A Hybrid Real-Time Framework for Efficient Fussell-Vesely Importance Evaluation Using Virtual Fault Trees and Graph Neural Networks

TL;DR

The paper tackles the high computational burden of Fussell-Vesely ($FV$) importance evaluation in complex systems by replacing traditional fault trees with an Interpretive Structural Modeling (ISM) based virtual fault tree that encodes dependencies among basic events. A Graph Convolutional Network (GCN/GNN) then rapidly computes FV importance in real time, enabling dynamic risk prioritization and decision support. The ISM-based structure reduces model complexity while preserving essential causal relationships, and the GNN learns from data to produce timely FV scores with favorable $MSE$, $RMSE$, $MAE$, and $R^{2}$ on validation. Experiments on a nuclear-power-plant-like case demonstrate improved accuracy and substantial time/energy efficiency gains, highlighting the framework's potential for real-time reliability assessment in dynamic environments.

Abstract

The Fussell-Vesely Importance (FV) reflects the potential impact of a basic event on system failure, and is crucial for ensuring system reliability. However, traditional methods for calculating FV importance are complex and time-consuming, requiring the construction of fault trees and the calculation of minimal cut set. To address these limitations, this study proposes a hybrid real-time framework to evaluate the FV importance of basic events. Our framework combines expert knowledge with a data-driven model. First, we use Interpretive Structural Modeling (ISM) to build a virtual fault tree that captures the relationships between basic events. Unlike traditional fault trees, which include intermediate events, our virtual fault tree consists solely of basic events, reducing its complexity and space requirements. Additionally, our virtual fault tree considers the dependencies between basic events rather than assuming their independence, as is typically done in traditional fault trees. We then feed both the event relationships and relevant data into a graph neural network (GNN). This approach enables a rapid, data-driven calculation of FV importance, significantly reducing processing time and quickly identifying critical events, thus providing robust decision support for risk control. Results demonstrate that our model performs well in terms of MSE, RMSE, MAE, and R2, reducing computational energy consumption and offering real-time, risk-informed decision support for complex systems.

Figures (12)

• Figure 1: Hybrid framework for real-time fussell-vesely importance evaluation integrating interpretive structural modeling and graph neural networks
• Figure 2: Simplified system diagram for a nuclear power plant
• Figure 3: Fault tree for the safety injection system in the case
• Figure 4: Fault tree for the containment spray system in the case
• Figure 5: The relationships among various variables needed to be consulted.