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International audience; This work is devoted to the robust analysis of the effects of geometric nonlinearities on the non-linear dynamic behavior of rotating detuned (intentionally mistuned) bladed disks in presence of unintentional mistuning (simply called mistuning). Mistuning induces uncertainties in the computational model, which are taken into account by a probabilistic approach. This paper presents a series of novel results of the dynamic behavior of such rotating bladed disks exhibiting nonlin-ear geometric effects. The structural responses in the time domain are analyzed in the frequency domain. The frequency analysis exhibits responses outside the frequency band of excitation. The confidence region of the stochastic responses allows the robustness to be analyzed with respect to uncertainties and also allows physical insights to be given concerning the structural sensitivity. The bladed disk structure is made up of 24 blades for which several different detuned patterns are investigated with and without mistuning.

Studying asymptotic properties for non autonomous partial differential equations is often challenging question due to the lack of general theory. We prove in this paper some monotony properties of a class of general non linear non autonomous size(age)-structured population dynamic models. Our results are applied to an example in order to show how one can prove some global asymptotic properties by using comparison principle.

We present a time-domain broadband beamforming based on a unimodular-upper polynomial matrix decomposition. The unimodular factor is the product of elementary $J$ - orthogonal matrices and a lower-triangular matrix with 1's on the diagonal, as in the constant matrix lower upper (LU) decomposition. This leads to a $J$ - orthogonal LU polynomial matrix decomposition, as a combination of two classical matrix factorization methods: Smith canonical form and LU Gaussian elimination. The inversion of the unimodular factor, for use as a pre/postfilter in the beamforming scheme, is immediate and can be achieved with O(1) complexity. The resulting reduced multiple-input multiple-output (MIMO) channel is exactly diagonal, leading to separate single-input single-output (SISO) channels with no cochannel inteference. There is no need to model the MIMO channel as a Laurent polynomial as usual, thus introducing unnecessary delays just for technical reasons. In addition, it turns out that each of the resulting SISO channels, except to the last channel, reduces to a simple additive noise channel, with no intersymbol interference (ISI), except for unprobable original MIMO channels. However, these very interesting features are to be balanced with the possible noise enhancement in the postfiltering step. The performance in terms of bit error rate (BER) is studied and compared with the QR-based frequency-domain and time-domain broadband beamforming. In particular, the proposed beamforming scheme can be used both in orthogonal frequency-division multiplexing (OFDM) and in single-carrier MIMO systems, without a cyclic prefix (CP). Meanwhile, the QR-based scheme requires a CP extension.

In this work, we use the concept of \(\mu \)-square-mean pseudo almost periodic and automorphic processes introduced by Diop et al. (Afr Mat 26(5):779–812, 2015) to discuss the existence and uniqueness of solutions for some semilinear integro-differential stochastic evolution equations. We provide an example to illustrate ours results.

International audience

This work concerns the nonlinear numerical analysis of mistuned blades for a rotating detuned bladed-disk structure with geometrical nonlinearities. The detuning phenomenon is taken into account through a deterministic approach by modifying material properties of some blades. A nonlinear reduced-order model is obtained by setting up a basis using a double projection method. The mistuning uncertainties are implemented through a nonparametric probabilistic approach for which the level of uncertainties is controlled by a hyperparameter. A numerical application is carried out on a bladed-disk structure made up of 24 blades whose finite element model has about 800,000 dofs exhibiting complex dynamic behaviors.

Massive MIMO is a promising technique for providing good spectral efficiency. However, the excessive feedback overhead is a major handicap in FDD Massive MIMO system. This paper presents an efficient lossless feedback overhead compression wich can achieve a compression ratio greater than 90% in Massive MIMO. The proposed method is based on the Lempel-ZivWelch (LZW) lossless compression algorithm and its performances are evaluated in several Massive MIMO configurations.

National audience; Dans cette recherche, nous présentons une méthodologie pour l’analyse dynamique des effets non linéaires géométriques pour une structure de roue aubagée, constituée d’aubes désaccordées involontairement et intentionnellement. Le désaccordage intentionnel est mis en place de manière déterministe en considérant plusieurs types d’aubes de propriétés matérielles différentes. Les incertitudes liées au désaccordage involontaire sont par ailleurs implémentées via une approche probabiliste non-paramétrique. La méthodologie est appliquée à une structure industrielle de roue aubagée afin de déterminer les répartitions des aubes permettant d’atténuer les effets d’amplification liés au désaccordageinvolontaire.

In this work, we introduce the concept of μ-pseudo almost automorphic processes in distribution. We use the μ-ergodic process to define the spaces of μ-pseudo almost automorphic processes in the square mean sense. We establish many interesting results on the functional space of such processes like a composition theorem. Under some appropriate assumptions, we establish the existence, the uniqueness and the stability of the square-mean μ-pseudo almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Levy noise. We provide an example to illustrate our results.

In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case when the functions forcing are both continuous and S2−almost automorphic. We provide an example to illustrate ours results.

In this work, we establish a new concept of square-mean pseudo almost periodic and automorphic processes using the measure theory. We use the \({\mu }\!-\)ergodic process to define the spaces of \({\mu }\!-\)pseudo almost periodic and automorphic processes in the square-mean sense. We establish many interesting results on those spaces like completeness and composition theorems. Then, we study the existence, the uniqueness, and the stability of the square-mean \({\mu }\!-\)pseudo almost periodic and automorphic solutions of the stochastic evolution equation. We provide an example to illustrate ours results.

International audience; The present paper describes a computational methodology adapted to the analysis of the nonlinear dynamical behavior of a detuned bladed disk. The context of the analysis is the following : (1) the detuning is taken into account by voluntarily breaking the cyclic symmetry of the structure with the use of a pattern constituted of different blade types; (2) the structure is assumed to undergo large strain/displacements induced by the geometrical nonlinear effects; (3) the prestresses and the gyroscopic effects induced by the rotating motion are considered in the nonlinear dynamical analysis. The computational strategy has to be compatible with the industrial context. Consequently, a particular attention is paid to the construction of an adapted nonlinear reduced-order model. Finally, the proposed methodology is applied on a complex bladed disk structure.

International audience; In the framework of linear dynamic analysis of bladed disks, the intentional mistuning has been identified as a technological way for reducing the sensitivity of the forced response of bladed disks to mistuning induced by the manufacturing tolerances and by the small variabilities of mechanical properties. The role played by the geometrical nonlinearities(Capiez-Lernout 2015) and dry friction in the dynamics of bladed disk has recently received a particular attention. In this paper, we present an analysis of the effects of geometrical nonlinearities on an intentional mistuned bladed disk. For that, a simplified bladed disk made up of 24 blades is defined for which a computational model is constructed by using the finite element method. Two different blades are used and allow for defining a pattern with 22 blades of type 1 and 2 blades of type 2. A projection basis is computed and a linear and a nonlinear reduced-order model (ROM) are constructed for the defined bladed disk. A comparison of the responses of the mistuned bladed disk computed with the linear ROM and with the nonlinear ROM is performed in order to analyze the role played by the nonlinearities on the intentional mistuning. The numerical results obtained show the significant influences of the nonlinear geometrical effects in the dynamical responses.

This paper propose an efficient Time Domain Quantization feedback for beamforming in WLAN MIMO-OFDM systems. This technic is based on Time Domain Beamforming and exploits the temporal properties of the MIMO channel. Simulations results in IEEE 802.11ac context with empirical ITU channel models show that whatever the bandwidth or MIMO configuration, the feedback overhead of the proposed quantization is shorter than that of the conventional Givens Rotation.

In this article we first establish a new representation formula for bounded solutions to a class of nonlinear second-order hyperbolic partial differential equations. Next, we use of our newly-established representation formula to establish the existence of bounded solutions to these nonlinear partial differential equations.

In this work, we establish a new concept of pseudo almost periodic processes in p-th mean sense using the measure theory. We use the μ-ergodic process to define the spaces of μ-pseudo almost periodic process in the p-th mean sense. We establish many interesting results on the functional space of such processes like completeness and composition theorems. The main objective of this paper is to use those results and some stochastic analysis approaches to study the existence, the uniqueness and the global attractiveness for a μ-pseudo almost periodic mild solution to a class of abstract stochastic evolution equations driven by fractional Brownian motion. We provide an example to illustrate our results.

This paper considers time-domain beamforming in MIMO convolutive systems, using the classical LU-based (Gauss elimination) polynomial matrix decomposition. As the pre- and postfilters are not paraunitary, the output signal-to-noise ratio is degraded compared to QR-based beamforming. We investigate the role of the postfilter on the noise enhancement and propose a simple and efficient solution. We show that a simple normalisation of the postfilter, using row balancing, is sufficient to significantly improve the conditioning of the system and thereby, the performance of the system. With the resulting performance increase, the LU-based polynomial matrix decomposition for MIMO beamforming becomes competitive as compared to its QR-based counterparts, in terms of bit error rate, for medium input SNR.

In this work, we use the measure theory to define and to study the spaces of Stepanov-like $$\mu $$ -pseudo almost ( $$S^{2}$$ - $$\mu $$ -pseudo almost) periodic and automorphic processes in the square mean sense. We establish many interesting results on the functional spaces of such processes like completeness and composition theorems. The main objective of this paper is to establish the existence, uniqueness and stability of square-mean $$\mu $$ -pseudo almost periodic (resp. automorphic) mild solution to a linear and semilinear case of the stochastic evolution equations in case when the functions forcing are both continuous and $$S^{2}$$ - $$\mu $$ -pseudo almost periodic (resp. automorphic) and verify some suitable assumptions. The technique analysis used to achieve the required results are the stochastic analysis theory, the composition theorems and the Banach fixed point theorem. We provide an example to illustrate ours results.

This paper presents a MIMO-OFDM " Beamforming " approach in a IEEE 802.11ac context. This technique of " Beamforming " has the same performance as the conventional technique while allowing to perform the precoding and postcoding at one time and whatever the number of OFDM subcarriers., Dans ce papier nous présentons une nouvelle approche de " Beamforming " en MIMO OFDM dans un contexte IEEE 802.11ac. La nouvelle technique de " Beamforming " présente les mêmes performances que la technique conventionnelle tout en permettant de réaliser le pré-codage et le post-codage en une seule fois et ce quelque soit le nombre de sous-porteuses OFDM.

The design of a six-aperture, 10-dB directional coupler using substrate integrated waveguide is presented. Size constraints precluded addition of holes in series, however, in parallel the addition enhanced performance without increasing size. Here, 10-dB coupling with ±2-dB coupling ripple and reflection coefficient exceeded that of 15 dB over 34% of bandwidth. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:23–27, 2014

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.

A 15-dB directional coupler is designed and fabricated using the substrate-integrated waveguide (SIW) technique and Bethe's holes method (BHM).The proposed design is a perfect candidate for design of highly integrated microwave and millimeter-wave circuits. Three holes with optimized radius are positioned on the conducting wall to achieve the desired coupling operating at X-band. A good agreement between experimental and simulation results is obtained. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:970–973, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26678

This paper deals with the dynamics of a cyclic system, representative of a bladed-disk subjected to dry friction forces, and exhibiting structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure, and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response, and suggests that further statistical investigations could be of great interest for the design of bladed disks, in terms of vibration mitigation and robustness.

This paper proposes an original approach to the reduced-order modelling of integrally bladed disks. It is proposed to build a reduction basis which is independent from the rotational speed, from only one modal, cyclic-symmetry calculation performed at rest, and a few static computations. Based on previous works, a polynomial expansion is used which leads to a parametric approximation of the stiffness matrix for the entire operating range. Furthermore, the Kirsch Combined Approximation (KCA) method is used for building the final reduction basis. This method is based on successive approximations of the negative binomial expansion applied to the reanalysis eigenproblem. After giving a general overview of the main theoretical aspects, the paper focuses on the reanalysis problem based on the combined approximations method. Finally, the application of the extended reduction method to the case of a real bladed disk is presented. It is shown that the use of combined approximations provides a very accurate estimation of a Campbell diagram, and allows substantial computational time savings.

International audience; This paper deals with the dynamical analysis and uncertainty quantification of a mistuned industrial rotating integrally bladed disk, for which the operating regime under consideration takes into account the nonlinear geometrical effects induced by large displacements and deformations. First, a dedicated mean nonlinear reduced-order model of the tuned structure is explicitly constructed using the finite element method. The random nature of the mistuning is then modeled by using the nonparametric probabilistic approach extended to the nonlinear geometric context. Secondly, a detailed dynamic analysis and uncertainty propagation are conducted in order to quantify the impact of the nonlinear geometrical effects on the mistuned structure. The results show that the dynamic amplification in the frequency band is significant outside the frequency band of excitation due to the presence of geometric nonlinearities combined with mistuning effects.

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 letter presents a dual-slot antenna etched on a substrate integrated waveguide. This antenna is designed, fabricated, and measured to operate at X-band. It uses two unequal slots in order to increase the bandwidth. The measured results show a bandwidth of 8.5%, which is twice that of the standard dual-slot antennas. Attractive features including low cost, compact size, and planar form make this antenna easy to integrate within microwave planar circuits.

International audience; The recent improvements in turbomachinery design requires the analysis of exceptional operating regime of bladed disks corresponding to geometrical nonlinear effects induced by the large displacements/deformations. In addition, the random nature of the mistuning has also to be modeled. First, a mean nonlinear reduced-order model of the tuned bladed disk is explicitly constructed in the context of the finite element method. The investigation is then devoted to the modeling of the mistuning through the nonparametric probabilistic approach extended to the nonlinear geometric context. The stochastic nonlinear equations are solved in the time domain using the Monte Carlo numerical simulation coupled with advanced arc-length methods adapted to high nonlinear response levels. Finally, the methodology is applied through a numerical example of a bladed disk and a nonlinear analysis is performed in both time and frequency domain.

International audience; Integrally bladed rotors dynamic properties are known to be particularly sensitive to small geometric discrepancies due to the machining process or in-service wear. In this context, it is straightforward that setting up accurate numerical models which take into account real mistuning patterns is a key issue in the prediction of forced response amplitudes under operating conditions. The present study focuses on an experimental bladed disk. Due to strong inter-blade coupling, the geometric mistuning is supposed to result in severe mode localization for the studied bladed disk, thus emphasizing the need of a realistic, predictive finite-element model. This paper describes the procedure which leads to the development and validation of a high-fidelity FE model for a realistic bladed disk, based on coordinate measurements by means of fringe projection. After giving an overview of the coordinate measurement and model building for the studied bladed disk, the comparison of cantilevered-blade and full disk calculated eigenfrequencies to individual blade and full disk in quasi-vacuum measurements are presented.

In the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technological methods to introduce detuning are based on modifying either the blade material properties, either the interface between blades and disk, or the blade shapes. This paper presents a robustness analysis of mistuning for a given detuning in blade geometry. Detuning is performed by modifying blade shapes. The different types of blades, obtained by those modifications, are then distributed on the disk circumference. A new reduced-order model of the detuned disk is introduced. It is based on the use of the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally, the robustness of the computational model responses with respect to uncertainties, is performed with a stochastic analysis using a nonparametric probabilistic approach of uncertainties which allows both the system-parameter uncertainties and the modeling errors to be taken into account.

International audience; The present study focuses on a sensitivity analysis of uncertain parameters for a mistuned bladed disk. After providing a general overview of the main theoretical aspects, this paper describes the way of computing the forced response with aeromechanical coupling. The bladed disk considered here is a representative naturally mistuned bladed disk whose geometry has been obtained by scan. A global sensitivity analysis is then performed using the Morris algorithm in order to rank a set of conservative and dissipative uncertain parameters in terms of their influence on the forced response level. Since a large number of response computations are needed for the sensitivity analysis, a reduced-order model that encompasses geometric mistuning is used.

International audience; A new reduction method for vibration analysis of intentionally mistuned bladed disks is presented. The method is built for solving the dynamic problem of cyclic structures with geometric modifications. It is based on the use of the cyclic modes of the different sectors, which can be obtained from a usual cyclic symmetry modal analysis. Hence the projection basis is constituted; as well as, on the whole bladed disk, each sector matrix is reduced by its own modes. The method is validated numerically on a real bladed disk model, by comparing free and forced responses of a full model finite element analysis to those of a reduced-order model using the new reduction method.