Automatic driving risk assessment method and system based on dynamic Bayesian network

Abstract

The invention discloses an automatic driving risk assessment method and system based on a dynamic Bayesian network, and the method comprises the steps: 1, recognizing a hazard event which may be caused by function missing through an HAZOP method according to each function on which an automatic driving system depends, and constructing a hazard graph model G = (V, E): enabling a root node and a child node of a node set V to represent a trigger node, the leaf node represents a hazardous event node, the trigger node causes occurrence of the hazardous event node, and the directed edge of the E comprises a directed edge of the trigger node pointing to the hazardous event node; 2, constructing a dynamic Bayesian network, and predicting the individual occurrence probability of each node in the hazard graph model in a future time period, the occurrence probability of child nodes on the basis of the occurrence of a father node, and the occurrence probability of the nodes between adjacent moments through the dynamic Bayesian network; and step 3, obtaining the risk value of the automatic driving system at the prediction moment. According to the invention, multi-dimensional quantitative evaluation of risks can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of risk assessment of automobile systems, and in particular to an automatic driving risk assessment method and system based on a dynamic Bayesian network. Background Art

[0002] The risk assessment problem of automobile systems, especially the risks that have not occurred but are potentially present in different environments, is a field with high uncertainty. In a complex and changeable driving environment, how to identify and assess the unmanifested risks of automobile systems, and under what conditions to adopt an autonomous driving degradation strategy, have become important issues that need to be urgently addressed in modern intelligent transportation systems. Due to the existence of uncertainty problems, traditional risk assessment methods have certain limitations in dealing with this type of complexity and uncertainty. To this end, dynamic Bayesian networks, as a probabilistic graphical model suitable for dealing with uncertainty problems, provide a more ideal solution framework.

[0003] Dynamic Bayesian networks can effectively capture the potential risks of automobile systems in different driving environments by modeling the dependencies between random variables. In order to cope with the dynamic changes in the driving environment, this paper proposes a driving environment risk assessment model based on discrete dynamic Bayesian networks. The model can quantitatively analyze the various uncertainties faced in the driving process in real time, and then evaluate the risk level in the current driving environment.

[0004] In practical applications, the construction of discrete dynamic Bayesian networks can not only help quantify and evaluate existing risks, but also assist in deciding whether the autonomous driving system has the ability to reduce the risk. By quantifying environmental risks, the model can provide quantitative evidence for the stability and safety of the system in a specific environment. In addition, the model can further evaluate whether it is necessary to take autonomous driving downgrade actions. When the autonomous driving system cannot effectively respond to risks in a specific environment, the model will generate corresponding decision recommendations to remind human drivers to intervene to improve overall driving safety.

[0005] For example, in the prior art one, a dynamic Bayesian network is used to evaluate the flight risks of unmanned aerial vehicles (UAVs), and error compensation is performed through cellular grid division and the moving average method to construct a multi-scale low-altitude airway risk map. Although this method has good real-time performance and accuracy, due to the introduction of a complex dynamic Bayesian network and fixed cellular grid division, the computational complexity is relatively high, and there may be certain limitations when dealing with complex geographical environments and real-time large-scale data processing. The main drawback is the relatively high computational complexity, especially when processing large-scale time-series data, which may affect the real-time performance. At the same time, the fixed cellular grid division lacks adaptability to complex geographical environments, and the singularity of its moving average method for error compensation limits the compensation effect in a changing environment. In addition, the method for optimizing risk factors is relatively limited and may not be able to fully meet the requirements of complex multi-dimensional flight environments.

[0006] Also for example, in the prior art two, the method of Constrained Maximum A Posteriori (CMAP) is introduced to learn the Conditional Probability Table (CPT) parameters of a dynamic Bayesian network, which is particularly suitable for situations where data is scarce or incomplete. This method combines convex optimization and Dirichlet priors, and by introducing qualitative constraints of expert judgment, it solves the problem that it is difficult to accurately learn CPT by pure data-driven methods. The CMAP method shows higher accuracy when dealing with scarce and incomplete data, especially in the case with expert constraints, significantly improving the performance of the inference model. However, there are some limitations in the prior art two when dealing with complex dynamic Bayesian networks. First, although the CMAP method solves some problems of parameter learning by introducing constraints and priors, the computational cost of its convex optimization process is relatively high, especially when dealing with large-scale networks or multiple variables. Second, the CMAP method relies heavily on expert judgment, which may lead to a decline in model performance in the absence of high-quality expert information.

[0007] Still for example, in the prior art three, real-time inference in an uncertain environment is achieved through an Adaptive Dynamic Bayesian Network (DBN). This solution combines adaptive variable structure and DBN, and can dynamically capture the dependencies and temporal changes between different information, adapting to complex changes and incomplete data in the environment. Its design goal is to improve the robustness and accuracy of inference, especially in the case of missing information, and it can perform effective risk assessment and decision-making. The prior art three has problems of high computational complexity and insufficient flexibility. The dynamic Bayesian network requires a large amount of computing resources, especially when dealing with large-scale data or complex scenarios, and the real-time performance is limited. In addition, the adaptability of the solution mainly depends on fixed nodes and temporal inference, with relatively low flexibility.

[0008] Prior Art Four proposed a bidirectional heuristic search algorithm for finding the optimal structure of a dynamic Bayesian network. This algorithm searches in the sequential graph space of the dynamic Bayesian network, combining forward and backward heuristic functions to ensure that the search process can converge to the global optimal solution. Experimental results show that compared with traditional unidirectional heuristic search algorithms, the bidirectional heuristic search algorithm needs to expand fewer states in most cases, has higher convergence efficiency and shorter running time. Although Prior Art Four reduces the number of search states and improves the convergence efficiency through bidirectional search, the computational complexity is still high. Especially when dealing with large-scale dynamic Bayesian networks, the memory consumption and running time will increase significantly. In addition, this solution has a high dependence on the selection and adjustment of the heuristic function, which may lead to poor performance when dealing with uncertain or high-dimensional data.

[0009] Prior Art Five proposed a new method for system risk definition and analysis based on an improved risk field model. This method uses the Gaussian pulse energy function to measure the change of risk energy in the system and models the risk field as an energy distribution similar to an electric field or a gravitational field. The key points include analyzing the risk potential and the risk field intensity, and explaining the interaction and coupling between different risks in the system through the superposition law. This method has been applied to regional environmental risk assessment and system-level risk modeling. Prior Art Five conducts risk analysis by analogy with physical fields (such as electric fields or gravitational fields), although it provides an intuitive explanation of risk energy distribution and coupling, this method is too dependent on static models and is difficult to dynamically capture the temporal evolution and complex interactions of risks. At the same time, although the superposition law of the risk field can explain the coupling effect of multiple risks, it appears limited when dealing with highly uncertain and real-time changing risks. Summary of the Invention

[0010] The purpose of the present invention is to provide a method and system for autonomous driving risk assessment based on a dynamic Bayesian network to overcome or at least mitigate at least one of the above-mentioned defects of the prior art.

[0011] To achieve the above object, the present invention provides a method for autonomous driving risk assessment based on a dynamic Bayesian network, which includes:

[0012] Step 1, according to the various functions relied on by the autonomous driving system, identify the hazard events that may be caused by function failures through the HAZOP method, and construct a hazard graph model G=(V, E): V represents the set of nodes, and the root node and child nodes of V tIt represents a hazard event node. The superscripts i and j represent the index numbers of the root node and the child node respectively, and the subscript t represents the time. The triggering node causes the hazard event node to occur. E represents the set of directed edges between two nodes in V. The directed edges include the directed edges from the triggering node to the hazard event node;

[0013] Step 2: According to the hazard graph model G, construct a dynamic Bayesian network, and predict the individual occurrence probability of each node in the hazard graph model G, the occurrence probability of the child node based on the occurrence of the parent node, and the occurrence probability of the node between adjacent time periods within the future time period through the dynamic Bayesian network;

[0014] Step 3: Obtain the risk value of the autonomous driving system at the prediction time according to the probability in Step 2.

[0015] Furthermore, the "occurrence probability of the child node based on the occurrence of the parent node" in Step 2 is obtained through P(Y t |pa(Y t )) set by Equation (1):

[0016]

[0017] In Equation (1), Y t represents the hazard event node at time t, pa(Y t ) represents the parent node of Y t , represents the jth child node at time t, represents 's parent node, represents the ith i ∈ {1,..., I}, the denominator represents the simultaneous occurrence probability of all the parent nodes of , and the numerator represents the simultaneous occurrence probability of all the parent nodes of and Y t .

[0018] Furthermore, the "occurrence probability of the node between adjacent time periods" in Step 2 is obtained through P(Y t |Y t-1 ) set by Equation (2):

[0019]

[0020] Among them, represents 's occurrence probability based on the occurrence of , represents Y t 's occurrence probability based on the occurrence of , and Π represents the product operation.

[0021] Further, step 3 includes:

[0022] Step 31, the probability of step 2, to obtain the prediction time T p The probability C of danger occurring;

[0023] Step 32, calculate the risk value risk of the autonomous driving system at the prediction time T p The risk value risk is related to C in step 31;

[0024] where C = P(Y Tp ), and its acquisition method specifically includes:

[0025] Discretize t according to k = 1, 2, …, T c , T c +1, …, T p For the known time period k = 1, 2, …, T c There are I root nodes and 2 hidden nodes and Y t , and for the prediction time period k = T c +1, …, T p There are I + a root nodes. Use the root node to represent the i-th observation node at the t-th moment, and use to represent the hidden node at the t-th moment from the i-th state of the hidden node at the t-th moment to the j-th state of the hidden node at the t + 1-th moment. The state transition probability forms the state transition probability table A. Within the known time period, Y The occurrence probability based on the occurrence at the known point pa(Y Tc ) is as follows Tc : As shown in Equation (3):

[0026]

[0027] where λ is the normalization factor; represents the prior probability within the known time period, which is calculated through Equation (4); represents the posterior probability within the unknown time period, which is calculated through Equation (5);

[0028]

[0029]

[0030] where represents The occurrence probability based on the simultaneous occurrence of the I trigger nodes at each time point within the known time period ; denote on the basis of the occurrence of the occurrence probability denote the time point T c of the hidden node the hidden node from the i-th state to the (t + 1)-th moment the transition probability of the j-th state denote the prior probability θ within the known time period k+1 (i) denote the unknown time period k + 1 = T c +2, …, Y p the posterior probability within +1 denote on the basis of the occurrence of the occurrence probability, Π denotes the product operation, and ∑ denotes the summation operation

[0031] Furthermore, in step 32, the risk value risk is also related to the probability Q of danger occurring in the autonomous driving system, Q = P s ·P or ·P and P s 、P or 、P and respectively denote the occurrence probabilities of the sequential structure, OR structure, and AND structure of the Bayesian network

[0032]

[0033]

[0034]

[0035] In the formula denote the occurrence probability on the basis of the occurrence of denote the individual occurrence probability denote on the basis of the simultaneous occurrence of all parent nodes of the occurrence probability

[0036] Furthermore, in step 32, the risk value risk is also related to the collision severity index S, as shown in formula (10);

[0037] risk = ω1·Q·S + ω2·C·S (10)

[0038] In the formula, both ω1 and ω2 are preset weight coefficients

[0039] ​The present invention also provides an autonomous driving risk assessment system based on a dynamic Bayesian network, which includes:

[0040] A hazard graph model unit, which is used to identify hazard events that may be caused by function failures through the HAZOP method according to the various functions relied on by the autonomous driving system, and construct a hazard graph model G=(V, E): V represents the set of nodes, the root node of V and the child nodes both represent trigger nodes, the leaf node Y t represents the hazard event node, the superscripts i and j respectively represent the index numbers of the root node and the child node, the subscript t represents the moment, the trigger node causes the hazard event node to occur, E represents the set of directed edges between two nodes in V, and the directed edge includes the directed edge pointing from the trigger node to the hazard event node;

[0041] A Bayesian network unit, which is used to construct a dynamic Bayesian network according to the hazard graph model G, and predict the individual occurrence probabilities of each node in the hazard graph model G, the occurrence probability of the child node on the basis of the occurrence of the parent node, and the occurrence probability between adjacent moments in the future time period through the dynamic Bayesian network;

[0042] A risk prediction unit, which is used to obtain the risk value of the autonomous driving system at the prediction moment according to the probabilities of the Bayesian network unit.

[0043] Further, the "occurrence probability of the child node on the basis of the occurrence of the parent node" is obtained through P(Y t |pa(Y t )) set by formula (1), and the "occurrence probability between adjacent moments of the node" is obtained through P(Y t |Y t-1 ) set by formula (2):

[0044]

[0045]

[0046] In the formula, Y t represents the hazard event node at moment t, pa(Y t ) represents the parent node of Y t , represents the jth child node at moment t, represents 's parent node, represents the ith i∈{1,..., I}, the denominator represents the simultaneous occurrence probability of all parent nodes of, the numerator represents the simultaneous occurrence probability of all parent nodes of and Y t simultaneously, represents on the basis of the occurrence of the occurrence probability, represents Y t on the basis of the occurrence of the occurrence probability, and Π represents the product operation.

[0047] Furthermore, the risk value risk is related to the probability C of danger occurring at the prediction time T p the probability Q of danger occurring in the autonomous driving system, and the collision severity index S, as shown in Equation (10);

[0048] risk = ω1·Q·S + ω2·C·S (10)

[0049] In the formula, both ω1 and ω2 are preset weight coefficients.

[0050] Due to the adoption of the above technical solutions, the present invention has the following advantages:

[0051] 1. System function deviation identification and hazard assessment based on HAZOP (the full English text is Hazard and Operability, and the full Chinese text is Hazard and Operability Analysis): The present invention adopts the HAZOP (Hazard and Operability Analysis) method to deeply identify function deviations in the autonomous driving system, and constructs a directed acyclic graph (DAG) in combination with risk assessment to clarify the trigger nodes of potential hazard events and their impacts. This process ensures that system function defects can be discovered and managed in a timely manner.

[0052] 2. Establishment of a multi-dimensional risk assessment framework: By inferring the probability of danger occurring, the severity of the situation, and the controllable situation in the dynamic Bayesian network system, the present invention realizes multi-dimensional quantitative assessment of risks. This framework can not only evaluate the current risks, but also predict the future development trends of risks, guiding the autonomous driving system to take preventive measures.

[0053] 3. Analysis of risk controllable situations: By calculating the occurrence probability of hazard events through the dynamic Bayesian network, this technology can evaluate the ability of the autonomous driving system to cope with specific risks, thereby analyzing whether these risks are within the controllable range of the system and guiding countermeasures.

[0054] 4. Flexibility of the variable structure dynamic Bayesian network: The present invention further proposes a variable structure dynamic Bayesian network, allowing the network structure or parameters to be dynamically adjusted with time, enhancing the system's risk prediction and management capabilities in complex and non-steady driving environments.

[0055] 5. Risk Management and Decision Support for Autonomous Driving Systems: This model can not only identify and quantify risks, but also support the decision-making of autonomous driving systems, especially in critical moments to help determine whether the driving authority should be switched from the autonomous driving system to manual driving, or whether a downgrading operation should be taken, etc. Description of the Drawings

[0056] Figure 1 is the system risk analysis flowchart of the variable structure dynamic Bayesian network.

[0057] Figure 2 is the hazard and operability analysis process.

[0058] Figure 3 is an example of the risk assessment hazard map model.

[0059] Figure 4 is the representation diagram of the dynamic Bayesian network, Figure 4 (a) represents the initial dynamic Bayesian network B1, Figure 4 (b) represents the dynamic Bayesian network B including two moments → .

[0060] Figure 5 is the change diagram of the system risk reasoning process.

[0061] Figure 6 is the representation diagram of the variable structure dynamic Bayesian network. Detailed Implementation Manner

[0062] In the drawings, the same or similar reference numerals are used to represent the same or similar elements or elements with the same or similar functions. The embodiments of the present invention will be described in detail below with reference to the drawings.

[0063] In the description of the present invention, the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the protection scope of the present invention.

[0064] The method for autonomous driving risk assessment based on a dynamic Bayesian network provided by the embodiment of the present invention includes:

[0065] Step 1, according to the various functions relied on by the autonomous driving system, identify the hazard events that may be caused by the lack of functions through the HAZOP method, and construct a hazard map model G=(V, E): V represents the set of nodes, and the root node of V and child nodes Both represent trigger nodes, and the leaf node Y t Represents a hazard event node. The superscripts i and j respectively represent the index numbers of the root node and the child node, and the subscript t represents the time. The trigger node causes the hazard event node to occur. E represents the set of directed edges between two nodes in V. The directed edge includes the directed edge from the trigger node to the hazard event node.

[0066] Step 2: According to the hazard graph model G, construct a dynamic Bayesian network, and predict the individual occurrence probability of each node in the hazard graph model G, the occurrence probability of the child node based on the occurrence of the parent node, and the occurrence probability between adjacent time moments of the node in the future time period through the dynamic Bayesian network.

[0067] Step 3: Obtain the risk value of the autonomous driving system at the prediction moment according to the probability in Step 2.

[0068] Through the quantitative analysis of the uncertain factors in the driving environment in the embodiments of the present invention, not only can the current risk level be accurately evaluated, but also a scientific basis is provided for the risk management and degradation strategy of the autonomous driving system. By predicting and managing potential risks, it is ensured that the risks of system function deficiencies can be timely identified and effectively addressed, thereby improving the safety and reliability of the autonomous driving system.

[0069] In one embodiment, as Figure 1 shown, the risk assessment scheme mainly analyzes the potential risks brought by the deficiencies of the key function items of the autonomous driving system. First, clarify the various functions relied on by the autonomous driving system, use the HAZOP method to identify the hazards that may be caused by the lack of functions, and construct a hazard graph model. The nodes in the hazard graph model represent different hazard events, and based on a large amount of hazard data caused by function deficiencies, the occurrence probability of these hazards is evaluated. As the inference basis in the dynamic Bayesian network. Through the inference ability of the dynamic Bayesian network, the hazard graph model can predict the potential occurrence probability in the future period of time and generate a quantitative risk assessment result. In order to comprehensively evaluate the system risk, the hazard graph model comprehensively considers the probability of occurrence of hazards (i.e., the frequency of risk occurrence), the severity (i.e., the possible consequences after the risk occurs), and the controllability (i.e., the system's response ability to risks) during the evaluation process to ensure that the analysis covers all aspects of risks. This scheme can provide scientific support for the risk management of the autonomous driving system, ensure that the risks of system function deficiencies can be identified in advance and effectively managed, and provide strong guarantees for the system's degradation strategy and operation safety.

[0070] As Figure 2As shown, in the process of functional analysis of an autonomous driving system, the HAZOP method can effectively evaluate the deviations that may occur during the production and use of the system and conduct qualitative risk assessment. The hazard analysis of the risks of the autonomous driving system by the HAZOP method is roughly divided into the following steps:

[0071] First, identify the potential risks of the autonomous driving system, divide the system into different functional units, analyze each unit independently, use the guide word list to identify the deviations between the system and the expected functions. By using guide words for each functional unit, review potential failure situations one by one. After discovering the deviations, enter the stage of analyzing the causes and consequences of the deviations. Finally, summarize all the deviations, causes, and consequences in a HAZOP analysis summary table. Through this systematic summary, decision-makers can comprehensively evaluate the safety of the entire system.

[0072] Specific measures include:

[0073] Extract the set of functional items. First, extract the set of autonomous driving functional items F related to the current driving task and confirm the set of possible functional abnormal modes B. The extraction process filters out the functional items irrelevant to the current driving task and retains the relevant set of functional items F. The abnormal mode set B consists of five elements: B1 represents the failure to provide the required function, B2 represents that the provided functional item is less than the value required by the task, B3 represents that the provided functional item exceeds the value required by the task, B4 represents that the provided functional item is earlier than the task requirement, and B5 represents that the provided functional item is later than the task requirement. Screen abnormal behaviors and summarize hazards. By combining the set of functional items F with the set of abnormal modes B, form the potential abnormal behavior function set Y (Y = F × B), which represents the set of functions with potential abnormalities. These abnormal behaviors may cause the driving task to not be completed normally, thus triggering dangerous behaviors.

[0074] The above analysis steps can be applied to specific functional scenarios of the autonomous driving system. Through hazard analysis and risk assessment, a complete example of the assessment process is formed. This process can effectively evaluate the potential risks of system functional abnormalities and provide a reference for countermeasures. At the same time, a hazard graph model can be established according to the analysis results.

[0075] When constructing the hazard graph model, the node without a father node is called the root node. The root node is not caused by any hazard event in the hazard graph model, and its generation reason may be the environmental impact on the sensor performance or the insufficient performance of the system's expected functions. The HAZOP method provides the relationship basis for constructing the hazard graph model of the system risk assessment method. Construct the hazard graph model according to the results obtained by the HAZOP method. Record the resulting final hazard event Y, divide the functional units, analyze the causes leading to Y as the father node pa(Y), then analyze the father node of pa(Y), and then search for the father node. If there is none, record it as the trigger node.

[0076] The hazard graph model G = (V, E) can be represented by a directed acyclic graph, where: V = {v1, v2, …, v n}, representing all node sets. Each node represents a specific condition or event that leads to the occurrence of a hazard event, such as sensor failure, environmental change, etc. These nodes are the prerequisites for the occurrence of the hazard event and form a path from the hazard event to the final hazard event Y. That is, the occurrence of a hazard event may lead to the occurrence of a certain hazard, and this hazard may in turn lead to the occurrence of the final hazard event Y.

[0077] To facilitate the description of the generation of the dynamic Bayesian network, for any node, a five-tuple is defined as the attribute set. The attribute set C = (Pa, ca, e, kt, p), where Pa represents the set of the father nodes of any node, and specific data can be obtained through the father nodes when performing probability calculations. ca represents the set of the child nodes of any node, representing the nodes of the related scenarios affected by the scenario of this node in the hazard graph model. e represents the set of directed edges of any node, recording the causal relationships between nodes. For any node, kt represents all the known events that may trigger the state change from the node to the next node. These events can be external environmental factors, system internal failures, or other identifiable risk factors. For the node and its corresponding set of nodes kt with known occurrence probabilities, p represents the occurrence probability of transferring from the current node to the next scenario node under the occurrence of these hazard events. It reflects the possibility of the system transferring to the next state and then proceeding to the next scenario node given the current node state and the nodes with known occurrence probabilities.

[0078] The hazard graph model records the complete path from certain specific hazard events B to the final hazard. Through the HAZOP method, it can be analyzed, including the hazard paths in known and unknown hazard scenarios. The hazard graph model shows all the prerequisites before the occurrence of the final hazard, including hazard events, scenarios, and the connections between scenarios. In the same hazard graph model, each unknown or known hazard event is independent of each other and does not affect the occurrence probability of other hazard events.

[0079] As Figure 3 shown, in the hazard graph model, the node without a father node is called the root node. The root node is not triggered by any hazard event in the graph, and its generation reason may be the environmental impact on the sensor performance or the insufficient performance of the system's expected function. According to the hazard graph model G, a dynamic Bayesian network (B 1 , B → ) is constructed, including the static Bayesian network B 1 at the initial moment and the static Bayesian networks B → including the current moment t and the previous moment t + 1. In B1 Among them, Figure 3 three root nodes are shown, which are respectively The hazard event node shows Y1, and the child nodes are represented as in B → Among them, Figure 3 the static Bayesian network at the current moment t shown includes three root nodes, three root nodes The hazard event node shows Y t , and the child nodes are represented as The static Bayesian network at the previous moment t+1 includes three root nodes, three root nodes The hazard event node shows Y t-1 , and the child nodes are represented as

[0080] In the hazard sequence, only a series of hazard events triggered in sequence can be regarded as valid hazard occurrences. The state of each hazard event is independent, and the state before triggering does not affect the state after triggering. Only the father node or ancestor node can affect the probability of the target node. If there are nodes n, father node pa(n), and node m, and pa(n) is not the father node of m at the same time, then pa(n) needs to satisfy P(n|pa(n),m) = P(n|pa(n)), that is, the probability of the occurrence of n is only affected by its father node pa(n) and not by other nodes. Furthermore, the probability of the occurrence of node m is only affected by its father node and not by the father node of n, that is, P(m|pa(n)) = P(m).

[0081] In the dynamic Bayesian network, it is necessary to calculate and evaluate the occurrence probability of nodes with unknown occurrence probabilities based on the prior probabilities of nodes with known occurrence probabilities. Assume that Y is the unknown final hazard event, and X i is the known i-th hazard event in the dynamic Bayesian network, and its prior probability P(X i ) is known, then there is Equation (11):

[0082]

[0083] In the formula, represents the occurrence probability of the hazard event on the basis of the occurrence of the node Y with unknown occurrence probability t , represents the simultaneous occurrence probability of the node Y with unknown occurrence probability t and the known i-th hazard event , P(Y t ) represents the occurrence probability of the node Y with unknown occurrence probability t .

[0084] In one embodiment, the "occurrence probability of a child node based on the occurrence of its parent node" in step 2 is set by P(Y t |pa(Y t )) obtained from Equation (1):

[0085]

[0086] In Equation (1), Y t represents the hazard event node at time t, and pa(Y t ) represents the parent node of Y t . represents the j-th child node at time t, represents 's parent node, represents the i-th i ∈ {1,..., I}, and the denominator represents the simultaneous occurrence probability of all the parent nodes of , while the numerator represents the simultaneous occurrence probability of all the parent nodes of and Y t .

[0087] For the I parent nodes of the child node 's parent node set where each parent node 's individual occurrence probability can be obtained directly or indirectly through prior probabilities, so that the occurrence probability table of the child node can be obtained. Furthermore, the occurrence probability table P(pa(Y t )) of all the parent nodes pa(Y t ) of Y t can be obtained. And so on, for the occurrence probability tables in the static Bayesian network at other times, based on , just adjust the subscript t of to the corresponding time.

[0088] The above prior probabilities are obtained through the prior probability table of the Bayesian network at time t, specifically including:

[0089] Obtaining the probability of a node with a known occurrence probability occurring dangerously which can be statistically obtained through a real database or simulation tests;

[0090] Obtaining M hazard nodes Prior probability table

[0091] Obtain all Y t-known Prior probability table P(Y t-known ), And so on, for the prior probability tables in the static Bayesian network at other times, on the basis of , just adjust the subscript t of to the corresponding time.

[0092] Indicates the probability of a minor collision occurring when the hazard event occurs. The system risk of autonomous driving is a process that changes with the environment. One aspect of the autonomous driving risk is related to the current environment and trigger nodes, and the other aspect is related to the occurrence probability at the previous time. In order to express and reason about such dynamic time-varying stochastic processes, the concept of dynamic Bayesian needs to be adopted.

[0093] The entire dynamic Bayesian network contains a finite number of times, and each time consists of a directed acyclic graph and an occurrence probability table. The dynamic Bayesian network is represented as (B1, B → ), where B1 is a Bayesian network that defines the probability distribution P(Y1) at the initial time, and B → is a Bayesian network that contains 2 times and defines the conditional distribution between variables at 2 adjacent times, that is,

[0094]

[0095] In the formula: Y t is the node Y at the t-th time; pa(Y t ) is the parent node of the node Y t . Each node in the second time in B → has an occurrence probability distribution P(Y t |pa(Y t )) for t > 0. The parent node pa(Y t ) of the node Y t can be in the same time as Y t , or it can be in the previous time. The edges within the same time can be understood as instantaneous effects, while the edges across times can be understood as time-varying effects, reflecting the passage of time. Figure 4 (a) represents the initial Bayesian network B1, Figure 4 (b) represents the Bayesian network B → that contains two times. At this time, i = 3,

[0096] The probability distribution B1 at the initial moment is as shown in Equation (13):

[0097]

[0098] Wherein, Y1 represents the hazard event Y at the initial moment t = 1, pa(Y1) represents the parent node of node Y1, represents the parent node of node Y1 the occurrence probability of node Y1 on the basis of the occurrence of the parent node represents the node the occurrence probability of all represents the first trigger node at the initial moment t = 1 represents the second trigger node at the initial moment t = 1 represents the third trigger node at the initial moment t = 1

[0099] The sequential structure, OR structure, and AND structure of the Bayesian network are combined with each other, and finally lead to hazards through a series of hazard paths. When performing risk assessment, in addition to referring to the occurrence probability of each node with an unknown occurrence probability, it is also necessary to comprehensively analyze the sequential structure, OR structure, and AND structure to obtain the final probability of the occurrence of the hazard.

[0100] In one embodiment, in step 32, the risk value risk is also related to the probability Q of the occurrence of danger in the autonomous driving system, Q = P s ·P or ·P and ,P s 、P or 、P and respectively represent the occurrence probabilities of the sequential structure, OR structure, and AND structure of the Bayesian network.

[0101] The method for obtaining the occurrence probability P s of the sequential structure of the static Bayesian network at the current moment t includes:[[]]

[0102] In the sequential structure, for the node with an unknown occurrence probability the occurrence probability is related to the probability of the parent node In the case where the parent node is a node with a known occurrence probability, that is, the prior probability of the parent node can be known, expressed as Then, the occurrence probability of the hazard event node is expressed as Equation (7):

[0103]

[0104] The occurrence probability P of the OR structure of the static Bayesian network at the current moment t or The acquisition method includes:

[0105] In the OR structure, the occurrence probability of the hazard event is composed of the probabilities of the occurrence hazards of the parent nodes. A new dynamic Bayesian network can be established for the conditions that trigger the hazard alone and analyzed separately using the sequential structure. Equation (8) gives the occurrence probability formula of the nodes with unknown occurrence probabilities in the OR structure, P or represents the occurrence probability of triggering Y under the condition that the node with unknown occurrence probability in the OR structure occurs.

[0106]

[0107] The occurrence probability P of the AND structure of the static Bayesian network at the current moment t and The acquisition method includes:

[0108]

[0109] In Equations (7) to (9), represents the occurrence probability based on the occurrence of , represents the individual occurrence probability, represents the occurrence probability based on the simultaneous occurrence of all the parent nodes of .

[0110] In one embodiment, the "occurrence probability of the node between adjacent moments" in step 2 is obtained through P(Y t |Y t-1 ) set by Equation (2):

[0111]

[0112] wherein, represents the occurrence probability based on the occurrence of , represents the occurrence probability of Y t based on the occurrence of , and Π represents the product operation.

[0113] Since autonomous driving can take measures on the trigger nodes, such as decelerating, changing lanes, autonomous driving degradation, etc., and the change of the scenario after taking measures leads to the change of the system risk, the inference of the system risk is a non-steady-state process, which can be regarded as composed of several different steady-state processes, such as Figure 5, for each of these steady-state processes, a traditional dynamic Bayesian network can be constructed. From one steady-state process to another, it reflects the risk response ability of the autonomous driving system, which is called the controllable situation of risk.

[0114] A variable-structure dynamic Bayesian network allows the network structure or parameters at each moment to be different. For example, Figure 5 is a simple variable-structure dynamic Bayesian network, where Figure 6 (a) is the initial Bayesian network B 1 , which defines the distribution P(Y1) at the initial moment. Figure 6 (b) is the network, which defines the occurrence probability P(Y t |Y t-1 ) at the moment when a certain structure changes. Among them, the number of nodes in the t-th moment increases by 1, and at the same time, the topological structure of the network also changes.

[0115] For the variable-structure discrete dynamic Bayesian network as Figure 6 shown, assuming that the network covers t moments, its Bayesian network structure at the t-th (t = 1, 2,..., T c , T c +1,..., T p ) moment is DBN t . When t = 1, 2,..., T c is the known time period, there are 3 observation nodes 2 hidden nodes and Y t . Among them, the hidden node refers to the node whose occurrence probability cannot be directly obtained, and its probability needs to be inferred through the occurrence probability of the known node. The hidden node corresponds to the node with the known occurrence probability such as etc.

[0116] When t = T c+1 , the network mutates. When t = T c +1,..., T p , it is the prediction time period, and there are 4 observation nodes Since the system risk at the current moment is only related to the original risk at the current moment, the dynamic risk at the current moment, and the new system risk at the previous moment. Let represent the i-th observation variable at the t-th moment, which only has a dependence relationship with other variables at this moment. Let represent the hidden node at the t-th moment from the i-th state of the hidden node at the t-th moment to the j-th state of the hidden node at the t + 1-th moment. The state transition probability table composed of such state transition probabilities is A.

[0117] In one embodiment, step 3 includes:

[0118] Step 31, obtaining the probability of step 2 at the prediction time T p The probability C of a danger occurring.

[0119] Step 32, calculating the risk value risk of the autonomous driving system at the prediction time T p The risk value risk is related to C in step 31.

[0120] Where C = P(Y Tp ), and the specific method for obtaining it includes:

[0121] Discretize t according to k = 1, 2,..., T c , T c +1,..., T p In the known time period k = 1, 2,..., T c There are I root nodes and 2 hidden nodes and Y t , in the prediction time period k = T c +1,..., T p There are I + a root nodes. Use the root node To represent the i-th observation node at the t-th moment, and use To represent the hidden node at the t-th moment The state transition probability from the i-th state of the hidden node at the t-th moment to the j-th state of the hidden node at the t + 1-th moment, and the state transition probability Composes the state transition probability table A. In the known time period k = 1, 2,..., T The occurrence probability of Y c On the basis of the known point pa(Y Tc ) occurring Tc Can be understood as an intermediate variable, indicating the occurrence probability of the hazard within the prediction time under the condition that the nodes with known occurrence probabilities occur within the known time period k = 1, 2,..., T As shown in Equation (3): c Where λ is the normalization factor;

[0122]

[0123] Where, λ is the normalization factor; Represents the prior probability within the known time period k = 1, 2,..., T c Which is calculated by Equation (4); Represents the posterior probability within the unknown time period k = T c +1,..., T p Which is calculated by Equation (5);

[0124]

[0125]

[0126] Among them, denotes the probability of occurrence on the basis of the I trigger nodes at each time point within the known time periods k = 1, 2, …, T c occurring simultaneously, whereas refers to the I nodes at t = 1 including etc., denotes the probability of occurrence on the basis of occurring, denotes the hidden node at time point T c the hidden node from the i-th state to the (t + 1)-th moment the transition probability of the j-th state, denotes the prior probability, θ, within the known time periods k = 1, 2, …, T c -1, k+1 (i) denotes the posterior probability within the unknown time periods k + 1 = T c + 2, …, T p + 1, denotes the probability of occurrence on the basis of occurring, where ∏ represents the product operation and ∑ represents the summation operation.

[0127] Next, taking I = 3 as an example, the method for obtaining P(Y Tp ) is described.

[0128] For the prior probability, as shown in Equation (14):

[0129]

[0130] where t = 1, 2, …, T c ; denotes all the moments, and the probability of occurrence of hazard Y on the basis of the occurrence of the three trigger nodes at each moment t

[0131] First, initialize as shown in Equation (15):

[0132]

[0133] ​​where: λ is the normalization factor, and η1(i) is the prior probability at the initial time point k = 1. is the occurrence probability of the hazard event at for the 3 observation nodes, and is the sum of all possible occurrences of the hazard event while is the occurrence probability of the hazard event when it occurs alone.

[0134] Then, iterative calculation is performed:

[0135]

[0136] where represents the probability that the three observation nodes at each time point within the known time period t = 1, 2,..., T c will cause the hazard to occur at time T c , and is the transition probability from the i-th state of the hidden node at the t-th time point to the j-th state of the hidden node at the (t + 1)-th time point.

[0137] For the posterior probability, as shown in Equation (17):

[0138]

[0139] where t = T c+1 ,..., T p , and c represents the probability that the occurrence of the hazard at time T will cause the occurrence of the event at the future prediction time observation node.

[0140] First, initialize:

[0141] θ t (i) = 1 (18)

[0142] Then, iterative calculation is performed:

[0143]

[0144] Combining the prior and posterior probabilities, the recursive inference algorithm for the discrete dynamic Bayesian network is obtained, namely

[0145]

[0146] Calculate according to the prior probability formula of the variable-structure dynamic Bayesian network and the posterior probability formula Then, according to the inference algorithm of the variable-structure discrete dynamic Bayesian network, calculate the probability value after corresponding measures are taken.

[0147] At the t-th second the occurrence probability is Equation (20):

[0148]

[0149] Substitute into the equation and analyze the data in the table to calculate the occurrence probability of accidents at all levels at the 0-T p seconds. Take measures at the T c moment and calculate the prediction period T c -T p the occurrence probability of accidents at all levels after the moment. For a future moment T p probability uncontrollable situation

[0150] In one embodiment, in step 32, the risk value risk is also related to the collision severity index (SeverityIndex) S, as shown in Equation (10);

[0151] risk = ω1·Q·S + ω2·C·S (10)

[0152] In the formula, Q·S is the product of the probability and severity of danger occurring at the current moment, and C·S is the product of the probability and severity of danger occurring within the prediction moment. The risk risk is the expected value of the risk severity from the current moment to the future moment. ω1 and ω2 are weight coefficients, which are adjusted according to historical data and the experience of similar systems. If historical data shows that the risk is higher in a certain period, the corresponding weight coefficient should be increased. Test the impact of different weight settings on the risk assessment results through sensitivity analysis to determine the most appropriate weight coefficient. The greater the risk value risk, the greater the risk of the system.

[0153] In one embodiment, define the collision severity index S as Equation (21):

[0154]

[0155] where v SV is the speed of the following vehicle, in meters per second (m / s), which reflects the speed of the rear vehicle before the collision; v TVis the target object speed, with the unit of meters per second (m / s), which is the speed of the object that may collide. If it is a stationary object, the speed is 0; a is the acceleration (or deceleration), usually a negative value, representing the deceleration during emergency braking, with the unit of meters per second squared (m / s 2 ).; d int represents certain important distances during deceleration or braking processes, usually can represent the stopping distance of the vehicle; θ: is the collision angle, with the unit of degrees (°), and the influence of the collision angle on the energy distribution is represented by cos(θ). θ = 0° represents a frontal collision; PDR (Packet Delivery Ratio) is the ratio that measures the successful arrival of data packets from the sender to the receiver. It can be used to evaluate the reliability of data transmission in the network. The higher the PDR, the more reliable the communication. The calculation formula of PDR is formula (22):

[0156]

[0157] In the formula, N received is the number of data packets successfully received by the receiver. N sent is the total number of data packets sent by the sender. If all the sent data packets successfully reach the receiver, the PDR value is close to 1. If there are data packet losses, the PDR value is less than 1, indicating that there is a packet loss phenomenon during the communication process. PDR is usually used to evaluate the effectiveness of data transfer between vehicles in autonomous driving or V2V communication. For example, if a vehicle sends an emergency braking signal to other vehicles, the higher the PDR, the more vehicles can receive the signal in time, reducing the potential collision risk.

[0158] T delay refers to the total time required for a data packet to reach the receiver from the sender. It includes multiple delay factors, such as propagation delay, processing delay, and queuing delay. T delay The lower the delay, the faster the system responds. T delay The calculation formula can be expressed as formula (23):

[0159] In the formula, T arrival,m is the time when the m-th data packet reaches the receiver. T sent,m : is the time when the m-th data packet is sent from the sender. N is the number of successfully received data packets. T delay The smaller the delay, the faster the communication response speed between vehicles, and the more timely the information can be transmitted. In an autonomous driving environment, a lower delay can ensure that vehicles communicate with each other in a very short time, thus reducing the potential collision risk. Delay is usually affected by various factors, such as the network bandwidth, the distance between vehicles, signal interference, etc.

[0160] An embodiment of the present invention further provides an autonomous driving risk assessment system based on a dynamic Bayesian network, which includes a hazard graph model unit, a Bayesian network unit, and a risk prediction unit, where:

[0161] The hazard graph model unit is used to identify hazard events that may be caused by function failures through the HAZOP method according to the various functions relied on by the autonomous driving system, and construct a hazard graph model G=(V, E): V represents the set of nodes, and the root node of V and the child nodes both represent trigger nodes, and the leaf node Y t represents a hazard event node. The superscripts i and j respectively represent the index numbers of the root node and the child node, and the subscript t represents the moment. The trigger node causes the hazard event node to occur. E represents the set of directed edges between two nodes in V, and the directed edge includes the directed edge from the trigger node to the hazard event node.

[0162] The Bayesian network unit is used to construct a dynamic Bayesian network according to the hazard graph model G, and predict the individual occurrence probabilities of each node in the hazard graph model G, the occurrence probability of the child node based on the occurrence of the parent node, and the occurrence probability between adjacent moments of the nodes in the future time period through the dynamic Bayesian network.

[0163] The risk prediction unit is used to obtain the risk value of the autonomous driving system at the prediction moment according to the probabilities of the Bayesian network unit.

[0164] The present invention proposes a driving environment risk assessment model based on a Bayesian network, which is specifically used to cope with the uncertain risks during driving. The model quantifies the risk level in the current driving environment through probability theory, so as to provide support for decision-making in a dynamic driving environment. On the one hand, the model can assist in judging whether the driving right should be transferred from the autonomous driving system to the driver; on the other hand, when the system detects that the dynamic risk faced by the driver exceeds a specific threshold, the model can actively intervene and prompt the autonomous driving system to take corresponding countermeasures. In addition, the model can also evaluate the controllability of the accident caused by the risk and improve the overall safety management.

[0165] Finally, it should be pointed out that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Those of ordinary skill in the art should understand that: the technical solutions recorded in the foregoing embodiments can be modified, or some of the technical features can be equivalently replaced; these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A risk assessment method for autonomous driving based on a dynamic Bayesian network, characterized in that: include: Step 1: Based on the functions that the autonomous driving system relies on, identify the hazardous events that may be caused by the lack of functions through the HAZOP method, and construct a hazard graph model G = (V, E): V represents a node set, and the root node of V is and child nodes Both represent trigger nodes, leaf nodes Y t represents the hazard event node, the superscripts i and j represent the index numbers of the root node and the child node respectively, the subscript t represents the time, the trigger node causes the hazard event node to occur, E represents the set of directed edges between two nodes in V, and the directed edges include the directed edges from the trigger node to the hazard event node; Step 2: Based on the hazard graph model G, a dynamic Bayesian network is constructed to predict the probability of occurrence of each node in the hazard graph model G in the future time period, the probability of occurrence of a child node based on the occurrence of the parent node, and the probability of occurrence of nodes between adjacent moments. Step 3: Based on the probability of step 2, obtain the risk value of the autonomous driving system at the prediction moment.

2. The method for risk assessment of autonomous driving based on dynamic Bayesian network according to claim 1, characterized in that: The "probability of occurrence of a child node based on the occurrence of the parent node" in step 2 is set by formula (1) P(Y t |pa(Y t ))get: In formula (1), Y t represents the hazard event node at time t, pa(Y t ) indicates Y t The parent node of represents the jth child node at time t, express The parent node of Indicates the i-th i∈{1,...,I}, the denominator represents The probability of all parent nodes occurring simultaneously, the numerator represents All parent nodes and Y t The probability of simultaneous occurrence.

3. The autonomous driving risk assessment method based on dynamic Bayesian network according to claim 1, characterized in that: The "probability of a node occurring between adjacent moments" in step 2 is set by formula (2) P(Y t |Y t-1 )get: in, express exist The probability of occurrence based on the occurrence, Represents Y t exist The probability of occurrence based on occurrence, ∏ represents the product operation.

4. The autonomous driving risk assessment method based on a dynamic Bayesian network as claimed in any one of claims 1 to 3, characterized in that: Step 3 includes: Step 31, the probability of step 2, obtain the predicted time T p The probability of danger occurring C; Step 32, calculate the predicted time T p The risk value risk of the autonomous driving system is related to C in step 31; Where C = P(Y Tp ), and the acquisition method thereof specifically includes: Set t according to k=1,2,…,T c ,T c +1,…,T p Discretize, in known time periods k = 1, 2, ..., T c There is 1 root node and 2 hidden nodes and Y t , in the prediction time period k = T c +1,…,T p There are I+a root nodes, use the root node represents the i-th observation node at the t-th time, and is expressed as Represents the hidden node at the tth moment The hidden node from the i-th state to the t+1-th moment The state transition probability of the jth state is given by the state transition probability Composition state transition probability table A, within a known time period Y Tc At a known point pa(Y Tc ) Probability of occurrence based on occurrence As shown in formula (3): Among them, λ is the normalization factor; represents the prior probability within a known time period, which is calculated by formula (4); represents the posterior probability in the unknown time period, which is calculated by formula (5); in, express I trigger nodes at each time point in a known time period The probability of occurrence based on simultaneous occurrence, express exist The probability of occurrence based on the occurrence, Indicates time point T c The hidden nodes Hidden nodes from the i-th state to the t+1-th moment The transition probability of the jth state is represents the prior probability within a known time period, θ k+1 (i) represents the unknown time period k+1=T c +2,…,T p +1 within the posterior probability, express exist The probability of occurrence based on occurrence, ∏ represents the product operation, and ∑ represents the sum operation.

5. The method for risk assessment of autonomous driving based on dynamic Bayesian network according to claim 4, characterized in that: In step 32, the risk value risk is also related to the probability Q of the automatic driving system causing danger, Q = P s ·P or ·P and , P s , P or , P and Respectively represent the occurrence probabilities of the sequential structure, OR structure, and AND structure of the Bayesian network; In the formula, express In happening Based on the probability of occurrence, express The probability of occurrence of a single express exist The probability of occurrence based on the simultaneous occurrence of all parent nodes.

6. The method for risk assessment of autonomous driving based on dynamic Bayesian network according to claim 5, characterized in that: In step 32, the risk value risk is also related to the collision severity index S, as shown in formula (10); risk=ω1·Q·S+ω2·C·S(10) Wherein, ω1 and ω2 are both preset weight coefficients.

7. An autonomous driving risk assessment system based on a dynamic Bayesian network, characterized in that: include: The hazard graph model unit is used to identify the hazard events that may be caused by the loss of functions according to the various functions that the autonomous driving system relies on, and to construct a hazard graph model G = (V, E): V represents a node set, and the root node of V is and child nodes Both represent trigger nodes, leaf nodes Y t represents the hazard event node, the superscripts i and j represent the index numbers of the root node and the child node respectively, the subscript t represents the time, the trigger node causes the hazard event node to occur, E represents the set of directed edges between two nodes in V, and the directed edges include the directed edges from the trigger node to the hazard event node; A Bayesian network unit is used to construct a dynamic Bayesian network based on the hazard graph model G, and predict the probability of occurrence of each node in the hazard graph model G in the future time period, the probability of occurrence of a child node based on the occurrence of a parent node, and the probability of occurrence of a node between adjacent moments through the dynamic Bayesian network; The risk prediction unit is used to obtain the risk value of the autonomous driving system at the prediction moment according to the probability of the Bayesian network unit.

8. The autonomous driving risk assessment system based on dynamic Bayesian network according to claim 7, characterized in that: The probability of a child node occurring based on the occurrence of the parent node is set by formula (1) P(Y t |pa(Y t )) is obtained, and the "probability of a node occurring between adjacent moments" is obtained by setting P(Y t |Y t-1 )get: Where Y t represents the hazard event node at time t, pa(Y t ) indicates Y t The parent node of represents the jth child node at time t, express The parent node of Indicates the i-th i∈{1,...,I}, the denominator represents The probability of all parent nodes occurring simultaneously, the numerator represents All parent nodes and Y t The probability of simultaneous occurrence, express exist The probability of occurrence based on the occurrence, Represents Y t exist The probability of occurrence based on occurrence, ∏ represents the product operation.

9. The autonomous driving risk assessment system based on dynamic Bayesian network according to claim 7 or 8, characterized in that: Risk value risk and prediction time T p The probability of danger occurring C, the probability of danger occurring in the autonomous driving system Q, and the collision severity index S are related, as shown in formula (10); risk=ω1·Q·S+ω2·C·S(10) Wherein, ω1 and ω2 are both preset weight coefficients.

10. The autonomous driving risk assessment system based on dynamic Bayesian network according to claim 9, characterized in that: C=P(Y Tp ), and the acquisition method thereof specifically includes: Set t according to k=1,2,…,T c ,T c +1,…,T p Discretize, in known time periods k = 1, 2, ..., T c There is 1 root node and 2 hidden nodes and Y t , in the prediction time period k = T c +1,…,T p There are I+a root nodes, use the root node represents the i-th observation node at the t-th time, and is expressed as Represents the hidden node at the tth moment The hidden node from the i-th state to the t+1-th moment The state transition probability of the jth state is given by the state transition probability Composition state transition probability table A, within a known time period Y Tc At a known point pa(Y Tc ) Probability of occurrence based on occurrence As shown in formula (3): Among them, λ is the normalization factor; represents the prior probability within a known time period, which is calculated by formula (4); represents the posterior probability in the unknown time period, which is calculated by formula (5); in, express I trigger nodes at each time point in a known time period The probability of occurrence based on simultaneous occurrence, express exist The probability of occurrence based on the occurrence, Indicates time point T c The hidden nodes Hidden nodes from the i-th state to the t+1-th moment The transition probability of the jth state is represents the prior probability within a known time period, θ k+1 (i) represents the unknown time period k+1=T c +2,…,T p +1 within the posterior probability, express exist The probability of occurrence based on the occurrence, ∏ represents the product operation, ∑ represents the sum operation; Q=P s ·P or ·P and , P s , P or , P and Respectively represent the occurrence probabilities of the sequential structure, OR structure, and AND structure of the Bayesian network; In the formula, express In happening Based on the probability of occurrence, express The probability of occurrence of a single express exist The probability of occurrence based on the simultaneous occurrence of all parent nodes.

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