Modern engineering systems, such as vehicles, aerospace structures, and large-scale infrastructures, are inherently multi-level systems, composed of interacting components and subsystems across different hierarchy levels. Throughout their lifecycle, these systems are subjected to various sources of uncertainty arising from material properties, manufacturing and assembly processes, operational loads, and model idealizations. Inadequate treatment of such uncertainties may lead to inaccurate performance predictions and unreliable design decisions, potentially resulting in system failures with significant economic and societal consequences. Therefore, it is crucial to understand how uncertainties propagate across different system levels and how they affect overall system reliability.

Hierarchical Bayesian Modeling (HBM) provides a rigorous probabilistic framework for uncertainty quantification in multi-level engineering systems by consistently fusing data and models across system hierarchies. Despite its strong theoretical foundation, the practical application of HBM to full-scale engineering systems remains computationally challenging. Existing inference techniques rely heavily on computationally expensive sampling algorithms, which become inefficient when dealing with high-dimensional parameter spaces and large numbers of system components. Moreover, incorporating system reliability analysis within the HBM framework requires the estimation of rare failure events, further increasing the computational burden and limiting its applicability to real-life engineering problems.

The present project aims to address these challenges by developing a computationally efficient HBM framework for uncertainty quantification and structural reliability analysis in multi-level engineering system design. By integrating advanced sampling algorithms, variational inference techniques, and machine learning-based surrogate models, the proposed framework will significantly reduce computational costs while maintaining high accuracy. The developed methodology will be systematically validated using simulated and experimental studies, supporting the development of high-fidelity digital twins and enabling reliability-informed design and decision-making for complex engineering systems.