A structural reliability analysis method under non-parameterized P-box based on double-loop deep learning models

Hao Hu

doi:10.1007/s00158-024-03854-3

2024-08-17

PRE

DOI：10.1007/s00158-024-03854-3

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摘要

En 中文

Structural reliability analysis, when accounting for non-parameterized probability box (P-box) uncertainty, typically entails multiple calls to performance functions and poses significant computational hurdles, largely attributable to its inherently nested double-loop structure. Therefore, this paper proposes a new reliability analysis method tailored for structures with uncertain parameters represented using non-parameterized P-boxes. This method leverages double-loop deep learning models to efficiently calculate both the upper and lower bounds of the failure probability. In the development phase of the double-loop deep learning model, an active learning function is devised that integrates the local prediction uncertainty of the deep learning model, based on the K-fold cross-validation principle with the proximity of training samples to candidate sample points. Different stopping criteria are formulated at distinct stages of the model construction process. Firstly, within the inner loop, a deep learning model is established to represent the original performance function in relation to the input parameters. Secondly, based on the inner-loop deep learning model for the performance function, an outer-loop deep learning model is established for the auxiliary response function corresponding to the P-box bound curves of the performance function response with respect to standard uniform distribution variables. Thirdly, utilizing the outer-loop deep learning approximate model, the Monte Carlo simulation technique is employed to compute the upper and lower bounds of the structural failure probability. Finally, the effectiveness of the proposed method is validated through the investigation of two numerical examples and a practical engineering problem. The influence of parameters in the active learning function, threshold values for stopping criteria, and the number of sample points on the computational results is deliberated.

Keyword:

Non-parameterized P-box

Reliability analysis

Deep learning

Adaptive updating

Double-loop surrogate model