2,521 research outputs found
Reliability-based design optimization using kriging surrogates and subset simulation
The aim of the present paper is to develop a strategy for solving
reliability-based design optimization (RBDO) problems that remains applicable
when the performance models are expensive to evaluate. Starting with the
premise that simulation-based approaches are not affordable for such problems,
and that the most-probable-failure-point-based approaches do not permit to
quantify the error on the estimation of the failure probability, an approach
based on both metamodels and advanced simulation techniques is explored. The
kriging metamodeling technique is chosen in order to surrogate the performance
functions because it allows one to genuinely quantify the surrogate error. The
surrogate error onto the limit-state surfaces is propagated to the failure
probabilities estimates in order to provide an empirical error measure. This
error is then sequentially reduced by means of a population-based adaptive
refinement technique until the kriging surrogates are accurate enough for
reliability analysis. This original refinement strategy makes it possible to
add several observations in the design of experiments at the same time.
Reliability and reliability sensitivity analyses are performed by means of the
subset simulation technique for the sake of numerical efficiency. The adaptive
surrogate-based strategy for reliability estimation is finally involved into a
classical gradient-based optimization algorithm in order to solve the RBDO
problem. The kriging surrogates are built in a so-called augmented reliability
space thus making them reusable from one nested RBDO iteration to the other.
The strategy is compared to other approaches available in the literature on
three academic examples in the field of structural mechanics.Comment: 20 pages, 6 figures, 5 tables. Preprint submitted to Springer-Verla
Forest Density Estimation
We study graph estimation and density estimation in high dimensions, using a
family of density estimators based on forest structured undirected graphical
models. For density estimation, we do not assume the true distribution
corresponds to a forest; rather, we form kernel density estimates of the
bivariate and univariate marginals, and apply Kruskal's algorithm to estimate
the optimal forest on held out data. We prove an oracle inequality on the
excess risk of the resulting estimator relative to the risk of the best forest.
For graph estimation, we consider the problem of estimating forests with
restricted tree sizes. We prove that finding a maximum weight spanning forest
with restricted tree size is NP-hard, and develop an approximation algorithm
for this problem. Viewing the tree size as a complexity parameter, we then
select a forest using data splitting, and prove bounds on excess risk and
structure selection consistency of the procedure. Experiments with simulated
data and microarray data indicate that the methods are a practical alternative
to Gaussian graphical models.Comment: Extended version of earlier paper titled "Tree density estimation
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