Emergent risks in complex systems: A Bayesian perspective on uncertainty and prediction

The digital and energy transitions in industrial systems introduce unprecedented complexity and uncertainty which are challenging to capture by traditional static risk assessment approaches. Current research addresses this issue by dynamic risk assessment through Bayesian Networks (BNs) which enable probabilistic modelling of the cyber-physical risk. However, BNs are mostly adopted at discrete time which come with inherent drawbacks such as the definition of static Conditional Probability Tables (CPTs), and the lack of support for temporal inference. Additionally, most of the existing literature tends to neglect the combined safety and security challenges arising from both digital and energy transitions. To account for these limitations, this study presents a novel probabilistic framework integrating Hidden Markov Models (HMMs) and continuous-time BNs to dynamically assess emergent risks in complex technological systems. By modelling latent states, transition probabilities, and system vulnerabilities, we demonstrate how to account for both aleatory and epistemic uncertainties, enabling the prediction of potential facility failures based on real-time industrial process data, and ultimately supporting a more adaptive and resilient risk assessment. The proposed framework is validated through a pressure system Proof of Concept (PoC), revealing critical insights into system resilience and early failure detection.