The pipelines that transport hazardous liquids (e.g., petroleum and petroleum products) across cities or countries are critical to the energy-supply infrastructure, and they are crucial for the reliable and secure operation of a city. Estimating the occurrence rate of serious pipeline accidents with sparse data is a challenging problem in pipeline safety management because serious hazardous liquid pipeline accidents are caused by a particular multidimensional sequence of events. In this paper, complex network theory was employed to detect the temporal structure of pipeline incidents and reveal the nonlinear connections between major accidents and their precursors. A database of hazardous liquid pipeline incidents in the US between 2010 and 2018 collected by the Pipeline Hazardous Material Safety Administration (PHMSA) of the US Department of Transportation was transformed into a complex network via the visibility graph algorithm. The temporal structure of the pipeline incident time series for different years and different companies was explored by applying complex network analysis. The results show the scale-free property and small-world topology of the constructed networks and provide the rationale for applying the hierarchical Bayesian model to predict the occurrence rate of major accidents in a pipeline system when there is sparse data. The benefits of using the hierarchical Bayesian model for estimating the occurrence rate were illustrated by comparing it with three different methods. Furthermore, posterior predictive checks were performed to validate whether the results of the hierarchical Bayesian model are consistent with the real data. The result indicates that it is reasonable to apply the hierarchical Bayesian model to estimate the occurrence rate of serious pipeline accidents when there is sparse data. Finally, practical applications of the temporal structure of the incidents were proposed for improved pipeline safety management. Our results provide the underlying new insights needed to enhance quantitative analyses of pipeline incidents.

在城市或国家之间运输危险液体（例如，石油和石油产品）的管道对于能源基础设施至关重要，对城市的可靠和安全运营也至关重要。用稀疏数据估计严重管道事故的发生率是管道安全管理中的一个难题，因为严重的危险液体管道事故是由特定的多维事件序列引起的。在本文中，复杂网络理论被用来检测管道事件的时间结构，并揭示重大事故与其前兆之间的非线性联系。由美国运输部管道危险物质安全管理局（PHMSA）收集的2010年至2018年美国危险液体管道事件数据库已通过可见度图算法转换为复杂网络。通过应用复杂的网络分析，探索了不同年份和不同公司的管道事件时间序列的时间结构。结果表明所构造网络的无标度特性和小世界拓扑结构，并为应用稀疏数据时应用层次贝叶斯模型预测管道系统中重大事故的发生率提供了依据。通过与三种不同方法进行比较，说明了使用分层贝叶斯模型估计发生率的好处。此外，进行后验预测检查以验证分层贝叶斯模型的结果是否与真实数据一致。结果表明，在数据稀疏的情况下，应用分层贝叶斯模型估计严重管道事故的发生率是合理的。最后，提出了事件时间结构的实际应用，以改善管道安全管理。我们的结果提供了增强管道事件定量分析所需的基础新见解。结果表明，在数据稀疏的情况下，应用分层贝叶斯模型估计严重管道事故的发生率是合理的。最后，提出了事件时间结构的实际应用，以改善管道安全管理。我们的结果提供了增强管道事件定量分析所需的基础新见解。结果表明，在数据稀疏的情况下，应用分层贝叶斯模型估计严重管道事故的发生率是合理的。最后，提出了事件时间结构的实际应用，以改善管道安全管理。我们的结果提供了增强管道事件定量分析所需的基础新见解。