LNG serves as a pivotal element within integrated energy systems, especially in coastal regions where the implementation of a stable and reliable LNG cold energy power generation system significantly elevates energy efficiency. This system can effectively meet concurrent demands for cold energy utilization and electricity supply while contributing to the mitigation of carbon emissions. However, the inherent complexity of the system coupled with the scarcity of historical operational data for the novel dual-Rankine cycle process renders conventional reliability assessment methodologies inadequate. This study proposes an integrated framework utilizing fuzzy Bayesian methods to address data scarcity during the early stages of equipment deployment. A hierarchical risk factor model, incorporating process decomposition, expert evaluations, and triangular fuzzy numbers, is developed to quantify uncertainties in failure probabilities. The Bayesian network models the causal relationships among equipment failure factors, allowing for the inference of overall system reliability from individual equipment performance. Through a case study of a LNG terminal in Zhoushan, this approach integrates sensitivity analysis with forward-backward reasoning methodologies to rigorously evaluate and quantify system reliability under operational conditions. The results show that under high load conditions within the 1000 h prior to overhaul, following long-term accumulated operation, the probability of complete system shutdown in the power generation system is 3.30%, while the probability of the LNG cold energy power generation system failing to operate fully due to aging-related faults is 8.24%, demonstrating the system’s strong reliability under extreme conditions. Critical risks identified through backward inference include the seawater pump SWP1, with a posterior failure probability of 59.92% during complete shutdown, and the propane-side pump SWP3, with a posterior failure probability of 32.29% when the cold energy power generation system can only operate in a single-cycle mode. This study provides an advanced methodological framework for risk management in newly constructed LNG cold energy power generation systems, playing a crucial role in promoting sustainable, low-carbon technologies in the energy sector.

The natural gas sector, as a pivotal transition fuel, is fundamentally constrained by the “Energy Trilemma”—the intertwined and often competing goals of energy security, affordability, and sustainability. Current research predominantly focuses on the demand side, leaving a significant gap in understanding the synergistic dynamics within production regions, which are critical to resolving this trilemma at its source. To address this gap, this study constructs a “Safety–Economy–Green” (S-E-G) evaluation framework aligned with the trilemma’s dimensions. Utilizing panel data (2011–2021) from four major Chinese natural gas production regions (Sichuan, Chongqing, Shaanxi, and Shanxi). By integrating the Entropy Weight Method, a Coupling Coordination Model, and Kernel Density Estimation, it delineates the system’s synergistic dynamics from both temporal and regional perspectives. The key findings are as follows: (1) Significant disparities and polarization are observed in the S and G dimensions, while the E dimension shows a narrowing gap, with its peak height increasing by 177.8% and bandwidth shrinking by 64.2%. G has emerged as a constraint on overall system coupling coordination. The persistently high coupling degree—rising from 0.87 in 2011 to 0.97 in 2021 while consistently exceeding the coordination degree, which increased from 0.45 to 0.62—underscores the continued need for improvement in synergistic development. (2) The coupling coordination degree of the S-E-G system underwent a three-stage evolution: rapid improvement (2011–2013, from 0.36 to 0.58 at 7.3% annually), fluctuating adjustment (2014–2017, between 0.58 and 0.66), and finally high-level stability (2018–2021, stabilizing at 0.76–0.80). (3) Obvious regional differentiation exists: Sichuan achieved a moderate level of 0.76 by 2021, Shaanxi maintained primary coupling coordination (0.6–0.7), while Chongqing and Shanxi remained marginal, fluctuating between 0.4 and 0.6. Enhancing subsystem coordination and implementing differentiated pathways are therefore essential for these regions’ sustainable development. The study suggests promoting the sustainable development of natural gas production regions by enhancing subsystem coordination and exploring differentiated pathways, thereby providing practical guidance for the energy transition of resource-based regions.