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

Abstract

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.

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

“…In general, the structure of a complex vibroacoustic system is composed of a main part called the master structure that is accessible to conventional modeling including uncertainties modeling, and a secondary part called the fuzzy substructure related to the structural complexity and including for example many equipment units attached to the master structure. In the present paper, we will not consider fuzzy substructures, and concerning fuzzy structure theory, we refer the reader to Chapter 15 of [41] for a synthesis, and to [96] for an extension of the theory to the modeling of an uncertain complex vibroacoustic system with fuzzy interface. At equilibrium, the structure occupies the three-dimensional bounded domain Ω S with a boundary ∂Ω S that is made up of a part Γ E that is the coupling interface between the structure and the external acoustic fluid, a part Γ that is a coupling interface between the structure and the internal acoustic fluid, and finally, a part Γ Z that is another part of the coupling interface between the structure and the internal acoustic fluid with acoustic properties.…”

“…Several works have been published concerning experimental validation of the nonparametric probabilistic approach of both the computational model-parameter uncertainties and the model uncertainties induced by modeling errors (e.g., [96,[106][107][108][109][110][111]). …”

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

“…This prior probability distribution is constructed by using the Maximum Entropy Principle [20] (from Information Theory [21]) for which the constraints are defined by the available information [13,14,22,15]. Since the paper [13], many works have been published in order to validate the nonparametric probabilistic approach of model uncertainties with experimental results (see for instance [23,24,25,26,27,28,15,29]), to extend the applicability of the theory to other areas [30,31,32,33,34,35,36,37,38,39,40,41], to extend the theory to new ensembles of positive-definite random matrices yielding a more flexible description of the dispersion levels [42], to apply the theory for the analysis of complex dynamical systems in the medium-frequency range, including vibroacoustic systems, [43,44,23,45,25,26,27,28,46,47,48,39], to analyze nonlinear dynamical systems (i) for local nonlinear elements [49,50,37,…”

“…(27). It should be noted that the posterior probability density function strongly depends on the choice of the stochastic model of the output additive noise B.…”

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

“…[3] for a synthesis, and to Ref. [8] for the extension of the theory to uncertain complex vibroacoustic system with fuzzy interface modeling. Consequently, the so-called "master structure" will be simply called here as "structure".…”