Hierarchical Learning-Based System Decomposition for Time-Dependent Structural System Reliability Assessment

Time-dependent reliability assessment of structural systems is challenging when degradation and multiple interacting failure modes govern failure. Under these conditions, the system limit state function (LSF) may be highly nonlinear, non-smooth, and available only implicitly through high-fidelity analysis. This paper proposes a system decomposition and hierarchical learning (DHL) framework to construct an evaluable surrogate system LSF for degradation-driven, time-variant reliability analysis. The structural system is decomposed into dominant failure modes and their connectivity. Artificial neural networks are trained hierarchically to learn the decomposed relationships. Mode-level surrogates approximate the LSF of each failure mode. A system-level surrogate then integrates the mode-level performance quantities and time to capture mode interaction and mechanism switching. The resulting surrogate is combined with Monte Carlo simulation and the probability density evolution method to compute time-dependent failure probabilities and, when required, the evolution of the system performance probability density. Two benchmark problems—a highly nonlinear parallel system and a rigid–plastic portal frame with correlated collapse mechanisms under degrading capacities—are used to evaluate the approach. DHL improves system-level surrogate fidelity relative to direct system-level ANN learning, with mean reliability prediction errors below 3.1% and 1.23% in the two benchmarks, respectively, while remaining compatible with both sampling-based and density-evolution propagation schemes.