Sylvain Lacaze

Fidelity maps for model update under uncertainty: Application to a piano soundboard

This paper presents a new approach for model updating based on fidelity maps. Fidelity maps are used to explicitly define regions of the random variable space within which the discrepancy between computational and experimental data is below a threshold value. It is shown that fidelity maps, built as a function of parameters to estimate and aleatory uncertainties, can be used to calculate the likelihood for maximum likelihood estimates or Bayesian update. The fidelity map approach has the advantage of handling numerous correlated responses at a moderate computational cost. This is made possible by the use of an adaptive sampling scheme to build accurate boundaries of the fidelity maps. Although the proposed technique is general, it is specialized to the case of model update for modal properties (natural frequencies and mode shapes). A simple plate and a piano soundboard finite element model with uncertainties on the boundary conditions are used to demonstrate the methodology.

Methods for high-dimensional and computationally intensive models

Complex simulation codes such as the ones used in aerospace industry are often computationally expensive and involve a large number of variables. These features significantly hamper the estimation of rare event probabilities. To reduce the computational burden, an analysis of the most important variables of the problem can be performed before applying rare event estimation methods. Another way to reduce this burden is to build a surrogate model of the computationally costly simulation code and to perform the probability estimation on this metamodel. In this chapter, we first review the main techniques used in sensitivity analysis and then describe several surrogate models that are efficient in the probability estimation context.

A generalized "max-min" sample for reliability assessment with dependent variables

This paper introduces a novel approach for reliability assessment with dependent variables. In this work, the boundary of the failure domain, for a computational problem with expensive function evaluations, is approximated using a Support Vector Machine and an adaptive sampling scheme. The approximation is sequentially refined using a new adaptive sampling scheme referred to as generalized “max-min”. This technique efficiently targets high probability density regions of the random space. This is achieved by modifying an adaptive sampling scheme originally tailored for deterministic spaces (Explicit Space Design Decomposition). In particular, the approach can handle any joint probability density function, even if the variables are dependent. In the latter case, the joint distribution might be obtained from copula. In addition, uncertainty on the probability of failure estimate are estimated using bootstrapping. A bootstrapped coefficient of variation of the probability of failure is used as an estimate of the true error to determine convergence. The proposed method is then applied to analytical examples and a beam bending reliability assessment using copulas.Copyright