  Stealth attacks pose potential risks to cyber-physical systems because they
are difficult to detect. Assessing the risk of systems under stealth attacks
remains an open challenge, especially in nonlinear systems. To comprehensively
quantify these risks, we propose a framework that considers both the
reachability of a system and the risk distribution of a scenario. We propose an
algorithm to approximate the reachability of a nonlinear system under stealth
attacks with a union of standard sets. Meanwhile, we present a method to
construct a risk field to formally describe the risk distribution in a given
scenario. The intersection relationships of system reachability and risk
regions in the risk field indicate that attackers can cause corresponding risks
without being detected. Based on this, we introduce a metric to dynamically
quantify the risk. Compared to traditional methods, our framework predicts the
risk value in an explainable way and provides early warnings for safety
control. We demonstrate the effectiveness of our framework through a case study
of an automated warehouse.
