Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels

Abstract

This paper deals with the experimental identification and the validation of a non-parametric probabilistic approach allowing model uncertainties and data uncertainties to be taken into account in the numerical model developed to predict low-and medium-frequency dynamics of structures. The analysis is performed for a composite sandwich panel representing a complex dynamical system which is sufficiently simple to be completely described and which exhibits, not only data uncertainties, but above all model uncertainties. The dynamical identification is experimentally performed for 8 panels. The experimental frequency response functions are used to identify the non-parametric probabilistic approach of model uncertainties. The prediction of the low-and medium-frequency dynamical responses obtained with the stochastic system is compared with the experimental measurements.

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,…”

“…Many works have been published in this field, such as [79] in micromechanics, [78] for the identification and prediction of stochastic dynamical systems in a polynomial chaos basis, [23] for the experimental identification of the nonparametric stochastic model of uncertainties in structural dynamics [134,24,29], in structural acoustics for the low-and medium-frequency ranges [26,28], in nonlinear structural dynamics [49,50]. The identification of the generalized probabilistic approach of uncertainties can be found in [56] and also below in Sections 5.3 and 6.…”

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

“…In this paper, it is assumed that parameter uncertainties and model uncertainties exist in the computational model. Consequently, we propose to use the nonparametric probabilistic approach of both parameter uncertainties and model uncertainties recently introduced (see [57] to [63]), constructed by using the maximum entropy principle [31,56], and for which experimental validations can be found in [8][9][10]18,19]. The maximum entropy principle was introduced by Shannon [56] in the construction of the information theory.…”

“…Consequently, the measurements of the frequency response functions in the frequency band of analysis are performed for a configuration corresponding to free-free conditions. This structure and the experiments are completely defined in [9], [10].…”

“…(6) The mean computational model is a finite element model with 12, 288 structural dofs (64×64 four-nodes finite elements for laminated plate bending). This mean computational model has been updated with respect to the mass density of each carbon-resine ply and to the Young moduli of each carbon-resin ply in order to update the eigenfrequecies of the first four elastic modes using the experimental values (see [9], [10]). Below, this updated mean computational model will simply be called the mean computational model.…”