Laurent Gagliardini

Structural-acoustic modeling of automotive vehicles in presence of uncertainties and experimental identification and validation

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.

Sound-Insulation Layer Modelling in Car Computational Vibroacoustics in the Medium-Frequency Range

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.

Fuzzy structure theory modeling of sound-insulation layers in complex vibroacoustic uncertain systems: Theory and experimental validation

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.

Nonparametric modeling of the variability of vehicle vibroacoustic behavior

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.

Stochastic modeling of the vibro‐acoustic behavior of production cars

Production cars ‐as any industrial product‐ are subject to various causes of variability including process uncertainties or product diversity. Many authors have shown that vibroacoustic problems sensitivity to small uncertainties increases dramatically with frequency until only statistical approaches remain relevant in the high frequency range. Moreover, modeling uncertainties due to numerous model simplifications induce similar dispersion effects on the computed responses. Both kind of uncertainties may be addressed when using a non‐parametric stochastic modeling, based on the random matrices theory. Such a modeling, appears to be very practicable for industrial vibroacoustic problems while relying on a strong mathematical background. In a first part, the application of the non‐parametric modeling of uncertainties to vibro‐acoustics problems will be addressed. Stochastic aspects are controlled by only 7 dispersion parameters that provide most of the dynamic behaviors that can be observed experimentally. ...

Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

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 equipment. A nonusual 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.

Virtual statistical energy analysis for vibroacoustic industrial prediction

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...

Sound-Insulation Layers Low-Frequency Modeling, Using the Fuzzy Structure Theory

Over the past few years, car manufacturers have improved their numerical models for the prediction of the trimmed body vibroacoustic response. In the lowfrequency band [20,200] Hz, sound-insulation layer modeling remains a critical topic. Recent work allows the connection of the structure and cavity through a transfer matrix computed from a FE model of the soundinsulation layer. Nevertheless, such an approach requires a FE model of sound-insulation layer, which may not be available in early design stages. Moreover, considering the uncertainty of the design itself, in addition to material uncertainty, a deterministic model may not be appropriate. In this paper, a simplified model of sound-insulation layers based on the fuzzy structure theory is proposed. The simplified model is obtained by performing a statistical averaging of the internal dynamical degrees of freedom of the sound-insulation layer and is governed by three parameters: the modal density, the coefficient of participating mass and the damping rate of the sound-insulation layer. In order to improve the prediction, the model errors introduced by the simplifications as well as material properties uncertainty are modeled using a nonparametric probabilistic approach. After the fuzzy model is set up theoretically, it is applied to a simplified case. The way how the fuzzy model’s parameters are related to design parameters will then be discussed. Finally, the application to a full trimmed body is presented.

Structure‐borne modeling of a vehicle in the mid‐frequency range using Virtual SEA: experimental validation

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 ...

Tire radiation in vehicle environment: A review of some source identification methods

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.