CN114186753A - Food safety risk prediction algorithm based on FTA-BN - Google Patents

Food safety risk prediction algorithm based on FTA-BN Download PDF

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CN114186753A
CN114186753A CN202111555559.7A CN202111555559A CN114186753A CN 114186753 A CN114186753 A CN 114186753A CN 202111555559 A CN202111555559 A CN 202111555559A CN 114186753 A CN114186753 A CN 114186753A
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林丹
梁启军
谢锋
陶光灿
吴锴
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Abstract

The invention discloses a food safety risk prediction algorithm based on FTA-BN, which comprises the steps of firstly, risk classification of food safety problems, secondly, establishment of a food safety fault tree model and conversion of a BN model, thirdly, forward reasoning analysis and prediction of food safety risk level, fourthly, reverse reasoning diagnosis to obtain failure paths and links, fifthly, analysis and judgment of sensitivity according to mutual information, and sixthly, derivation of a final fault path; according to the method, the food safety risk problem is quantitatively analyzed from a supply chain system by aiming at the characteristics of coupling relation and uncertainty existing among risk factors of each link of food safety and combining the advantages of a fault tree analysis method and a Bayesian network, the food safety problem is comprehensively and deeply analyzed through an improved FTA-BN model, and a theoretical basis is provided for researching food risk sequencing and key path control.

Description

Food safety risk prediction algorithm based on FTA-BN
Technical Field
The invention relates to the technical field of food safety, in particular to a food safety risk prediction algorithm based on FTA-BN.
Background
In recent years, the food safety problem is getting more and more serious and is widely concerned by people, and as the food safety is directly related to social safety and economic development, the food safety risk is accurately analyzed, so that the method has important significance for reducing accident loss and perfecting a food safety control system;
scholars at home and abroad make much research on food safety risk assessment, developed countries such as the United states and Japan pay attention to the whole process of a supply chain from farmland to dining table, and the harmfulness assessment technology is adopted, so that the characteristic description and the intake amount assessment are focused. Domestic food safety risk assessment mostly focuses on methods such as an evaluation index system, a quantity model and the like, and focuses on qualitative analysis;
the conventional research on food safety risk evaluation is mainly based on comprehensive evaluation of a model, and the research on food safety accident inducement and internal logic relationship is less, so that the invention provides a food safety risk prediction algorithm based on FTA-BN to solve the problems in the prior art.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a food safety risk prediction algorithm based on FTA-BN, and the food safety risk prediction algorithm based on FTA-BN comprehensively and deeply analyzes the food safety problem through an improved FTA-BN model, thereby providing a theoretical basis for researching food risk sequencing and key path control.
In order to realize the purpose of the invention, the invention is realized by the following technical scheme: an FTA-BN based food safety risk prediction algorithm comprises the following steps:
classifying risks causing food safety problems in each link of a supply chain according to human-machine-ring-pipe sources by utilizing a historical event analysis method and according to main reasons causing food safety events in the past year;
secondly, constructing a fault tree model of the food safety problem by taking the food safety problem as a top event and taking risk factors of each link as bottom events, and converting the fault tree model according to a Bayesian network to obtain a BN (boron nitride) model of the food safety problem;
analyzing the causal logic relationship of each node from the top event to the bottom event of the BN model by forward reasoning, calculating by using a joint probability distribution formula to obtain a joint probability, obtaining a risk occurrence probability from the joint probability, and predicting the risk level of food safety;
fourthly, reversely reasoning from a bottom event to a top event of the BN model, calculating the posterior probability of other variables according to given variable information, and diagnosing to obtain a path and a link which cause system failure;
fifthly, mutual information of a BN model root node and a BN model leaf node is calculated, and the sensitivity of the BN model root node to the leaf node is analyzed and judged according to the size of a mutual information value;
and step six, acquiring a fault point combination influencing the food safety problem in the Bayesian network, solving a problem link by utilizing a maximum posterior hypothesis problem in the Bayesian network according to the posterior probability of the combination state, and finally deducing a fault path.
The further improvement lies in that: in the first step, the risks of food safety problems are divided into four types of artificial risks, equipment risks, environmental risks and management risks according to the source of the human-machine-ring-pipe.
The further improvement lies in that: given set of nodes in the third step, V ═ V1，V2，…，ViAnd then the joint probability distribution formula is represented by the following formula.
Figure BDA0003418512680000021
The further improvement lies in that: the risk level for predicting food safety in the third step is specifically divided into evidential variable risk prediction and evidential variable risk prediction, and when the probability of occurrence of a food safety problem T is represented by P (T7 ═ 1);
the evidentiary variable risk prediction is calculated by
Figure BDA0003418512680000031
The evidence variable risk prediction is calculated by
Figure BDA0003418512680000032
Vi∈Vc,vi∈(0,1)
In the formula Vi(i is more than or equal to 1 and less than or equal to m-1) is a root node, VcSet of nodes being evidence variables, viE (0, 1) is the occurrence or non-occurrence, m is the number of nodes in the Bayesian network, n is the number of nodes with known states, P (V)1＝v1，V2＝v2，…，Vn＝vnT ═ 1) denotes the joint probability of a risk factor with a known state and a risk event occurring simultaneously, P (V)1＝v1，V2＝v2，…，Vn＝vn) Represents the joint probability of a state-known event and P (T ═ 1) represents the likelihood of a risk event occurring.
The further improvement lies in that: the posterior probability calculation formula in the fourth step is expressed by the following formula
Figure BDA0003418512680000033
Wherein P (V)j＝1|VcT ═ 1) is the posterior probability of the jth node, Vj∈Vc，vi∈(0，1)。
The further improvement lies in that: the V iscWhen the event is an empty set, calculating the posterior probability of each basic event, finding out the reasons causing the fault and diagnosing with pertinence; the V iscWhen the fault occurs, the fault is gradually ranked based on multiple evidence variables in a non-empty set mannerAnd (5) checking the fault and finding out the fault position.
The further improvement lies in that: mutual information between the BN model root node and the BN model leaf node in the step five is represented by the following formula
Figure BDA0003418512680000041
In the formula P (v)i，vj) Is v isiAnd vjJoint probability of P (v)i) And P (v)j) Are each viAnd vjThe leaf nodes have strong probability dependence on the root nodes if the mutual information value is large, and therefore key risks are identified, and process control points are clearly analyzed.
The further improvement lies in that: the concrete derivation method in the sixth step is
S1, firstly determining the problem link of the fault, and solving the problem link by using the maximum posterior hypothesis problem in the Bayesian network according to the posterior probability of the combined state of the fault sources of the link
In the case where the conditional probability table is switched by a logical AND gate
Figure BDA0003418512680000042
In the case where the conditional probability tables are switched by logical OR gates
Figure BDA0003418512680000043
In the formula
Figure BDA0003418512680000044
The fault node set of the i intermediate links comprises j fault nodes; x is the number ofjIs composed of
Figure BDA0003418512680000045
A state value of the corresponding failed node; vcA set of nodes that are evidence variables; v. ofcTo be corresponding toTaking a value of an evidence node;
Figure BDA0003418512680000046
a jth failed node representing an i-intermediate link; tau isiRepresenting the fault probability of the intermediate link;
s2, finding out specific fault node according to the problem link, namely calculating posterior probability of father node of the link and solving
Figure BDA0003418512680000051
The posterior probability is proportional to the probability of the parent node failing, and the final failure path is deduced according to the posterior probability.
The invention has the beneficial effects that: according to the method, the food safety risk problem is quantitatively analyzed from a supply chain system by combining the advantages of a fault tree analysis method and a Bayesian network according to the characteristics of coupling relationship and uncertainty existing among risk factors of each link of food safety;
the method for searching weak links by adopting posterior probability measures the dependence degree of risk factors and risk events by utilizing mutual information capable of fusing prior information and posterior probability, identifies risk control points, proposes link control as a core, and reversely identifies causative paths inducing the risk events by combining maximum posterior hypothesis problems and maximum posterior probability.
The food safety problem is comprehensively and deeply analyzed through the improved FTA-BN model, and a theoretical basis is provided for exploring food risk sequencing and key path control.
Drawings
FIG. 1 is a prediction flow chart of the present invention.
FIG. 2 is a tree structure diagram illustrating the failure of the food safety problem according to the present invention.
Fig. 3 is a BN model architecture diagram of the present invention.
Detailed Description
In order to further understand the present invention, the following detailed description will be made with reference to the following examples, which are only used for explaining the present invention and are not to be construed as limiting the scope of the present invention.
Example one
According to fig. 1, 2 and 3, the present embodiment provides an FTA-BN-based food safety risk prediction algorithm, which includes the following steps:
the method comprises the following steps of firstly, dividing risks causing food safety problems in all links of a supply chain into four types of artificial risks, equipment risks, environmental risks and management risks according to human-machine-ring-pipe sources by utilizing a historical event analysis method and according to main reasons causing food safety events in the past year;
secondly, constructing a fault tree model of the food safety problem by taking the food safety problem as a top event and taking risk factors of each link as bottom events, and converting the fault tree model according to a Bayesian network to obtain a BN (boron nitride) model of the food safety problem;
step three, analyzing the causal logic relationship of each node from the top event to the bottom event of the BN model in a forward reasoning way, calculating by using a joint probability distribution formula to obtain a joint probability, and giving a node set V as { V ═ V { (V })1，V2，…，ViA joint probability distribution formula is represented by the following formula;
Figure BDA0003418512680000061
obtaining risk occurrence probability from the joint probability, predicting the risk level of food safety, wherein the risk level of food safety is specifically divided into evidentiary variable risk prediction and evidential variable risk prediction, and when the probability of occurrence of a food safety problem T is represented by P (T7 ═ 1);
the evidentiary variable risk prediction is calculated by
Figure BDA0003418512680000062
The evidence variable risk prediction is calculated by
Figure BDA0003418512680000063
Vi∈Vc,vi∈(0,1)
In the formula Vi(i is more than or equal to 1 and less than or equal to m-1) is a root node, VcSet of nodes being evidence variables, viE (0, 1) is the occurrence or non-occurrence, m is the number of nodes in the Bayesian network, n is the number of nodes with known states, P (V)1＝v1，V2＝v2，…，Vn＝vnT ═ 1) denotes the joint probability of a risk factor with a known state and a risk event occurring simultaneously, P (V)1＝v1，V2＝v2，…，Vn＝vn) Represents the joint probability of the known-state events, P (T ═ 1) represents the probability of occurrence of the risk events, and the food safety risks are classified into 5 levels according to their occurrence probability, as shown in table 1;
table 1 food safety risk ratings
Grade Descriptor word Quantitative measure of likelihood
Is lower than Is rarely generated The occurrence probability is less than or equal to 1 percent
Is low in Low probability of occurrence The occurrence probability is more than 1 percent and less than or equal to 5 percent
Medium and high grade May happen The occurrence probability is more than 5 percent and less than or equal to 10 percent
Height of Is likely to happen The occurrence probability is more than 10 percent and less than or equal to 20 percent
Super high Is often generated 20% < probability of occurrence
Fourthly, reasoning reversely from the bottom event of the BN model to the top event, calculating the posterior probability of other variables according to given variable information, and diagnosing to obtain the path and the link causing the system failure, wherein a posterior probability calculation formula is represented by the following formula
Figure BDA0003418512680000071
Wherein P (V)j＝1|VcT ═ 1) is the posterior probability of the jth node, Vj∈Vc，vi∈(0，1)；VcWhen the event is an empty set, calculating the posterior probability of each basic event, finding out the reasons causing the fault and diagnosing with pertinence; vcWhen the fault occurs, gradually troubleshooting the fault and finding out the fault position based on multiple evidence variables;
step five, calculating mutual information of the BN model root node and the BN model leaf node, and expressing the mutual information by the following formula
Figure BDA0003418512680000081
In the formula P (v)i，vj) Is v isiAnd vjJoint probability of P (v)i) And P (v)j) Are each viAnd vjThe probability dependency of leaf nodes on root nodes is strong when the mutual information value is largeIdentifying key risks, determining process control key points, and analyzing and judging the sensitivity of the leaf nodes according to the size of the mutual information values;
step six, obtaining a fault point combination influencing food safety problems in the Bayesian network, solving a problem link by utilizing a maximum posterior hypothesis problem in the Bayesian network according to the posterior probability of a combination state, and finally deducing a fault path
S1, firstly determining the problem link of the fault, and according to the posterior probability of the combined state of the fault source of the link, utilizing the maximum posterior hypothesis problem solving link in the Bayesian network under the condition that the conditional probability table is converted by the logic AND gate
Figure BDA0003418512680000082
In the case where the conditional probability tables are switched by logical OR gates
Figure BDA0003418512680000083
In the formula
Figure BDA0003418512680000084
The fault node set of the i intermediate links comprises j fault nodes; x is the number ofjIs composed of
Figure BDA0003418512680000085
A state value of the corresponding failed node; vcA set of nodes that are evidence variables; v. ofcTaking values for corresponding evidence nodes;
Figure BDA0003418512680000086
a jth failed node representing an i-intermediate link; tau isiRepresenting the fault probability of the intermediate link;
s2, finding out specific fault node according to the problem link, namely calculating posterior probability of father node of the link and solving
Figure BDA0003418512680000087
The posterior probability is proportional to the probability of the parent node failing, and the final failure path is deduced according to the posterior probability.
Example two
According to fig. 1, 2 and 3, the present embodiment provides an example analysis of the FTA-BN-based food safety risk prediction algorithm, which is performed by taking pork food in 2009-2014 as an example. The initial probability of each node is obtained by collecting pork safety event data which occur in 2009-2014 and consulting experts, as shown in table 2, then is compared and analyzed with information and data published by Chinese food safety net, national food and drug administration and media news, and is repeatedly corrected by experts, so that the prior probability of each node causing pork food safety problems in 2009-2014 is finally determined, as shown in table 3, the established BN reasoning analysis model is utilized, and pork food safety problems are comprehensively analyzed based on a route of risk prediction, fault diagnosis, weak link and key path
Table 22009-2014 years raw material production link safety event data
Event(s) Data of Event(s) Data of Event(s) Data of
Unqualified raw material 0 Profession function 12 Cognitive errors 0
Harmful input product 119 Counterfeiting 0 General problem parts 217
Improper additive 23 Unqualified personnel and sanitary environment 0 Percent of pass 94.29
Unqualified agricultural input products 43 Improper disposal of waste 24 - -
Improper storage 0 Selling defective products 0 - -
Improper processing 0 Force of supervision 26 - -
Improper packaging 0 Environmental factors 3 - -
TABLE 3 Prior probability and posterior probability of events
Figure BDA0003418512680000101
Risk prediction based on forward reasoning
Based on the constructed BN model, under the prior probability of root nodes, the occurrence probability of pork food safety risk is calculated to be 2.41% by using an evidentiary variable risk prediction calculation formula, and the pork food safety in recent years belongs to low-level risk according to the food safety risk probability classification, so that the quality and the safety level condition of the pork food at the present stage of China are relatively met. When the state of a certain node is known, the probability of occurrence of food safety risk events under different conditions can be calculated by using an evidence variable risk prediction calculation formula. If no label mark is found during processing of a batch of meat products, the probability of occurrence of the safety risk of the meat products is calculated to be 11.73%, and as shown in table 4, it can be known that the occurrence of a plurality of risk factors is more likely to cause food safety problems
TABLE 4 prediction of probability of occurrence of food safety problem
Figure BDA0003418512680000102
Risk diagnosis based on reverse reasoning
If pork food safety problems appear in the market, the posterior probability of risk factors can be calculated through reverse reasoning of BN, and accident cause investigation is carried out. For example, in 2011, clenbuterol event P (T ═ 1) ═ 1 in diplex, a posterior probability calculation formula is used to obtain a posterior probability of risk factors, and as shown in table 3, it is found that food monitoring capacity is insufficient and X is in each link10、X37、X2、X23The posterior probability value of (2) is large, and the investigation can be carried out from the several risk factors. Through investigation, if the healthy and handsome pigs are released to the market in the breeding link due to the supervision negligence, P (Y)11 ═ 1) ═ 1; when an accident occurs, P (T is 1) is 1, and the breeding link is not well supervised P (Y)1When the number is 1), updating the BN network, calculating the posterior probability of the root node, and finding that the most probable cause of the accident is X2(addition of hazardous input), followed by X1(improper application of the element), the two risk factors are heavily investigated until the cause of the accident is found. According to investigation of relevant departments, the clenbuterol event is caused by forbidden use of clenbuterol in a breeding link and career neglecting, and is consistent with an analysis result.
Sensitivity analysis
In practice, weak link monitoring of food safety often depends on practical experience of experts, a writer adopts MI indexes to measure the influence degree of each risk factor on a risk event, an optimized control sequence representing the 'importance degree' of the risk factors is constructed, and predictive control over key links in a food chain is achieved. The risk factor sensitivity ranking for each link is shown in table 5. It can be seen from Table 3 that the MI values are ranked top by Y4>Y8>X10>X37>Y2>Y6>X2>X23>X9>X42The method has great influence on risk events, is a weak link in a food chain, and needs key management and control when preventing food safety problems.
TABLE 5 ranking of Risk factor sensitivity of links
Figure BDA0003418512680000111
As can be seen from table 5, in the supply chain link, the most significant link affecting pork food safety is the processing link, and then the consumption link, and the less significant link is the raw material production, storage, transportation/circulation link, wherein the hysteresis of the supervision system is the main reason of frequent events, and the supervision link should be used as a key control point in the future to optimize the supervision system and improve the monitoring capability of various risks.
In the raw material production link, farmers or enterprises are numerous and widely distributed, the admission threshold is low, and food problems are easily caused by benefit driving. Wherein Y is2(insufficient monitoring capability of production link), X2(addition of harmful input product) X1(inappropriate amounts of elements applied) is a major risk cause.
In the processing link, because the organization form of processing enterprises is mainly in the small, scattered and low pattern, and the technical means and moral deficiency of some microminiature processing enterprises and the supervision are difficult, the processing enterprises become a high-risk link of pork food safety problems. Wherein Y is4(insufficient monitoring capability of processing link), X10(using nonconforming starting materials), X9The occurrence probability of improper additive is high, and the additive is a main cause for failure of the processing link.
The circulation link comprises transportation and storage, the pork products need to be transported for many times from cultivation to dining table, the related links are many, food pollution can be caused by carelessness, and Y is large in occurrence probability6(insufficient monitoring ability of circulation link), X23(improper storage of the finished product).
The consumption links comprise food sale and catering, the market is dispersed, the intensification degree is low, and the food consumption is increasingly diversified and convenient, so that the food quality is difficult to control, and the food consumption is also a frequent area with food safety problems. The main cause of pork food safety problem is Y8(insufficient monitoring capability in food safety consumption link), X37(sale of defective product), X42(unqualified sale and catering environments).
Key causation path
The accident path with the maximum risk possibility is identified in a plurality of accident chains, so that the main points of risk control can be further defined. And finding out accident chains which are most likely to cause food safety problems in each link by using a probability value calculation formula converted from a logic AND gate and an OR gate by using the conditional probability table, as shown in table 6.
TABLE 6 Key Path of each Link
Figure BDA0003418512680000131
As can be seen from Table 6, the path most likely to cause a risk event is X for the processing segment10→C21→B2(Y4)→A2→ T, followed by X in the consumption segment37→C41→B4(Y8)→A4→ T, X of the circulation segment23→C31→B3(Y6)→A3→ T, X in production section2→C11→B1(Y2)→A1→ T. The occurrence probability of the method is higher than 8.00%, the risk level is medium or higher, and the risk occurrence probability is higher, so that key risk management and control are carried out on key cause paths of all links in daily life, and risk awareness is strengthened.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. An FTA-BN based food safety risk prediction algorithm is characterized by comprising the following steps:
classifying risks causing food safety problems in each link of a supply chain according to human-machine-ring-pipe sources by utilizing a historical event analysis method and according to main reasons causing food safety events in the past year;
secondly, constructing a fault tree model of the food safety problem by taking the food safety problem as a top event and taking risk factors of each link as bottom events, and converting the fault tree model according to a Bayesian network to obtain a BN (boron nitride) model of the food safety problem;
analyzing the causal logic relationship of each node from the top event to the bottom event of the BN model by forward reasoning, calculating by using a joint probability distribution formula to obtain a joint probability, obtaining a risk occurrence probability from the joint probability, and predicting the risk level of food safety;
fourthly, reversely reasoning from a bottom event to a top event of the BN model, calculating the posterior probability of other variables according to given variable information, and diagnosing to obtain a path and a link which cause system failure;
fifthly, mutual information of a BN model root node and a BN model leaf node is calculated, and the sensitivity of the BN model root node to the leaf node is analyzed and judged according to the size of a mutual information value;
and step six, acquiring a fault point combination influencing the food safety problem in the Bayesian network, solving a problem link by utilizing a maximum posterior hypothesis problem in the Bayesian network according to the posterior probability of the combination state, and finally deducing a fault path.
2. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: in the first step, the risks of food safety problems are divided into four types of artificial risks, equipment risks, environmental risks and management risks according to the source of the human-machine-ring-pipe.
3. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: given set of nodes in the third step, V ═ V1，V2，…，ViAnd then the joint probability distribution formula is represented by the following formula.
Figure FDA0003418512670000021
4. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: the risk level for predicting food safety in the third step is specifically divided into evidential variable risk prediction and evidential variable risk prediction, and when the probability of occurrence of a food safety problem T is represented by P (T7 ═ 1);
the evidentiary variable risk prediction is calculated by
Figure FDA0003418512670000022
The evidence variable risk prediction is calculated by
Figure FDA0003418512670000023
Vi∈Vc,vi∈(0,1)
In the formula Vi(i is more than or equal to 1 and less than or equal to m-1) is a root node, VcSet of nodes being evidence variables, viE (0, 1) is the occurrence or non-occurrence, m is the number of nodes in the Bayesian network, n is the number of nodes with known states, P (V)1＝v1，V2＝v2，…，Vn＝vnT ═ 1) denotes the joint probability of a risk factor with a known state and a risk event occurring simultaneously, P (V)1＝v1，V2＝v2，…，Vn＝vn) Represents the joint probability of a state-known event and P (T ═ 1) represents the likelihood of a risk event occurring.
5. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: the posterior probability calculation formula in the fourth step is expressed by the following formula
Figure FDA0003418512670000031
Wherein P (V)j＝1|VcT ═ 1) is the posterior probability of the jth node, Vj∈Vc，vi∈(0，1)。
6. An FTA-BN based food safety risk prediction algorithm according to claim 5 wherein: the V iscWhen the event is an empty set, calculating the posterior probability of each basic event, finding out the reasons causing the fault and diagnosing with pertinence; the V iscWhen the fault occurs, the fault is gradually checked and the fault position is found out based on multiple evidence variables.
7. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: mutual information between the BN model root node and the BN model leaf node in the step five is represented by the following formula
Figure FDA0003418512670000032
In the formula P (v)i，vj) Is v isiAnd vjJoint probability of P (v)i) And P (v)j) Are each viAnd vjThe leaf nodes have strong probability dependence on the root nodes if the mutual information value is large, and therefore key risks are identified, and process control points are clearly analyzed.
8. An FTA-BN based food safety risk prediction algorithm according to claim 1 wherein: the concrete derivation method in the sixth step is
S1, firstly determining the problem link of the fault, and solving the problem link by using the maximum posterior hypothesis problem in the Bayesian network according to the posterior probability of the combined state of the fault sources of the link
In the case where the conditional probability table is switched by a logical AND gate
Figure FDA0003418512670000041
In the case where the conditional probability tables are switched by logical OR gates
Figure FDA0003418512670000042
In the formula
Figure FDA0003418512670000043
The fault node set of the i intermediate links comprises j fault nodes; x is the number ofjIs composed of
Figure FDA0003418512670000044
A state value of the corresponding failed node; vcA set of nodes that are evidence variables; v. ofcTaking values for corresponding evidence nodes;
Figure FDA0003418512670000045
a jth failed node representing an i-intermediate link; tau isiRepresenting the fault probability of the intermediate link;
s2, finding out specific fault node according to the problem link, namely calculating posterior probability of father node of the link and solving
Figure FDA0003418512670000046
The posterior probability is proportional to the probability of the parent node failing, and the final failure path is deduced according to the posterior probability.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116263878A (en) * 2022-10-09 2023-06-16 北京理工大学 Lithium ion battery thermal runaway risk prediction method and device
WO2024181079A1 (en) * 2023-03-01 2024-09-06 栗田工業株式会社 Situation diagnosis assistance system for water treatment facilities

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116263878A (en) * 2022-10-09 2023-06-16 北京理工大学 Lithium ion battery thermal runaway risk prediction method and device
WO2024181079A1 (en) * 2023-03-01 2024-09-06 栗田工業株式会社 Situation diagnosis assistance system for water treatment facilities

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