Self-adaptive hybrid uncertainty integration method via deterministic analytic formula

Data uncertainty and model uncertainty are two critical factors that affect the credibility of deep learning-based reliability analysis. However, existing research has paid little attention to integrating these two distinct uncertainties with theoretical guarantees. To bridge this gap, this paper presents a self-adaptive hybrid uncertainty integration method built on a dual-level structure. Relying on the first-level uncertainty quantification, deterministic analytic formulas of integrated uncertainty are obtained through affine and convolutional layers in the second level, which can adaptively capture the interaction between data and model uncertainties. Experimental results indicate that the analytical integrated uncertainty offers a comprehensive evaluation by effectively consolidating data and model uncertainties. The approach also shows a high degree of consistency with uncertainty estimates derived from Monte Carlo Sampling, thereby enhancing the credibility of system reliability analysis.