Marine liquefied natural gas transportation system toughness evaluation method based on dynamic Bayesian network

Abstract

The invention discloses an offshore liquefied natural gas transportation system toughness evaluation method based on a dynamic Bayesian network, and relates to the technical field of marine transportation. Comprising the steps of defining a steady-state system, determining a system function and a dependency relationship, constructing a dynamic Bayesian network in combination with robustness, redundancy, quick responsiveness and resource allocation capability of the system and external interference factors, then establishing a Markov chain to obtain probability parameters, and realizing dynamic quantization and calculating a toughness index through a DBN. According to the method, a time change function of 4R characteristics and interference factors is integrated, a dynamic toughness model closer to the actual operation condition of a sea transportation LNG transportation system is constructed, quantifiable probability distribution and time recovery functions are given to all categories, a DBN is embedded, a dynamic toughness curve is generated based on the framework, and the dynamic toughness of the sea transportation LNG transportation system is improved. And the influence degree of various interruption factors on the system toughness can be intuitively presented.

Description

Technical Field

[0001] This invention relates to the field of maritime transportation technology, and more specifically to a method for assessing the resilience of offshore liquefied natural gas transportation systems based on dynamic Bayesian networks. Background Technology

[0002] Liquefied natural gas (LNG) has become a clean and efficient energy source globally in recent years (Thomson et al., 2015). In countries striving to achieve emission reduction targets, significantly increasing LNG imports has become a common trend. In the maritime LNG supply chain, LNG carriers play a crucial role due to their large capacity and low cost. However, maritime LNG carriers face threats from multiple sources, including human factors, technological advancements, and the environment.

[0003] Safety and risk management research on liquefied natural gas (LNG) carriers has attracted widespread attention. Vanem et al. (2008) established a basic probabilistic risk assessment system for maritime operations using fault tree analysis (FTA), and derived the frequency of collision-induced cargo loss (2.8 × 10⁻⁶ per ship per year). This probabilistic method was subsequently used by Li to derive the frequency of cargo loss due to collisions (2.8 × 1 per ship per year) through fault tree analysis (FTA). This probabilistic method was later improved by Li et al. (2021) by embedding decision tree networks (DBNs) into real-time automatic identification systems (AIS) and meteorological data, reducing prediction uncertainty by 38%. Zhou et al. (2017) proposed an enhanced fault tree model for LNG carrier leaks, integrating fault tree analysis, human factor reliability analysis, and Monte Carlo simulation results, incorporating human factor analysis to achieve comprehensive risk assessment. Abdussamie et al. (2018) quantified the collision and grounding risks of LNG carriers during ocean voyages through fault tree analysis and Monte Carlo simulation, identified key failure modes, and proposed a graded risk control scheme to support safety management decisions. Jin et al. (2024) achieved risk indicator quantification and hierarchical formulation of safety measures by adopting a personalized semantic group failure mode and impact analysis framework, demonstrating further development of the methodology.

[0004] In addition, shipping routes also face numerous risks. Baksh et al. (2018) constructed a Bayesian network (BN) framework, combined with fault data specific to the Arctic region, to quantify the navigation risks of polar shipping routes, providing scenario-based fault analysis and evidence-driven safety management solutions for maritime operations in cold regions. Jiang and Lu (2020) proposed a decision-based Bayesian network method to quantify and predict channel-specific accident risks and identify key fault points to achieve proactive maritime safety management. Kulkarni et al. (2020) identified dominant fault mechanisms and assessed the evolution of risk assessment paradigms through longitudinal analysis of Baltic Sea accident data, proposing a forward-looking safety management strategy for high-density waterways. Fu et al. (2021) used bibliometrics and systematic reviews to map the risk factors of Arctic navigation accidents, integrating empirical evidence for route risk quantification, causal fault analysis, and precise safety governance for polar shipping corridors. Wen et al. (2022) used entropy theory to quantify the vulnerability of the Eurasian shipping network, achieving route risk assessment and proactive safety management.

[0005] Huang et al. (2023) categorized and benchmarked quantitative risk assessment models for maritime transport, clarified methodological gaps, and proposed a data-driven framework for route risk assessment, failure analysis, and safety management. For strategic maritime chokepoints, Jiang et al. (2023) developed a fuzzy evidence-based reasoning model to quantify the multidimensional vulnerability of key straits and canals; this model not only generates accurate risk indicators but also prioritizes failure scenarios and implements actionable safety control measures.

[0006] However, previous risk assessment studies have mainly focused on analyzing known hazards and their corresponding consequences in the pre-disruption phase (Zio, 2016). Francis and Bekera (2014) proposed a resilience-oriented index system that integrates absorptive capacity, adaptive capacity, and recovery capacity. By addressing the limitations of probabilistic loss quantification and system recovery characterization, they demonstrated the advantages of the resilience framework compared to traditional risk analysis. Hosseini et al. (2016) defined engineering resilience as the inherent ability of a system to adjust its function when disturbed. Liu et al. (2023) explored methods to translate maritime supply chain resilience from concept to practice, constructed a supply chain resilience framework, and used a hybrid AHP-QFD-DEMATEL method to analyze the most critical resilience factors. Wang and Yuan (2022) proposed a maritime-waterway resilience framework that simultaneously quantifies the system's performance and recovery costs after disturbance, providing a rigorous and cost-effective basis for assessing and improving the adaptability of shipping channel transportation systems. Li et al. (2024), through a systematic review of existing literature, defined the concept of maritime logistics resilience, extracted its 4R characteristics, and proposed an innovative evaluation index system. Although the aforementioned studies offer different definitions of resilience, they all point out that its essence lies in the system's ability to maintain or restore its function when encountering disturbances. This provides a theoretical basis and practical guidance for assessing and improving the resilience of maritime liquefied natural gas transportation systems.

[0007] Dynamic Bayesian Networks (DBNs) have gained significant attention in the field of resilience assessment due to their ability to model multi-state systems and temporal dynamics. Recent applications demonstrate their practical value in the resilience assessment of critical infrastructure. Leclercq et al. (2021) used DBNs to assess resilience by modeling the state of a system as it evolves over time, thereby enhancing predictive capabilities. Building on this approach, Zinetullina et al. (2021) integrated Functional Resonance Analysis (FRAM) with DBNs to model the adaptive behavior of chemical process systems affected by perturbations, identifying key functional interactions across time scales. Similarly, Caetano et al. (2024) quantified infrastructure resilience using DBNs, utilizing evidence propagation to update system state probabilities during perturbations. Zhang et al. (2021) fused finite element degradation results into dynamic Bayesian Networks, establishing a real-time updating framework for the resilience assessment of mechanical structures. An et al. (2023) integrated multi-stage STAMP with DBNs to provide a time-evolving resilience metric for emergency response systems. Chen et al. (2023) used DBN to quantify the multidimensional evolution of urban resilience in Fujian Province, China, and to diagnose its recovery capacity.

[0008] Previous research on maritime liquefied natural gas (LNG) transportation systems has primarily focused on risk assessment, often neglecting the dynamic changes of disturbance factors. This results in an inability to accurately capture the dynamic characteristics of the system, thus reducing the precision of resilience assessments. Furthermore, existing studies often treat LNG carriers or maritime transport systems as independent research objects, leading to a severe lack of comprehensive quantitative analysis of integrated maritime LNG transportation systems.

[0009] Therefore, proposing a resilience assessment method for offshore liquefied natural gas transportation systems based on dynamic Bayesian networks to address the difficulties in existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In view of this, the present invention provides a method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network. It integrates the 4R characteristics and the time variability of disturbance factors to construct a dynamic resilience model that is closer to the actual operating conditions of the marine LNG transportation system. Each category is assigned a quantifiable probability distribution and a time recovery function, and a dynamic recovery network (DBN) is embedded in it. This framework generates dynamic resilience curves, which can intuitively present the degree of influence of various interruption factors on the system resilience.

[0011] To achieve the above objectives, the present invention provides the following technical solution: A method for assessing the resilience of offshore liquefied natural gas transportation systems based on dynamic Bayesian networks includes the following steps: The maritime liquefied natural gas transportation system is divided into three levels: the physical transportation layer, the governance layer, and the ship service layer, and a stable operating state is defined. Based on the 4R framework, the system resilience is decomposed into four functional components: robustness, redundancy, rapid response, and resource allocation capability, and the interference factors affecting the functional components are identified. Construct a dynamic Bayesian network, using functional components and disturbance factors as network nodes, to quantitatively assess the dynamic evolution of system resilience over time; A Markov chain model with four states S1, S2, S3, and S4 is established, and the probability of the system being in each state is calculated by the state transition probability matrix. A DBN is constructed to realize dynamic quantization and calculate the resilience index. Based on the node probabilities in dynamic Bayesian networks and the state transition probabilities in Markov chain models, the final evaluation results are obtained by analyzing the impact of changes in disturbance factors on resilience and / or recovery time.

[0012] Optionally, the maritime liquefied natural gas transportation system can be divided into three levels: the physical transportation layer, the governance layer, and the ship service layer, and the specific content of a stable operating state can be defined as follows: The first level is the physical transport layer, which is used to track the entire process from the initial production facility to the final delivery point, involving navigation and cargo storage. The second level is the governance level, which covers the system through which individuals and institutions jointly govern public affairs through various mechanisms; The third level is the ship service layer, which includes power supply, fuel security, communication and emergency response. When the physical transport layer, governance layer, and ship service layer are all in good working order, the system is in a stable operating state.

[0013] Optionally, the 4R framework includes robustness (R1), redundancy (R2), rapid responsiveness (R3), and resource allocation capability (R4); among which, Robustness R1 refers to the degree of stress a system can withstand while maintaining a specific level of stability; Redundancy R2 refers to the amount of remaining resources used to mitigate damage; Rapid responsiveness (R3) refers to the system's ability to manage losses and prevent potential damage during the recovery process, and is measured by the slope of the function curve. Resource allocation capacity (R4) is an indicator that reflects the contribution of human factors to the recovery operation.

[0014] Optional interfering factors include natural factors, human factors, geopolitical risks, and terrorist attacks.

[0015] Optionally, a dynamic Bayesian network can be constructed, using functional components and disturbance factors as network nodes, to quantitatively evaluate the dynamic evolution of system resilience over time. Dynamic Bayesian networks introduce a time dimension into their structure, enabling them to capture and analyze the evolution of the system over time. The Bayesian formula is as follows:

[0016] in, Let be the likelihood probability. For prior probability, As evidence; The state of a node at time t depends not only on its parent node within the same time segment, but also on the state at time t-1 and the state of its parent node in the previous step, thus defining the dynamic evolution relationship over time:

[0017] in, Let be the set of states of all nodes at time t. Let be the set of states of all nodes at time t-1. The total number of nodes. For probability, Let be the state of the i-th node at time t. Let i be the state of the i-th node at time t-1. Let i be the i-th node at time t. The set of parent nodes, For time t-1, the first The set of parent nodes of each node.

[0018] Optionally, fuzzy hierarchical analysis can be used to quantify the influence of parent nodes on child nodes in the form of conditional probabilities.

[0019] Optionally, a Markov chain model with four states S1, S2, S3, and S4 is established, where, S1 represents the state in which the system maintains its normal functional level under interference; S2 represents a state where the system's functionality has partially degraded; S3 represents a state of severe system dysfunction; S4 indicates that the system has successfully transitioned from a damaged state to the recovery process.

[0020] Optionally, the probability of the system being in each state is calculated using the state transition probability matrix. The specific details of constructing a DBN to achieve dynamic quantization and calculate resilience indicators are as follows: The resilience value R(t) of the system at a specific moment is defined as the sum of the probability P(S1) that the system is in state S1 and the probability P(S4) that the system is in state S4 at that moment, that is: R(t) = P(S1) + P(S4).

[0021] As can be seen from the above technical solution, compared with the prior art, the present invention provides a method for assessing the resilience of offshore liquefied natural gas transportation systems based on dynamic Bayesian networks, which has the following beneficial effects: (1) This invention establishes the relationship between the four factors of system robustness, redundancy, rapid response and resource allocation capability (4R) and time series. Through comprehensive sensitivity analysis, the key factors affecting system resilience are successfully identified. (2) This invention integrates the 4R characteristics and the time function of interference factors to construct a dynamic resilience model that is closer to the actual operation of the LNG transportation system. The interference factors are divided into four categories: natural disasters, human factors, geopolitical risks and terrorist attacks. Each category is given a quantifiable probability distribution and time recovery function and embedded in DBN. Based on this framework, a dynamic resilience curve is generated, which can intuitively present the degree of influence of various interference factors that cause system interruption on resilience. (3) The present invention can accurately assess the impact of a single indicator on the overall resilience. The main factors that reduce the resilience of the system (marked by a baseline deviation of more than 0.5%) include: N6 (port management and operation efficiency), N11 (local and government support), N8 (automatic identification system and communication for ships), N1 (ship and transportation technology) and N5 (supply chain redundancy). Therefore, promoting digital collaborative governance between the government and ports and improving the reliability and redundancy of technology can significantly enhance the safety performance of the system. (4) Under normal conditions, the system resilience index shows a much higher sensitivity to changes in failure rate (λ2) and self-repair rate (μ1) than to interruption failure rate (λ1) or external intervention repair rate (μ2). The results indicate that long-term system resilience mainly depends on resource allocation capability and redundancy during normal operation, rather than robustness or rapid response capability under extreme conditions. Therefore, system design, maintenance procedures and policy formulation should prioritize improving human-machine collaboration efficiency, while redundancy should be regarded as a dynamic resource, and it should be recognized that pursuing maximum robustness will lead to diminishing marginal benefits and cost inefficiency, thereby avoiding resource waste. Attached Figure Description

[0022] To more clearly illustrate the embodiments of the present invention or the existing technical solutions, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0023] Figure 1 A flowchart of a method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network, provided by this invention; Figure 2 A functional schematic diagram illustrating the change in resilience over time during an interruption of the system provided by this invention; Figure 3 A schematic diagram of a dynamic Bayesian model for capturing system resilience provided by the present invention; Figure 4 A schematic diagram illustrating the process of constructing dynamic Bayesian transition probabilities based on Markov chains, provided for this invention. Figure 5 The structured decision tree model for time resilience assessment provided by this invention; Figure 6 A time-series evolution diagram of the system resilience provided by the present invention; Figure 7 A schematic diagram illustrating the change of probability over time for different states of the system provided by this invention; Figure 8a The system provided by the present invention The probability distribution that changes over time; Figure 8b The system provided by the present invention The probability distribution that changes over time; Figure 8c The system provided by the present invention The probability distribution that changes over time; Figure 8d The system provided by the present invention The probability distribution that changes over time; Figure 9 The influence of the 4R factors provided by this invention on the system toughness; Figure 10 Sensitivity analysis of the 4R factors provided by this invention on recovery time (to 90%); Figure 11 Sensitivity analysis of interference factors provided for this invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] See Figure 1 As shown, this invention discloses a method for assessing the resilience of offshore liquefied natural gas transportation systems based on dynamic Bayesian networks, comprising the following steps: The maritime liquefied natural gas transportation system is divided into three levels: the physical transportation layer, the governance layer, and the ship service layer, and a stable operating state is defined. Based on the 4R framework, the system resilience is decomposed into four functional components: robustness, redundancy, rapid response, and resource allocation capability, and the interference factors affecting the functional components are identified. Construct a dynamic Bayesian network, using functional components and disturbance factors as network nodes, to quantitatively assess the dynamic evolution of system resilience over time; A Markov chain model with four states S1, S2, S3, and S4 is established, and the probability of the system being in each state is calculated by the state transition probability matrix. A DBN is constructed to realize dynamic quantization and calculate the resilience index. Based on the node probabilities in dynamic Bayesian networks and the state transition probabilities in Markov chain models, the final evaluation results are obtained by analyzing the impact of changes in disturbance factors on resilience and / or recovery time.

[0026] Furthermore, the maritime liquefied natural gas (LNG) transportation system is divided into three levels: the physical transportation layer, the governance layer, and the ship service layer, and the specific content of a stable operating state is defined as follows: The first level is the physical transport layer, which is used to track the entire process from the initial production facility to the final delivery point, involving navigation and cargo storage. The second level is the governance level, which covers the system through which individuals and institutions jointly govern public affairs through various mechanisms; The third level is the ship service layer, which includes power supply, fuel security, communication and emergency response. When the physical transport layer, governance layer, and ship service layer are all in good working order, the system is in a stable operating state.

[0027] Furthermore, the 4R framework includes robustness (R1), redundancy (R2), rapid responsiveness (R3), and resource allocation capability (R4); among which, Robustness R1 refers to the degree of stress a system can withstand while maintaining a specific level of stability; Redundancy R2 refers to the amount of remaining resources used to mitigate damage; Rapid responsiveness (R3) refers to the system's ability to manage losses and prevent potential damage during the recovery process, and is measured by the slope of the function curve. Resource allocation capacity (R4) is an indicator that reflects the contribution of human factors to the recovery operation.

[0028] Furthermore, disruptive factors include natural factors, human factors, geopolitical risks, and terrorist attacks.

[0029] Furthermore, a dynamic Bayesian network is constructed, with functional components and disturbance factors as network nodes, to quantitatively evaluate the dynamic evolution of system resilience over time. Dynamic Bayesian networks introduce a time dimension into their structure, enabling them to capture and analyze the evolution of the system over time. The Bayesian formula is as follows:

[0030] in, Let be the likelihood probability. For prior probability, As evidence; The state of a node at time t depends not only on its parent node within the same time segment, but also on the state at time t-1 and the state of its parent node in the previous step, thus defining the dynamic evolution relationship over time:

[0031] in, Let be the set of states of all nodes at time t. Let be the set of states of all nodes at time t-1. The total number of nodes. For probability, Let be the state of the i-th node at time t. Let i be the state of the i-th node at time t-1. Let i be the i-th node at time t. The set of parent nodes, For time t-1, the first The set of parent nodes of each node.

[0032] Specifically, a Bayesian Network (BN) is a probabilistic model constructed in the form of a Directed Acyclic Graph (DAG). This structure consists of nodes interconnected by arcs, where nodes represent variables and arcs represent conditional dependencies between variables. A particularly noteworthy characteristic of this model is its powerful causal reasoning ability, especially suitable for uncertain systems, allowing it to infer the possible causes behind observed effects. Furthermore, Bayesian Networks exhibit remarkable adaptability: the model's probability distribution is dynamically updated when new evidence is introduced, thus deepening our understanding of the network. Dynamic Bayesian Networks (DBNs) are an important extension of Bayesian Networks. This model introduces a time dimension into its structure, enabling it to capture and analyze the evolution of the system over time, thereby mapping the probabilistic causal relationships between variables. This system can perform both predictive and diagnostic analyses. It must be noted that diagnostic analyses can combine observed evidence and simulate system operation in real time. Therefore, whenever new evidence appears, the probability values ​​of all nodes can be updated accordingly.

[0033] Specifically, using functional states can more accurately represent resilience, and the 4R factors are integrated into the functional curve at different time intervals. For example... Figure 2 As shown, the initial stage t0 represents the state of the system before it encounters damage. This stage does not yet incorporate the 4R factors, and its core objective is to assess the system's initial performance. From time point t1 onwards, the assessment focuses on the impact of specific hazard levels on the degree of damage to each functional branch (R1, R2, R3, R4) of the system. This assessment continues until time point t4, at which point the system's functionality will stabilize in a new state. By analyzing the functional curves, the response performance of the four functions of the system under disturbance can be evaluated.

[0034] Specifically, such as Figure 3As shown, the network structure and its component connections are presented using GeNIe software. Color coding is used to distinguish different variables in the network: pink nodes represent static variables and are assigned an unconditional probability table (UPT). Some elements are considered static and remain constant throughout the analysis; conversely, green, red, and yellow nodes represent dynamic variables. The conditional probability table (CPT) can be constructed based on expert assignments or empirical statistical data. The core function of the CPT is to assess the necessary probability values ​​for the system's resilience at a subsequent time step t+1. The assessment criteria include the system's current operating state (time t) and external factors, covering variables related to system interruption and recovery. To control the exponential growth of parameters, iterative compression techniques are applied to the CPT. Throughout the process, the accuracy of Bayesian inference is maintained.

[0035] Furthermore, fuzzy hierarchical analysis is used to quantify the influence of parent nodes on child nodes in the form of conditional probabilities.

[0036] Furthermore, a Markov chain model with four states S1, S2, S3, and S4 is established, where... S1 represents the state in which the system maintains its normal functional level under interference; S2 represents a state where the system's functionality has partially degraded; S3 represents a state of severe system dysfunction; S4 indicates that the system has successfully transitioned from a damaged state to the recovery process.

[0037] Furthermore, the specific details of constructing a DBN to achieve dynamic quantization and calculate resilience indicators by calculating the probability of the system being in each state through the state transition probability matrix are as follows: The resilience value R(t) of the system at a specific moment is defined as the sum of the probability P(S1) that the system is in state S1 and the probability P(S4) that the system is in state S4 at that moment, that is: R(t) = P(S1) + P(S4).

[0038] Specifically, such as Figure 2 As shown, four different states (S1, S2, S3, and S4) are defined and used to evaluate resilience. The transition probabilities between these states depend on the system's performance metrics (i.e., robustness, redundancy, rapid response, and resource allocation capability) under the influence of external disturbances in each time period.

[0039] Figure 4 It describes the transition process between specified states, which helps to understand the overall process more comprehensively. Figure 4 This paper systematically explains the programmatic transformation from the Markov chain framework to Dynamic Bayesian Networks (DBNs). Parameters , , and These correspond to the four elements R1, R2, R3, and R4 in the 4R model. A Database of Resilience (DBN) is then constructed to represent the evolution of the "resilience" node under the influence of the recovery attribute node. The "resilience" node is discretized into four mutually exclusive states (S1, S2, S3, and S4), and its probabilistic evolution is conditionally constrained by the recovery attribute node. For example, the transition probability between states S1 and S2 derived from the Markov chain is directly mapped to the corresponding conditional probability in the DBN, thus explicitly incorporating the influence of robustness.

[0040] Once the system reaches stability in the new steady state S4, the subsequent cycle will begin. The transition probability from S4 to S1 is denoted as... This corresponds to the nominal failure rate of the system under standard operating conditions. The steady-state failure rate λ is derived from the mean time between failures (MTBF), and its relationship is λ = 1 / MTBF. Similarly, the constant repair rate μ is defined as the reciprocal of the mean time to repair (MTTR), and its expression is μ = 1 / MTTR.

[0041] The allocation of transition probabilities is correspondingly guided by the system's resilience, which is reflected in the fundamental properties of the 4Rs. For example, when robustness is high, the system function in time... to The probability of degradation between these intervals is low. Therefore, when the mean time between failures (MTBF) increases, the corresponding... The value decreases, thereby reducing the probability of transitioning from state S1 to S2. Improvements in redundancy and fast response correspond to... and The value increases. Furthermore, resource allocation capabilities... It has a buffering effect. Figure 4 This demonstrates all the transition probabilities required for the model.

[0042] Specifically, resilience is defined as the sum of S1 and S4, that is, resilience is defined as the probability that the system, within each time step, during and after each interruption, will maintain its specified high-performance (normal) state or successfully recover from a low-performance (abnormal) state to a normal state. Two basic cases can be distinguished: (1) Provide sufficient robustness to absorb damage caused by interruptions, thereby increasing the probability of remaining in the desired functional state (S1) or minimizing the magnitude of performance degradation. A state represents the probability that the system will remain in a specific functional state.

[0043] (2) When disturbances are unavoidable and severe, redundancy and rapid response can enable recovery from the damaged state (S2) to the enhanced resilience state (S4). The probability of recovery from the damaged state to the expected functional state is reflected by the probability of state S4.

[0044] Resilience is quantified by summing states S1 and S4, a method adopted as the definition of resilience probability within the current framework. Furthermore, the system calculates the recovery time required to regain 90% of the lost resilience after damage and uses this as a time indicator to capture the time-varying characteristics of system resilience. For example, when resilience drops to 0.5, the time required to recover to 0.95 needs to be calculated, which is equivalent to recovering 0.45 units (0.5 × 0.9) from the lowest value of 0.5.

[0045] In one specific embodiment, the following is included: The liquefied natural gas (LNG) shipping route from Ras Lafan Port in Qatar to Yangkou Port in Jiangsu, China, plays a vital role in the global LNG shipping network and has become an important maritime trade channel for the import and export of LNG.

[0046] The functionality of a maritime liquefied natural gas (LNG) transport system refers to its ability to safely, timely, and cost-effectively transport LNG from export terminals to import terminals. However, the effectiveness of this function is highly susceptible to impairment when the system experiences disruptions. In such cases, performance degradation typically manifests as voyage delays, deviations from planned routes, cargo loss, or complete service interruption. Therefore, resilience assessments must measure the system's ability to maintain or rapidly restore its intended functionality under specific disruption scenarios.

[0047] To assess resilience, an evaluation system was constructed using the 4R framework. The fundamental attribute is robustness, assessed through three indicators: vessel age, annual failure rate, and typhoon resistance capability. Systems with vessels under five years old and an annual failure rate of less than one incident are considered highly robust. Another key attribute is redundancy, quantified through two core indicators: the number of available alternative routes and tank redundancy rate. Systems with at least three feasible alternative routes and a tank redundancy rate exceeding 30% are considered highly redundant. The framework also incorporates rapid response capability, assessed through emergency response capabilities and early warning system effectiveness. Excellent rapid response capability is demonstrated by the ability to arrive at the rescue site within 30 minutes; this standard is verified through quarterly emergency drills. The final attribute is resource allocation capability, measured by the number of established mutual assistance agreements (MCAs) and training compliance rate. Systems maintaining at least two MCAs and achieving a training compliance rate exceeding 90% are considered to have high resource allocation capability.

[0048] The Fuzzy Hierarchical Analysis (FAHP) method is used to quantify the influence of parent nodes on child nodes in the form of conditional probabilities. This method uses a fuzzy logic system to manage uncertainty and constructs a formal framework that can handle fuzzy and uncertain data.

[0049] FAHP is used to assess the importance of each confounding factor. This method uses fuzzy quantization to convert expert opinions into specific numerical values, and then constructs corresponding pairwise comparison matrices within the FAHP framework. The weights of these factors may vary significantly across different systems, depending on the specific operating environment and external influencing conditions. Figure 5 The process of converting a Markov chain into a DBN is demonstrated, and all relevant confounding factors are presented. Within this framework, the assigned importance weights indicate the degree of influence a parent node exerts on its child nodes, thus reflecting the corresponding conditional probabilities. The weights in Table 2 are derived using the following method: First, the language is converted into triangular fuzzy numbers according to the semantic-numerical mapping rules described in Table 1. Then, eleven domain experts are invited to conduct pairwise evaluations of the relative importance of the selected parameters. Finally, the scores are summarized, and the node sensitivities are ranked. After comparing all parameters, the conversion scores for the 4R parameters are obtained. The weights of each parameter are calculated using interval analysis. This method is based on the assumption that the contributions of each parent node to its child nodes are independent and do not inhibit each other. Therefore, the "Noisy-OR" function quantifies the probabilistic relationship between parent and child nodes through conditional probabilities, and its mathematical expression is:

[0050] in, For variables Results in isolated context Marginal activation probability, variable Restricted to the set of Boolean values ​​[0, 1], when Setting it to 1 indicates that the factor is in a "high" state. Therefore, the complete conditional probability diagram (CPT) can be obtained through a small number of expert estimates.

[0051] Table 1. Transformation standards based on triangular fuzzy numbers

[0052] Table 2. Weight distribution of important parameters affecting 4R and interference factors in DBN

[0053] like Figure 6As shown, the system resilience decreased significantly, dropping to a low of 0.5 at t=10 minutes, and then recovering to 0.95 after 37 minutes. Decreased robustness leads to a more significant decrease in system resilience, while improved robustness effectively mitigates this loss. When the resilience parameter approaches 1.0, redundancy and rapid response play crucial roles, jointly contributing to a dynamic equilibrium, ultimately enabling the system to stabilize in the final state S4 with a probability of 0.956 after 100 minutes. The core conclusion of the analysis is that even when the system resilience has recovered to 90%, the internal optimization process continues. Finally, the system reaches a steady state at t=47 minutes and maintains this level.

[0054] In this embodiment, the system recovery function takes 100 minutes, which corresponds to the stabilization period. For example... Figure 7 As shown, the system resilience exhibits a specific pattern over time: at t=14 minutes, the probability of state S1 drops to nearly 0.2; furthermore, the probabilities of state S2 and S3 peak at 8 minutes and 13 minutes, respectively, at 0.339 and 0.182. The probability of state S4 drops to its lowest value of 0.5 at t=10 minutes, then rises sharply, stabilizing at 0.97 at t=60 minutes. These data validate the effectiveness of the proposed model, and the changes in system resilience are entirely consistent with theoretical expectations.

[0055] To identify the main factors affecting resilience assessment, a sensitivity analysis was conducted on the established model. Figure 8a The system provided by the present invention The probability distribution that changes over time; Figure 8b The system provided by the present invention The probability distribution that changes over time; Figure 8c The system provided by the present invention The probability distribution that changes over time; Figure 8d The system provided by the present invention Probability distribution that changes over time; such as Figure 9 As shown, the influence of the 4R factors on the system's toughness variation is revealed. Sensitivity analysis of the four parameters indicates that under normal operating conditions, the failure rate ( ) and self-repair rate ( Fluctuations in the failure rate (FRR) can lead to significant changes in system resilience; while the failure rate under interruption conditions (FRR) Corresponding changes and external intervention repair rate () The changes in ( ) are relatively small. Therefore, precise calibration and This is crucial for ensuring the reliability of resilience assessments. For example... Figure 10 As shown, after a system outage caused by interference, the sensitivity analysis of the 4R factors on the recovery of 90% resilience is compared with... Figure 6 The observational data show a high degree of agreement. Further analysis indicates that... The amplification effect of the disturbance amplitude is significantly better than that of other variables. When As volatility increases, the system's recovery period from interruption to full recovery becomes significantly longer. In contrast, the recovery periods for the other three variables show smaller increases, a trend that continues in... Figure 9 This is especially evident in the curve comparison.

[0056] The number of nodes for each interference factor in the dynamic Bayesian network is consistent with that in Table 3. For example... Figure 11 As shown, the two curves illustrate the comparison of final stability resilience under different parameter settings. The black baseline (value: 0.979) corresponds to the optimal resilience scenario, characterized by all nodes listed in Table 3 being in a "high" state. The red curve shows how the system resilience gradually deteriorates when a single node (in a "low" state) fails, while the remaining nodes operate normally (in a "high" state). When node 6 (port management and operational efficiency) fails, the resilience drops to its lowest point, followed by decreases at nodes 11, 8, 12, 1, and 5. The rate of change for the remaining nodes is small (<0.5%), indicating that these factors have a limited impact on system resilience. Figure 9 It can serve as the basis for resource allocation decisions, ensuring stable operational efficiency throughout all stages of a disruption event (i.e., before, during, and after the event). To build a highly resilient system, key resources should be invested in improving port management and operational efficiency, local government and government support, Automatic Identification Systems (AIS) and communications, international collaboration and coordination, shipping technology, and supply chain redundancy.

[0057] Table 3. Nodes contributing to the 4R principle and interference factors

[0058] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0059] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for assessing the resilience of offshore liquefied natural gas transportation systems based on dynamic Bayesian networks, characterized in that, Includes the following steps: The maritime liquefied natural gas transportation system is divided into three levels: the physical transportation layer, the governance layer, and the ship service layer, and a stable operating state is defined. Based on the 4R framework, the system resilience is decomposed into four functional components: robustness, redundancy, rapid response, and resource allocation capability, and the interference factors affecting the functional components are identified. Construct a dynamic Bayesian network, using functional components and disturbance factors as network nodes, to quantitatively assess the dynamic evolution of system resilience over time; A Markov chain model with four states S1, S2, S3, and S4 is established, and the probability of the system being in each state is calculated by the state transition probability matrix. A DBN is constructed to realize dynamic quantization and calculate the resilience index. Based on the node probabilities in dynamic Bayesian networks and the state transition probabilities in Markov chain models, the degree of influence of changes in disturbance factors on resilience and / or recovery time is analyzed through sensitivity analysis to obtain the final evaluation results.

2. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, The maritime liquefied natural gas (LNG) transportation system is divided into three layers: the physical transportation layer, the governance layer, and the ship service layer. The specific content of a stable operating state is defined as follows: The first level is the physical transport layer, which is used to track the entire process from the initial production facility to the final delivery point, involving navigation and cargo storage. The second level is the governance level, which covers the system through which individuals and institutions jointly govern public affairs through various mechanisms; The third level is the ship service layer, which includes power supply, fuel security, communication and emergency response. When the physical transport layer, governance layer, and ship service layer are all in good working order, the system is in a stable operating state.

3. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, The 4R framework includes robustness (R1), redundancy (R2), rapid response (R3), and resource allocation capability (R4); among them, Robustness R1 refers to the degree of stress a system can withstand while maintaining a specific level of stability; Redundancy R2 refers to the amount of remaining resources used to mitigate damage; Rapid responsiveness (R3) refers to the system's ability to manage losses and prevent potential damage during the recovery process, and is measured by the slope of the function curve. Resource allocation capacity (R4) is an indicator that reflects the contribution of human factors to the recovery operation.

4. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, Disruptive factors include natural factors, human factors, geopolitical risks, and terrorist attacks.

5. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, The specific content of constructing a dynamic Bayesian network, using functional components and disturbance factors as network nodes, to quantitatively evaluate the dynamic evolution of system resilience over time is as follows: Dynamic Bayesian networks introduce a time dimension into their structure, enabling them to capture and analyze the evolution of the system over time. The Bayesian formula is as follows: in, Let be the likelihood probability. For prior probability, As evidence; The state of a node at time t depends not only on its parent node within the same time segment, but also on the state at time t-1 and the state of its parent node in the previous step, thus defining the dynamic evolution relationship over time: in, Let be the set of states of all nodes at time t. Let be the set of states of all nodes at time t-1. The total number of nodes. For probability, Let be the state of the i-th node at time t. Let i be the state of the i-th node at time t-1. Let i be the i-th node at time t. The set of parent nodes, For time t-1, the first The set of parent nodes of each node.

6. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 5, characterized in that, Fuzzy hierarchical analysis is used to quantify the influence of parent nodes on child nodes in the form of conditional probabilities.

7. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, Construct a Markov chain model with four states S1, S2, S3, and S4, where... S1 represents the state in which the system maintains its normal functional level under interference; S2 represents a state where the system's functionality has partially degraded; S3 represents a state of severe system dysfunction; S4 indicates that the system has successfully transitioned from a damaged state to the recovery process.

8. The method for assessing the resilience of a marine liquefied natural gas transportation system based on a dynamic Bayesian network according to claim 1, characterized in that, The specific details of constructing a DBN to achieve dynamic quantization and calculate resilience indicators by calculating the probability of the system being in each state using the state transition probability matrix are as follows: The resilience value R(t) of the system at a specific moment is defined as the sum of the probability P(S1) that the system is in state S1 and the probability P(S4) that the system is in state S4 at that moment, that is: R(t) = P(S1) + P(S4).

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