Adaptive kernel operator learning for spatiotemporal full-field reliability analysis with mixed random inputs
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The material properties and external loads of engineering structures inevitably exhibit significant spatial and temporal variability; simplifying these into homogeneous random variables severely underestimates failure probability by neglecting localized weak regions. Conventional surrogate approaches address this by incorporating spatial random fields, yet first discretize them via spectrum methods, introducing truncation errors that become prohibitive for fields with short correlation lengths. This paper proposes a kernel operator learning framework for spatiotemporal full-field reliability analysis that encodes all three categories of uncertain inputs, namely, random variables, stochastic processes, and spatial random fields, through anisotropic product kernels on a latent Gaussian process regressor, bypassing explicit dimensionality reduction. An active learning strategy is further developed, combining an integrated variance reduction term weighted toward the zero level set with a sign-misclassification exploitation term, terminated by a level-set stability criterion. The framework is validated on benchmark problems with mixed random inputs, demonstrating accurate full-field failure probability estimation with a small number of training samples.
