In densely populated venues, early warning signs of safety accidents triggered by portable flammable items (e.g., power banks) are often difficult to detect. This challenge necessitates effective security patrol inspections. Although recent research has focused on optimizing patrol routes, resource allocation, and deploying unmanned aerial vehicles, manual inspections remain the primary method. Moreover, visual obstructions caused by high crowd density and structural limitations further complicate the detection process. Consequently, the optimal allocation of security patrol personnel is critical for enhancing early warning sign detection. This paper addresses the impact of visual obstructions and investigates how the number of security patrol personnel influences detection efficiency in densely populated venues.

This study examined the effect of the number of security patrol personnel on the efficiency of early warning sign detection and explored the underlying mechanisms. The investigation was conducted in three steps. First, behavior rules for pedestrians and security patrol personnel were established using the classical social force model. These rules were tailored to reflect the characteristics of densely populated venues and incorporated key factors such as interpersonal interactions and environmental constraints. Second, a dynamic visual field model for security patrol personnel was developed under three conditions: unobstructed vision, obstructed vision with non-overlapping blind spots, and obstructed vision with overlapping blind spots. By dynamically calculating the visual coverage area in real time, the model enabled adaptive adjustments of the visual field in response to changes in crowd density and obstructions. Third, eight sets of scenarios were designed based on variations in crowd density and typical spatial factors of densely populated venues. MATLAB was used to simulate detection times when one to eight security patrol personnel patrolled along random paths with early warning signs placed at random locations and their visual field trajectories recorded. Two hundred simulation runs were performed to ensure the robustness and reliability of the results.

The simulation shows that the dynamic visual field model effectively monitors crowd density within a specified range along the patrol direction. The model dynamically calculates the visual coverage area while accounting for both unobstructed vision and overlapping blind spots, thereby enabling adaptive adjustments to maintain optimal monitoring conditions. Moreover, the simulation data reveals that increasing the number of patrol personnel significantly reduces the time required to detect early warning signs. However, the improvement effects exhibit a trend of diminishing effects, following a negative power-law relationship as personnel numbers increase. In larger spaces or high-density environments, a fixed number of patrol personnel require substantially longer detection times, whereas a moderate increase in personnel yields more effective reductions in detection time. Furthermore, the simulations demonstrates that as the number of patrol personnel increases, the time required for the average visual coverage to reach its upper limit gradually decreases and eventually stabilizes. This finding suggests that the marginal benefit of adding extra personnel declines beyond a certain point, thereby limiting further reductions in detection time. The diminishing marginal effect is especially pronounced in smaller venues or environments with lower crowd density.

This study clarifies how the number of security patrol personnel affects the efficiency of early warning sign detection under visual obstruction conditions and provides insights into the underlying mechanisms. The findings help improve detection efficiency in densely populated venues and offer theoretical and methodological support for developing more effective patrol strategies.

The operational safety resilience of urban lifeline systems refers to their ability to maintain critical functions and recover swiftly when faced with multiple disruptive events during their operational period. This resilience is crucial for ensuring the safe and uninterrupted operation of these critical systems. However, existing resilience evaluation methods often risk inaccuracies under multi-event scenarios, making it challenging to accurately assess the systems' overall resilience. To address this issue, this paper proposes a comprehensive resilience evaluation model and methodology tailored for urban lifeline systems during their operational phase. The approach considers multi-event contexts and is built on a detailed analysis of resilience mechanisms. It incorporates key factors such as resistance, recovery, and adaptability.

This study presents an evaluation method for assessing the operational safety resilience of urban lifeline systems under multi-event scenarios. The methodology is structured around three main steps: analyzing resilience mechanisms, constructing a resilience evaluation model for multi-event contexts, and applying the method in a case study. First, using resilience curve theory, scenario assumptions and theoretical deductions were used to analyze the specific roles and effects of resistance, recovery, and adaptability during operational performance loss and recovery under both single and multiple disruptive event scenarios. This analysis facilitated a systematic understanding of the resilience mechanisms governing urban lifeline systems. Second, building on existing resilience metrics, the study identified misjudgment risks and limitations in current resilience evaluation models. This led to the development of an enhanced model that integrates the advantages of existing methods. The improved model accounts for resilience mechanisms, computational efficiency, and reasonable distribution. An exponential function was utilized to establish an evaluation model for urban lifeline system resilience during the operational period. Key components, including system performance indicator settings, performance calculations, the resilience evaluation model, and a comprehensive resilience judgment matrix, were incorporated to form a "four-step" evaluation process tailored to multi-event scenarios. Finally, the methodology was validated through a case study on the Hong Kong (China) MTR East Rail Line from 2005 to 2009. Service performance indicators for the metro system were identified, and the causes of annual changes in comprehensive resilience levels were calculated and analyzed. The results demonstrated the feasibility and effectiveness of the proposed evaluation method.

The research results revealed the following insights: (1) During the operational period, the resilience mechanisms of urban lifeline systems differ significantly between single and multiple disruptive events. In single-event scenarios, the system primarily relies on resistance to mitigate or eliminate disruptions and uses recovery to restore functionality. In contrast, in multiple-event scenarios, the system leverages adaptability, continuously optimizing resistance and post-event recovery. This enhances its capacity to respond to regular, extreme, or unknown events. (2) The proposed evaluation model, incorporating key resilience factors like resistance, recovery, and adaptability, assesses the comprehensive resilience level of the system throughout its operational period. It also measures the average resilience in single-event scenarios and cumulative resilience under multiple events. (3) Practical application demonstrates that a high average resilience in single-event scenarios does not necessarily correlate with high cumulative or comprehensive resilience. Enhancing comprehensive resilience is a long-term, dynamic process that relies on adaptability to repeatedly refine system resistance and recovery. This approach minimizes the impact of disruptive events and accelerates recovery. These findings validate the feasibility and effectiveness of the proposed evaluation method.

This method enhances the safe operation of urban lifeline systems and serves as a valuable methodological reference for future research on resilience enhancement strategies. It also holds significant potential for application in the resilience analysis of complex coupled systems.