Predicting transitions across macroscopic states for railway systems

Railways are classic instances of complex socio-technical systems, whose defining characteristic is that they exist and function by integrating (continuous-time) interactions among technical components and human elements. Typically, unlike physical systems, there are no governing laws for describing their dynamics. Based purely on micro-unit data, here we present a data-driven framework to analyze macro-dynamics in such systems, leading us to the identification of specific states and prediction of transitions across them. It consists of three steps, which we elucidate using data from the Dutch railways. First, we form a dimensionally reduced phase-space by extracting a few relevant components, wherein relevance is proxied by dominance in terms of explained variance, as well as by persistence in time. Secondly, we apply a clustering algorithm to the reduced phase-space, resulting in the revelation of states of the system. Specifically, we identify ‘rest’ and ‘disrupted’ states, for which the system operations deviates respectively little and strongly from the planned timetable. Third, we define an early-warning metric based on the probability of transitions across states, predict whether the system is likely to transit from one state to another within a given time-frame and evaluate the performance of this metric using the Peirce skill score. Interestingly, using case studies, we demonstrate that the framework is able to predict large-scale disruptions up to 90 minutes beforehand with significant skill, demonstrating, for the railway companies, its potential to better track the evolution of large-scale disruptions in their networks. We discuss that the applicability of the three-step framework stretches to other systems as well—i.e., not only socio-technical ones—wherein real-time monitoring can help to prevent macro-scale state transitions, albeit the methods chosen to execute each step may depend on specific system-details.

铁路系统是复杂社会技术系统（socio-technical systems）的典型范例，其核心特征在于通过整合技术组件与人为要素间的连续时间交互作用而存在并运行。与物理系统不同，这类系统通常不存在可描述其动力学行为的统一定律。本研究仅基于微观单元数据，提出了一套面向该类系统宏观动力学分析的数据驱动框架，可实现特定状态的识别与状态间跃迁的预测。

该框架包含三个步骤，我们将以荷兰铁路的实测数据为例进行阐释。第一步，通过提取若干关联分量构建降维相空间（phase-space）；此处的关联性以解释方差占比优势及时域持续性作为衡量依据。第二步，对降维相空间应用聚类算法，以此揭示系统的各类运行状态。具体而言，我们识别出“停运”与“故障中断”两类状态：前者对应的系统运营与既定时刻表偏差极小，后者则偏差显著。第三步，基于状态间跃迁概率定义预警指标，预测系统在指定时间范围内从某一状态跃迁至另一状态的可能性，并采用皮尔斯技能评分（Peirce skill score）对该指标的性能进行评估。

值得注意的是，通过案例研究我们证实，该框架可提前最高90分钟实现高精度的大规模运营中断预测，表明其可帮助铁路企业更好地追踪其路网内大规模中断事件的演化进程。本研究进一步讨论表明，这套三步框架的适用范围不仅局限于社会技术系统，亦可推广至其他可通过实时监测助力防范宏观尺度状态跃迁的系统，尽管各步骤所选用的具体方法可能需结合系统的专属特性进行调整。