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With electromobility, vehicles are becoming quieter due to the presence of electric motors that replace internal combustion engines. The interior cabin noise of electric vehicles is characterized by high-frequency components that can be annoying and unpleasant. Therefore, it is essential to analyse the NVH behaviour of e-powertrains early in the design-phase. However, this induces inherent uncertainties during the design process related to the operating conditions, geometrical parameters, measurement techniques, etc. that need to be quantified with fast and comprehensive stochastic models.In this work, we first present a deterministic framework to provide first-order estimations of the e-powertrain’s interior whining noises, combining both the airborne & structure-borne contribution with data-driven NVH transfers meta-models. Subsequently, stochasticity is induced in the deterministic models considering random sampling of operating conditions and the chosen geometrical parameters for the e-machine under assessment. At each stage, metamodels (or surrogates), developed in the Bayesian framework, take into account the uncertainties which are propagated from operating conditions to whining noise contribution inside the cabin. The work is demonstrated on an interior permanent magnet synchronous motor which is widely used in electric vehicles traction drives.

This work seeks an effective data reduction method for matrices of Frequency Response Functions (FRF) in a way that preserves, as much as possible, the physical interpretation of FRFs in the full targeted frequency range. Also, this reduction method is wished able to cope with the different sources of uncertainties linked to the definition of the mechanical system whose FRFs are processed. It is shown that a Bayesian formulation of Independent Component Analysis (ICA) serves this purpose. It is used here to decompose a FRF matrix as a sum of frequency independent matrices multiplied by a frequency dependent scalar component. On the one hand, the independence property of this processing allows the scalar component to be concentrated in a narrow frequency range, on the other hand the chosen Bayesian approach presents itself as the most natural way to take into account uncertainties in the input FRFs whether they are due to measurement errors or structural uncertainties. Moreover, the probabilistic framework is shown to provide credible intervals on the estimation of the decomposition factors, thus allowing some considerations on the reliability of the processing and the development of a straightforward thresholding method to enhance the data reduction. A first application on measured automotive vibro-acoustic transfer functions shows the reduction performance of the approach and its interest when trying to analyse the measurements. A second application on non-parametric random FRFs computed through a stochastic finite element model illustrates the capacity of the proposed approach to take into account the uncertainty of the FRFs data and to propagate it to the factors of the decomposition.

Online event via MS Teams, ISSN: 0148-7191, e-ISSN: 2688-3627; International audience

Current approaches in the automotive domain to predict booming noise essentially target extreme loading conditions. This is useful when mechanical strength is of concern, but not representative of the actual vehicle usage. Usage is however important when addressing acoustic annoyance. One issue in this respect is the lack of databases representative of the diversity of client usages and, therefore, of the excitation forces applied to the vehicle in real usage conditions. This paper introduces a possible answer to this problem. First, it proposes a measurement protocol to estimate the excitation forces in real usage responsible of booming noise. Second, it provides an array of algorithms to analyze the large amount of data collected during the measurement step. In particular, an ad hoc Independent Component Analysis algorithm is introduced to extract excitation components specific to well-defined operating condition regions, thus providing insights in the excitation behaviour, as well as data reduction. Next, the excitation components are modelled as a function of the vehicle operating conditions with a Radial Basis Function network. A meta-model of the excitations in real usage conditions is thus obtained, composed of two levels: the analysis level and the modelling level. The proposed methodology is developed in the Bayesian framework. In addition to its advantages linked to the trivial introduction of prior knowledge, the Bayesian framework is found particularly useful for propagating uncertainties throughout the successive steps of the approach.

International audience

International audience; Improvement of vibroacoustic models prediction capabilities requires an adapted indicator to compare experimental measurements with the results of the computational model. When dealing with highly uncertain objects such as series production cars, a probabilistic approach is mandatory to be able to describe the dispersion of experimental results. Moreover, a probabilistic non-parametric model also account for modeling uncertainties and simplifications that are part of any engineering process. The proposed approach deals with Frequency Response Functions since FRFs are the common way to handle vibroacoustic models. When considering multiple input and outputpoints configuration, FRFs are frequency dependent complex matrices. Since the probabilistic modeling is available in current vibroacoustic software, collections of random realizations of the FRF matrix can be computed from the existing FE model. The model’s likelihood naturally appears as the probability of a measured quantity to be part of its model. It is a single number that can advantageously be used as an indicator of the model‘s relevance regarding measurements. A novel complex FRF matrix statistical reduction is proposed, allowing the model’s likelihood computation. This reduction relies on the separation of statistically independent components such that the probability of the whole is the product of the probability of the components. The reduction is performed by a two stage Independent Component Analysis, first along the frequencies and second on frequency independent complex matrices. For each of the components, the joint probability density function of the complex coefficient is constructed from the various realization of the considered FRF matrix. The projection of any experimental or computed matrix on the components basis provides the complex coefficients which probabilities are known. The product of the componentprobabilities is the model’s likelihood. The proposed approach is applied to a mid-size vehicle body.

National audience; Dans un contexte probabiliste, l’amélioration des capacités de prédiction des modèles vibroacoustiques nécessite un indicateur adapté pour comparer les mesures avec les prédictions. La comparaison est faite en utilisant la vraisemblance, dès qu’elle peut être estimée pour un résultat donné. L’analyse repose principalement sur des fonctions de réponse en fréquence complexes à valeurs matricielles qui peuvent être mesurées et calculées. Une réduction statistique est proposée. Cette réduction statistique présente en plus de la réduction des données, une analyse du comportement physique du système étudié.

International audience; Improvement of vibroacoustic models prediction capabilities in a probabilistic context requires a adapted metric to compare experimental results with stochasitic computations. The likelihood appears as the natural tool to compare experiments with probabilistic computations as soon as the probability of a given result may be computed. Since vibroacoustic analysis mainly rely on complex Frequency Response Functions ([FRF] = {ω → [FRF(ω)]}) matrices that can be easily measured and computed, the likelihood of such complex and frequency dependent matrices is investigated. A two stage statistical reduction, based on Indepen-dant Components Analysis, is proposed in order to separate statisticaly independent components with complex amplitudes which probability may be computed independently one from each others. Bi-dimensional probability density fonctions of the complex components amplitudes are deduced from a Monte-Carlo simulation of a non-parametric stochastic model, using MSC/NASTRAN. The proposed statistical reduction presents many interesting properties regarding the physical understanding of FRF matrices as well as a numerical aspects.

International audience; This work deals with an extension of the reduced order models (ROMs) that are classically constructed by modal analysis in linear structural dynamics of complex structures for which the computational models are assumed to be uncertain. Such an extension is based on a multilevel projection strategy consisting in introducing three reduced-order bases (ROBs) that are obtained by using a spatial filtering methodology of local displacements. This filtering involves global shape functions for the kinetic energy. The proposed multilevel stochastic ROM is constructed by using the nonparametric prob-abilistic approach of uncertainties. It allows for affecting a specific level of uncertainties to each type of displacements associated with the corresponding vibration regime, knowing that the local elastic modes are more sensitive to uncertainties than the global elastic modes. The proposed methodology is applied to the computational model of an automobile structure, for which the multilevel stochastic ROM is identified with respect to experimental measurements. This identification is performed by solving a statistical inverse problem.

International audience; The fuzzy structure theory was introduced 20 years ago in order to model the effects of complex subsystems imprecisely known on a master structure. This theory was only aimed at structural dynamics. In this paper, an extension of that theory is proposed in developing an elastoacoustic element useful to model sound-insulation layers for computational vibroacoustics of complex systems. The simplified model constructed enhances computation time and memory allocation because the number of physical and generalized degrees of freedom in the computational vibroacoustic model is not increased. However, these simplifications introduce model uncertainties. In order to take into account these uncertainties, the nonparametric probabilistic approach recently introduced is used. A robust simplified model for sound-insulation layers is then obtained. This model is controlled by a small number of physical and dispersion parameters. First, the extension of the fuzzy structure theory to elastoacoustic element is presented. Second, the computational vibroacoustic model including such an elastoacoustic element to model sound-insulation layer is given. Then, a design methodology to identify the model parameters with experiments is proposed and is experimentally validated. Finally, the theory is applied to an uncertain vibroacoustic system.

International audience; This paper is devoted to the construction of a stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics. The considered structure is characterized by the fact that it exhibits, in the low frequency range, not only the classical global elastic modes but also numerous local elastic modes which cannot easily be separated from the global elastic modes. A new adapted generalized eigenvalue problem is introduced and allows a global vector basis to be constructed for the global displacements space. This method requires to decompose the domain of the structure into sub-domains. Such a decomposition is carried out using the Fast Marching Method. This global vector basis is then used to construct the reduced-order computational model. Since there are model uncertainties induced by modeling errors in the computational model, the nonparametric probabilistic approach of uncertainties is used and implemented in the reduced-order computational model. The methodology is applied to an automotive vehicle.

Open Access Journal; International audience; A reduced-order model is constructed to predict, for the low-frequency range, the dynamical responses in the stiff parts of an automobile constituted of stiff and flexible parts. The vehicle has then many elastic modes in this range due to the presence of many flexible parts and equipments. A non-usual reduced-order model is introduced. The family of the elastic modes is not used and is replaced by an adapted vector basis of the admissible space of global displacements. Such a construction requires a decomposition of the domain of the structure in subdomains in order to control the spatial wave length of the global displacements. The Fast Marching Method is used to carry out the subdomain decomposition. A probabilistic model of uncertainties is introduced. The parameters controlling the level of uncertainties are estimated solving a statistical inverse problem. The methodology is validated with a large computational model of an automobile.

International audience; In a recent work [Journal of Sound and Vibration 323 (2009) 849-863] the authors presented an energy-density field approach for the vibroacoustic analysis of complex structures in the low and medium frequency ranges. In this approach, a local vibroacoustic energy model as well as a simplification of this model were constructed. In this paper, firstly an extension of the previous theory is performed in order to include the case of general input forces and secondly, a structural partitioning methodology is presented along with a set of tools used for the construction of a partitioning. Finally, an application is presented for an automotive vehicle.

International audience; In a previous article, a simplified low- and medium-frequency model for uncertain automotive sound-insulation layers was developed and experimentally identified and validated. This model is based on a stochastic elastoacoustic element whose mean part comes from an extension of the fuzzy structures theory and depends on three physical parameters: the modal density, the damping rate and the participating mass. A non-parametric probabilistic approach is used to build the uncertainty-accounting stochastic simplified model. This model takes into account the modelling and system-parameters uncertainties and depends on three dispersion parameters. In this paper, the insulation simplified model is implemented in an industrial stochastic vibroacoustic model of a car. An experimental database of tests on vehicles has been carried out and is compared with the predictions. The analysis of these results shows the relevance of the proposed methodology for complex vibroacoustics industrial computational models.

International audience; In this paper, an energy-density field approach applied to the vibroacoustic analysis of complex industrial structures in the low- and medium-frequency ranges is presented. This approach uses a statistical computational model. The analyzed system consists of an automotive vehicle structure coupled with its internal acoustic cavity. The objective of this paper is to make use of the statistical properties of the frequency response functions of the vibroacoustic system observed from previous experimental and numerical work. The frequency response functions are expressed in terms of a dimensionless matrix which is estimated using the proposed energy approach. Using this dimensionless matrix, a simplified vibroacoustic model is proposed. (C) 2009 Elsevier Ltd. All rights reserved.

International audience; A new energy-density field approach is proposed for low- and medium-frequency vibroacoustic analysis of complex industrial structures, using a probabilistic computational model. The observed structure is composed of a trimmed body coupled and its internal cavity. The objective of this paper is to take advantage of some statistical properties of the frequency response functions to build a simplified vibroacoustic model. In this approach, the Frequency Response Functions (FRF) of the vibroacoustic system are expressed as the product of a dimensionless "smooth" matrix and local mobilities or impedances, depending on their type (acoustical, vibratory or vibroacoustic). The stochastic computational model of the vibroacoustic system is obtained from the reduced mean computational model and is using a nonparametric probabilistic approach.

International audience; We present a methodology to perform the identification and validation of complex uncertain dynamical systems using experimental data, for which uncertainties are taken into account by using the nonparametric probabilistic approach. Such a probabilistic model of uncertainties allows both model uncertainties and parameter uncertainties to be addressed by using only a small number of unknown identification parameters. Consequently, the optimization problem which has to be solved in order to identify the unknown identification parameters from experiments is feasible. Two formulations are proposed. The first one is the mean-square method for which a usual differentiable objective function and an unusual non-differentiable objective function are proposed. The second one is the maximum likelihood method coupling with a statistical reduction which leads us to a considerable improvement of the method. Three applications with experimental validations are presented in the area of structural vibrations and vibroacoustics.

International audience; The design of cars is mainly based on the use of computational models to analyze structural vibrations and internal acoustic levels. Considering the very high complexity of such structural-acoustic systems, and in order to improve the robustness of such computational structural-acoustic models, both model uncertainties and data uncertainties must be taken into account. In this context, a probabilistic approach of uncertainties is implemented in an adapted computational structural-acoustic model. The two main problems are the experimental identification of the parameters controlling the uncertainty levels and the experimental validation. Relevant experiments have especially been developed for this research in order to constitute an experimental database devoted to structural vibrations and internal acoustic pressures. This database is used to perform the experimental identification of the probability model parameters and to validate the stochastic computational model. (C) 2008 Acoustical Society of America.

Structural damping is known as one of the most efficient design variable in order to reduce structure‐borne noise. At low and medium frequencies (100‐500 Hz), the vibro‐acoustic behavior of the car is essentially governed by large panels as windshield, roof or front panel for example. In order to improve the car body design regarding cost, weight, performances and reliability, one must have a good understanding of the damping performances of these large panels submitted to various operating conditions. In a previous paper, the authors have proposed an improved method for structural damping numerical assessment of structural elements with non uniform damping using a stochastic distribution of input forces. In the present paper, this method is applied to quantify the structural damping of a multi‐layered windshield at low and medium frequencies. Effects of the geometry, of the viscoelastic properties of the PVB layer and of the windshield glue bead on the total damping properties will be studied.

In the mid‐frequency range (200‐2000 Hz), difficulty is encountered when modeling car body vibroacoustic interactions, mainly due to the complexity of automotive design. Analytical Statistical Energy Analysis (ASEA) is efficient to bring to the fore regions of interest regarding NVH design but was proven to be accurate only above 2000 Hz. To overcome ASEA limitations at lower frequencies, Virtual SEA (VSEA) technique was introduced to translate the dynamic information contained in a finite element (FE) model into an SEA model. Any FE model, whatever its complexity, can thus be processed thanks to an automatic sub‐structuring algorithm and a built‐in VSEA modal synthesis solver, fast leading to robust numerical SEA model. VSEA also addresses structure‐borne noise problems by coupling structural VSEA subsystems to analytical acoustic subsystems through a virtual wave number. Investigation of damping and trim treatment effects on mixed acoustic and structural subsystems are thus possible. While reviewing VSE...

The REBECA research project aims at defining new architectural concepts and reduction strategies of vehicle external noise emission regarding the international pass‐by noise certification standard (ISO 362). The first task of the project is to qualify and quantify the major contributor of the external emission, the tires/road surface source. To this end, a 3D array composed of 164 microphones has been set up in the near and far field around vehicle. Measurements have been performed for several operational conditions with the use of a chassis dyno in a semi‐anechoic chamber. A review and a comparison of some source identification methods has been led including experimental FRFs based on inverse techniques (Nelson), conventional and optimized beamforming approaches (Elias, Dougherty, Brooks and Humphreys, Ravetta) and inverse BEM method (Hamdi, Omrani). This study permits to identify the more appropriate microphone array technique with respect to source identification robustness, power level and directivity radiation reconstruction in the far field.

Virtual SEA is a modeling process using FE computations to build an SEA model including equivalent masses, modal densities, and CLF, but excluding DLF since damping modeling in the mid‐high frequency range is still an open issue. This technique, previously proposed by some of the authors, is applied to a production vehicle in the range 200‐1000 Hz. The actual vehicle is simultaneously measured at a subset of the FE nodes. The automated sub‐structuring provided by Virtual SEA (20 subsystems at 630Hz) is used to favorably position 64 sensors on the body. Next, an experimental SEA procedure is performed: a full transfer matrix is measured between more than 1000 excitation (hammer) locations and the sensors. In order to compensate for structural heterogeneity, input mobilities are measured at every point and used to normalize the transfer matrix As all measurement points are associated to FE nodes, computed input mobilities can be compared to measurements. Finally, the SEA model identification is carried out for both experimental and virtual SEA. As far as damping (DLF) can only be known experimentally, comparisons of the numerical and experimental approach only concern the orher SEA parameters (CLFs, modal densities ...) and transfer functions.

Due to a new pass‐by noise regulation, Vehicle exterior noise will have to be reduced in the coming years. This may be achieved by optimizing underbody and underhood absorption and screening apertures. There is then a need for numerical techniques able to predict sound reduction related to acoustic absorption and transmission loss changes. Through a work supported by ADEME and headed by PSA, energy‐based predictive techniques such as Analytical Statistical Energy Analysis (ASEA) and discretized Energy Flow Analysis (DEFA) were tested against the actual physical problem to be solved through a series of benchmarks. Both theories are compared across several simple acoustic problems. It is concluded that both methods do not fit to the initial acoustic optimization requirement due to their intrinsic assumptions that restrict their applicative range. More fitted numerical techniques are now investigated: among new candidates, the Virtual SEA (VSEA) technique that allows the creation of a numerical model of coupled acoustic cavities from the finite element global modes without the serious limitations of ASEA and a matrix approach based on Craigh‐Bampton substructuration of the cavities.

International audience; In order to improve the robustness of vibroacoustic numerical predictions, one introduces a model of random uncertainties. The random uncertainty modelling relies on a nonparametric approach providing random system realizations with a maximum entropy. This approach only requires a few uncertainty parameters but takes into account data errors as well as model errors. It appears to be well adapted to study the variability of structural-acoustic systems; the implementation of the method for this class of problem is presented here for the first time. Practically, the paper deals with a classical low frequency vibroacoustic modelling such as used for booming noise predictions. The application of the nonparametric approach to vehicle uncertainties modelling shows the sensitivity of the vibroacoustic frequency responses to structural and cavity uncertainties as well as coupling interface uncertainties. Flexible parts appear to be more sensitive to random uncertainties than stiff parts. The sensitivity of the structural modes to structural random uncertainties is also shown in a stochastic MAC table.

Semi-Plenary Lecture; International audience; The paper deals with the robustness of uncertain computational elastoacoustic models in low- and medium-frequency ranges. The elastoacoustic system is made up of a heterogeneous viscoelastic structure coupled with an internal acoustic cavity filled with a dissipative acoustic fluid. A reduced mean elastoacoustic model is deduced from the mean finite element model by using the modal approach with the structural modes of the structure and the acoustic modes of the acoustic cavity. Data uncertainties and model uncertainties are taken into account by using a nonparametric probabilistic approach for the structure, for the acoustic cavity and for the vibroacoustic coupling interface. The main objectives of this paper are (1) to present experimental validation of the nonparametric probabilistic approach of model uncertainties and to propose methods to perform the experimental identification of the probabilistic model parameters, (2) to analyze the robustness of computational elastoacoustic models with respect to model and data uncertainties, (3) to study uncertainty propagation through complex elastoacoustic systems. Two experimental configurations are analyzed with the stochastic computational elastoacoustic model. The first experimental configuration is made up of a composite sandwich panel coupled with an acoustic cavity constituted of a simple rigid box. Experimental measurements have been performed for 8 manufactured composite panels. The second experimental configuration is a car made up of a complex heterogeneous structure coupled with a complex acoustic cavity. Experimental measurements have been performed for 22 manufactured cars of the same type with optional extra.

International audience; This paper deals with the construction of a multilevel stochastic reduced-order model (ROM) devoted to the robust dynamical analysis of complex structures in a broad frequency band. In particular, we are interested in complex structures characterized by the presence of several structural scales (such as a stiff main body supporting flexible parts). In such a case, in addition to the usual global elastic modes (long-wavelengthmodes), numerous local elastic modes (associated with the flexible parts) appear. These local elastic modes, which are numerous in the low-frequency band already, exhibit high-frequency behavior, namely high modal density, small wavelength, and high sensitivity to uncertainty. In such a context, the low- , medium-, and highfrequency (LF, MF, HF) vibration regimes overlap. The objectives are to adapt the modeling of uncertainty to each vibration regime and, also, to deal with the unusually high dimension of the classic ROMs, which is due to the numerous local elastic modes. Thanks to a spatial filtering method of local displacements (that is based on the use of global polynomial shape functions for the kinetic energy), three successive filterings allow three families of displacements to be constructed, namely the LF-, MF-, and HF-type displacements. The filtering of the most local displacements allows the final dimension of the proposed ROM to be reduced. The multilevel reduced-order basis that is obtained yields a multilevel ROM. Using the nonparametric probabilistic approach of uncertainties with this ROM allows for obtaining a stochastic ROM for which the levels of uncertainty can be controlled independently for each type of displacements.The methodology is applied to a detailed finite element model of a car for which FRF measurements are available on a broad frequency band. Unlike a classic stochastic ROM constructed with the nonparametric approach, for which the probability law of each random reduced matrix is controlled by a unique dispersion hyperparameter, three hyperparameters are introduced for each random matrix of the multilevel stochasticROM. These stochastic ROMs are identified with respect to the measurements and are compared.