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To date, the analysis of high-dimensional, computationally expensiveengineering models remains a difficult challenge in risk and reliabilityengineering. We use a combination of dimensionality reduction and surrogatemodelling termed partial least squares-driven polynomial chaos expansion(PLS-PCE) to render such problems feasible. Standalone surrogate modelstypically perform poorly for reliability analysis. Therefore, in a previouswork, we have used PLS-PCEs to reconstruct the intermediate densities of asequential importance sampling approach to reliability analysis. Here, weextend this approach with an active learning procedure that allows for improvederror control at each importance sampling level. To this end, we formulate anestimate of the combined estimation error for both the subspace identified inthe dimension reduction step and surrogate model constructed therein. Withthis, it is possible to adapt the design of experiments so as to optimallylearn the subspace representation and the surrogate model constructed therein.The approach is gradient-free and thus can be directly applied to blackbox-type models. We demonstrate the performance of this approach with a seriesof low- (2 dimensions) to high- (869 dimensions) dimensional example problemsfeaturing a number of well-known caveats for reliability methods besides highdimensions and expensive computational models: strongly nonlinear limit-statefunctions, multiple relevant failure regions and small probabilities offailure.

Sequential active learning of low-dimensional model representations for reliability analysis