Efficient reliability analysis using prediction-oriented active sparse polynomial chaos expansion

In this paper, a prediction-oriented active sparse polynomial chaos expansion (PAS-PCE) is proposed for reliability analysis. Instead of leveraging on additional techniques to reduce the problem dimensionality and/or to obtain the local error estimates, which has been done in the majority of existing PCE-based methods, this study first makes use of the Bregman-iterative greedy coordinate descent in effectively solving the least absolute shrinkage and selection operator based regression for sparse PCE approximation with a small set of initial samples. Then, the local variance distribution of the performance function is predicted using the approximated PCE. By maximizing an optimality measure that balances the exploration of design space and exploitation of the PCE characteristics, a recently proposed learning function is subsequently adopted for selecting the optimal samples one by one from a candidate pool to cover the limit state surface regions proportionally to the predicted local variance. The performance of the proposed PAS-PCE is assessed on four numerical examples of varying complexity and input dimensionality through comparison with several state-of-the-art active learning methods based on a variety of surrogate models. Results show that the proposed method is superior to the benchmark algorithms in terms of both accuracy and efficiency for reliability analysis.