Quadrature based dynamic event tree construction using FMU-driven piecewise deterministic Markov process for dynamic probabilistic risk assessment

Dynamic Probabilistic Risk Assessment (DPRA) methods are increasingly important to evaluate nuclear plant systems characterized by strong coupling between continuous physical dynamics, digital control logic, and stochastic component failures. Conventional sampling-based approaches, including Monte Carlo and next-event Piecewise Deterministic Markov Process (PDMP) methods, often require a prohibitive number of system simulations to resolve rare, time-dependent failure sequences. This work introduces a Quadrature based Dynamic Event Tree (QDET) framework that deterministically constructs weighted event-tree trajectories by discretizing hazard space rather than sampling failure times. The method preserves deterministic system evolution by coupling to a Functional Mock-up Unit (FMU) representation of the plant and control system and uses snapshot-based state restoration to avoid redundant simulations. The approach is formulated within a PDMP framework and enforces strict probability mass conservation while controlling combinatorial tree growth through quadrature, pruning, and cause ranking. The QDET method is validated against analytical solutions and Monte Carlo results using cold-standby and time-dependent K-out-of-N examples, demonstrating accurate probability estimation with orders-of-magnitude fewer system evaluations. The framework is further applied to the NRC Digital Feedwater Control System (DFWCS) benchmark under a realistic 24-hour power maneuver. The results show order-of-magnitude agreement with published benchmark failure probabilities and identify physically interpretable dominant risk contributors for both high- and low-level failure modes. These results demonstrate that QDET provides an efficient, deterministic, and scalable DPRA methodology suitable for high-fidelity digital control systems and advanced reactor applications.