11 Random Vibrations of Large Finite Element Systems

Scalable uncertainty and reliability analysis by integration of advanced Monte Carlo simulation and generic finite element solvers

“…(6) -and the boundary conditions, are affected by uncertainties, then the concepts introduced in Section 2.2 may be used to rationally represent these uncertainties. In this case, the numerical schemes for the analysis of the uncertainty associated with the quantities of interest of the structural analysis, are termed as Stochastic Finite Element methods (SFEM) [17][18][19]2].…”

“…for instance [1]). While a large portion of the associated efforts have focussed on shedding light on the fundamental and theoretical aspects and on the application of the uncertainty analysis methods to strongly simplified, reduced-order models of structures, significant progress has also been made recently in the rational treatment of uncertainties in large FE models of complex structures [2].…”

On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach

“…However, quantifying those statistics is often far from trivial or even impossible since that information is not always known. Therefore a distinction can be made between parametric [36] and nonparametric approaches such as the random matrix theory [37,38], in which the latter does not introduce the uncertainties during the construction of the mathematical-mechanical model but directly into the matrix coefficients. In non-probabilistic approaches, on the other hand, the properties are assumed to adopt a value within a conservative interval of possible values and no assumption is made regarding the probability distribution within this interval.…”

Imprecise probabilities in engineering analyses

“…In order to derive predictions regarding structural behavior and reliability, it is crucial to represent the uncertainty and imprecision appropriately according to the underlying empirical information which is available. To capture variation of structural parameters, established probabilistic models and powerful simulation techniques are available for engineers, which are widely applicable to real-world problems; for example, see [1,2,3]. The required probabilistic modeling can be realized via classical mathematical statistics if sucient data of a suitable quality are available.…”