Adaptive and uncertainty-aware surrogate modeling for reliability analysis of nonlinear dynamic systems

Reliability analysis of nonlinear inelastic dynamic systems under uncertainty remains a critical challenge, owing to the path-dependent, high-dimensional nature of the problem. To this end, this paper proposes an adaptive and uncertainty-aware surrogate modeling framework comprising three synergistic components. The first component is the aLSTM–SNGP surrogate model, an uncertainty-aware surrogate for nonlinear dynamic systems that integrates an attention-enhanced LSTM (aLSTM) encoder with a Spectral-normalized Neural Gaussian Process (SNGP) predictor, jointly optimized through end-to-end co-training. The aLSTM encoder processes excitation sequences and system parameters together, capturing temporal dependencies while implicitly reducing dimensionality; the SNGP predictor provides scalable uncertainty-aware prediction through random Fourier feature approximation. The second component develops two surrogate-based failure probability estimation methods: Method I (aLSTM-SNGP-MCS) based on direct Monte Carlo simulation, and Method II (aLSTM-SNGP-IS) based on importance sampling with an adaptively constructed proposal density that concentrates sampling effort in failure-prone regions. The third component is an adaptive exploration–exploitation refinement strategy that iteratively refines the surrogate model by combining active learning with an alternating training scheme of full training and local fine-tuning. The framework is validated under stochastic seismic excitations through two examples: a numerical example based on a six-story nonlinear inelastic shear building model with Bouc-Wen hysteresis, and a practical engineering example based on a nine-story SAC steel frame represented by a nonlinear finite element model. Results demonstrate that both methods yield accurate failure probability estimates while significantly reducing the number of evaluations to the simulation model relative to crude Monte Carlo simulation, with Method II outperforming Method I.