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Rotorcraft–pilot coupling (RPC) denotes inter- play between pilot and helicopter (or tiltrotor) that may give rise to adverse phenomena. These are usually divided into two main classes: pilot-induced oscillations driven by flight dynamics and behavioural processes, and pilot- assisted oscillations (PAO) caused by unintentional actions of pilot on controls, owing to involuntary reaction to seat vibrations. The aim of this paper is the development of mathematical helicopter models suited for analysis of RPC phenomena. In addition to rigid-body dynamics, RPCs (especially PAO) are also related to fuselage structural dynamics and servoelasticity; however, a crucial role is played by main rotor aeroelasticity. In this work, the aeroelastic behaviour of the main rotor is simulated through a novel finite-state modeling that may conve- niently be applied for rotorcraft stability and response analyses, as well as for control synthesis applications. Numerical results, first are focused on the validation of the proposed novel main rotor model, and then present appli- cations of the developed comprehensive rotorcraft model for the RPC analysis of a Bo-105-type helicopter. Specif- ically, these deal with the stability of vertical bouncing, which is a PAO phenomenon caused by coupling of ver- tical pilot seat acceleration with collective control stick, driven by inadvertent pilot actions. Further, considering quasi-steady, airfoil theory with wake inflow correction and three-dimensional, potential-flow, boundary element method approaches, the sensitivity of PAO simulations to different aerodynamic load models applied within the main rotor aeroelastic operator is also investigated.

This work deals with an extension of the classical construction of reduced-order models (ROMs) that are obtained through modal analysis in computational linear structural dynamics. It is based on a multilevel projection strategy and devoted to complex structures with uncertainties. Nowadays, it is well recognized that the predictions in structural dynamics over a broad frequency band by using a finite element model must be improved in taking into account the model uncertainties induced by the modeling errors, for which the role increases with the frequency. In such a framework, the nonparametric probabilistic approach of uncertainties is used, which requires the introduction of a ROM. Consequently, these two aspects, frequency-evolution of the uncertainties and reduced-order modeling, lead us to consider the development of a multilevel ROM in computational structural dynamics, which has the capability to adapt the level of uncertainties to each part of the frequency band. In this thesis, we are interested in the dynamical analysis of complex structures in a broad frequency band. By complex structure is intended a structure with complex geometry, constituted of heterogeneous materials and more specifically, characterized by the presence of several structural levels, for instance, a structure that is made up of a stiff main part embedding various flexible sub-parts. For such structures, it is possible having, in addition to the usual global-displacements elastic modes associated with the stiff skeleton, the apparition of numerous local elastic modes, which correspond to predominant vibrations of the flexible sub-parts. For such complex structures, the modal density may substantially increase as soon as low frequencies, leading to high-dimension ROMs with the modal analysis method (with potentially thousands of elastic modes in low frequencies). In addition, such ROMs may suffer from a lack of robustness with respect to uncertainty, because of the presence of the numerous local displacements, which are known to be very sensitive to uncertainties. It should be noted that in contrast to the usual long-wavelength global displacements of the low-frequency (LF) band, the local displacements associated with the structural sub-levels, which can then also appear in the LF band, are characterized by short wavelengths, similarly to high-frequency (HF) displacements. As a result, for the complex structures considered, there is an overlap of the three vibration regimes, LF, MF, and HF, and numerous local elastic modes are intertwined with the usual global elastic modes. This implies two major difficulties, pertaining to uncertainty quantification and to computational efficiency. The objective of this thesis is thus double. First, to provide a multilevel stochastic ROM that is able to take into account the heterogeneous variability introduced by the overlap of the three vibration regimes. Second, to provide a predictive ROM whose dimension is decreased with respect to the classical ROM of the modal analysis method. A general method is presented for the construction of a multilevel ROM, based on three orthogonal reduced-order bases (ROBs) whose displacements are either LF-, MF-, or HF-type displacements (associated with the overlapping LF, MF, and HF vibration regimes). The construction of these ROBs relies on a filtering strategy that is based on the introduction of global shape functions for the kinetic energy (in contrast to the local shape functions of the finite elements). Implementing the nonparametric probabilistic approach in the multilevel ROM allows each type of displacements to be affected by a particular level of uncertainties. The method is applied to a car, for which the multilevel stochastic ROM is identified with respect to experiments, solving a statistical inverse problem. The proposed ROM allows for obtaining a decreased dimension as well as an improved prediction with respect to a classical stochastic ROM, Ce travail de recherche présente une extension de la construction classique des modèles réduits (ROMs) obtenus par analyse modale, en dynamique numérique des structures linéaires. Cette extension est basée sur une stratégie de projection multi-niveau, pour l'analyse dynamique des structures complexes en présence d'incertitudes. De nos jours, il est admis qu'en dynamique des structures, la prévision sur une large bande de fréquence obtenue à l'aide d'un modèle éléments finis doit être améliorée en tenant compte des incertitudes de modèle induites par les erreurs de modélisation, dont le rôle croît avec la fréquence. Dans un tel contexte, l'approche probabiliste non-paramétrique des incertitudes est utilisée, laquelle requiert l'introduction d'un ROM. Par conséquent, ces deux aspects, évolution fréquentielle des niveaux d'incertitudes et réduction de modèle, nous conduisent à considérer le développement d'un ROM multi-niveau, pour lequel les niveaux d'incertitudes dans chaque partie de la bande de fréquence peuvent être adaptés. Dans cette thèse, on s'intéresse à l'analyse dynamique de structures complexes caractérisées par la présence de plusieurs niveaux structuraux, par exemple avec un squelette rigide qui supporte diverses sous-parties flexibles. Pour de telles structures, il est possible d'avoir, en plus des modes élastiques habituels dont les déplacements associés au squelette sont globaux, l'apparition de nombreux modes élastiques locaux, qui correspondent à des vibrations prédominantes des sous-parties flexibles. Pour ces structures complexes, la densité modale est susceptible d'augmenter fortement dès les basses fréquences (BF), conduisant, via la méthode d'analyse modale, à des ROMs de grande dimension (avec potentiellement des milliers de modes élastiques en BF). De plus, de tels ROMs peuvent manquer de robustesse vis-à-vis des incertitudes, en raison des nombreux déplacements locaux qui sont très sensibles aux incertitudes. Il convient de noter qu'au contraire des déplacements globaux de grande longueur d'onde caractérisant la bande BF, les déplacements locaux associés aux sous-parties flexibles de la structure, qui peuvent alors apparaître dès la bande BF, sont caractérisés par de courtes longueurs d'onde, similairement au comportement dans la bande hautes fréquences (HF). Par conséquent, pour les structures complexes considérées, les trois régimes vibratoires BF, MF et HF se recouvrent, et de nombreux modes élastiques locaux sont entremêlés avec les modes élastiques globaux habituels. Cela implique deux difficultés majeures, concernant la quantification des incertitudes d'une part et le coût numérique d'autre part. L'objectif de cette thèse est alors double. Premièrement, fournir un ROM stochastique multi-niveau qui est capable de rendre compte de la variabilité hétérogène introduite par le recouvrement des trois régimes vibratoires. Deuxièmement, fournir un ROM prédictif de dimension réduite par rapport à celui de l'analyse modale. Une méthode générale est présentée pour la construction d'un ROM multi-niveau, basée sur trois bases réduites (ROBs) dont les déplacements correspondent à l'un ou l'autre des régimes vibratoires BF, MF ou HF (associés à des déplacements de type BF, de type MF ou bien de type HF). Ces ROBs sont obtenues via une méthode de filtrage utilisant des fonctions de forme globales pour l'énergie cinétique (par opposition aux fonctions de forme locales des éléments finis). L'implémentation de l'approche probabiliste non-paramétrique dans le ROM multi-niveau permet d'obtenir un ROM stochastique multi-niveau avec lequel il est possible d'attribuer un niveau d'incertitude spécifique à chaque ROB. L'application présentée est relative à une automobile, pour laquelle le ROM stochastique multi-niveau est identifié par rapport à des mesures expérimentales. Le ROM proposé permet d'obtenir une dimension réduite ainsi qu'une prévision améliorée, en comparaison avec un ROM stochastique classique

To obtain satisfactory dynamic characteristics and enhance numerical simulation efficiency, an improved reduced-order transfer-function model of an electric pitch drive system (EPDS) for a wind turbine is proposed. First, a detailed transfer-function model of an EPDS is developed on the basis of its mathematical model. Thereafter, the improved reduced-order transfer-function model for an EPDS is derived from the detailed model by transfer-function approximation, sensitivity analysis, and block diagram reduction. The frequency-domain characteristics of the proposed model and their effects on the stability of the pitch angle control system are also analyzed and compared with that of a first-order transfer-function model. Finally, the dynamic characteristics of an EDPS using the improved model are analyzed and verified by a practical EPDS test platform. Furthermore, based on the FAST-MATLAB/Simulink co-simulation tool, simulation comparisons are performed on the loading characteristics of a wind turbine to further validate its availability in it. Results show that the improved model is superior to the first-order model for the performance analysis of a wind turbine pitch angle controller, and it also can meet the requirements of large-scale loading simulations for wind turbines both in terms of the precision and the time efficiency.

International audience; Commonly, the low-frequency range [1] is characterized by the presence of a few dozen isolated eigenfrequencies that are associated with global modes, in which case the modal analysis method leads to an effective and efficient small-dimension reduced-order model (ROM). We present a new method for the robust prediction of frequency response functions (FRF) of complex structures exhibiting a high modal density. We consider complex structures for which there are more than hundreds or thousands modes in the low-frequency range. This unusual feature can be due to the presence of several structural scales within the complex geometry of the structure. Small flexible components attached to the stiff skeleton of the structure induce the presence of numerous local modes intertwined with the usual global modes of the stiff skeleton. For such complex structures, besides the absence of separation of scales, the global displacements (or global modes) cannot easily be identified because coupled with the large-amplitude local displacements (or local modes). First, the proposed method [2] allows for constructing a ROM of smaller dimension, which is obtained by introducing a subspace of global displacements. The construction of the latter is based on the introduction of high-degree polynomial shape functions. The basis of the global-displacements subspace is constituted of the eigenmodes calculated using such an approximation for the kinetic energy. The choice of the polynomial degree allows for controlling the filtering between the so-called global and local displacements, as well as the resulting dimension and accuracy of the so-called global ROM. Furthermore, it is well known that local displacements are in general more sensitive to uncertainties than global displacements. The nonparametric probabilistic approach [3] allows all sources of uncertainty to be globally accounted for by randomizing each reduced matrix whose probability density function, constructed applying the maximum entropy principle, is parameterized by a unique dispersion hyperparameter. In order to separately control the uncertainty level of the displacements of each of the scales, we propose a multilevel ROM, based on the introduction of orthogonal subspaces. The basis of each of these subspaces is constructed by using, notably, the aforementioned polynomial approximation for the kinetic energy, with an adapted polynomial degree. Each basis is constituted of displacements associated with a given structural scale. Then, the multilevel stochastic ROM is obtained by setting different dispersion hyperparameters for constructing the random matrix blocks associated with each scale. The method is applied to the complex computational model of a car and the dispersion hyperparameters of a multilevel stochastic ROM composed of three scales are identified with respect to experimental FRF measurements over a wide frequency band.[1] R. Ohayon and C.Soize, 1998, Structural acoustics and vibration, Academic Press.[2] O. Ezvan, A. Batou, and C. Soize, Multilevel reduced-order computational model in structural dynamics for the low- and medium-frequency ranges, Computers and Structures 160 (2015) 111-125.[3] C.Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics 15(3) (2000) 277-294.

ISBN: 978-618-82844-0-1; International audience; The paper is devoted to model uncertainties (or model form uncertainties) induced by modeling errors in computational sciences and engineering (such as in computational structural dynamics, fluid-structure interaction, and vibroacoustics, etc.) for which a parametric high-fidelity computational model (HFM) is used for addressing optimization problems (such as a robust design optimization problem), which are solved by introducing a parametric reduced-order model (ROM) constructed using an adapted reduced-order basis (ROB) derived from the parametric HFM. Two main methodologies are available to take into account such modeling errors. The first one is the usual output-predictive error method that has been introduced for many years. This approach can induce some difficulties because the parametric HFM and ROM do not learn from data. The second one is the nonparametric probabilistic approach of model uncertainties introduced in the framework of structural dynamics fifteen years ago. This approach is adapted, but is mainly limited to linear operators of the parametric HFM. The present paper deals with this challenging problem and proposes a novel nonparametric probabilistic approach of the modeling errors for any parametric nonlinear HFM for which a parametric nonlinear ROM can be constructed from the HFM. The methodology proposed consists in substituting the deterministic ROB with a stochastic ROB for which the probability measure in constructed on a subset of a compact Stiefel manifold. The stochastic model depends on a small number of hyperparameters for which the identification is performed by solving a statistical inverse problem. An application is presented in nonlinear computational structural dynamics.

In this paper, the proper orthogonal decomposition and the Arnoldi-based Krylov subspace methods are applied to the magnetodynamic finite element analysis of power electronic converters. The performance of these two model order reduction techniques is compared both in frequency and time domain. Moreover, two original, adaptive and automated greedy snapshots selection methods are investigated using either local or global quantities for selecting the snapshots (frequencies or time steps). ispartof: pages:1-6 ispartof: 2016 IEEE International Energy Conference (ENERGYCON) pages:1-6 ispartof: IEEE International Energy Conference (ENERGYCON) location:Leuven, BELGIUM date:4 Apr - 8 Apr 2016 status: published

© 2016. American Geophysical Union. All Rights Reserved. The topography, and the biotic and abiotic parameters are typically upscaled to make watershed-scale hydrologic-biogeochemical models computationally tractable. However, upscaling procedure can produce biases when nonlinear interactions between different processes are not fully captured at coarse resolutions. Here we applied the Proper Orthogonal Decomposition Mapping Method (PODMM) to downscale the field solutions from a coarse (7 km) resolution grid to a fine (220 m) resolution grid. PODMM trains a reduced-order model (ROM) with coarse-resolution and fine-resolution solutions, here obtained using PAWS+CLM, a quasi-3-D watershed processes model that has been validated for many temperate watersheds. Subsequent fine-resolution solutions were approximated based only on coarse-resolution solutions and the ROM. The approximation errors were efficiently quantified using an error estimator. By jointly estimating correlated variables and temporally varying the ROM parameters, we further reduced the approximation errors by up to 20%. We also improved the method's robustness by constructing multiple ROMs using different set of variables, and selecting the best approximation based on the error estimator. The ROMs produced accurate downscaling of soil moisture, latent heat flux, and net primary production with O(1000) reduction in computational cost. The subgrid distributions were also nearly indistinguishable from the ones obtained using the fine-resolution model. Compared to coarse-resolution solutions, biases in upscaled ROM solutions were reduced by up to 80%. This method has the potential to help address the long-standing spatial scaling problem in hydrology and enable long-time integration, parameter estimation, and stochastic uncertainty analysis while accurately representing the heterogeneities.

This thesis studies projection-based reduced-order models (ROMs) in the context of computational fluid dynamics. Proper Orthogonal Decomposition (POD) is employed to compute the reduced-order basis from snapshots, which are assumed to represent the finite element solution of a partial differential equation. All investigations involve either convection-diffusion-reaction equation or the incompressible Navier-Stokes equations. The main contribution of the thesis can be divided into three parts. Firstly, a Streamline-Upwind Petrov-Galerkin reduced-order model (SUPG-ROM) is investigated theoretically and numerically for convection-dominated convection-diffusion- reaction equations. Numerical analysis is utilized to propose the scaling of the stabilization parameter for the SUPG-ROM. Two approaches are used: One based on the underlying finite element discretization and the other one based on the POD truncation. The resulting SUPG-ROMs and the standard Galerkin ROM are studied numerically on several convection-dominated test problems aiming at answering several questions. One of the choices for the stabilization parameter is recommended. Secondly, an alternative approach for the computation of the ROM initial condition is derived for problems, for which the standard approach, that is usually used in the literature, results in the ROM initial condition being polluted by spurious oscillations. The principal idea of the method consists in modifying the conventional ROM initial condition in a post-processing step by a filtering procedure. Numerical studies are performed in order to investigate the influence of the filtered initial condition on the ROM results. With respect to the minimum and maximum values of the ROM solution, which characterize the under- and overshoots, ROM results could be partly significantly improved compared to the results obtained with the standard ROM initial condition. Thirdly, three velocity- pressure reduced-order models (vp-ROMs) for incompressible flows are investigated numerically. One method computes the ROM pressure solely based on the velocity POD modes, whereas the other two ROMs use pressure modes as well. One of the latter methods denoted by SM-ROM is developed within the framework of this dissertation. Moreover, the impact of the snapshot accuracy as well as of utilizing different linearization techniques on the ROM results is investigated numerically. Based on weakly divergence-free velocity snapshots, SM-ROM could reproduce the results of the finite element simulations in many cases better than the other vp-ROMs. Together with the fact that SM-ROM does not need any specification of additional pressure boundary conditions, which is required in the other methods, SM-ROM can be considered to be superior to other vp-ROMs for the computation of the ROM pressure., Diese Dissertation beschäftigt sich mit projektionsbasierten ordnungsreduzierten Modellen (ROMs) im Rahmen der numerischen Strömungsmechanik. Proper Orthogonal Decomposition (POD) wird zur Berechnung der ordnungsreduzierten Basis aus den sogenannten Schnappschüssen eingesetzt. Es wird angenommen, dass die Schnappschüsse die Finite-Elemente-Lösung einer partiellen Differentialgleichung darstellen. Der Beitrag der vorliegenden Dissertation besteht aus drei Teilen. Erstens wird ein Streamline-Upwind Petrov-Galerkin ordnungsreduziertes Modell, bezeichnet als SUPG-ROM, für konvektionsdominante Konvektions-Diffusions-Reaktions-Gleichungen sowohl theoretisch als auch numerisch untersucht. Mittels numerischer Analyse wird die Skalierung der Stabilisierungsparameter für SUPG-ROMs vorgeschlagen. Dabei werden zwei Ansätze verwendet: Der eine basiert auf der zugrundeliegenden Finite-Elemente-Diskretisierung und der andere auf der räumlichen Auflösung im Zusammenhang mit POD. Die resultierenden SUPG-ROMs und das übliche Galerkin ROM werden mittels mehrerer konvektionsdominanter Testbeispiele untersucht. Zweitens wird ein alternativer Ansatz für die Berechnung der ROM- Anfangsbedingung für Probleme entwickelt, bei welchen der Standard-Ansatz, der in der Regel in der Literatur verwendet wird, eine durch Störschwingungen verfälschte Anfangsbedingung erzeugt. Die Grundidee des Verfahrens besteht darin, die herkömmliche ordnungsreduzierte Anfangsbedingung in einem Nachbearbeitungsschritt durch ein Filterverfahren zu modifizieren. Der Einfluss der gefilterten ROM-Anfangsbedingung auf die ROM-Ergebnisse wird numerisch untersucht. In Bezug auf die Minimal- und Maximalwerte der ordnungsreduzierten Lösung, die als Maß für Unter- und Überschwingungen dienen, konnten die ROM-Ergebnisse im Vergleich zu denen mit üblichen ROM- Anfangsbedingungen zum Teil deutlich verbessert werden. Drittens werden drei ordnungsreduzierte Modelle für Geschwindigkeit und Druck (vp-ROMs) für inkompressible Strömungen numerisch untersucht. Eines dieser Verfahren berechnet den ROM-Druck allein auf der Grundlage der POD-Moden für die Geschwindigkeit, während die beiden anderen vp-ROMs auch die POD-Basiselemente für den Druck verwenden. Eine der letztgenannten Methoden, bezeichnet als SM- ROM, wurde im Rahmen dieser Arbeit entwickelt. Des Weiteren wird die Auswirkung der Genauigkeit der Schnappschüsse sowie verschiedener Linearisierungsansätze auf die ROM-Ergebnisse numerisch untersucht. Für die im schwachen Sinne divergenzfreien Geschwindigkeits-Schnappschüsse konnte SM-ROM die Ergebnisse der Finite-Elemente-Simulationen in vielen Fällen am besten approximieren. Unter Berücksichtigung, dass SM-ROM im Gegensatz zu den anderen vp-ROMs keine Angabe zusätzlicher Druckrandbedingungen benötigt, lässt sich hieraus ableiten, dass SM-ROM im Vergleich zu den zwei anderen untersuchten vp-ROMs am besten zur Berechnung des POD-Drucks geeignet ist.

The conventional concepts of a loss factor and complex-valued elastic moduli are used to study wave attenuation in a visco-elastic layer. The hierarchy of reduced-order models is employed to assess attenuation levels in various situations. For the forcing problem, the attenuation levels are found for alternative excitation cases. The differences between two regimes, the low frequency one, when a waveguide supports only one propagating wave, and the high frequency one, when several waves are supported, are demonstrated and explained. The conventional concepts of a loss factor and complex-valued elastic moduli are used to study wave attenuation in a visco-elastic layer. The hierarchy of reduced-order models is employed to assess attenuation levels in various situations. For the forcing problem, the attenuation levels are found for alternative excitation cases. The differences between two regimes, the low frequency one, when a waveguide supports only one propagating wave, and the high frequency one, when several waves are supported, are demonstrated and explained.

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy.

International audience; We present the construction of a multilevel stochastic reduced-order model devoted to the robust prediction of frequency response functions of complex linear dy-namical systems that are characterized by the presence of several structural scales in which there are local displacements in addition to the usual global displacements, and which are associated with the distinct low-, medium-, and high-frequency bands. As the levels of uncertainties are different in the three frequency bands, a multilevel stochastic reduced-order model using several orthogonal subspaces associated with the several types of displacements is developed. The objective of the paper is to demonstrate the capability of the multilevel stochastic reduced-order model to adapt the stochastic modeling of uncertainties to each one of the three frequency bands.

The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark-Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various parametric bifurcation diagrams (c) 2016 Elsevier B.V. All rights reserved.

International audience; The present work presents an improvement of a computational methodology for the uncertainty quantifi-cation of structures in presence of geometric nonlinearities. The implementation of random uncertainties is carried out through the nonparametric probabilistic framework from a nonlinear reduced-order model. With such usual modeling, it is difficult to analyze the influence of uncertainties on the nonlinear part of the operators with respect to its linear counterpart. In order to adress this problem, an approach is proposed to take into account uncertainties for both the linear and the nonlinear operators. The methodology is then validated in the context of the linear and nonlinear mistuning of an industrial integrated bladed-disk.

The propulsion shafting is one typically continuous, elastic and stepped body. To design an active controller for propulsion shafting by applying the modern control theory, an accurate reduced-order model with lumped parameters is required. This research concentrated on the reduced-order modelling method for longitudinal vibration control of a direct transfer marine propulsion shafting. The longitudinal vibration modes of the propulsion shafting were determined with one-dimension elastic wave approach based on its continuous model in advance. Taking into account of the unobservability and uncontrollability of mode nodes, the nodes of the neglected low highest mode were selected as locations of the reduced-order model mass points. By modifying mode shapes of the reduced-order model with sensitivity analysis, the reduced-order model can accurately represent the first low order modes of the continuous propeller-shafting system, enabling the effectiveness of controller design in the physical state space.

International audience; The two-dimensional Burgers' equations are solved here using the A Priori Reduction method. This method is based on an iterative procedure which consists in building a basis for the solution where at each iteration the basis is improved. The method is called a priori because it does not need any prior knowledge of the solution, which is not the case if the standard Karhunen-Loéve decomposition is used. The accuracy of the APR method is compared with the standard Newton-Raphson scheme and with results from the literature. The APR basis is also compared with the Karhunen-Loéve basis.

International audience; Large-amplitude non-linear vibrations of micro- and nano-electromechanical resonant sensors around their primary resonance are investigated. A comprehensive multiphysics model based on the Galerkin decomposition method coupled with the averaging method is developed in the case of electrostatically actuated clamped-clamped resonators. The model is purely analytical and includes the main sources of non-linearities as well as fringing field effects. The influence of the higher modes and the validation of the model is demonstrated with respect to the shooting method as well as the harmonic balance coupled with the asymptotic numerical method. This model allows designers to investigate the sensitivity variation of resonant sensors in the non-linear regime with respect to the electrostatic forcing.

International audience; The present work aims at developing a mathematical model in order to reproduce hemodynamics changes due to liver surgeries. First, a 0D closed-loop model is developed, to simulate hepatectomy and compute post-operative average values. Due to the closed loop, the surgery impact both on and from the whole circulation can be captured, including bleeding and infusion. Then, a one-dimensional artery model is implemented to improve the closed-loop model and simulate better the changes in arterial waveforms due to surgery.

International audience; In structural dynamics, the use of the vibration eigenmodes (elastic modes) allows for obtaining an accurate small-dimension reduced-order model (ROM) for the low-frequency range analysis. For some complex structures with distinct structural levels (presence of flexible parts attached to a stiff master part), numerous local elastic modes are intertwined with the usual global elastic modes, yielding high-dimension ROM. To circumvent this difficulty, a general method is proposed in order to construct a small-dimension ROM whose reduction vector basis is constituted of the global displacements only. The method is applied to an automobile complex structure.

In this work, a solution strategy based on the use of Pad´e approximants is investigated for efficient solution of parametric finite element problems such as, for example, frequency sweep analyses. An improvement to the Pad´e-based expansion of the solution vector components is proposed, suggesting the advantageous a priori estimate of the poles of the solution. This allows for the intervals of approximation to be chosen a priori in connection with the Pad´e approximants to be used. The choice of these approximants is supported by the Montessus de Ballore theorem, proving the convergence of a series of approximants with fixed denominator degrees. An acoustic case study is presented in order to illustrate the potential of the approach proposed by the authors.

International audience; The recent improvements in turbomachinery design combined to the unavoidable requirements of kerosene savings require to analyze the exceptional operating regime of bladed disks, for which large deformations and large displacements can occur. It seems then quite appropriate to consider the geometrically nonlinear effects in the computational models dedicated to the analysis of mistuned turbomachinery bladed-disks. A special attention has to be first given to the case of geometrically nonlinear tuned bladed disks. The large set of nonlinear coupled differential equations issued from the finite element model of the tuned structure has to necessarily be solved in the time domain, leading us to establish a reduced-order strategy. The operators of the corresponding mean nonlinear reduced-order model are then deduced from its explicit construction as shown in the context of three-dimensional solid finite elements. One also has to focus on the modeling of the external load, corresponding to a frequency band chosen for the excitation, which has to be selected according to usual turbomachinery criterions. The external load has to be defined in the time domain but has to represent a uniform sweep in the frequency domain. We then propose to implement the mistuning uncertainties by using the nonparametric probabilistic framework. We then obtain a stochastic reduced-order model, which requires to solve a reasonable set of uncertain nonlinear coupled differential equations in the time domain, yielding appropriate efficient and dedicated algorithms to be constructed. Such computational strategy provides an efficient computational tool, which is applied on a finite element model of an industrial centrifugal compressor with a large number of degrees of freedom. This allows new high complex dynamical behaviors to be put in evidence.

This paper presents a methodology for the identification of a reduced-order model (ROM) for the perturbation aeroelastic analysis of fixed wings in transonic flight. It is based on a linearized, frequency-domain, boundary-field integral equation for the solution of the unsteady perturbation potential flow about steady-state reference wing configurations. The resulting transfer functions between structural Lagrangean variables and generalized aerodynamic forces are approximated by means of rational expressions, and the aeroelastic ROM is identified by coupling them with the structural operator. With the aeroelastic operator recast in a reduced-order form, transonic flutter boundaries are detected through a classical eigenvalue analysis and the time-domain state–space aeroelastic model is also obtained. Applications of the methodology presented to a widely known aeroelastic test case reveal a remarkable agreement with the measured speed and frequency of flutter.

A stabilizing control technique for an inverted-double pendulum system consisting of two elastic links connected in series is developed, using a reduced-order model considering only the first vibration mode of the upper elastic beam, and applying an H∞ controller design method for a mixed sensitivity problem that can consider multiplicative perturbations at the input port and is characterized by a settling function. It is found that although the coupling effect of different natural frequencies between the two flexible beams makes the stabilization problem more difficult, it is possible to stabilize the system by a feedback control using only the system’s output signals that include the vibration signal of the upper elastic beam. Furthermore, it is concluded that the more different the lowest natural frequencies of the two elastic beams are, the more easily the system can be stabilized.