Efficient reliability analysis based on deep learning-enhanced surrogate modelling and probability density evolution method

An improved method, termed as the AL-DLGPR-PDEM, is presented to address high-dimensional reliability problems. The novelty of this work lies in developing a complete framework for combining the deep learning (DL) architectures, serving as the utility of dimension reduction, and the Gaussian process regression (GPR), resulting in the so-called DLGPR model. First, the parameters of both the DL and the GPR are inferred using a joint-optimization scheme, rather than the traditional two-step, separate-training scheme. Second, the network configuration of the DLGPR is optimally determined by using a grid-search procedure involving cross-validation, instead of an empirical setting manner. On this basis, the DLGPR is adaptively refined via an active learning (AL)-based sampling strategy, so as to gain the desired DLGPR using as fewer training samples as possible. Eventually, the finalized DLGPR is evaluated at the whole representative point set, thereby the probability density evolution method (PDEM) is conducted accordingly. Two numerical examples are investigated. The first one tackles with the static reliability analysis of a planner steel frame, where the case of small failure probabilities is also considered; the second one addresses the dynamic reliability analysis of the steel frame under fully non-stationary stochastic seismic excitation. Comparisons against other existing reliability methods are conducted as well. Results demonstrate that the proposed AL-DLGPR-PDEM achieves a fair tradeoff between accuracy and efficiency for dealing with high-dimensional reliability problems in both static and dynamic analysis examples.