An Alternative Formulation for Design Under Uncertainty

A novel formulation for design under uncertainty is presented, which is based on the computation of the mean value and the minimum of the function. The aim of the method is to exert a stronger control on the system output variability in the optimization loop at a moderate cost. This would reduce post-processing analysis of the PDF of the resulting optimal designs, by converging rapidly to the interesting individuals. In other words, in the set of designs resulting from the optimization, the new approach should be capable of discarding poor-performance design. Also, no a priori assumption of optimal PDF is made. The preliminary results presented in the paper proves the benefit of the new formulation

Investigation of model uncertainties in Bayesian structural model updating

Model updating procedures are applied in order to improve the matching between experimental data and corresponding model output. The updated, i.e. improved, finite element (FE) model can be used for more reliable predictions of the structural performance in the target mechanical environment. The discrepancies between the output of the FE-model and the results of tests are due to the uncertainties that are involved in the modeling process. These uncertainties concern the structural parameters, measurement errors, the incompleteness of the test data and also the FE-model itself. The latter type of uncertainties is often referred to as model uncertainties and is caused by simplifications of the real structure that are made in order to reduce the complexity of reality. Several approaches have been proposed for taking model uncertainties into consideration, where the focus of this manuscript will be set on the updating procedure within the Bayesian statistical framework. A numerical example involving different degrees of nonlinearity will be used for demonstrating how this type of uncertainty is considered within the Bayesian updating procedure

Modeling of the variability of fatigue crack growth using cohesive zone elements

► Cohesive zone elements allow to model fatigue crack initiation and growth. ► An algorithm reducing extensively the simulation time with little loss of accuracy was developed. ► The variability inherent in the fatigue life was assessed using a random field model. ► Both crack initiation and propagation are described by the same model

Data and model uncertainties in complex aerospace engineering systems

ABSTRACT: The dynamical analysis of complex mechanical systems is in general very sensitive to random uncertainties. In order to treat the latter in a rational way and to increase the robustness of the dynamical predictions, the random uncertainties can be represented by probabilistic models. The structural complexity of the dynamical systems arising in these fields results in large finite element models with significant random uncertainties. Parametric probabilistic models capture the uncertainty in the parameters of the numerical model of the structure, which are often directly related to physical parameters in the actual structure, e.g. Young’s modulus. Model uncertainties would have to be modeled separately. On the other hand, the proposed nonparametric model of random uncertainties represents a global probabilistic approach which, in addition, takes directly into account model uncertainty, such as that related to the choice of a particular type of finite element. The uncertain parameters of the structure are not modeled directly by random variables (r.v.’s); instead, the probability model is directly introduced from the generalized matrices of a mean reduced matrix model of the structure by using the maximum entropy principle (Soize 2001). In this formulation the global scatter of each random matrix is controlled by one real positive scalar called dispersion parameter