafe or overly conservative designs. Motivated by the previous challenge, in this thesis work we present a robust and efficient framework for finite element model (FEM) updating based on ensemble-Kalman inversion (EnKI). The EnKI-FEM updating framework is used to obtain suitable parameters to inform a ROM from data generated using high-fidelity FEM simulations. Since high-fidelity SSI simulations call for accurate and computationally efficient capabilities, as a part of this work, we developed Seismo-VLAB, a simple, fast, and extendable C++ finite element software to optimize large-scale simulations of dynamic and nonlinear SSI problems. The EnKI-FEM updating framework is thus integrated in Seismo-VLAB allowing to identify any parameter of the ROM without compromising accuracy. The so-generated ROM are finally employed to propose a new dimensionless frequency mapping to estimate the soil impedance for time domain analysis and to investigate soil-structure-interaction effects at a regional-scale. The presented methodology is general enough and it can be extended to more complex structural and/or geotechnical systems, allowing to construct highly-accurate ROM in a simple manner.