Automatic train supervision (ATS) systems are a core safety component in metro operations. Its redundant design results in extremely scarce failure data, rendering traditional data-driven risk analysis ineffective. Consequently, existing studies often substitute reliability analysis for risk analysis. To overcome the limitations of static and vague reliability methods, this study employs the van der Pol equation to dynamically quantify inherent risk oscillations in ATS systems, providing managers with actionable control measures. Our paper begins by analyzing ATS risk characteristics and examining the feasibility of using the van der Pol equation to model risk state changes. Then, we establish a risk state equation derived from this framework and analyze the system’s risk dynamics. Finally, to control risk, we integrate a risk control function into the equation. A case study of Beijing Metro Line 2 demonstrates the method’s applicability. The proposed methodology enables accurate risk state judgment, potential risk prediction, and precise control implementation. By applying differential equation theory, it reduces reliance on historical data or expert knowledge while addressing inaccuracies from missing critical data. This work establishes a novel framework for system risk control and offers practical guidance for operators.
Yu et al. (Tue,) studied this question.