Important material logistics risk evaluation method based on multi-dimensional dynamic Bayesian network

Abstract

The invention relates to the technical field of logistics risk identification, in particular to an important material logistics risk evaluation method based on a multi-dimensional dynamic Bayesian network, by defining basic events and intermediate events and drawing a Dulan dynamic fault tree, the logic relation and the time sequence among risk factors in the logistics process can be visually displayed, and the risk evaluation accuracy is improved. And key risk points and weak links can be quickly identified. Events in the dynamic fault tree are converted into nodes in the Bayesian network, directed edges are used for connection, and the multi-dimensional dynamic Bayesian network is constructed. By means of the step, mathematization and modeling of the risk assessment method are achieved, and a basis is provided for follow-up quantitative analysis and calculation. The multi-dimensional dynamic Bayesian network can process data with multiple dimensions and dynamic characteristics, so that risk assessment is more refined and intelligent. Through the network, a plurality of risk factors and dynamic relations among the risk factors can be comprehensively considered, and a more accurate risk assessment result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of logistics risk identification, and in particular to an important material logistics risk assessment method based on a multidimensional dynamic Bayesian network. Background Art

[0002] Logistics risk identification is a critical component of supply chain management, particularly in the logistics of critical materials. Accurately identifying and managing potential risk factors is crucial. The modern logistics environment is complex, involving multiple factors, including personnel, equipment, and the environment. These factors, individually or in combination, can impact the efficiency and safety of logistics operations. Therefore, a thorough understanding and identification of these risk sources is fundamental to effective risk management.

[0003] The current method for identifying logistics risks involves identifying risk factors that may affect the safety of material logistics based on the characteristics and actual conditions of material logistics. Identified risk factors are used as nodes, and a directed acyclic graph is established based on the dependencies between them. Prior probabilities are assigned to each risk factor node, and collected data is used to estimate the conditional probability table in the Bayesian network. Real-time risk factor data is input into the Bayesian network model, and probabilistic reasoning is performed using Bayes' theorem and the conditional probability table to calculate the probability of material logistics risks caused by each risk factor. Based on the reasoning results, the probability of future material logistics risks is predicted, and corresponding risk management strategies and decisions are formulated accordingly. Problems include:

[0004] 1. There are real-time issues

[0005] In the field of material logistics, real-time performance is crucial for risk assessment and decision-making. However, traditional Bayesian networks may have limitations in processing real-time data, as shown below:

[0006] Data update delays: Traditional Bayesian network models are typically built and trained based on historical data, so they can experience update delays when processing real-time data. When new data is generated, the model may not be immediately updated to reflect the latest risk profile.

[0007] Limited real-time reasoning capabilities: Although Bayesian networks can perform probabilistic reasoning, their reasoning capabilities may be limited in real-time environments. This is especially true in dynamic scenarios like material logistics, where traditional Bayesian networks may not be able to quickly reason and make decisions based on new data and information.

[0008] 2. There are dynamic issues

[0009] Material logistics risks are dynamic and are affected by many factors, such as weather, traffic conditions, and market demand. Problems that traditional Bayesian networks may encounter when dealing with such dynamic changes include:

[0010] Insufficient model adaptability: Traditional Bayesian network models are typically built based on static datasets and therefore may exhibit insufficient adaptability when dealing with dynamically changing risks. When risk factors change, the model may not be able to accurately capture and represent such changes.

[0011] Inability to capture risk trends: In the field of material logistics, risk trends are crucial for risk assessment and decision-making. However, traditional Bayesian networks may not effectively capture and represent the changing trends of risk over time and in different environments. This can lead to biased predictions of future risks.

[0012] 3. There is a problem of single dimension

[0013] Material logistics risks often stem from more than one factor. Traditional Bayesian networks, such as fault tree analysis and discrete-time Bayesian networks, typically only process data in a single dimension. These methods often fail to fully consider the complex relationships and dynamic changes among various factors within a system when describing system stability.

[0014] Due to their single-dimensional nature, traditional methods may not accurately capture all characteristics of system stability. For example, in the stability analysis of electrical or wireless communication systems, system stability may be affected by multiple factors (such as time, temperature, and pressure). Considering only one factor may result in inaccurate conclusions.

[0015] Difficulty and significance of problem solving:

[0016] First, a dynamic fault tree model of failure time is constructed. This requires a deep understanding of the system's operational processes and dynamic fault tree theory. MDBN uses unit transition functions and impulse functions to serialize the dynamic logic gates of the constructed dynamic fault tree, requiring deep knowledge of statistics and advanced mathematics. MDBN assumes that each influencing factor independently calculates the failure probability of the system under the influence of each factor, such as node importance. This requires statistical analysis of event failure data under different influencing factors, applying statistical knowledge to derive failure probabilities, and then combining these probabilities with calculation formulas for inference. Furthermore, to accurately describe the system's dynamic and multidimensional characteristics, a deep understanding and analysis of the system is required. The reasoning and calculation process of MDBN involves complex mathematical operations and algorithms, placing high demands on computing resources.

[0017] Solving these problems has certain significance for the actual situation

[0018] 1. Improve system stability:

[0019] MDBN can comprehensively consider the influencing factors of multiple dimensions and capture the dynamic characteristics of the system, thereby more accurately assessing the system's stability. This helps to promptly identify potential problems and take appropriate measures to avoid system failures or malfunctions.

[0020] 2. Optimize decision support:

[0021] MDBN can analyze the system status in real time and predict future trends, providing decision makers with timely and accurate information support, helping them make more informed decisions.

[0022] 3. Promote technological development:

[0023] The research and application of MDBN will promote the development of related technologies, including statistics, probability theory, machine learning, and artificial intelligence, which will help improve the technical level and innovation capabilities of the entire field.

[0024] The existing Chinese patent document CN202110439493.9 discloses a logistics risk assessment model method, device, equipment and medium based on dynamic Bayesian, which includes: determining a set of candidate risk influencing factors associated with each logistics link; selecting formal risk influencing factors from the set of candidate risk influencing factors; determining the initial state category and prior probability value of each formal risk influencing factor; constructing a static Bayesian network for logistics risk assessment; constructing the state transition relationship between each logistics link and the transition probability that changes over time; adding transition probability to the static Bayesian network to construct a dynamic Bayesian network for logistics risk assessment; and completing the assessment of the risk and total risk of each logistics link in the logistics process based on the dynamic Bayesian network for logistics risk assessment. Summary of the Invention

[0025] The purpose of the present invention is to provide an important material logistics risk assessment method based on a multidimensional dynamic Bayesian network in the context of the "post-mass infectious disease era". By defining basic events and intermediate events and drawing a Dugan dynamic fault tree, this paper can intuitively display the logical relationship and time sequence between various risk factors in the logistics process, which helps to quickly identify key risk points and weak links. The events in the dynamic fault tree are converted into nodes in the Bayesian network and connected with directed edges to construct a multidimensional dynamic Bayesian network. This step realizes the mathematization and modeling of the risk assessment method, and provides a basis for subsequent quantitative analysis and calculation. The multidimensional dynamic Bayesian network can process data with multiple dimensions and dynamic characteristics, making risk assessment more refined and intelligent. Through this network, a variety of risk factors and their dynamic relationships can be comprehensively considered to obtain more accurate risk assessment results.

[0026] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0027] A method for evaluating the risk of important material logistics based on a multidimensional dynamic Bayesian network comprises the following steps:

[0028] S1: Identification of logistics risks of important materials in the context of the “post-pandemic infectious disease era”;

[0029] S2: Construction of Dugan fault tree for important material logistics process;

[0030] S3: Construction of multidimensional dynamic Bayesian network for important material logistics processes;

[0031] S4: Multidimensional dynamic Bayesian network evaluation and analysis of important material logistics processes.

[0032] Furthermore, step S1 includes the following sub-steps:

[0033] S1.1: Analyze the logistics process of important materials, which is divided into five links: processing and packaging, receiving and warehousing, warehouse management, sorting and outbound delivery, and transportation and distribution;

[0034] S1.2: Organize and analyze the direct causes of transportation system failure in accident cases, and identify risk factors from the three levels of people, machines, and environment.

[0035] Furthermore, step S2 includes the following sub-steps:

[0036] S2.1: Define basic events and intermediate events for the important material logistics process risk factors identified in S1, and number the events;

[0037] S2.2: Based on events and numbers, draw a Dugan dynamic fault tree for the important material logistics process.

[0038] Furthermore, step S3 includes the following sub-steps:

[0039] S3.1: Convert the events in the Dugan dynamic fault tree of the important material logistics process into nodes in the Bayesian network according to the "mapping rules between Dugan dynamic fault tree analysis and continuous-time Bayesian network";

[0040] S3.2: Use directed edges to connect nodes and draw a multidimensional dynamic Bayesian network for the logistics process of important materials.

[0041] Furthermore, step S4 includes the following sub-steps:

[0042] S4.1: Time-continuous construction of Bayesian networks, i.e., using unit transition functions and impulse functions to describe the time series relationship between root node failures and leaf node failures;

[0043] The input of the unit step function can express the failure time of the input event, and obtain the quantitative relationship between the failure distribution of the output event and the failure time of each input event. The unit step function is defined as follows:

[0044]

[0045] where t i ,t j Represents x respectively i ,x j The moment when the root node is unavailable; u(t i -t j ) is a unit step function, which represents the time series when the leaf nodes are unavailable.

[0046] The impulse function is defined as follows:

[0047]

[0048] This function has the property that the definite integral is 1 in the integral domain:

[0049]

[0050] where t T Represents the time when child node T is unavailable. When t T =t i It means that when the root node x i Failure time t i Child node T also fails. T ≠t i When it means that the child node T is not in x i The moment of failure is failure.

[0051] S4.2: Calculation of leaf node failure probability in multidimensional dynamic Bayesian networks;

[0052] In addition to the time factor, the root node x i (i=1,2,...,n) is also affected by many other interference factors, such as human operation, environment, etc. Let these other interference factors be e j (j=1,2,...,m), with Z i (t) is the time when node i is affected by interference factor e j The state variables at time t after the impact.

[0053]

[0054] When Zi When (t) is 1, the root node x i There is no failure after the interference factor, and when the root node is only affected by the time factor, the probability of no failure is:

[0055]

[0056] Represents when the root node x i The state variable is only affected by the time factor. P[A] represents the probability of event A occurring. F i (t i ) represents the time factor t i Affects the root node x i The failure probability distribution function.

[0057] The probability of no failure when affected by other factors is:

[0058]

[0059] Represents when the root node x i The state variable affected by other factors, F j (e j ) represents the interference factor e j Affects the root node x i The failure probability distribution function.

[0060] When m influencing factors are independent of each other, the root node x i Failure probability distribution function F i (t i ,e1,e2,...,e m )for:

[0061]

[0062] Calculating the partial derivatives of each factor variable in formula (7), we can get the root node x i The probability density function of is:

[0063]

[0064] Based on formula (8) and the Bayesian network reasoning method, combined with the unavailable order of the root node and leaf nodes in the system Bayesian network, the leaf node x can be obtained. i The probability density function that is not available is:

[0065]

[0066] r is the number of conditional probability tables, Ξl is the lower integral domain of sequence number l, R(l)=u(ti -t j ) is a unit step function, i and j represent any two nodes, P (l) (t T ) is the impulse function of leaf node T with sequence number l.

[0067] Based on the probability density function of the root node being unavailable, the probability density distribution function of the child node being unavailable can be obtained as follows:

[0068]

[0069] S4.3: Calculation of posterior probability of root nodes in multidimensional dynamic Bayesian networks;

[0070] Based on the unique reverse reasoning ability of the Bayesian network, the posterior probability of the intermediate node or root node within a specific task time range can be effectively calculated in a multi-dimensional dynamic Bayesian network structure when a leaf node fails. The posterior probability formula is:

[0071]

[0072] Among them F T (T M ,e1,e2,…,e m ) is the leaf node T at task time T M The probability of failure within .

[0073] S4.4: Multidimensional dynamic Bayesian network importance analysis;

[0074] The probabilistic importance of a root node reflects the importance of the root node component in the system. Due to economic and time constraints, it is impossible for managers to improve the security of all processes simultaneously. Therefore, probabilistic importance provides managers with an optimized ranking of root node security, allowing them to prioritize improving root nodes with high probabilistic importance. The probabilistic importance of a root node is:

[0075]

[0076] Among them F T (t i ,e1,e2,…,e m ) represents the failure probability distribution function of leaf node T under the influence of time and multiple factors, F i (t i ,e1,e2,…,e m ) represents the root node x i Failure probability distribution function affected by time and other factors.

[0077] Beneficial effects of the present invention:

[0078] The present invention significantly improves the real-time dynamic response capability of the risk assessment process by constructing a multidimensional dynamic Bayesian network (MDBN). In a complex logistics environment, risk factors are highly time-varying and uncertain. By combining the advantages of a dynamic fault tree (Dugan fault tree) and a Bayesian network, the MDBN can quickly process newly acquired real-time data. Specifically, the MDBN model uses mathematical tools such as unit transition functions and impulse functions to update the conditional probabilities of risk factors in real time and adjust the dependencies between network nodes. The originally discrete time periods are made continuous. This allows the model to be dynamic and the failure probability of each time root node to be obtained. The MDBN not only improves the adaptability of the model, but also can reflect changes in risk conditions in the logistics process in real time, thereby providing decision makers with real-time risk assessment information and decision support.

[0079] The present invention is different from existing methods in that it adds the dimension of the degree of impact of mass infectious diseases to the dimension of working hours. When constructing a dynamic fault tree model, the key links of the material logistics process are carefully analyzed to enhance the accuracy and comprehensiveness of risk assessment. In actual application, the logistics process is decomposed into five major links: processing and packaging, receiving and warehousing, warehouse management, sorting and outbound transportation and distribution, and the risk factors are comprehensively analyzed from the three aspects of people, machines, and environment. This fine-grained analysis method is effectively integrated into MDBN, enabling the model to capture and analyze the complex causal relationships and time series characteristics between various links and factors. And by adding dimensions, it can not only reflect the failure probability of the system over time, but also the failure probability of the system can be seen under the changes in the severity of mass infectious diseases. Therefore, MDBN improves the accuracy of risk assessment and can more accurately identify and quantify potential risks in the logistics process.

[0080] The present invention achieves an intelligent upgrade of risk assessment methods through the application of multi-dimensional dynamic Bayesian networks, greatly optimizing the decision support system. MDBN not only supports traditional probabilistic reasoning, but also can perform multi-dimensional causal inference based on the dynamic behavior of complex systems. In terms of specific technical implementation, MDBN constructs a time-continuous network structure, comprehensively considers multiple risk factors and their dynamic interactions, making the risk assessment process more intelligent and sophisticated. Through posterior probability calculation, managers can prioritize key risk nodes based on the probability ranking provided by the model when leaf nodes fail, thereby improving the efficiency and pertinence of resource allocation.

[0081] Faced with a highly complex and rapidly changing logistics environment, particularly in the context of pandemics, MDBN demonstrates exceptional adaptability and application value. By incorporating pandemic severity as an analytical dimension, MDBN is able to capture the dynamics of supply chain changes at different pandemic stages and quantify their impact on systemic risk. This analytical capability not only extends the limitations of traditional Bayesian networks in handling time-series problems but also provides a more comprehensive perspective for risk management in complex dynamic environments. By assessing the failure probability of logistics nodes under different pandemic states, MDBN provides policymakers and business managers with data-driven decision-making and facilitates the development of more effective risk management strategies.

[0082] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0084] Figure 1 A schematic diagram of the Dugan fault tree for the important material logistics process constructed by the present invention;

[0085] Figure 2 Schematic diagram of the mapping rules between Dugan dynamic fault tree analysis and continuous-time Bayesian network;

[0086] Figure 3 This is a schematic diagram of the multidimensional dynamic Bayesian network of the important material logistics process constructed by the present invention;

[0087] Figure 4 Schematic diagram of the failure probability distribution of leaf nodes over working time;

[0088] Figure 5 Schematic diagram of the failure probability distribution of leaf node T with working time and severity of mass infectious diseases; DETAILED DESCRIPTION

[0089] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0090] Example 1

[0091] The method for evaluating the risk of important material logistics based on a multidimensional dynamic Bayesian network described in this embodiment includes the following steps:

[0092] S1: Identification of logistics risks of important materials in the context of the “post-pandemic infectious disease era”;

[0093] S2: Construction of Dugan fault tree for important material logistics process;

[0094] S3: Construction of multidimensional dynamic Bayesian network for important material logistics processes;

[0095] S4: Multidimensional dynamic Bayesian network evaluation and analysis of important material logistics processes.

[0096] In this embodiment, step S1 includes the following sub-steps:

[0097] S1.1: Analyze the logistics process of important materials. The process can be generally divided into five main links: processing and packaging, receiving and warehousing, warehouse management, sorting and outbound delivery, and transportation and distribution;

[0098] S1.2: Organize and analyze the direct causes of transportation system failure in accident cases, and identify risk factors from the three levels of people, machines, and environment.

[0099] In this embodiment, step S2 includes the following sub-steps:

[0100] S2.1: Define basic events and intermediate events for the important material logistics process risk factors identified in S1, and number the events;

[0101] S2.2: Based on events and numbers, draw a Dugan dynamic fault tree for the important material logistics process.

[0102] Table 1 Basic event numbers and failure rates of important material logistics processes identified in this embodiment

[0103]

[0104] Table 2: Intermediate event numbers of important material logistics processes identified in this embodiment

[0105] serial number Intermediate Events serial number Intermediate Events BI Other personnel errors B7 Weather reasons B2 Driver error B8 External causes B3 Vehicle defects Al Human error B4 Packaging issues A2 Equipment failure B5 Loading and unloading issues A3 Environmental factors B6 Warehouse equipment issues T Logistics process of important materials

[0106] In this embodiment, step S3 includes the following sub-steps:

[0107] S3.1: Convert the events in the Dugan dynamic fault tree of the important material logistics process into nodes in the Bayesian network according to the "mapping rules between Dugan dynamic fault tree analysis and continuous-time Bayesian network";

[0108] S3.2: Use directed edges to connect nodes and draw a multidimensional dynamic Bayesian network for the logistics process of important materials.

[0109] In this embodiment, step S4 includes the following sub-steps:

[0110] S4.1: Time-continuous construction of Bayesian networks, i.e., using unit transition functions and impulse functions to describe the time series relationship between root node failures and leaf node failures;

[0111] The input of the unit step function can express the failure time of the input event, and obtain the quantitative relationship between the failure distribution of the output event and the failure time of each input event. The unit step function is defined as follows:

[0112]

[0113] where t i ,t j Represents x respectively i ,x j The moment when the root node is unavailable; u(t i -t j ) is a unit step function, which represents the time series when the leaf nodes are unavailable.

[0114] The impulse function is defined as follows:

[0115]

[0116] This function has the property that the definite integral is 1 in the integral domain:

[0117]

[0118] where t T Represents the time when child node T is unavailable. When t T =t i It means that when the root node x i Failure time t i Child node T also fails. T ≠t i When it means that the child node T is not in x i The moment of failure is failure.

[0119] S4.2: Calculation of leaf node failure probability in multidimensional dynamic Bayesian networks;

[0120] In addition to the time factor, the root node x i (i=1,2,...,n) is also affected by many other factors, such as human operation, environment, etc. Let these other interference factors be e j (j=1,2,...,m), with Zi (t) is the time when node i is affected by interference factor e j The state variables at time t after the impact.

[0121]

[0122] When Z i When (t) is 1, the root node x i There is no failure after the interference factor, and when the root node is only affected by the time factor, the probability of no failure is:

[0123]

[0124] Represents when the root node x i The state variable is only affected by the time factor. P[A] represents the probability of event A occurring. F i (t i ) represents the time factor t i Affects the root node x i The failure probability distribution function.

[0125] The probability of no failure when affected by other factors is:

[0126]

[0127] Represents when the root node x i The state variable affected by other factors, F j (e j ) represents the interference factor e j Affects the root node x i The failure probability distribution function.

[0128] When m influencing factors are independent of each other, the root node x i Failure probability distribution function F i (t i ,e1,e2,...,e m )for:

[0129]

[0130] Calculating the partial derivatives of each factor variable in formula (7), we can get the root node x i The probability density function of is:

[0131]

[0132] Based on formula (8) and the Bayesian network reasoning method, combined with the unavailable order of the root node and leaf nodes in the system Bayesian network, the leaf node x can be obtained.i The probability density function that is not available is:

[0133]

[0134] r is the number of conditional probability tables, Ξl is the lower integral domain of sequence number l, R(l)=u(t i -t j ) is a unit step function, i and j represent any two nodes, P (l) (t T ) is the impulse function of leaf node T with sequence number l.

[0135] Based on the probability density function of the root node being unavailable, the probability density distribution function of the child node being unavailable can be obtained as follows:

[0136]

[0137] S4.3: Calculation of posterior probability of root nodes in multidimensional dynamic Bayesian networks;

[0138] Based on the unique reverse reasoning ability of the Bayesian network, the posterior probability of the intermediate node or root node within a specific task time range can be effectively calculated in a multi-dimensional dynamic Bayesian network structure when a leaf node fails. The posterior probability formula is:

[0139]

[0140] Among them F T (T M ,e1,e2,…,e m ) is the leaf node T at task time T M The probability of failure within .

[0141] S4.4: Multidimensional dynamic Bayesian network importance analysis;

[0142] The probabilistic importance of a root node reflects the importance of the root node component in the system. Due to economic and time constraints, it is impossible for managers to improve the security of all processes simultaneously. Therefore, probabilistic importance provides managers with an optimized ranking of root node security, allowing them to prioritize improving root nodes with high probabilistic importance. The probabilistic importance of a root node is:

[0143]

[0144] Among them F T (t i ,e1,e2,…,e m ) represents the failure probability distribution function of leaf node T under the influence of time and multiple factors, F i (t i,e1,e2,…,e m ) represents the root node x i Failure probability distribution function affected by time and other factors.

[0145] Example 2

[0146] like Figure 4 , Figure 5 As shown in the figure, this embodiment uses a multidimensional dynamic Bayesian network (MDBN) to conduct an in-depth and systematic analysis of the failure probability of leaf nodes within the task time. As an extended Bayesian network model, MDBN not only retains the advantages of traditional Bayesian networks in handling uncertainty problems, such as probabilistic reasoning and causal inference, but also achieves comprehensive modeling of dynamic systems and complex dependencies by introducing the dimensions of time and the impact of mass infectious diseases.

[0147] The core functionality of MDBN lies in its ability to capture complex dependencies that evolve over time and accurately assess the failure probability of leaf nodes over different time periods. This capability is particularly important when addressing time-series problems, as it can reveal the dynamic evolution patterns hidden behind the data. Using MDBN, one can intuitively see the increasing trend in leaf node failure probability over time, which helps better understand the dynamic behavior of the system and provides strong support for subsequent decision-making and optimization.

[0148] In contrast, traditional Bayesian networks (BNs) have significant limitations when dealing with continuous-time analysis problems. Traditional BNs can typically only analyze prior probabilities at fixed time points, and fail to fully consider the impact of time factors on the data. This limitation prevents traditional BNs from capturing and reflecting the dynamic evolution of the problem, making it impossible to accurately assess the failure risk of leaf nodes in different time periods. Therefore, when faced with problems with time series characteristics, the application of traditional BNs is often unsatisfactory.

[0149] Multidimensional Dynamic Bayesian Networks, with their powerful dynamic modeling and multivariate analysis capabilities, demonstrate significant advantages in analyzing changes in leaf node failure probabilities. By introducing the time dimension, MDBNs can more accurately assess the failure risk of leaf nodes over different time periods, providing decision makers with more comprehensive and accurate information support, offering valuable insights and reference for practical applications.

[0150] like Figure 5As shown, MDBN, as an advanced probabilistic graphical model, not only demonstrates exceptional capabilities in time series analysis, accurately capturing and quantifying the dynamic trends in leaf node failure probabilities over time, but also significantly enhances the depth and breadth of problem analysis through its unique multidimensional analysis capabilities. Specifically, MDBN achieves a comprehensive characterization of the dynamic behavior of complex systems by integrating time series data with multidimensional feature information. This study specifically selected the key dimension of "severity of mass infectious diseases" to further explore the variation patterns of leaf node failure probabilities under different infectious disease backgrounds.

[0151] Compared to traditional static Bayesian networks (BNs), their inherent limitation is that they can only process static data at a single point in time, ignoring the dynamic nature of time series data and the interactions between multiple factors. This single-dimensional analysis method is inadequate when faced with complex systems such as mass infectious diseases that involve numerous variables and change rapidly over time. Therefore, the selection of "severity of mass infectious diseases" as an analysis dimension is based on its profound impact on multiple aspects such as socioeconomic activities, resource allocation, and public behavior. It is an indispensable key factor in assessing the risk of leaf node failure.

[0152] In practical applications, by constructing an MDBN model that incorporates the severity dimension of a pandemic, we observed significant differences in the failure probability of leaf nodes at different stages of a pandemic (e.g., mild, moderate, and severe). For example, during the peak of a pandemic, the failure probability of leaf nodes increased significantly due to factors such as resource constraints and supply chain disruptions. However, after the pandemic was effectively controlled, the failure probability decreased as economic activity gradually resumed. This finding not only validates the effective application of MDBN in complex dynamic systems but also provides decision makers with more accurate, data-based risk management strategy recommendations.

[0153] It can be seen that the multidimensional dynamic Bayesian network, with its powerful multidimensional data analysis capabilities and sensitive capture of dynamic changes, provides a powerful tool for in-depth understanding of the complex mechanisms of leaf node failure probability. Through case analysis, its application value in the specific dimension of the severity of mass infectious diseases is further demonstrated. This not only enriches theoretical research in related fields, but also provides scientific basis and practical guidance for addressing possible future risk identification.

[0154] Example 3

[0155] This experiment is compared to a discrete-time Bayesian network (DTBN). Both the DTBN and the multidimensional dynamic Bayesian network used in this invention require a dynamic fault tree model based on an analysis of the system's functional structure. The difference is that the DTBN can only analyze in a single dimension and cannot consider the changes in the failure probability of the root and leaf nodes in different dimensions.

[0156] The DTBN with m nodes is expressed as: N = < <V,T n ,G>,P>. Where, V={V1,V2,…,V m}, is a node set, mainly including root nodes, intermediate nodes and leaf nodes; T n ={[t0,t1),[t1,t2),…,[t n ,+∞)}, indicating that a timeline is divided into n+1 time intervals, and the time interval length Δ=T n / n; G is the directed edge between nodes, indicating the relationship between variables.

[0157] Assuming that the node V follows an exponential distribution (failure rate is λ), the failure probability of the node V at any time interval i within the task time is:

[0158]

[0159] When the node V is in the time interval [t n ,+∞), then the node V is in the task time [t0,t n ) is not invalid, that is:

[0160]

[0161] The logic behind DTBN's conversion of a fault tree into a Bayesian model is the same as that of MDBN. Fussell-Vesely (FV) importance is used to calculate importance, indicating the impact of a unit failure on the system.

[0162]

[0163] Where: P(T=1) is the probability of system failure; P(T=1|x i =0) is the unit x i The probability that a system will fail if no faults occur.

[0164] In this experiment, the task time is set to 10,000 hours and divided into 6 segments. The failure probability of leaf node T in each segment is calculated using discrete-time Bayesian network, as shown in Table 3.

[0165] Table 3. Failure probability of leaf nodes in each time period

[0166] Time period 1 2 3 4 5 6 7 Failure probability 0.12488 0.07238 0.08089 0.04599 0.04778 0.08757 0.54051

[0167] As shown in Table 3, the failure probability of leaf node T during the task time is 0.45949, and the failure probability outside the task time is 0.54051.

[0168] Using the multidimensional dynamic Bayesian network analysis method, according to the unit transition function and pulse function corresponding to the logic gates of the root node and the leaf node, from the calculation formulas (3)-(6), when only considering the influence of the system failure probability on the working time, the failure probability change curve of the leaf node T with the working time t can be obtained as follows: Figure 4 As shown. Figure 4 It can be seen that when the mission time is 10,000 hours, the failure probability of the leaf node is 0.4595, which is the same as the calculation result of the discrete-time Bayesian network analysis method in Table 3.

[0169] Considering the combined influence of working time and the degree of mass infectious disease on the system failure probability, the distribution curve of the leaf node T failure probability under the influence of multiple factors can be obtained as follows: Figure 5 As shown. Figure 5 It can be seen that when considering that the system failure probability is jointly affected by working hours and the severity of mass infectious diseases, the multidimensional dynamic Bayesian network analysis method can show the changing trend of the failure probability with working hours and the severity of mass infectious diseases, which is more advantageous.

[0170] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for evaluating the risk of important material logistics based on a multidimensional dynamic Bayesian network, characterized in that: The following steps are involved: S1: Risk identification of important material logistics in the post-pandemic era; S2: Construction of Dugan fault tree for important material logistics process; S3: Construction of multidimensional dynamic Bayesian network for important material logistics processes; S4: Multidimensional dynamic Bayesian network evaluation and analysis of important material logistics processes.

2. The important material logistics risk assessment method based on a multidimensional dynamic Bayesian network according to claim 1 is characterized by: The step S1 includes the following sub-steps: S1.1: Analyze the logistics process of important materials, which is divided into five links: processing and packaging, receiving and warehousing, warehouse management, sorting and outbound delivery, and transportation and distribution; S1.2: Organize and analyze the direct causes of transportation system failure in accident cases, and identify risk factors from the three levels of people, machines, and environment.

3. The important material logistics risk assessment method based on a multidimensional dynamic Bayesian network according to claim 1 is characterized by: The step S2 includes the following sub-steps: S2.1: Define basic events and intermediate events for the important material logistics process risk factors identified in S1, and number the events; S2.2: Based on events and numbers, draw a Dugan dynamic fault tree for the important material logistics process.

4. The important material logistics risk assessment method based on a multidimensional dynamic Bayesian network according to claim 1 is characterized in that: The step S3 includes the following sub-steps: S3.1: Convert the events in the Dugan dynamic fault tree of the important material logistics process into nodes in the Bayesian network according to the "Mapping rules between Dugan dynamic fault tree analysis and continuous-time Bayesian network"; S3.2: Use directed edges to connect nodes and draw a multidimensional dynamic Bayesian network for the logistics process of important materials.

5. The important material logistics risk assessment method based on multidimensional dynamic Bayesian network according to claim 1 is characterized in that: The step S4 includes the following sub-steps: S4.1: Time-continuous construction of Bayesian networks, i.e., using unit transition functions and impulse functions to describe the time series relationship between root node failures and leaf node failures; The input of the unit step function expresses the failure time of the input event, and the failure distribution of the output event is quantitatively related to the failure time of each input event. The unit step function is defined as follows: where t i ,t j Represents x respectively i ,x j The moment when the root node is unavailable; u(t i -t j ) is a unit step function, indicating the time series of unavailable leaf nodes; The impulse function is defined as follows: This function has the property that the definite integral is 1 in the integral domain: where t T Represents the time when child node T is unavailable. When t T =t i It means that when the root node x i Failure time t i Child node T also fails; when t T ≠t i When it means that the child node T is not in x i The moment of failure is failure; S4.2: Calculation of leaf node failure probability in multidimensional dynamic Bayesian networks; In addition to the time factor, the root node x i (i=1,2,...,n) is also affected by interference factors, including but not limited to human operation factors and environmental factors. Let the interference factor be e j (j=1,2,...,m), with Z i (t) is the time when node i is affected by interference factor e j The state variables at time t after the impact; When Z i When (t) is 1, the root node x i There is no failure after the interference factor, and when the root node is only affected by the time factor, the probability of no failure is: Represents when the root node x i The state variable is only affected by the time factor. P[A] represents the probability of event A occurring. F i (t i ) represents the time factor t i Affects the root node x i Failure probability distribution function; The probability of no failure when affected by other factors is: Represents when the root node x i The state variable affected by other factors, F j (e j ) represents the interference factor e j Affects the root node x i Failure probability distribution function; When m influencing factors are independent of each other, the root node x i Failure probability distribution function F i (t i ,e1,e2,...,e m )for: Calculate the partial derivatives of each factor variable in formula (7) and get the root node x i The probability density function of is: Based on formula (8) and the Bayesian network reasoning method, combined with the unavailable order of the root node and leaf nodes in the system Bayesian network, we can get the leaf node x i The probability density function that is not available is: r is the number of conditional probability tables, Ξl is the lower integral domain of sequence number l, R(l)=u(t i -t j ) is a unit step function, i and j represent any two nodes, P (l) (t T ) is the impulse function of leaf node T with sequence number l; Based on the probability density function of the root node being unavailable, the probability density distribution function of the child node being unavailable is obtained as follows: S4.3: Calculation of posterior probability of root nodes in multidimensional dynamic Bayesian networks; Based on the unique reverse reasoning ability of the Bayesian network, the posterior probability of the intermediate node or root node within a specific task time range is calculated in a multidimensional dynamic Bayesian network structure when a leaf node fails. The posterior probability formula is: Among them F T (T M ,e1,e2,…,e m ) is the leaf node T at task time T M Failure probability within S4.4: Multidimensional dynamic Bayesian network importance analysis; Select the root node with high probability importance for priority promotion; the probability importance of the root node is: Among them F T (t i ,e1,e2,…,e m ) represents the failure probability distribution function of leaf node T under the influence of time and multiple factors, F i (t i ,e1,e2,…,e m ) represents the root node x i Failure probability distribution function affected by time and other factors.

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