A safety assessment method for temporary grandstand structures based on Bayesian network models

Abstract

The present invention discloses a method for safety assessment of temporary grandstand structures based on a Bayesian network model. The steps include: 1) establishing a Bayesian network topology structure for safety assessment of temporary grandstands; 2) generating a junction tree according to the Bayesian network topology structure; 3) obtaining the prior probabilities of the root nodes and the conditional probability tables of the non-root nodes of the Bayesian network; 4) quantifying the junction tree; 5) assessing the safety of the temporary grandstand structure according to the quantified junction tree. The present invention proposes a method for safety assessment of temporary grandstand structures based on a Bayesian network. By utilizing the powerful functions of the Bayesian network, the purpose of safety assessment of the overall structure of the temporary grandstand can be achieved.

Description

Technical Field

[0001] The present invention relates to the field of grandstand structure evaluation, and specifically to a method for safety evaluation of temporary grandstand structures based on a Bayesian network model. Background Art

[0002] Temporary grandstand structures are widely used in large-scale public events at home and abroad. According to statistics, in 2012 alone, more than 10,000 temporarily erected grandstands were registered in first- and second-tier cities in China, a 240% increase compared to 2011. However, during the rapid development of temporary grandstands in recent decades, collapse accidents still occur from time to time, threatening people's lives. Therefore, it is of great significance to carry out research on the safety evaluation of temporary grandstand structures.

[0003] At present, the research on temporary grandstand structures mostly focuses on local refined research, such as analyzing how to prevent the collapse of temporary grandstands from the perspectives of node structure, support layout, mechanical properties, etc., but lacks a systematic analysis of the causes of temporary grandstand accidents from a macroscopic and overall perspective. The main reason is that there are many risk factors causing temporary grandstand structure accidents, and it is difficult to find a method that can coordinate all risk factors and give a reasonable systematic evaluation. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for safety evaluation of temporary grandstand structures based on a Bayesian network model, including the following steps:

[0005] 1) Establish a Bayesian network topology structure for the safety evaluation of temporary grandstands;

[0006] The Bayesian network topology structure in the present invention includes a root node layer, an intermediate node layer, and a leaf node layer. Each layer corresponds to a basic event (a risk factor causing a temporary grandstand safety accident), an intermediate event (connecting the basic event and the top event as an intermediate bridge), and a top event (a temporary grandstand safety accident); the nodes at the same level are independent of each other.

[0007] Three typical structural safety accidents are selected for the leaf node layer of the Bayesian network: overall overturning of the grandstand, collapse of the grandstand, and excessive deformation of the grandstand (the deformation value exceeds the preset threshold); six intermediate events are selected for the intermediate node layer of the Bayesian network: insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity; eleven typical safety accident risk factors are selected for the root node layer of the Bayesian network: strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connection, assembly error, component size deviation, and too low temperature.

[0008] 2) Generate a junction tree according to the Bayesian network topology structure;

[0009] The steps for generating a junction tree according to the Bayesian network topology structure include:

[0010] 2.1) Remove the directions of each connection line in the Bayesian network topology structure, and then add undirected edges to connect each pair of parents to obtain a moral graph;

[0011] 2.2) Use the BuildCT algorithm to eliminate nodes in sequence to obtain several cluster nodes;

[0012] Among them, the method for determining the elimination order is the minimum fill-in search method; the method for judging the number of fill-in edges during the elimination process is: the number of edges that need to be added to make all variables connected to variable V connected pairwise is the number of fill-in edges.

[0013] 2.3) Connect the cluster nodes obtained after elimination in sequence, and connect adjacent cluster nodes with separator nodes (the separator nodes save the information shared by adjacent cluster nodes) to finally generate a junction tree;

[0014] For each variable V, there is at least one cluster node in the junction tree that contains V and the parents of V;

[0015] For each pair of nodes N and node W in the junction tree, each node on the path between them contains the intersection N ∩ W.

[0016] 3) Determine the prior probability of the root node of the Bayesian network and the conditional probability table of non-root nodes.

[0017] The prior probability of the root node of the Bayesian network and the conditional probability table of non-root nodes are determined by experts in the field based on existing data and engineering experience.

[0018] 4) Quantify the junction tree;

[0019] The steps for quantifying the junction tree include:

[0020] 4.1) Create a table φ(T) for each cluster node and separator node. The table includes all combinations of n variables, add a column to record the probability distribution of each table, and set each value in this column to 1;

[0021] 4.2) Determine a cluster for each variable V, and the cluster contains V and the parents of V; update φ(T) by multiplying φ(T) by P(V|the parents of V), i.e., φ(T) ← φ(T)P(V|the parents of V);

[0022] This step can be understood as an assignment process, and the prior probability of the root node and the conditional probability of non-root nodes are stored in φ(T) through assignment for subsequent information passing.

[0023] 4.3) Pass information (taking cluster node C i and C jTaking the connection through the separation point S as an example):

[0024] 4.3.1) Copy the separation point table;

[0025] φ(S C ) ← φ(S) (7)

[0026] 4.3.2) Marginalize the cluster node C i , to obtain a new separation point table φ(S)

[0027]

[0028] 4.3.3) Calculate the new table φ(C j ) of C j )

[0029]

[0030] 4.4) Propagate information in both directions until a consistent junction tree is obtained. The junction tree encodes the joint probability distribution P(U) as the product of the cluster tables divided by the product of the separation point tables, i.e.:

[0031]

[0032] 5) According to the quantized junction tree, evaluate the safety of the temporary stand structure, including predicting the occurrence probability of risk events of the temporary stand and diagnosing the key risk factors leading to the risk event C j .

[0033] The steps for predicting the occurrence probability of risk events of the temporary stand include:

[0034] a) Predict the occurrence probability of risk events before the use of the temporary stand. At this time, the occurrence probability P(A i ), i = 1, 2,..., 11 are prior probabilities (determined by expert experience). Marginalize any cluster node in the quantized junction tree that contains the leaf node to be predicted, so as to calculate the occurrence probability P(C j = 1), j = 1, 2, 3, which is the occurrence probability of the risk event C j predicted before the use of the temporary stand; j ;

[0035] b) Predict the occurrence probability of risk events during the use of the temporary stand. If a risk factor A i is detected to have occurred during the use of the temporary stand, then its occurrence probability P(A i) Update the value to 1, and keep the prior probabilities for the occurrence probabilities of other root nodes. Re-quantize the junction tree. Marginalize any cluster node in the quantized junction tree that contains the leaf node to be predicted, so as to calculate the probability of the leaf node C to be predicted j The probability P(C j = 1|A i = 1), j = 1, 2, 3. The obtained result is the occurrence probability of the risk event of the temporary stand during use when a known risk-causing factor A i occurs.

[0036] The steps for diagnosing the key risk-causing factors that lead to the risk event C j include:

[0037] a) Obtain the state (occurrence / non-occurrence) of the leaf node C j , j = 1, 2, 3;

[0038] b) Assume that the leaf node C j occurs, find all clusters that contain this leaf node, and add an evidence column to the table of each variable in these clusters, set the rows corresponding to the cases where the corresponding leaf node has occurred to 1, and the others to 0;

[0039] c) Multiply the probability distribution by the evidence column to obtain a new probability distribution, and perform two-way message passing on the junction tree again to obtain a consistent junction tree;

[0040] d) Standardize the table of any cluster node or separator point that contains the root node A i , and the probability information of this root node can be obtained, that is:

[0041]

[0042] Among them, the probability P(A i , C j = 1) is as follows:

[0043]

[0044] P(A i |C j = 1) is the probability of each root node A j occurring when the leaf node C i occurs. Among them, the event A i corresponding to the maximum probability value j is the key risk-causing factor that leads to the risk event C.

[0045] The technical effect of the present invention is remarkable. The present invention proposes a temporary stand structure safety assessment method based on a Bayesian network. By utilizing the powerful function of the Bayesian network, the purpose of conducting a safety assessment on the overall structure of the temporary stand can be achieved. The Bayesian network is a product of the combination of probability theory and graph theory, and is mainly developed for the research of uncertainty problems in the field of artificial intelligence. The outstanding feature of the Bayesian network is that it uses quantitative probability values ​​to describe the uncertainty in various forms of variables, and also uses probability rules to realize network reasoning and learning, which can link the prior probability of an event and its posterior probability. By using the forward reasoning and reverse reasoning functions of the Bayesian network, the temporary stand structure can be analyzed in an all-round and systematic manner, thereby achieving the purpose of conducting a safety assessment on the overall structure of the temporary stand.

[0046] The present invention proposes a safety assessment method for temporary stand structures based on Bayesian networks. By using the forward reasoning function of the Bayesian network, the failure probability of the temporary stand structure can be predicted in advance so that measures can be taken to prevent it in advance; based on the reverse reasoning function of the Bayesian network, post-event cause diagnosis can be achieved, key risk factors can be identified, and the cause of the accident can be found out. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A technical roadmap for the present invention to use Bayesian network to conduct safety assessment on temporary stand structures;

[0048] Figure 2 The Bayesian network topology for the temporary stand;

[0049] Figure 3 It is the prior probability of the root node and the conditional probability table of non-root nodes;

[0050] Figure 4 is a deontic graph generated by the Bayesian network topology;

[0051] Figure 5 It is the process of elimination;

[0052] Figure 6 is a connection tree generated by the Bayesian network topology;

[0053] Figure 7 Predict the probability of risk events before using the temporary stands;

[0054] Figure 8 It is the probability prediction of risk events under the condition of A1 (strong wind) occurrence;

[0055] Figure 9 is the posterior probability of each root node when the overall overturning of the known stands (C1) occurs;

[0056] Figure 10The posterior probability of each root node when the known grandstand collapse (C2) occurs;

[0057] Figure 11 The posterior probability of each root node when the known excessive grandstand deformation (C3) occurs; Detailed implementation manners

[0058] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above technical idea of the present invention, various substitutions and changes made according to ordinary technical knowledge and customary means in the art shall be included within the protection scope of the present invention.

[0059] Embodiment 1:

[0060] Refer to Figures 1 to 11 , a temporary grandstand structure safety assessment method based on a Bayesian network model, comprising the following steps:

[0061] 1) Establish a Bayesian network topology structure for temporary grandstand safety assessment;

[0062] The Bayesian network topology structure in the present invention includes a root node layer, an intermediate node layer, and a leaf node layer. Each layer corresponds to a basic event (a risk factor causing a temporary grandstand safety accident), an intermediate event (connecting the basic event and the top event as an intermediate bridge), and a top event (a temporary grandstand safety accident); nodes at the same level are independent of each other.

[0063] Three typical structural safety accidents are selected for the leaf node layer of the Bayesian network: overall overturning of the grandstand, collapse of the grandstand, and excessive grandstand deformation (the deformation value exceeds the preset threshold); six intermediate events are selected for the intermediate node layer of the Bayesian network: insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity; eleven typical safety accident risk factors are selected for the root node layer of the Bayesian network: strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connection, assembly error, component size deviation, and too low temperature.

[0064] The content of each layer of nodes in the Bayesian network topology structure is obtained by experts analyzing historical data and combining with actual engineering experience.

[0065] 2) Generate a junction tree according to the Bayesian network topology structure;

[0066] The steps of generating a junction tree according to the Bayesian network topology structure include:

[0067] 2.1) Remove the direction of each connection line in the Bayesian network topology structure, and then add undirected edges to connect each pair of parents to obtain a moral graph;

[0068] 2.2) Use the BuildCT algorithm to eliminate nodes one by one, obtaining several clusters of nodes;

[0069] Adopt the minimum missing edge search method to determine the order of node deletion. Minimum missing edge search method: Delete the node with the fewest missing edges, and on this basis, further search and delete the node with the fewest missing edges, and so on until the moral graph reaches the simplest form (which can be a single cluster node) and stops.

[0070] Thus, it can be seen that the elimination order is not directly given before elimination, but is determined during the elimination process, and the elimination order is not unique.

[0071] Method for judging the number of missing edges: The number of edges that need to be added to make all variables connected to variable V connected to each other pairwise is the number of missing edges. Take Figure 5 h) in as an example. Before adding edges, the variables connected to A8 are B4, B5, A9, and A10, but these five variables are not connected to each other pairwise. An additional edge A10 - B4 needs to be added. After that, all variables connected to A8 are connected to each other pairwise, that is, the number of missing edges of variable A8 is 1.

[0072] 2.3) Connect the cluster nodes obtained after elimination in sequence, and connect adjacent cluster nodes with a separator (the separator preserves the information shared by adjacent cluster nodes), and finally generate a junction tree;

[0073] For each variable V, there is at least one cluster node in the junction tree that contains V and the parents of V;

[0074] For each pair of nodes N and node W in the junction tree, each node on the path between them contains the intersection N ∩ W.

[0075] 3) Determine the prior probability of the root node of the Bayesian network and the conditional probability table of non - root nodes.

[0076] The prior probability of the root node of the Bayesian network and the conditional probability table of non - root nodes are determined by experts in this field based on existing data and engineering experience.

[0077] 4) Quantify the junction tree;

[0078] The steps for quantifying the junction tree include:

[0079] 4.1) Create a table φ(T) for each cluster node and separator. The table includes all combinations of n variables, add a column to record the probability distribution of each table, and set each value in this column to 1;

[0080] 4.2) Determine a cluster for each variable V, where the cluster contains V and the parents of V; update φ(T) by multiplying φ(T) by P(V | the parents of V), i.e., φ(T) ← φ(T)P(V | the parents of V);

[0081] This step can be understood as an assignment process: by assignment, the prior probability of the root node and the conditional probability of non-root nodes are stored in φ(T) for subsequent information passing.

[0082] 4.3) Pass information (taking the example of cluster nodes C i and C j connected through the separating point S):

[0083] 4.3.1) Copy the separating point table;

[0084] φ(S C ) ← φ(S)(1)

[0085] 4.3.2) Marginalize the cluster node C i to obtain a new separating point table φ(S)

[0086]

[0087] 4.3.3) Calculate the new table φ(C k ) of C j

[0088]

[0089] 4.4) Pass information in both directions until a consistent junction tree is obtained. The junction tree encodes the joint probability distribution P(U) as the product of cluster tables divided by the product of separating point tables, i.e.:

[0090]

[0091] 5) According to the quantized junction tree, evaluate the safety of the temporary stand structure, which can implement forward reasoning and backward reasoning functions, corresponding to the prediction of the occurrence probability of risk events of the temporary stand structure and the diagnosis of key risk factors leading to risk events of the temporary stand structure respectively.

[0092] The steps for predicting the occurrence probability of risk events of the temporary stand structure include:

[0093] a) Predict the occurrence probability of risk events before the temporary stand is used. At this time, the occurrence probability P(A i ), i = 1, 2,..., 11 is the prior probability. Marginalize any cluster node in the quantized junction tree that contains the leaf node to be predicted, so as to calculate the probability P(C j ) of the occurrence of the leaf node C j= 1), j = 1, 2, 3, which is the risk event C predicted before the temporary stand is used j The probability of occurrence;

[0094] b) Prediction of the probability of occurrence of risk events during the use of the temporary stand. If a risk-causing factor A i has occurred during the use of the temporary stand, then update the value of its probability of occurrence P(A i ) to 1. The probabilities of occurrence of other root nodes still take the prior probabilities, and re-quantify the join tree. Marginalize any cluster node in the quantified join tree that contains the leaf node to be predicted, so as to calculate the probability of occurrence of the leaf node C j The probability of occurrence P(C j = 1|A i = 1), j = 1, 2, 3. The obtained result is the probability of occurrence of the risk event of the temporary stand under the known occurrence state of a risk-causing factor A i during the use of the temporary stand.

[0095] The steps for diagnosing the key risk-causing factors leading to the structural risk events of the temporary stand include:

[0096] a) Obtain the state (occurrence / non-occurrence) of the leaf node C j where j = 1, 2, 3;

[0097] b) Assume that the leaf node C j occurs, find all the clusters that contain this leaf node, and add an evidence column to the table of each variable in these clusters, set the rows corresponding to the cases where the corresponding leaf node has occurred to 1, and the others to 0;

[0098] c) Multiply the probability distribution by the evidence column to obtain a new probability distribution, and perform two-way message passing on the join tree again to obtain a consistent join tree;

[0099] d) Standardize the table of any cluster node or separator point that contains the root node A i , and the probability information of this root node can be obtained, that is:

[0100]

[0101] Among them, the probability P(A i , C j = 1) is as follows:

[0102]

[0103] P(A i |C j = 1) is the probability of each root node A j under the condition that the leaf node C iThe probability of occurrence, where the event A corresponding to the maximum probability value i , which is the key risk factor leading to the risk event C of the temporary stand structure j .

[0104] Embodiment 2:

[0105] A safety assessment method for temporary stand structures based on a Bayesian network model, comprising the following steps:

[0106] 1) Establish a Bayesian network topology for temporary stand safety assessment;

[0107] The Bayesian network topology in the present invention includes a root node layer, an intermediate node layer, and a leaf node layer. Each layer corresponds to a basic event (a risk factor leading to a temporary stand safety accident), an intermediate event (connecting the basic event and the top event as an intermediate bridge), and a top event (a temporary stand safety accident); the nodes at the same level are independent of each other.

[0108] Three typical structural safety accidents are selected for the leaf node layer of the Bayesian network: overall overturning of the stand, collapse of the stand, and excessive deformation of the stand (the deformation value exceeds the preset threshold); six intermediate events are selected for the intermediate node layer of the Bayesian network: insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity; eleven typical safety accident risk factors are selected for the root node layer of the Bayesian network: strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connection, assembly error, component size deviation, and too low temperature.

[0109] The content of each layer of nodes in the Bayesian network topology is obtained by experts analyzing historical data and combining with actual engineering experience.

[0110] 2) Generate a junction tree according to the Bayesian network topology;

[0111] The steps of generating a junction tree according to the Bayesian network topology include:

[0112] 2.1) Remove the direction of each connection line in the Bayesian network topology, and then add undirected edges to connect each pair of parents to obtain a moral graph;

[0113] 2.2) Use the BuildCT algorithm to eliminate nodes in turn to obtain several cluster nodes;

[0114] 2.3) Connect the cluster nodes obtained after elimination in turn, and connect adjacent cluster nodes with a separator (the separator preserves the information shared by adjacent cluster nodes), and finally generate a junction tree;

[0115] For each variable V, at least one cluster node in the junction tree contains V and the parents of V;

[0116] For each pair of nodes N and node W in the junction tree, each node on the path between them contains the intersection N ∩ W.

[0117] 3) Determine the prior probabilities of the root nodes of the Bayesian network and the conditional probability tables of the non-root nodes.

[0118] The prior probabilities of the root nodes of the Bayesian network and the conditional probability tables of the non-root nodes are determined by experts in the field based on existing data and engineering experience.

[0119] 4) Quantize the junction tree;

[0120] The steps for quantizing the junction tree include:

[0121] 4.1) Create a table φ(T) for each cluster node and separator, which includes all combinations of n variables, add a column to record the probability distribution of each table, and set each value in this column to 1;

[0122] 4.2) Determine a cluster for each variable V, which contains V and the parents of V; update φ(T) by multiplying φ(T) by P(V|the parents of V), i.e., φ(T) ← φ(T)P(V|the parents of V);

[0123] 4.3) Pass messages (taking the example of cluster node C i and C j connected through separator S):

[0124] 4.3.1) Copy the separator table;

[0125] φ(S C ) ← φ(S)(1)

[0126] 4.3.2) Marginalize cluster node C i , to obtain a new separator table φ(S)

[0127]

[0128] 4.3.3) Calculate the new table φ(C j ) of C j )

[0129]

[0130] 4.4) Pass messages in both directions until a consistent junction tree is obtained. The junction tree encodes the joint probability distribution P(U) as the product of the cluster tables divided by the product of the separator tables, i.e.:

[0131]

[0132] 5) Evaluate the structural safety of the temporary grandstand according to the quantified junction tree. Based on the forward reasoning function of the Bayesian network, the probability of the occurrence of risk events in the temporary grandstand structure can be predicted.

[0133] The steps for predicting the probability of the occurrence of risk events in the temporary grandstand structure include:

[0134] a) Predict the probability of the occurrence of risk events before the temporary grandstand is used. At this time, the occurrence probabilities P(A i ), i = 1, 2,..., 11 are prior probabilities. Marginalize any cluster node in the quantified junction tree that contains the leaf node to be predicted, so as to calculate the probability P(C j ) of the occurrence of the leaf node C j = 1), j = 1, 2, 3, which is the predicted probability of the occurrence of risk event C j before the temporary grandstand is used;

[0135] b) Predict the probability of the occurrence of risk events during the use of the temporary grandstand. If a risk-causing factor A i has occurred during the use of the temporary grandstand, update the value of its occurrence probability P(A i ) to 1, and the occurrence probabilities of other root nodes still take the prior probabilities, and re-quantify the junction tree. Marginalize any cluster node in the quantified junction tree that contains the leaf node to be predicted, so as to calculate the probability P(C j ) of the occurrence of the leaf node C j = 1|A i = 1), j = 1, 2, 3. The obtained result is the probability of the occurrence of risk events in the temporary grandstand under the known occurrence state of a certain risk-causing factor A i during the use of the temporary grandstand.

[0136] Embodiment 3:

[0137] A method for evaluating the structural safety of a temporary grandstand based on a Bayesian network model, comprising the following steps:

[0138] 1) Establish a Bayesian network topology structure for the safety evaluation of the temporary grandstand;

[0139] The Bayesian network topology structure in the present invention includes a root node layer, an intermediate node layer, and a leaf node layer. Each layer corresponds to a basic event (a risk-causing factor leading to a safety accident of the temporary grandstand), an intermediate event (connecting the basic event and the top event as an intermediate bridge), and a top event (a safety accident of the temporary grandstand); the same level is independent of each other.

[0140] Three typical structural safety accidents are selected for the leaf node layer of the Bayesian network: overall overturning of the stand, collapse of the stand, and excessive deformation of the stand (the deformation value exceeds the preset threshold); six intermediate events are selected for the intermediate node layer of the Bayesian network: insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity; eleven typical risk factors for safety accidents are selected for the root node layer of the Bayesian network: strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connections, assembly errors, component size deviations, and too low temperature.

[0141] The node content of each layer of the Bayesian network topology structure is obtained by experts analyzing historical data and combining with actual engineering experience.

[0142] 2) Generate a join tree according to the Bayesian network topology structure;

[0143] The steps of generating a join tree according to the Bayesian network topology structure include:

[0144] 2.1) Remove the direction of each connection line in the Bayesian network topology structure, and then add undirected edges to connect each pair of parents to obtain a moral graph;

[0145] 2.2) Use the BuildCT algorithm to eliminate nodes in turn to obtain several cluster nodes;

[0146] 2.3) Connect the cluster nodes obtained after elimination in turn, and connect adjacent cluster nodes with separator nodes (the separator nodes save the information shared by adjacent cluster nodes), and finally generate a join tree;

[0147] For each variable V, at least one cluster node in the join tree contains V and the parents of V;

[0148] For each pair of nodes N and node W in the join tree, each node on the path between them contains the intersection N ∩ W.

[0149] 3) Determine the prior probability of the root nodes of the Bayesian network and the conditional probability tables of non-root nodes

[0150] The prior probability of the root nodes of the Bayesian network and the conditional probability tables of non-root nodes are determined by experts in this field based on existing data and engineering experience.

[0151] 4) Quantify the join tree;

[0152] The steps of quantifying the join tree include:

[0153] 4.1) Create a table φ(T) for each cluster node and separator node. The table includes all combinations of n variables, add a column to record the probability distribution of each table, and set each value in this column to 1;

[0154] 4.2) Determine a cluster for each variable V, where the cluster contains V and the parents of V; update φ(T) by multiplying it with P(V|the parents of V), i.e., φ(T) ← φ(T)P(V|the parents of V);

[0155] 4.3) Pass messages (taking the example of cluster nodes C i and C j connected through the separating point S):

[0156] 4.3.1) Copy the separating point table;

[0157] φ(S C ) ← φ(S) (1)

[0158] 4.3.2) Marginalize the cluster node C i , to obtain a new separating point table φ(S)

[0159]

[0160] 4.3.3) Calculate the new table φ(C j ) j )

[0161]

[0162] 4.4) Pass messages in both directions until a consistent join tree is obtained. The join tree encodes the joint probability distribution P(U) as the product of the cluster tables divided by the product of the separating point tables, i.e.:

[0163]

[0164] 5) Evaluate the safety of the temporary stand structure based on the quantized join tree. According to the reverse inference function of the Bayesian network, the key risk factors leading to the risk events of the temporary stand structure can be diagnosed.

[0165] The steps for diagnosing the key risk factors leading to the risk events of the temporary stand structure include:

[0166] a) Obtain the state (occurrence / non-occurrence) of the leaf node C j , j = 1, 2, 3;

[0167] b) Assume that the leaf node C j occurs, find all the clusters containing this leaf node, and add an evidence column to the table of each variable in these clusters, setting the rows corresponding to the cases where the corresponding leaf node has occurred to 1 and the others to 0;

[0168] c) Multiply the probability distribution by the evidence column to obtain a new probability distribution, and re-perform two-way message passing on the join tree to obtain a consistent join tree;

[0169] d) Standardize any cluster node or separation point table containing the root node A i , and the probability information of this root node can be obtained, that is:

[0170]

[0171] where the probability P(A i , C j = 1) is as follows:

[0172]

[0173] P(A i |C j = 1) is the probability of each root node A j occurring under the condition that the leaf node C i occurs. Among them, the event A i corresponding to the maximum probability value is the key risk factor leading to the temporary stand structure risk event C j .

[0174] Example 4:

[0175] A safety assessment method for temporary stand structures based on a Bayesian network model includes the following:

[0176] Step 1, establish a Bayesian network for temporary stand safety assessment. To establish this network, the following three aspects need to be considered:

[0177] Determine the node content. Take the accident types of the temporary stand structure and the reasons causing accidents in the temporary stand structure as the content of each node, and note that the nodes at the same level should be mutually independent;

[0178] Determine the form of the topological structure. Considering the characteristics of the temporary stand structure, build the topological structure into three layers: the root node layer, the intermediate node layer, and the leaf node layer, and create connections between the nodes according to the causal relationship between the nodes at each layer;

[0179] Determine the probability of the nodes. The probability of the nodes includes the prior probability of the root nodes and the conditional probability of the non-root nodes. Based on this probability information, Bayesian network reasoning can be realized.

[0180] The above three aspects of content are all obtained by experts in the relevant field analyzing historical data and combining with actual engineering experience. Finally, the Bayesian network topological structure as shown in Figure 2 and as shown in Figure 3The prior probability of the root node and the conditional probability table information of non-root nodes shown. Among them, three typical structural safety accidents, namely, overall overturning of the stand, collapse of the stand, and excessive deformation of the stand, are selected for the leaf node layer of the topological structure; six intermediate events, namely, insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity, are selected for the intermediate node layer; eleven most original risk factors leading to accidents of temporary stands, such as strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connections, assembly errors, component size deviations, and too low temperature, are selected for the root node layer. The entire Bayesian network topological structure is divided into three layers with a total of 20 nodes.

[0181] Next, use the junction tree algorithm to perform inference analysis on the Bayesian network:

[0182] Step 2, generate a junction tree from the Bayesian network topological structure. The implementation of this step includes the following contents: construct a moral graph, perform elimination using the BuildCT algorithm, distinguish cluster nodes, and establish a junction tree. Next, I will elaborate on the implementation process of this step in combination with Figure 4 Figure 5 detail.

[0183] First, remove the direction of each connection in the topological structure, and then connect each pair of parents by adding undirected edges to obtain a moral graph as shown in Figure 4 where the "dotted line" is the edge added when generating the moral graph from the topological structure. Subsequently, use the BuildCT algorithm to perform elimination on variables in sequence. The elimination order is ρ = {A1, C1, A2, A3, A4, A6, A5, B1, C2, A11, A7, C3, A8, A9, A10}, and the elimination process is as shown in Figure 5 where the "double-line dot" is the edge added during the elimination process. Then, connect the cluster nodes obtained during the elimination process in sequence, and connect adjacent cluster nodes with a separator (the separator preserves the information shared by adjacent cluster nodes). Finally, obtain a junction tree as shown in Figure 6 The junction tree needs to meet the following two conditions:

[0184] For each variable V, there is at least one cluster node in the junction tree that contains V and the parents of V;

[0185] For each pair of nodes N and W in the junction tree, each node on the path between them contains the intersection N ∩ W.

[0186] By observation, Figure 6 the junction tree shown meets these two conditions.

[0187] Step 3, quantify the junction tree. Quantifying the junction tree includes the following two aspects:

[0188] Initialize the junction tree

[0189] (1) Create a table for each cluster node and separator, which will encode all combinations of n variables. Add a column to record the probability distribution of the table (joint distribution) φ(T), and set each value in this column to 1. The symbol φ is used to represent the table of distribution values;

[0190] (2) Determine a cluster for each variable V, which contains V and the parents of V. Multiply φ(T) by P(V|the parents of V), and for

[0191] φ(T) ← φ(T)P(V|the parents of V)

[0192] 2. Pass messages to obtain a consistent junction tree. Take the example of cluster nodes C i and C j connected through separator S. The specific calculation process is as follows:

[0193] (1) Copy the separator table:

[0194] φ(S C ) ← φ(S)

[0195] (2) Marginalize cluster node C i , to obtain a new separator table.

[0196]

[0197] (3) Calculate the new table of the adjacent cluster node C i of C j , and divide the product of the old table of C j and the separator table by the old separator table:

[0198]

[0199] (4) Pass messages in both directions until a consistent junction tree is obtained.

[0200] As Figure 6 shown, where the dashed line represents the message collection phase, the solid line represents the message distribution phase, and the numbers on the line represent the message passing order. After the message collection and distribution phases, the junction tree satisfies:

[0201] (1) The tree encodes the joint probability distribution as the product of the cluster tables divided by the product of the separator tables:

[0202]

[0203] (2) The separator and the adjacent clusters are consistent, and the separator can be obtained by marginalizing any adjacent cluster.

[0204]

[0205] Step 4, write a junction tree algorithm program to conduct inference and analysis from the following two aspects

[0206] 1. Forward inference

[0207] Forward inference means predicting the probability of leaf nodes when the state of the root node is known. The calculation idea is as follows: First, initialize the junction tree, then obtain a consistent junction tree through two stages of message collection and message distribution, and finally marginalize any cluster node containing a certain leaf node to obtain the probability of this leaf node occurring. When some emergency situations occur on-site, such as strong wind suddenly acting on the temporary grandstand structure, just change the probability of strong wind occurrence in the program to 1, and then the probabilities of three risk events occurring in the temporary grandstand can be re-predicted to define the alarm level and take early precautions.

[0208] 2. Backward inference

[0209] Backward inference means inferring the probability of the root node occurring when the occurrence of some leaf nodes is known. The calculation idea is as follows: Assume that the leaf node C j occurs. First, quantify the junction tree. After obtaining a consistent junction tree, add a column to the table of each variable in the cluster with evidence, set 1 for the rows corresponding to the states with evidence, and set 0 for the others. Then, perform the initialization process again. When initializing, multiply the probability distribution by the evidence column to obtain a new probability distribution, and then re-obtain a consistent junction tree through two stages of message collection and message distribution. After the tree is consistent, the probability information of this root node can be obtained by normalizing any cluster node or separator table containing a certain root node. If the probability information of a certain root node A i is required, the following marginalization operation needs to be performed first (C is the cluster node table containing node A i ):

[0210]

[0211] Subsequently, normalize P(A i , C j = 1) to obtain P(A i |C j = 1):

[0212]

[0213] P(A i |C j = 1) is the probability of each root node A j occurring when the leaf node C i occurs. The event A i corresponding to the maximum probability value is the event that causes the risk event C jKey risk factors.

[0214] Write code for calculation according to the above idea and analyze the results.

[0215] Example 5:

[0216] A safety assessment method for temporary grandstand structures based on a Bayesian network model, comprising the following steps:

[0217] 1) Establish a Bayesian network topology for the safety assessment of temporary grandstands;

[0218] The Bayesian network topology includes several levels of nodes; nodes at the same level are independent of each other.

[0219] The content of the nodes in the Bayesian network topology includes the accident types of the temporary grandstand structure and the reasons for the accidents of the temporary grandstand structure.

[0220] The content of the top-level leaf nodes in the Bayesian network topology is selected as the overall overturning of the grandstand, the collapse of the grandstand, and excessive deformation of the grandstand; the judgment criteria for excessive deformation of the grandstand include: the difference area between the current temporary grandstand structure and the temporary grandstand structure without faults is greater than the preset threshold;

[0221] The content of the bottom-level root nodes in the Bayesian network topology is selected as strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connections, assembly errors, component size deviations, and low temperature. The content of the bottom-level root nodes in the Bayesian network topology is obtained through expert experience. The calculation of the prior probability of the root nodes is also completed based on the fuzzy set theory relying on expert experience.

[0222] The probability of the Bayesian network nodes includes the prior probability of the root nodes and the conditional probability of the non-root nodes.

[0223] 2) Generate a junction tree according to the Bayesian network topology;

[0224] The steps for generating a junction tree according to the Bayesian network topology include:

[0225] 2.1) Remove the direction of each connection line in the Bayesian network topology, and then add undirected edges to connect each pair of parents to obtain a moral graph;

[0226] 2.2) Use the BuildCT algorithm to eliminate nodes in turn to obtain several cluster nodes; among them, the method for determining the elimination node order includes the minimum deficiency edge search method; the criteria for adding edges during the elimination process include: if the other nodes connected to the node are pairwise connected, no edge is added, otherwise, an edge is added to make the other nodes pairwise connected;

[0227] 2.3) Connect the cluster nodes obtained after elimination in sequence, connect adjacent cluster nodes with separator points, and the separator points save the information shared by adjacent cluster nodes, thereby generating a junction tree;

[0228] For each variable V, at least one cluster node in the junction tree contains V and the parents of V;

[0229] For each pair of nodes V and W in the junction tree, each node on the path between them contains the intersection V ∩ W.

[0230] 3) Quantize the junction tree;

[0231] The steps for quantizing the junction tree include:

[0232] 3.1) Create a table φ(T) for each cluster node or separator point. The table includes all combinations of n nodes and a column for recording the probability distribution of the table φ(T), and each value in this column is set to 1;

[0233] 3.2) Determine a cluster for each variable V, where the cluster contains V and the parents of V; update the table φ(T) by multiplying φ(T) by P(V|the parents of V), i.e., φ(T) ← φ(T)P(V|the parents of V);

[0234] 3.3) Copy the separator point table;

[0235] 3.4) Marginalize the cluster node C i , to obtain a new separator point table φ(S), i.e.:

[0236]

[0237] where S is the new separator point;

[0238] 3.5) Calculate the new table φ(C i ) of the adjacent cluster node C j of the marginalized cluster node C j , i.e.:

[0239]

[0240] 3.6) Pass information in two directions until a consistent junction tree is obtained; the junction tree encodes the joint probability distribution P(U) as the product of the cluster tables divided by the product of the separator point tables, i.e.:

[0241]

[0242] where S j represents the separator point;

[0243] The separator point φ(S) in the junction tree is as follows:

[0244]

[0245] 4) Evaluate the safety of the temporary stand structure according to the quantified join tree.

[0246] The steps for evaluating the safety of the temporary stand structure include:

[0247] a) Obtain the state of the root node A a where a is a natural number;

[0248] b) Marginalize any cluster node in the quantified join tree that contains the leaf node to be predicted, so as to calculate the probability P(C k = 1|A k = 1) that the leaf node to be predicted occurs; the probability of the leaf node to be predicted occurring is negatively correlated with the safety of the temporary stand structure; k is a natural number. a

[0249] The steps for evaluating the safety of the temporary stand structure include:

[0250] a) Obtain the state of the leaf node that has occurred;

[0251] b) Determine the cluster related to the leaf node that has occurred, and add an evidence column to the table of each variable in this cluster, set 1 for the row corresponding to the obtained state, and set 0 for the others;

[0252] c) Multiply the probability distribution by the evidence column to obtain a new probability distribution, and re-quantify the join tree to obtain a consistent join tree;

[0253] d) Standardize the table of any cluster node or separator point that contains a certain root node, and the probability information of this root node can be obtained, that is:

[0254]

[0255] where the probability P(V, e) is as follows:

[0256]

[0257] The probability information of the said root node is negatively correlated with the safety of the temporary stand structure.

[0258] The steps for evaluating the safety of the temporary stand structure include:

[0259] a) Calculate the importance I RAW (X i ), the importance I RRW (X i ), and the importance I BW (X i ) of the change measure, that is:

[0260]

[0261]

[0262]

[0263] In the formula, I RAW (X i ) is used to evaluate the degree of influence of the occurrence or non-occurrence of the root node content X i on the occurrence probability of the leaf node T; I RAW (X i ) is positively correlated with the degree of influence of the occurrence or non-occurrence of the root node content X i on the occurrence probability of the leaf node T; When I RRW (X i ) > 1, the root node content X i reduces the structural safety of the temporary stand; When I RRW (X i ) < 1, the root node content X i increases the structural safety of the temporary stand; I BW (X i ) is used to measure the change range of the occurrence probability value of T when X i occurs and does not occur; P(T = 1|X i = 0), P(T = 1|X i = 1) respectively represent the occurrence probability values of T when X i does not occur and occurs; P(T = 1) represents the occurrence probability value of T;

[0264] b) According to the importance degree of the risk promotion value I RAW (X i ), the importance degree of the risk reduction value I RRW (X i ), and the importance degree of the change measurement I BW (X i ), judge the degree of influence of the root node content on the leaf node, so as to determine the root node content that affects the structural safety of the temporary stand.

[0265] Example 6:

[0266] A simulation analysis of a method for evaluating the structural safety of a temporary stand based on a Bayesian network model is as follows:

[0267] 1. Write code for forward inference calculation to predict the occurrence probability of risk events of the temporary stand structure:

[0268] 1.1) Before the temporary stand is used: Substitute the prior probability as the occurrence probability of the root node into the calculation to predict the occurrence probability of the risk event C j (such asFigure 7 As shown in the figure. It can be seen from the figure that the most likely risk event predicted before the use of the grandstand is C1 (overall overturning of the grandstand). The grandstand structure in this example is built in an area where strong winds often occur. Therefore, the overturning of the grandstand is the main type of accident that needs to be considered. The most likely risk event calculated by the code is also the overall overturning of the grandstand, which is consistent with the facts and verifies the rationality of this method.

[0269] 1.2) During the use of the temporary grandstand: When a certain condition of the structure is known, such as when it is known that strong wind (A1) acts on the structure, the probability of the leaf node occurring can also be quickly calculated (as Figure 8 shown in the figure). It can be seen from the figure that when strong wind exists, the risk of the grandstand overturning instantly increases to 10.5%, which is much greater than the probabilities of the grandstand collapsing and excessive deformation. Therefore, the management personnel should always pay attention to the wind force and wind speed in this area so as to take corresponding measures as early as possible.

[0270] The prediction function of the Bayesian network has very important guiding significance for the safety operation and maintenance of the temporary grandstand. Engineers only need to establish a Bayesian accident network in advance, and then according to the real-time conditions of risk-causing factors such as strong wind, foundation problems, and crowd activities monitored on site, input the corresponding values of the risk-causing factors into the Bayesian network, and then the probability of the risk event occurring can be predicted and the warning level of the grandstand accident can be defined.

[0271] 2. The reverse reasoning function of the Bayesian network can quickly diagnose the key risk-causing factors leading to the risk events of the temporary grandstand structure. In the code, the probabilities of C1 (overall overturning of the grandstand), C2 (collapse of the grandstand), and C3 (excessive deformation of the grandstand) are respectively set to 1, and the posterior probability values of each root node under different risk event occurrences are obtained through reverse reasoning, such as Figure 9 shown in Figures 10 and 11.

[0272] Before the use of the temporary grandstand, the key risk-causing factors leading to the risk events can be diagnosed through reverse reasoning, so as to clarify the control points during the use process and take corresponding preventive measures as early as possible. If a certain risk event occurs during the use of the temporary grandstand, the risk-causing factors with larger posterior probability values should be checked first in order to quickly find out the cause of the accident and accumulate experience for the construction, use, and safety operation and maintenance of the temporary grandstand.

Claims

1. A safety assessment method for temporary grandstand structures based on a Bayesian network model, characterized in that, It includes the following steps: 1) Establish a Bayesian network topology for the safety assessment of the temporary grandstand; 2) Generate a junction tree according to the Bayesian network topology; 3) Obtain the prior probabilities of the root nodes and the conditional probability tables of the non-root nodes of the Bayesian network; 4) Quantify the junction tree; 5) Evaluate the structural safety of the temporary grandstand according to the quantified junction tree; The Bayesian network topology includes several levels of nodes; the nodes at the same level are independent of each other; The content of the nodes of the Bayesian network topology includes the accident types of the temporary grandstand structure and the reasons for the accidents occurring in the temporary grandstand structure; The content of the top-level leaf nodes of the Bayesian network is selected as the overall overturning of the grandstand, the collapse of the grandstand, and excessive deformation of the grandstand; The judgment criterion for excessive deformation of the grandstand is: the deformation value exceeds the preset threshold; The content of the intermediate-level nodes of the Bayesian network is selected as insufficient foundation bearing capacity, resonance, overloading, insufficient structural stability, insufficient structural stiffness, and insufficient structural bearing capacity; The content of the bottom-level root nodes of the Bayesian network is selected as strong wind, foundation waterlogging, insufficient geological condition investigation, unreasonable foundation treatment, crowd jumping activities, excessive crowd density, initial geometric defects of components, unreasonable connections, assembly errors, component size deviations, and too low temperature; The content of each layer of nodes of the Bayesian network is obtained by experts based on existing data and actual engineering experience; The steps for generating a junction tree according to the Bayesian network topology include: 1) Remove the directions of each connection line in the Bayesian network topology, and then add undirected edges to connect each pair of parents to obtain a moral graph; 2) Use the BuildCT algorithm to eliminate nodes in turn to obtain several cluster nodes; among them, the method for determining the elimination order is the minimum fill-in search method; the method for judging the number of fill-in edges during the elimination process is: the number of edges that need to be added to connect all variables connected to variable V pairwise is the number of fill-in edges; 3) Connect the cluster nodes obtained after elimination in turn, and connect adjacent cluster nodes with separator nodes to generate a junction tree; the separator nodes save the information shared by adjacent cluster nodes; For each variable V, there is at least one cluster node in the junction tree that contains V and the parents of V; For each pair of nodes N and node W in the junction tree, each node on the path between them contains the intersection N∩W; The prior probabilities of the root nodes and the conditional probability tables of the non-root nodes of the Bayesian network are determined by experts in this field based on existing data and engineering experience; The steps for quantifying the junction tree include: 1) Create a table φ(T) for each cluster node or separator node, which includes all combinations of n nodes and a column for recording the probability distribution of the table φ(T), and each value in this column is set to 1; 2) Determine a cluster for each variable V, and the cluster contains V and the parents of V; update φ(T) by multiplying φ(T) by P(V|the parents of V) to get φ(T)←φ(T)P(V|the parents of V); 3) Pass messages: 3.1) Copy the separation point table φ(S C ): φ(S C ) ← φ(S)(1) 3.2) Marginalized cluster node C i , to obtain a new separation point table φ(S) 3.3) Calculate C j for the new table φ(C j ): 4) Pass messages in two directions until a consistent junction tree is obtained; the junction tree encodes the joint probability distribution P(U) as the product of the cluster tables divided by the product of the separator node tables, that is:

2. The safety assessment method for temporary grandstand structures based on a Bayesian network model according to claim 1, characterized in that, The steps for evaluating the structural safety of temporary grandstands include: using the forward reasoning ability of the Bayesian network to predict the occurrence probability of risk events of temporary grandstands; the specific implementation steps are as follows: 1) Predict the probability of the occurrence of risk events before the use of the temporary grandstand; at this time, the probability of occurrence of the root node P(A i ), where the values of i = 1, 2,..., 11 are prior probabilities. Marginalize any cluster node in the quantified join tree that contains the leaf node to be predicted, so as to calculate the probability of the occurrence of the leaf node C j P(C j = 1), where j = 1, 2, 3, which is the probability of the occurrence of the risk event C j predicted before the use of the temporary grandstand; 2) Prediction of the occurrence probability of risk events during the use of the temporary grandstand; if a risk-causing factor A is detected during the use of the temporary grandstand i has occurred, then update the value of its occurrence probability P(A i ) to 1, and the occurrence probabilities of other root nodes still take the prior probabilities, and re-quantify the junction tree; marginalize any cluster node in the quantified junction tree that contains the leaf node to be predicted, so as to calculate the probability P(C j ) of the leaf node C j =1|A i =1), j = 1, 2, 3, which is the occurrence probability of the risk event of the temporary grandstand in the known occurrence state of a certain risk-causing factor A i during the use of the temporary grandstand.

3. A safety assessment method for temporary grandstand structures based on a Bayesian network model according to claim 1, characterized in that, The steps for evaluating the structural safety of temporary grandstands include: using the reverse reasoning ability of Bayesian networks to diagnose the key risk factors leading to risk event C j ; the specific implementation steps are as follows: 1) Obtain leaf node C j The state it is in, where j = 1, 2, 3; the states include occurring and not occurring; 2) Assume leaf node C j Occurs, find all clusters that contain this leaf node, and add an evidence column to the table of each variable in these clusters, setting the rows corresponding to the cases where the corresponding leaf node has occurred to 1 and the others to 0; 3) Multiply the probability distribution by the evidence column to obtain a new probability distribution, and perform two-way message passing on the junction tree again to obtain a consistent junction tree; 4) Standardize any cluster node or separation point table containing the root node A i to obtain the probability information of this root node, that is: Among them, the probability P(A i ,C j =1) is as follows: P(A i |C j = 1) is the probability of each root node A j occurring under the condition that leaf node C i occurs. Among them, the event A corresponding to the maximum probability value i , is the key risk factor leading to risk event C j .

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