Mixed loss-guided modular regression for dependent system reliability

Complex structural systems frequently exhibit multi-source failure interdependencies under coupled multi-physics loading, posing significant challenges for accurate reliability evaluation. Traditional analytical models often overlook such dependencies and physical constraints, leading to biased predictions and limited scalability. To address these challenges, we propose an innovative mixed loss-guided modular regression (ML-MR) framework that seamlessly integrates component-level failure physics and mode-level failure mechanisms into a hierarchical modular architecture. In this method, the multi-component, multi-mode complex problem is first decomposed into several coordinated, physically interpretable sub-problems; moreover, an innovative data-physics mixed loss function embedding physical constraints (i.e., boundaries, monotonicity) guides accurate model training across modular datasets, while a Copula-based dependency model at the system level. An aeroengine blade-disc system is chosen as an engineering case study to validate the proposed method, comparative experiments confirm that the ML-MR significantly outperforms the direct regressions and modular regressions, delivering superior accuracy alongside substantial reductions in computational demands. Unlike existing physics-informed surrogates, ML-MR introduces a hybrid data-physics loss that embeds constraints during training, ensuring interpretable system reliability predictions. By merging modular decomposition and physics-informed learning, this study provides a scalable, interpretable, and physics-consistent solution for system-level reliability evaluation, shedding a light on accurate evaluation for complex high-reliability systems.