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Uncertainty propagation analysis for non-parameterized probability box based on distance-aware deep learning model
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DOI：10.1016/j.probengmech.2026.103966.png)
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Abstract
En 中文
The uncertainty propagation analysis task for non-parameterized probability boxes (P-boxes) involves a dual-layer nested problem combining probability propagation analysis and interval analysis. Constructing two stage surrogate models serves as the primary framework to address the non-parameterized P-box uncertainty propagation analysis. The inner layer builds an approximate model of the response function concerning input parameters, based on which the outer layer establishes a surrogate model for auxiliary responses corresponding to the bounds of the cumulative distribution function (CDF) for response function with respect to a series of standard uniform distribution variables. This paper proposes a distance-aware deep learning surrogate model-based method for non-parameterized P-box uncertainty analysis to efficiently obtain the upper and lower bounds of the response function's CDF. First, during surrogate model construction, we employ the spectral-normalized neural Gaussian process (SNGP) to characterize the predictive uncertainty of deep learning, which possesses distance awareness meaning that samples farther from training dataset exhibit greater prediction uncertainty. Second, the deep learning model's prediction uncertainty serves as an active learning function to adaptively identify optimal sample for augmenting the training dataset until stopping criteria are met. Third, the upper and lower bounds of CDF for the response function is computed using Monte Carlo simulation with the outer-layer deep learning model. Finally, two numerical examples validate the effectiveness of the proposed method.
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