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26
“Uncertainty-noise” Le Mans
Acoustique
&
Techniques n° 40
n the last years, numerical simulations have been more
and more intensively used in industrial design processes to
assess the vibro-acoustic behavior of various components. The
problem of constructing an appropriate numerical model from
a real physical configuration is however complex and directly
involves several sources of uncertainties. In this context, non-
deterministic methods can be defined as any methods aimed
at qualifying or quantifying the uncertainty on response or
performance indicators supported by a specific problem.
The uncertainty sources can be classified in the three following
categories [1,2] :
- First, the lack of knowledge in the physical process or the
complexity of this process forces the designer to define
a set of modeling assumptions during the construction of
the mathematical model. Modeling errors result from these
assumptions. Practice and intuition of the designer as well
as sophistication of the model generally tend to reduce the
modeling error.
- The second source of uncertainty is linked to the numerical
errors involved by the computational implementation of the
mathematical model. The numerical methods (interpolation,
integration, equation solving, etc.) are generally selected on
the base of their convergence properties (which should lead
to a reduction of the numerical error as soon as the size of
the numerical model is increased). This refinement however
results in higher computational requirements. Depending on
the numerical method, some procedures are available to
estimate this numerical error. It can thus be said that, basically,
this second source of uncertainty is linked to the efficiency of
the available computing tools.
- The third source that involves uncertainty is related to
the totally unknown or intrinsically variable parameters of
the mathematical model as well as to their experimental
identification. The resort to laboratory or experimental
procedures suggests that the exact knowledge of the
parameters is not possible. In fact, these procedures always
need an answer to representativeness issues, reproducibility
features and measurement errors. In some circumstances
(especially in the early design phase), only rough descriptions
(in terms of intervals or linguistic values (‘low’, ‘high’)) of
material and/or geometrical parameters are available. A
finer classification of model parameter uncertainties is often
made: uncertainty on loads or excitations, uncertainties on
strength properties and uncertainties on material, mechanical
and geometrical properties of the model.
This convenient description should not be taken as sufficient
as these three uncertainty sources are not independent. It is,
for instance, difficult to reduce the first uncertainty source
without increasing the last one, as a complex model very
often relies on an important number of parameters. A good
example is provided by porous materials [3] : the most simple
model relies on a concept of equivalent fluid (assuming a
rigid skeleton) while more sophisticated models are relying
Sources of uncertainties in vibro-acoustic
simulations
Jean-Pierre Coyette
Benoît Van Den Nieuwenhof
Free Field Technologies S.A.
Place de l’Université, 16
1348 Louvain-la-Neuve
BELGIUM
The paper addresses the main sources of uncertainties in vibro-acoustic simulations. Such
simulations involve the selection of a particular continuous model already characterized by some
simplifications of the real physical behavior. Material data, geometrical parameters and boundary
conditions (as, for example, excitations) are additional sources of uncertainty. Last but not least,
the discretization process supporting the numerical model introduces additional errors related to
computational algorithms (interpolation, integration, equation solving). The paper reviews these
uncertainties for numerical methods (FEM, SEA) traditionally used for vibro-acoustic simulations.
Some trends for securing vibro-acoustic simulations in such a context are also presented.
Cet article présente les sources principales d’incertitudes dans les simulations vibro-acoustiques.
De telles simulations impliquent la sélection d’un modèle continu particulier déjà caractérisé
par quelques simplifications du comportement physique réel. Les données matérielles, les
paramètres géométriques et les conditions aux limites (comme, par exemple, des excitations)
sont des sources supplémentaires d’incertitudes. Dernière et non des moindres, la méthode de
discrétisation qui sous-tend le modèle numérique introduit des erreurs supplémentaires relatives
aux algorithmes informatiques (interpolation, intégration, résolution d’équations).
L’article passe en revue ces incertitudes pour des modèles numériques (FEM, SEA)
traditionnellement utilisés pour des simulations en vibro-acoustique. Quelques orientations pour
sécuriser les simulations vibro-acoustiques dans un tel contexte sont aussi présentées.
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