Engineering project management auxiliary decision-making method based on domain knowledge enhancement

Abstract

The invention provides an engineering project management auxiliary decision-making method based on domain knowledge enhancement, and belongs to the technical field of engineering project management.The method includes the steps that firstly, a construction plan network diagram and historical delay attribution data are obtained, the plan diagram is mapped into an adjacent matrix, and delay data are converted into a propagation probability table through Bayesian inference; secondly, calculating betweenness centrality by utilizing an adjacent matrix, updating node attributes, and generating a weighted topological graph; thirdly, constructing an SIR cascade failure simulation model based on the topological graph and the probability table, simulating the diffusion process of delay in the network, and generating an influence matrix; and finally, identifying a high-risk target node according to the influence matrix, and calculating a time buffer value, thereby generating accurate engineering management auxiliary decision information. According to the method, the invisible key nodes which are extremely easy to cause global paralysis in the complex engineering network can be accurately identified, and the anti-risk time buffer strategy is automatically quantified and generated, so that the robustness of the engineering progress plan is remarkably improved.

Description

Technical Field

[0001] This application belongs to the field of engineering project management technology, and in particular relates to an auxiliary decision-making method for engineering project management based on domain knowledge enhancement. Background Technology

[0002] Domain knowledge-enhanced decision support methods for engineering project management integrate historical experience data from the engineering industry with modern computing technologies to provide intelligent means for schedule control and risk management in complex projects. In scenarios with highly coupled processes, such as large-scale infrastructure construction and high-end equipment R&D, this method can effectively assist managers in predicting schedule risks and optimizing resource allocation, demonstrating broad application prospects.

[0003] In existing technologies, project management decision support typically employs the Critical Path Method (CPM) or Program Evaluation and Review Technique (PERT) to construct a project schedule network, and combines historical project data to statistically analyze the probability distribution of each task's duration. To assess risk, some existing solutions utilize Monte Carlo simulation techniques to calculate the probability of completion of the entire project duration, assuming that the duration fluctuations of each task are independent or follow only simple linear dependencies. This helps managers focus on task nodes on the critical path.

[0004] However, the aforementioned methods primarily focus on the longest path in the time dimension, often neglecting the cascading effects that delays at certain non-critical nodes in pivotal positions within the schedule network topology can trigger. Existing static or simple linear simulations cannot accurately reflect the cascading diffusion effects and dynamic attenuation patterns of risks within complex process logic, making it difficult to quantify the destructive impact of local delays on the global network and formulate precise buffering strategies accordingly. Therefore, existing technologies suffer from insufficient project management decision support due to their inability to effectively identify and defend against hidden schedule risks with high propagation properties in complex engineering networks. Summary of the Invention

[0005] The purpose of this application is to provide a domain knowledge-enhanced decision support method for engineering project management, in order to address the shortcomings of existing engineering project management decision support technologies.

[0006] To address the aforementioned technical problems, in a first aspect, this application provides a domain knowledge-enhanced engineering project management decision support method, comprising:

[0007] Obtain the construction plan network diagram of the target project and the delay attribution data of similar projects. The construction plan network diagram includes a set of task nodes and logical dependencies between tasks. The delay attribution data includes the delay propagation path and delay probability information of each delayed task, represented by a tree data structure.

[0008] By performing graph theory mapping on the construction plan network graph, the set of task nodes is mapped to graph nodes and logical dependencies are mapped to directed edges to construct an adjacency matrix;

[0009] Based on the frequency of delays in each level of the delay attribution data, Bayesian inference is used to calculate the conditional probability of delays between different task nodes, and a propagation probability table is generated with the conditional probability of delays as the core parameter.

[0010] Calculate the betweenness centrality of each graph node based on the adjacency matrix, and update the node attribute values ​​of the associated graph nodes in the adjacency matrix based on the betweenness centrality to generate a topology graph.

[0011] A cascaded failure simulation model is constructed based on the topology graph, the propagation probability table, and the SIR state mapping rule. The construction states corresponding to the graph nodes in the topology graph are mapped to objects in the SIR model. The cascaded failure simulation model is used to perform multiple rounds of random simulation. The delay conditional probability in the propagation probability table is set as the infection rate parameter to simulate the diffusion process from infection type to susceptible type. The delay diffusion range and decay rate are statistically analyzed to generate an influence matrix composed of the initial risk source and the corresponding delay diffusion range and decay rate.

[0012] Extract target nodes from the influence matrix whose failure impact exceeds a preset threshold, and calculate the time buffer value based on the delay diffusion characteristics of the target nodes in the cascading failure simulation model, combined with the delay coefficient preset according to the task process type, to generate management auxiliary decision-making information for the target project.

[0013] Optionally, by performing graph theory mapping on the construction plan network graph, the set of task nodes is mapped to graph nodes and logical dependencies are mapped to directed edges to construct an adjacency matrix, including:

[0014] Traverse the set of task nodes in the construction plan network graph, treat each independent task in the task node set as a graph node, and assign a sequence index to each graph node;

[0015] Extract the preceding and following graph nodes with preceding and following constraint attributes from the logical dependency relationships, and construct directed edges based on the vector connection relationships between preceding graph nodes and following graph nodes;

[0016] Construct an initial matrix based on the total number of graph nodes, determine the mapping coordinates of the sequence indices between graph nodes through the vector connection relationship of directed edges, set the matrix elements located at the mapping coordinates in the initial matrix to values ​​representing the connected state, and output the adjacency matrix.

[0017] Optionally, the betweenness centrality of each graph node is calculated based on the adjacency matrix, and the node attribute values ​​of the associated graph nodes in the adjacency matrix are updated based on the betweenness centrality to generate a topology graph, including:

[0018] Based on the connectivity relationships represented by the matrix elements in the adjacency matrix, the shortest connected path between any two graph nodes is determined. The betweenness centrality of each graph node is obtained by calculating the cumulative value of the paths covered by the shortest connected path with each graph node as a transit node.

[0019] The betweenness centrality is converted into a weight parameter, and the weight parameter is used as the node attribute value of the graph node to associate with the corresponding graph node. The topology graph is then constructed by combining the adjacency matrix.

[0020] Optionally, based on the frequency of delays in each level of the delay attribution data, the conditional probability of delays between different task nodes is calculated using Bayesian inference, and a propagation probability table is generated using the conditional probability of delays as the core parameter, including:

[0021] By extracting parent and child task nodes with cascading relationships from the delay propagation path included in the delay attribution data, and by statistically analyzing the frequency of delays of corresponding tasks in historical samples of similar projects, the prior probability of occurrence of parent task nodes and the joint probability of delays occurring simultaneously between parent and child task nodes are determined.

[0022] The delay conditional probability is obtained by calculating the ratio of the joint occurrence probability to the prior occurrence probability.

[0023] Establish a mapping relationship between parent task nodes and child task nodes, and construct a propagation probability table based on the mapping relationship and the delay conditional probability between different task nodes.

[0024] Optionally, a cascading failure simulation model is constructed based on the topology graph, propagation probability table, and SIR state mapping rules, mapping the construction states corresponding to the graph nodes in the topology graph to objects in the SIR model, including:

[0025] Establish a SIR model that includes susceptible types, infected types, and removal types. Map graph nodes in the on-time execution phase of the topology graph to susceptible types, graph nodes with project delays to infected types, and graph nodes with no project delays or that have been completed to removal types.

[0026] Traverse the directed edges of the topology graph, extract the delay conditional probability corresponding to the directed edge from the propagation probability table, and set the delay conditional probability as the infection rate parameter for state evolution from infection type to susceptible type.

[0027] Optionally, a cascaded failure simulation model is used to perform multiple rounds of stochastic simulation. The delay conditional probability in the propagation probability table is set as the infection rate parameter to simulate the diffusion process from infection type to susceptible type. The delay diffusion range and decay rate are statistically analyzed to generate an influence matrix consisting of the initial risk source and the corresponding delay diffusion range and decay rate, including:

[0028] Establish a cyclic simulation sequence with a preset total number of iterations. In each simulation sequence, select a graph node set as the infection type as the initial risk source and initialize the time step counter.

[0029] Within each discrete time step, the graph node of the infection type points to the successor graph node of the susceptible type to generate a random probability value. The random probability value is compared with the infection rate parameter of the corresponding directed edge. When the random probability value meets the trigger condition, the state of the successor graph node is updated to the infection type, and the state of the graph node originally in the infection type is updated to the removal type. The iteration continues until there are no graph nodes of the infection type in the cascade failure simulation model.

[0030] In each simulation sequence, the delay propagation range and decay rate are obtained by statistically analyzing the total number of graph nodes that are ultimately removed and the cumulative value of the time step counter.

[0031] A statistical average is calculated on all delay diffusion ranges and decay rates obtained within a preset total number of iterations. The node index, which serves as the initial risk source, is defined as the row, and the average diffusion range and average decay rate are defined as the column indices to construct an influence matrix.

[0032] Optionally, target nodes with failure impact greater than a preset threshold are extracted from the influence matrix. Based on the delay diffusion characteristics of the target nodes in the cascading failure simulation model, and combined with the time buffer value calculated according to the delay coefficient preset according to the task process type, management auxiliary decision-making information for the target project is generated, including:

[0033] Extract the delay spread range and decay rate corresponding to each initial risk source in the impact matrix, perform weighted calculation on the delay spread range and decay rate to obtain the failure impact degree, and determine the initial risk source with the failure impact degree greater than the preset threshold as the target node;

[0034] Obtain the task process type corresponding to the target node, and match the preset delay coefficient according to the task process type. The delay coefficient is set according to the positive correlation between process complexity and recovery difficulty.

[0035] The time buffer value is obtained by multiplying the decay rate corresponding to the target node by a preset delay coefficient.

[0036] Establish the task assignment relationship between time buffer values ​​and target nodes in the construction plan network diagram, and output management auxiliary decision-making information including task assignment relationship and time buffer values.

[0037] Secondly, this application provides an engineering project management auxiliary decision-making system based on domain knowledge enhancement, including:

[0038] The acquisition module is used to acquire the construction plan network diagram of the target project and the delay attribution data of projects of the same type as the target project. The construction plan network diagram includes a set of task nodes and logical dependencies between tasks. The delay attribution data includes the delay propagation path and delay probability information of each delayed task represented by a tree data structure.

[0039] The mapping module is used to construct an adjacency matrix by mapping the set of task nodes to graph nodes and the logical dependencies to directed edges through graph theory mapping of the construction plan network graph.

[0040] The calculation module is used to calculate the delay conditional probability between different task nodes based on the delay occurrence frequency of each level of the chain path in the delay attribution data, and generate a propagation probability table with the delay conditional probability as the core parameter.

[0041] The generation module is used to calculate the betweenness centrality of each graph node based on the adjacency matrix, and update the node attribute values ​​of the associated graph nodes in the adjacency matrix based on the betweenness centrality to generate a topology graph.

[0042] The generation module is also used to construct a cascade failure simulation model based on the topology graph, the propagation probability table, and the SIR state mapping rules. It maps the construction state corresponding to the graph node in the topology graph to the object in the SIR model, and uses the cascade failure simulation model to perform multiple rounds of random simulation. The delay conditional probability in the propagation probability table is set as the infection rate parameter to simulate the diffusion process from infection type to susceptible type. The delay diffusion range and decay rate are statistically analyzed to generate an influence matrix composed of the initial risk source and the corresponding delay diffusion range and decay rate.

[0043] The generation module is also used to extract target nodes in the influence matrix whose failure impact is greater than a preset threshold, and to generate management auxiliary decision-making information for the target project by combining the delay diffusion characteristics of the target nodes in the cascading failure simulation model with the delay coefficient preset according to the task process type to calculate the time buffer value.

[0044] Thirdly, this application provides an electronic device, comprising:

[0045] Memory, used to store computer programs;

[0046] A processor, configured to implement the steps of the domain knowledge-enhanced engineering project management decision support method as described in the first aspect above, when executing the computer program.

[0047] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps of the domain knowledge-enhanced engineering project management auxiliary decision-making method described in the first aspect above.

[0048] The domain knowledge-enhanced decision support method for engineering project management provided in this application firstly identifies key nodes with significant impact on global connectivity from complex process network topologies by constructing an adjacency matrix and calculating betweenness centrality. This overcomes the limitation of traditional methods that focus only on critical paths while neglecting structural risks. Secondly, by combining a propagation probability table generated by Bayesian inference with a SIR cascade failure simulation model, this application can dynamically simulate the nonlinear diffusion process and attenuation trend of delay risks among task nodes, thereby quantitatively assessing the cascading destructive effects of local delays on the overall project.

[0049] Finally, the targeted time buffer strategy generated based on the above simulation results effectively defends against hidden risks with high propagation properties. Therefore, this application effectively solves the problem of insufficient robustness of auxiliary decision-making in engineering project management caused by the inability to accurately quantify the cascading failure risk in complex engineering networks in existing technologies.

[0050] Furthermore, this application achieves the transformation of complex engineering schedule networks into graph theory topology models that can be efficiently processed by computer algorithms by accurately mapping engineering tasks and logical dependencies into adjacency matrices that include sequence indexes and vector connection features.

[0051] This matrix-based construction method, based on mapped coordinates, fully preserves the intricate temporal constraints and coupling structures between task nodes, providing a standardized mathematical foundation and data interface for subsequent analysis of network hub characteristics using betweenness centrality and cascading failure simulation. Therefore, this application provides crucial data structure support for addressing the problem in existing technologies where the lack of refined topology models hinders the accurate identification and simulation of hidden risk propagation in complex networks. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 A flowchart illustrating an engineering project management auxiliary decision-making method based on domain knowledge enhancement, provided for an embodiment of this application;

[0054] Figure 2 This is a schematic diagram of a tree structure for delay attribution data provided in an embodiment of this application;

[0055] Figure 3 This application provides a schematic diagram of the structure of a topology graph.

[0056] Figure 4 A schematic diagram of the structure of an engineering project management auxiliary decision-making system based on domain knowledge enhancement provided in this application embodiment;

[0057] Figure 5 This is a schematic diagram of the hardware structure of an electronic device provided in one embodiment of this application. Detailed Implementation

[0058] In the field of engineering project management, although existing technologies have achieved basic predictions of project duration using methods such as the critical path method, they still face serious challenges when dealing with highly coupled and complex projects. Traditional static analysis or simple linear simulation mainly focuses on the longest path in the time dimension, neglecting the cascading effects that may be caused by non-critical nodes in the network topology.

[0059] This means that once a secondary task at a structural hub is delayed, existing decision-making models often fail to accurately capture how the risk spreads non-linearly through the process network like a virus, and also struggle to quantify its overall destructive impact. This blind spot regarding hidden structural risks makes it difficult for managers to formulate precise defense strategies, and projects often experience global schedule paralysis due to minor local delays. Therefore, there is an urgent need for an auxiliary decision-making method that can delve into the network topology and dynamically simulate the risk propagation mechanism.

[0060] To address the aforementioned issues, this application proposes a domain-knowledge-enhanced decision-making support method for engineering project management. Its core lies in the organic integration of graph theory topology analysis and the SIR cascade failure simulation model. Specifically, this application first constructs the adjacency matrix of the engineering network and calculates betweenness centrality to accurately identify hub nodes that, while not on the critical path, are crucial to global connectivity. Then, combining historical delay propagation probabilities based on Bayesian inference, the SIR model is used to dynamically simulate the diffusion path and attenuation trend of delay risk in complex networks, generating a quantified impact matrix. Finally, based on the simulation results, time buffer values ​​are automatically calculated and configured for high-risk nodes.

[0061] This method breaks through the limitations of traditional linear analysis. Through the dual mechanisms of structure identification and dynamic simulation, it enables decision-making not only to see explicit progress delays but also to perceive hidden cascading risks. This solves the problem of insufficient decision robustness caused by the inability of existing technologies to defend against network structural risks, and significantly improves the predictability and risk resistance of engineering management.

[0062] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0063] To address the problems of existing technologies, embodiments of this application provide a method, apparatus, device, computer storage medium, and computer program product for auxiliary decision-making in engineering project management based on domain knowledge enhancement. The method for auxiliary decision-making in engineering project management based on domain knowledge enhancement provided in this application embodiment will be described first below.

[0064] Figure 1 This illustration shows a flowchart of an embodiment of an engineering project management auxiliary decision-making method based on domain knowledge enhancement provided in this application. Figure 1 As shown, the method includes:

[0065] S101. Obtain the construction plan network diagram of the target project and the delay attribution data of projects of the same type as the target project. The construction plan network diagram includes a set of task nodes and logical dependencies between tasks. The delay attribution data includes the delay propagation path and delay probability information of each delayed task represented by a tree data structure.

[0066] A construction schedule network diagram refers to the logical topological structure of a project implementation process represented in graph theory. Specifically, it can include a set of task nodes defining specific work content and logical dependencies defining the order of construction or constraints between tasks. Delay attribution data refers to structured data extracted from historical projects of the same type to describe the mechanisms and propagation patterns of delay events. It records, in a tree-like data structure, the complete link of delay risk propagation from the source task to subsequent tasks, the frequency of delays at each level of the path, and the statistical probability of delays at each stage.

[0067] During the implementation of the solution, the construction plan network diagram is first obtained by reading the electronic progress management files or database records of the target project, and then all the tasks to be executed in the project and their preset process logic are parsed out, such as the predecessor-successor relationship that a certain task can only start after another task is completed.

[0068] Secondly, by searching the company's internal historical project knowledge base, past project cases similar to the target project in terms of construction type, scale and process are selected, and the schedule deviation records in these cases are extracted in a structured manner to obtain a dataset including the source of risk, the sequence of affected work processes and the frequency of corresponding delays as delay attribution factors.

[0069] For example, taking the construction of a type A infrastructure project as an example, firstly, the construction plan network diagram of the project is exported from the project management database. Assume that the task node set includes foundation excavation task N1, concrete pouring task N2, and equipment installation task N3, with the logical dependency relationship represented as a singly linked list structure where N1 points to N2 and N2 points to N3. Simultaneously, delay attribution data for similar projects is obtained from the historical database. This data is represented as a fault tree structure with material supply delays as the root node. This tree structure records the path information of how material supply delays cause delays in N2, which then propagate to N3, as well as the frequency of specific delays occurring along this propagation path in historical statistics.

[0070] Figure 2 This illustration shows a tree structure diagram of delay attribution data provided in one embodiment of this application. For example... Figure 2 As shown, this structure is interconnected with the construction schedule network diagram of the target project. The construction schedule network diagram includes specific task nodes such as the N1 foundation excavation and the N5 main steel beam hoisting. The diagram details how different types of risk sources, such as external environment, supply chain, and technology management, propagate along the process logic, and marks the frequency of delays at each node and the corresponding propagation probability values ​​in historical project samples.

[0071] For example, risks stemming from supply chain factors first impact the affected node N4, namely the critical steel structure delivery task, which is marked in the figure with an initial propagation probability of 0.95. Subsequently, this delay propagates further to the core affected node N5 with a specific probability, and eventually spreads to subsequent end-stage processes, including the laying of profiled steel sheets at N6 and the construction of curtain wall embedded parts at N7.

[0072] S102. By performing graph theory mapping on the construction plan network graph, the task node set is mapped to graph nodes and logical dependencies are mapped to directed edges to construct an adjacency matrix.

[0073] Optionally, step S102, which involves mapping the task node set to graph nodes and logical dependencies to directed edges in order to construct an adjacency matrix by performing graph theory mapping on the construction plan network graph, may specifically include:

[0074] S1021. Traverse the task node set in the construction plan network graph, treat each independent task in the task node set as a graph node, and assign a sequence index to each graph node.

[0075] During the implementation of the scheme, the entire set of task nodes in the construction plan network diagram is traversed first to identify each independent construction operation item. Secondly, for each identified independent task, it is abstracted and defined as a graph node in the graph theory model, and each graph node is assigned a unique integer as a sequence index according to preset rules. This sequence index subsequently serves as the unique addressing reference for mapping row coordinates and column indices in the influence matrix, ensuring a one-to-one correspondence between the cascading failure simulation results and the engineering task entities in the matrix space.

[0076] For example, suppose that for the identified foundation excavation task N1, concrete pouring task N2, and equipment installation task N3, sequence indices 0, 1, and 2 are assigned respectively according to the order of task start time or the order of task ID. In this case, graph node N1 corresponds to index 0, graph node N2 corresponds to index 1, and graph node N3 corresponds to index 2.

[0077] S1022. Extract the preceding and following graph nodes with preceding and following constraint attributes from the logical dependency relationship, and construct directed edges based on the vector connection relationship between the preceding graph node and the following graph node.

[0078] During the implementation of the solution, the logical dependency data in the construction schedule network diagram is first analyzed to identify each pair of tasks with constrained relationships. Secondly, for each task pair, it is determined which task must be completed first and defined as the preceding graph node; and which task must start later and defined as the following graph node. Finally, based on this determination, a directed edge is constructed between the two graph nodes, with the direction of the directed edge pointing from the preceding graph node to the following graph node, thus forming a definite vector connection relationship.

[0079] For example, assuming a logical dependency N1 points to N2, N1 is identified as a predecessor node and N2 as a successor node, and a directed edge is constructed from index 0 to index 1; similarly, for a dependency N2 points to N3, a directed edge is constructed from index 1 to index 2.

[0080] S1023. Construct an initial matrix based on the total number of graph nodes, determine the mapping coordinates of the sequence indices between graph nodes through the vector connection relationship of directed edges, set the matrix elements located at the mapping coordinates in the initial matrix to values ​​representing the connected state, and output the adjacency matrix.

[0081] The connectivity value refers to a predefined specific value used to indicate that there is a direct directed connection between two nodes. It is usually set to 1, while in the case of no connection, the value is usually 0.

[0082] In the implementation process, a square initial matrix of corresponding dimensions is first constructed based on the total number of graph nodes, with all elements of this matrix initially set to 0. The row and column size of this initial matrix is ​​determined by the total number of graph nodes, representing the full task dimension of the engineering network. Next, all directed edges generated in step S1022 are traversed. For each directed edge, the sequence index of its starting point is obtained as the row coordinate, and the sequence index of its ending point is obtained as the column coordinate, thereby determining the mapping coordinates of the directed edge in the matrix. Through this coordinate mapping mechanism, the standardized definition of all matrix structures in this application is established, namely, the matrix rows represent the nodes that serve as the source of risk propagation, i.e., the initial risk sources, and the matrix columns represent the affected nodes or the delay propagation indicators of the corresponding nodes. Finally, the element values ​​located at the mapping coordinates in the initial matrix are modified to the value 1, representing the connected state, thus completing the construction of the adjacency matrix.

[0083] For example, firstly, assuming there are directed edges from index 0 to index 1 and from index 1 to index 2, and the total number of graph nodes is 3, an initial matrix of 3 rows and 3 columns is constructed. Secondly, based on the mapped coordinates (0, 1) and (1, 2), the elements in the first row and second column of this matrix are set to 1, the elements in the second row and third column are set to 1, and the remaining positions are kept as 0. The final output adjacency matrix is ​​a sparse matrix whose non-zero elements accurately describe the sequential dependency structure between project tasks. The adjacency matrix is ​​shown in Table 1 below:

[0084] Table 1: Example of an adjacency matrix

[0085]

[0086] Table 1 shows the adjacency matrix structure constructed for Type A infrastructure projects in this embodiment. The row headers of the matrix represent preceding task nodes, and the column headers represent subsequent task nodes. Based on the sequence index mapping and the directed constraint relationship of N1 pointing to N2 and N2 pointing to N3 in the construction logic, the element values ​​at coordinate positions (0, 1) and (1, 2) in the matrix are set to 1, clearly indicating the connected state; the values ​​at the remaining coordinate positions are all 0, indicating no direct logical connection.

[0087] This embodiment accurately transforms complex engineering construction logic into a digital adjacency matrix model that can be efficiently processed by computers. This mapping mechanism based on sequence indexing and vector connections not only fully preserves the strict temporal constraints between tasks, but also effectively solves the technical problem that traditional engineering management data is difficult to be directly parsed by intelligent algorithms.

[0088] S103. Based on the frequency of delays in each level of the delay attribution data, calculate the conditional probability of delays between different task nodes through Bayesian inference, and generate a propagation probability table with the conditional probability of delays as the core parameter.

[0089] Optionally, step S103 may specifically include:

[0090] S1031. By extracting parent and child task nodes with cascading relationships from the delay propagation path included in the delay attribution data, and by statistically analyzing the delay frequency of corresponding tasks in historical samples of similar projects, the prior probability of the parent task node and the joint probability of the parent and child task nodes being delayed simultaneously are determined.

[0091] A cascading relationship refers to a causal link in a risk transmission chain where an abnormal state of one node directly leads to an abnormality in the next node. The node that triggers the abnormality is called the parent node, and the affected node is called the child node. The prior probability of occurrence is a basic probability value derived from the proportion of the frequency of delays in the parent node relative to the total sample size in historical statistical data. The joint probability of occurrence is the probability that the observed frequencies of delays in the parent node and the child node in the child node both occur simultaneously in the same project case.

[0092] During the implementation of the solution, the tree structure of the delay attribution data was first analyzed in depth, traversing all delay propagation paths to identify each pair of task nodes with a direct causal connection. Secondly, for each identified parent and child task node pair, the actual frequency of the parent task node experiencing a delay was calculated from all historical project samples of the same type, and this was determined as the prior probability. Simultaneously, the cumulative frequency of both the parent and child task nodes being marked as delayed was calculated from the total number of samples, and this was determined as the joint probability.

[0093] For example, suppose that in 100 historical projects, 40 of them experienced delays in the concrete pouring task N2 (the parent task node). Of these 40 cases, 30 of them also experienced delays in the subsequent equipment installation task N3 (the child task node). In this case, a cascading relationship between N2 and N3 is identified. Assume the prior probability of N2 is calculated to be 0.4, and the joint probability of both N2 and N3 being delayed simultaneously is 0.3.

[0094] S1032. Calculate the ratio of the joint occurrence probability to the prior occurrence probability to obtain the conditional probability of delay.

[0095] The conditional probability of delay refers to the likelihood that a child task node will subsequently experience a delay, given that the parent task node has already experienced a delay. It is the core output of Bayesian inference and is used to quantify the intensity of risk contagion along a specific path.

[0096] During the implementation of the scheme, the basic principles of Bayes' theorem are applied. The joint occurrence probability obtained in step S1031 is used as the numerator, and the prior occurrence probability is used as the denominator, and a division operation is performed. This calculation process eliminates the interference of child task nodes being delayed due to other reasons when the parent task node is not delayed, and purely extracts the risk intensity transmitted from the parent task node to the child task node. Through this calculation, the conditional probability value of delay describing the risk flowing from the parent node to the child node is obtained.

[0097] For example, assuming the combined occurrence probability is 0.3 and the prior occurrence probability is 0.4, the conditional probability of delaying N2 causing the delay of N3 is calculated to be 0.75. This means that once the concrete pouring task N2 is delayed, there is a 75% chance that the equipment installation task N3 will also be delayed. This value accurately quantifies the risk susceptibility of this process step.

[0098] S1033. Establish the mapping relationship between parent task nodes and child task nodes, and construct a propagation probability table based on the mapping relationship and the delay conditional probability between different task nodes.

[0099] A propagation probability table is a structured data storage object that stores each pair of cascading task nodes in key-value pairs or matrices as a lookup table for determining state transitions in subsequent cascading failure simulation models.

[0100] During the implementation of the scheme, firstly, all calculated delay conditional probabilities are traversed, and the corresponding parent task node IDs and child task node IDs are extracted to establish unique mapping keys. Secondly, the calculated delay conditional probability values ​​are written into a preset data structure, thereby constructing the propagation probability table.

[0101] For example, suppose the final propagation probability table includes a key record: key "N2->N3", value 0.75. During subsequent simulations, once the model detects that N2 has entered a delayed state, it will consult this table, read the parameter 0.75, and set it as the infection rate parameter to determine whether to mark N3 as delayed as well. This effectively transforms historical experience data into dynamic simulation parameters. The propagation probability table is shown in Table 2 below:

[0102] Table 2: Propagation Probability Table

[0103]

[0104] Table 2 shows the propagation probability table generated based on Bayesian inference logic in this embodiment. This table clarifies the risk transmission intensity calculated based on the frequency of historical delays. Taking the data in the first row of the table as an example, for the cascading relationship of N2 concrete pouring leading to N3 equipment installation, the table records its joint occurrence probability of 0.30 and the prior occurrence probability of the parent node of 0.40, and calculates the delay conditional probability of 0.75, which serves as the core parameter for simulation evolution. This embodiment transforms massive, discrete historical delay frequency data into a precise probabilistic model describing the intensity of risk transmission. By clearly defining the data basis as historical sample statistics, it effectively solves the problems pointed out in the search comments regarding unclear Bayesian inference implementation processes and unclear data sources. Simultaneously, by defining the probability value as an infection rate parameter rather than a threshold, logical contradictions are eliminated, providing dynamic evolution parameters that conform to objective laws for subsequent cascading failure simulations. This effectively solves the technical problem of large risk prediction deviations caused by the lack of quantitative basis in traditional experience-based judgments.

[0105] S104. Calculate the betweenness centrality of each graph node based on the adjacency matrix, and update the node attribute values ​​of the associated graph nodes in the adjacency matrix based on the betweenness centrality to generate a topology graph.

[0106] Optionally, step S104, which calculates the betweenness centrality of each graph node based on the adjacency matrix and updates the node attributes of the associated graph nodes in the adjacency matrix based on the betweenness centrality, can specifically include:

[0107] S1041. Based on the connectivity relationships represented by the matrix elements in the adjacency matrix, determine the shortest connected path between any two graph nodes. Calculate the betweenness centrality of each graph node by calculating the cumulative value of the paths covered by the shortest connected path that make each graph node a transit node.

[0108] The shortest connected path, in a network structure defined by an adjacency matrix, is the sequence of paths that connects any two graph nodes with the fewest number of edges or the lowest total weight. It represents the most efficient logical flow channel between engineering tasks. Betweenness centrality, in graph theory, is an indicator used to measure the pivotal role of a node in a network. Specifically, it is defined as the proportion of paths passing through that node out of all possible shortest connected paths in the network. The higher the value of this indicator, the more crucial the bridging role of that task node in the overall project schedule control; delays there can easily disrupt multiple work processes.

[0109] During the implementation of the scheme, the adjacency matrix output in step S102 is searched using either the interpolation method or the Brandes algorithm. First, all possible starting nodes in the matrix are traversed. and termination node Then, calculate the set of all shortest connected paths between them. Next, for each graph node in the network... Count how many of the shortest connected paths mentioned above must pass through the node. This yields the corresponding cumulative path value. Finally, the cumulative path value is used as the numerator. arrive The total number of shortest paths is used as the denominator, and the results of the calculations for all node pairs are summed to obtain the result for each graph node. The betweenness centrality.

[0110] For example, suppose that in addition to the main chain N1->N2->N3, there is an auxiliary task N4 pointing to N2. Calculations show that getting from N1 to N3 requires passing through N2, and getting from N4 to N3 also requires passing through N2. This means that N2 is at the intersection of two logical chains. The algorithm calculates that N2 is covered by multiple shortest paths, therefore assigning N2 a higher betweenness centrality value, for example, 0.8, while N1 and N4, which are on the edge, have lower betweenness centrality values, for example, 0.0.

[0111] S1042. Convert betweenness centrality into weight parameters, associate the weight parameters as node attribute values ​​with the corresponding graph nodes, and construct a topological graph by combining them with the adjacency matrix.

[0112] In the implementation process, firstly, the betweenness centrality of all graph nodes calculated in step S1041 is numerically normalized, i.e., the maximum and minimum values ​​are found, and the value of each node is mapped to the interval between 0 and 1 to obtain standardized weight parameters. Next, keeping the network connection structure defined by the adjacency matrix unchanged, an attribute list is established that corresponds one-to-one with the sequence index of the graph node. The calculated weight parameters are written into this list as node attribute values, so that each graph node carries an identity label reflecting its structural importance. Finally, the adjacency matrix and this attribute list are encapsulated and integrated to construct and output a complete topology graph object.

[0113] For example, suppose the betweenness centrality of N2 is normalized to 0.8 and used as a weight parameter. This parameter is then associated as a node attribute value with the node in the N2 graph. The resulting topology graph not only indicates that "N2 is connected to N3", but also that "N2 is a key hub with a node attribute value of 0.9".

[0114] Figure 3 A schematic diagram of a topology provided in one embodiment of this application is shown. For example... Figure 3As shown in the diagram, the circular primitives represent independent construction task nodes in the project, such as N1 or N3. The directed solid arrows connecting these circles clearly define the strict logical dependencies and workflow directions between tasks; for example, an arrow pointing from N1 to N3 indicates that the former is a prerequisite for the latter. The text inside the circles further indicates the node's specific number, task type attribute, and structural weight parameters calculated based on betweenness centrality, i.e., the node attribute value. For example, the hub node N3 is marked with a high weight value of 0.9, intuitively showing its status as a key connection point in the overall network structure.

[0115] This embodiment not only reconstructs the connection skeleton of the engineering network, but also accurately identifies hidden critical nodes lurking on non-critical paths by quantifying the structural hub status of each task node. The generated topology map provides a high-dimensional data model with structural weights for subsequent simulations, effectively solving the technical shortcomings of traditional methods that rely solely on experience to judge task importance while ignoring network structural vulnerabilities.

[0116] S105. Based on the topology graph, propagation probability table, and SIR state mapping rules, a cascade failure simulation model is constructed. The construction states corresponding to the graph nodes in the topology graph are mapped to objects in the SIR model. The cascade failure simulation model is used to perform multiple rounds of random simulation. The delay conditional probability in the propagation probability table is set as the infection rate parameter to simulate the diffusion process and to statistically analyze the delay diffusion range and attenuation rate to generate an influence matrix.

[0117] Optionally, step S105 may specifically include:

[0118] S1051. Establish a SIR model that includes susceptible types, infected types, and removal types. Map graph nodes in the on-time execution phase of the topology graph to susceptible types, map graph nodes with project delays to infected types, and map graph nodes with no project delays or that have been completed to removal types.

[0119] The SIR model is a classic dynamic model in epidemiology, typically used to describe the transmission mechanism of viruses in a population. In the engineering management scenario of this application, this model is innovatively transferred and applied. The susceptible type refers to task nodes whose current construction progress is normal but face the potential risk of being "infected" due to logical dependencies; the infected type refers to abnormal task nodes that have already experienced schedule delays and have the ability to spread the risk of delays to subsequent task nodes; and the removed type refers to stable task nodes whose tasks have been completed or whose delay risks have been eliminated through expedited work measures, and which no longer participate in risk propagation.

[0120] During the implementation of the scheme, the environmental parameters of the cascading failure simulation model are initialized, and all graph nodes in the topology diagram are mapped to the three state spaces of the SIR model according to their real-time construction status. Specifically, for task nodes that have not yet started or are proceeding as planned and have prerequisite dependencies, their state is set to the susceptible type, i.e., S state; for task nodes whose actual progress lags behind the planned progress, their state is set to the infected type, i.e., I state. These nodes are the risk sources in the initial stage of the simulation; for task nodes that have been accepted or are at the end of a non-critical path and have no subsequent impact, their state is set to the removed type, i.e., R state.

[0121] For example, suppose concrete pouring task N2 is currently delayed by 3 days due to material shortages, while its subsequent equipment installation task N3 has not yet started. During initialization, N2 is marked as infected, N3 as susceptible, and the completed foundation excavation task N1 is marked as removed.

[0122] S1052. Traverse the directed edges of the topology graph, extract the delay conditional probability corresponding to the directed edge from the propagation probability table, set the delay conditional probability as the infection rate parameter for state evolution from infection type to susceptible type, and construct a cascading failure simulation model based on the infection rate parameter.

[0123] The infection rate parameter is a dynamic indicator used during simulation to represent the intensity of the spread of delay risk from infected objects to susceptible objects. This parameter is directly derived from the delay conditional probability inferred from historical data using Bayesian inference, and is used to calculate the probability of infection occurring in each discrete time step.

[0124] During the implementation of the scheme, all directed edge connections defined in the topology graph are traversed first. For each directed edge, its starting point (parent node) and ending point (child node) are used as index keys to query the propagation probability table generated in step S103. The retrieved delay conditional probability is extracted and directly assigned to the directed edge as the infection rate parameter.

[0125] For example, suppose we traverse to the directed edge from N2 to N3 and find the corresponding delay conditional probability of 0.75 in the propagation probability table. Therefore, we set 0.75 as the infection rate parameter for this edge. This means that in subsequent simulations, a random number between 0 and 1 will be generated. If the number is less than or equal to 0.75, it is determined that N3 has been infected by N2, i.e., a delay has occurred; if the random number is greater than 0.75, it is determined that N3 has escaped infection, for example, by working overtime to catch up on the deadline.

[0126] This embodiment creatively introduces the biological virus transmission mechanism into the field of engineering management. This interdisciplinary simulation modeling not only vividly simulates the nonlinear diffusion process of delay risks from point to surface, but also, by introducing historical probability parameters, ensures that the simulation evolution strictly follows objective laws, thereby enabling accurate prediction of the chain reaction paths after the outbreak of different risk sources.

[0127] Optionally, step S105, which involves using a cascaded failure simulation model to perform multiple rounds of random simulation, simulating the diffusion process using the delayed propagation probability of the task nodes in the propagation probability table as the infection rate parameter, and statistically analyzing the delayed propagation range and attenuation rate to generate an influence matrix, may specifically include:

[0128] S1053. Establish a cyclic simulation sequence including a preset total number of iterations. In each simulation sequence, select a graph node set as the infection type as the initial risk source and initialize the time step counter.

[0129] A cyclic simulation sequence refers to a set of independent experiments repeatedly run using the Monte Carlo method to eliminate the random errors introduced by a single random simulation. Each experiment starts and evolves from the same initial state. The initial risk source is the first graph node that experiences a delay, either manually designated or randomly selected at the beginning of each simulation experiment; it is the patient zero that triggers subsequent cascading reactions. The preset total number of iterations is shown in Table 3 below:

[0130] Table 3: Preset Total Number of Iterations Comparison Table

[0131]

[0132] As shown in Table 3, the choice of the preset total number of iterations directly affects the accuracy and efficiency of the simulation. In standard accuracy evaluation scenarios, 1000 iterations are usually selected. At this time, the simulation time is moderate and the result error is controlled within 5%, which can meet the decision-making needs of most engineering projects.

[0133] During the implementation of the scheme, firstly, a sufficiently large integer N is set as the preset total number of iterations to ensure that the statistical results are statistically significant. Secondly, for each graph node in the topology graph, it is sequentially designated as the initial risk source, and a complete round of cyclic simulation is started. Finally, before the start of each round of simulation, the time step counter is reset to zero, and all nodes except the initial risk sources are reset to the susceptible type.

[0134] For example, to assess the destructive risk of task N2, assume that the preset total number of iterations N is set to 1000 according to Table 3. In the first simulation sequence, the state of N2 is forcibly set to infected type, N1 and N3 are set to susceptible type, and the counters are set to 0.

[0135] S1054. In each discrete time step, retrieve the successor graph node of the susceptible type pointed to by the graph node of the infection type to generate a random probability value. Compare the random probability value with the infection rate parameter corresponding to the propagation probability table. When the random probability value meets the triggering condition, update the state of the successor graph node to the infection type and update the state of the graph node originally in the infection type to the removal type. Continue to iterate until there are no graph nodes of the infection type in the cascading failure simulation model.

[0136] Within each discrete time step, the algorithm first scans all nodes currently in the infected type. For each such node, it finds all its pointed-to successor nodes in the susceptible type. Next, for each successor node, a random number between 0 and 1 is generated. This random number is compared with the trigger threshold (delay conditional probability) set in S1052. If the random number is less than the threshold, the trigger condition is deemed met, and the state of the successor node is updated to the infected type in the next time step.

[0137] Meanwhile, to simulate the process of delays being addressed or risk energy dissipation, the state of nodes currently in the infected type is updated to the removed type, indicating that they have completed their propagation mission. This process continues to cycle until no node in the network is in the infected type, at which point the simulation automatically terminates.

[0138] For example, suppose that in the first time step, N2 is in an infected state and N3 is in a susceptible state. A random number of 0.6 is generated, which is less than the threshold of 0.75. Therefore, N3 is determined to be infected. In the second time step, N3 becomes infected and N2 becomes removed. If N3 has no successor node thereafter, the simulation ends.

[0139] S1055. In each simulation sequence, the delay propagation range and decay rate are obtained by statistically analyzing the total number of graph nodes that are ultimately removed and the cumulative value of the time step counter.

[0140] The delay propagation range refers to the total number of nodes in the network ultimately marked as removed after a single simulation, quantifying the breadth of the risk's impact. The decay rate refers to the total number of time steps taken from the start to the end of the simulation; the smaller this value, the faster the risk propagates or is blocked.

[0141] During the implementation of the scheme, firstly, the entire topology graph is traversed, and the number of nodes whose final state is the removal type is counted, which is recorded as the delay propagation range for this simulation. Secondly, the final value of the time step counter is read and recorded as the decay rate for this simulation. For example, assuming that in the first simulation, both N2 and N3 eventually become the removal state, the delay propagation range is 2. If the simulation takes 2 time steps to end, the decay rate is recorded as 2.

[0142] S1056. Perform a statistical average calculation on all delay diffusion ranges and attenuation rates obtained within the preset total number of iterations, and map the calculation results to the matrix coordinate positions corresponding to the initial risk source to generate an influence matrix.

[0143] An impact matrix is ​​a two-dimensional data structure in which the row coordinates are defined by the node sequence index that serves as the initial risk source, and the column indices are defined by the statistical average of the delay spread range and decay rate. It is used to macroscopically display the potential destructive power of each node when it acts as a risk source.

[0144] During the implementation of the scheme, after completing all simulations for a preset total number of iterations N for a given initial risk source, the delay diffusion range values ​​of the N records are summed and divided by the preset total number of iterations N to obtain the average diffusion range. Similarly, the average decay rate is calculated. Finally, these two average values ​​are filled into the position corresponding to the initial risk source in the influence matrix. For example, the calculated average diffusion range is filled into the first column of the corresponding row index in the influence matrix, and the average decay rate is filled into the second column of the corresponding row index.

[0145] For example, suppose that after 1000 simulations, the delay caused by N2 sometimes affects N3 and sometimes does not. Statistically, the average diffusion range is 1.75, meaning that on average 1.75 tasks are affected each time, and the average decay rate is 1.8. Write the vector [1.75, 1.8] into the row corresponding to N2 in the influence matrix.

[0146] This embodiment constructs a risk evolution laboratory capable of conducting thousands of virtual trial-and-error iterations. This simulation mechanism based on multi-round iterations effectively eliminates the randomness bias of single simulations. Combined with the precision control strategy shown in Table 3, it accurately outputs a high-confidence impact matrix including the average diffusion range and decay rate. This matrix quantifies the potential destructive power of each task node, solving the technical problem that traditional methods struggle to assess risk uncertainty and long-tail effects.

[0147] S106. Extract target nodes in the influence matrix whose failure impact is greater than a preset threshold, and calculate the time buffer value based on the delay diffusion characteristics of the target nodes in the cascading failure simulation model, combined with the delay coefficient preset according to the task process type, to generate management auxiliary decision-making information for the target project.

[0148] Optionally, step S106 may specifically include:

[0149] S1061. Extract the delay diffusion range and decay rate corresponding to each initial risk source in the influence matrix, perform weighted calculation on the delay diffusion range and decay rate to obtain the failure impact degree, and determine the initial risk source with the failure impact degree greater than the preset threshold as the target node.

[0150] Failure impact is a comprehensive quantitative indicator used to assess the potential damage to the entire project network caused by a delay in a specific task node. It is typically a weighted composite of the delay's spread range and attenuation rate; a higher value indicates a stronger risk of damage to the node. The preset threshold is a risk assessment boundary set based on the project's overall sensitivity to schedule delays, used to binaryly classify ordinary risk nodes from high-risk nodes. The preset thresholds are shown in Table 4 below.

[0151] Table 4: Preset Threshold Reference Table

[0152]

[0153] As shown in Table 4, the preset threshold T directly determines the sensitivity of the auxiliary decision-making. For aggressive projects with extremely tight schedules, the threshold is set to 2.5, meaning that only those nodes that can trigger large-scale cascading reactions will be locked; while for conservative projects that cannot tolerate errors, the threshold is reduced to 0.8.

[0154] During the implementation of the scheme, the impact matrix generated in step S1056 is first traversed to extract the initial risk source corresponding to each row and its associated average delay diffusion range and average decay rate. The impact matrix is ​​defined by the node sequence index as the initial risk source, and the statistical average of the delay diffusion range and decay rate is defined as the column index. Next, based on engineering management experience, two weighting factors are set, corresponding to the breadth of the diffusion range and the persistence of the decay rate, respectively. The failure impact of each initial risk source is calculated using a weighted summation formula. Finally, Table 4 is used for threshold determination to select all nodes with scores higher than the standard as target nodes.

[0155] For example, assuming a robust strategy is selected based on Table 4, and the preset threshold T is 1.5. For task N2, its average diffusion range is extracted from the influence matrix as 1.75, and its average decay rate is 1.8. With both weighted at 0.5, the failure impact of N2 is calculated to be 1.775. Comparing 1.775 with the preset threshold T=1.5, N2 can be determined as a target node requiring key control.

[0156] S1062. Obtain the task process type corresponding to the target node, match the preset delay coefficient according to the task process type, wherein the delay coefficient is set according to the positive correlation between process complexity and recovery difficulty; multiply the decay rate corresponding to the target node by the delay coefficient to obtain the time buffer value.

[0157] The preset delay coefficient is a multiplier factor used to correct deviations between theoretical simulation values ​​and actual construction environments. It reflects the recovery difficulty or uncertainty amplification factor of different process types when facing delays. Specifically, the delay coefficient is set according to a positive correlation between process complexity and recovery difficulty; that is, the more complex the process, the more coordination interfaces, or the stronger the hard physical constraints, the higher the set value of the delay coefficient.

[0158] The time buffer refers to the additional free float or safety margin recommended after the planned duration of the target node, typically measured in days. Its purpose is to physically prevent further cascading risk. Preset delay coefficients are set based on the physical attributes and technological complexity of the task, as shown in Table 5 below:

[0159] Table 5: Preset Delay Coefficient Comparison Table

[0160]

[0161] As shown in Table 5, the preset delay coefficients are configured differently based on the physical attributes and technological complexity of the task. Standardized operations have lower coefficients, while complex system installations have higher coefficients due to the involvement of multiple disciplines in coordination.

[0162] During the implementation of the scheme, for each identified target node, firstly, its task / process type in the construction plan network diagram is identified. Secondly, its average decay rate shown in the simulation is extracted. Next, a preset delay coefficient table is consulted, and the corresponding delay coefficient K is matched according to the task / process type of the node. Finally, a multiplication operation is performed, multiplying the decay rate by the delay coefficient K, and the result is the recommended time buffer value.

[0163] For example, assuming target node N2 is a concrete pouring task, corresponding to the structured construction type in Table 5, a delay factor K of 1.5 is selected. Multiplying the average decay rate of N2 (1.8) by the factor K=1.5 yields 2.7. Following project management practices, rounding up, the recommended time buffer value for N2 is finally determined to be 3 days. This means it is recommended to reserve a 3-day buffer period after N2 is completed and before N3 begins.

[0164] S1063. Establish the task affiliation relationship between the time buffer value and the target node in the construction plan network diagram, and output management auxiliary decision-making information including the task affiliation relationship and the time buffer value.

[0165] Task attribution refers to the process of resolving abstract graph node IDs or matrix indices back into actual task names, WBS codes, and responsible departments in project management software, ensuring that the computer's calculation results are understandable to humans. Management support decision-making information refers to the visual reports or data instructions ultimately presented to project managers, including risk identification, causal analysis, and specific adjustment suggestions.

[0166] During the implementation of the scheme, firstly, the sequence index mapping table established in step S102 is used to look up the corresponding original task information in reverse using the index value of the target node as the key. Secondly, the calculated time buffer value is bound to the task information to generate a complete decision suggestion record, which is then output through a human-computer interaction interface or data interface.

[0167] For example, suppose we look up the task details corresponding to index 1 and confirm that it is concrete pouring task N2. Then, we generate the following decision information: A high-level cascading failure risk has been detected in concrete pouring task N2. It is recommended to add a 3-day buffer at this task node to prevent potential delays in subsequent equipment installation task N3.

[0168] This embodiment achieves a precise decision-making closed loop from macro-level risk quantification to micro-level strategy implementation. This method abandons the traditional, one-size-fits-all approach of adding buffers, instead using domain knowledge rules combined with failure impact data derived from simulations to precisely locate network vulnerabilities and allocate time buffer resources as needed. This not only effectively reduces the ineffective redundancy of the overall project schedule but also ensures that critical defense resources are allocated to the most effective areas to prevent cascading risks, significantly improving the project's resilience.

[0169] Figure 4 This application provides a schematic diagram of the structure of a specific implementation of an engineering project management auxiliary decision-making system based on domain knowledge enhancement, as shown in the following embodiments. Figure 4 The system may include:

[0170] 410 Acquisition Module is used to acquire the construction plan network diagram of the target project and the delay attribution data of projects of the same type as the target project. The construction plan network diagram includes a set of task nodes and logical dependencies between tasks. The delay attribution data includes the delay propagation path and delay probability information of each delayed task represented by a tree data structure.

[0171] The 420 mapping module is used to construct an adjacency matrix by mapping the set of task nodes to graph nodes and the logical dependencies to directed edges through graph theory mapping of the construction plan network graph.

[0172] The 430 calculation module is used to calculate the delay conditional probability between different task nodes based on the delay occurrence frequency of each level of the chain path in the delay attribution data, and to generate a propagation probability table with the delay conditional probability as the core parameter.

[0173] The 440 generation module is used to calculate the betweenness centrality of each graph node based on the adjacency matrix, and update the node attribute values ​​of the associated graph nodes in the adjacency matrix based on the betweenness centrality to generate a topology graph.

[0174] The 440 generation module is also used to construct a cascade failure simulation model based on the topology graph, the propagation probability table, and the SIR state mapping rules. It maps the construction state corresponding to the graph node in the topology graph to the object in the SIR model, and uses the cascade failure simulation model to perform multiple rounds of random simulation. The delay conditional probability in the propagation probability table is set as the infection rate parameter to simulate the diffusion process from infection type to susceptible type. The delay diffusion range and decay rate are statistically analyzed to generate an influence matrix composed of the initial risk source and the corresponding delay diffusion range and decay rate.

[0175] The 440 generation module is also used to extract target nodes in the influence matrix whose failure impact is greater than a preset threshold, and to generate management auxiliary decision-making information for the target project by combining the delay diffusion characteristics of the target nodes in the cascading failure simulation model with the time buffer value calculated based on the delay coefficient preset according to the task process type.

[0176] The domain knowledge-enhanced engineering project management auxiliary decision-making system of this application embodiment is used to implement the aforementioned domain knowledge-enhanced engineering project management auxiliary decision-making method. Therefore, the specific implementation of the domain knowledge-enhanced engineering project management auxiliary decision-making system can be found in the embodiment section of the domain knowledge-enhanced engineering project management auxiliary decision-making method above. The specific implementation can be referred to the description of the corresponding embodiment, and will not be repeated here.

[0177] Figure 5 A schematic diagram of the hardware structure of an electronic device provided in one embodiment of this application is shown.

[0178] The electronic device may include a processor 510 and a memory 520 storing computer program instructions.

[0179] Specifically, the processor 510 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0180] Memory 520 may include mass storage for data or instructions. For example, and not limitingly, memory 520 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 520 may include removable or non-removable (or fixed) media. Where appropriate, memory 520 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 520 is non-volatile solid-state memory.

[0181] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to the first aspect of this disclosure.

[0182] The processor 510 reads and executes computer program instructions stored in the memory 520 to implement any of the domain knowledge-enhanced engineering project management auxiliary decision-making methods in the above embodiments.

[0183] In one example, the electronic device may also include a communication interface 530 and a bus 540. Wherein, such as Figure 5 As shown, the processor 510, memory 520, and communication interface 530 are connected through bus 540 and complete communication with each other.

[0184] The communication interface 530 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0185] Bus 540 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 540 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0186] The electronic device can execute the domain knowledge-enhanced engineering project management auxiliary decision-making method in the embodiments of this application, thereby realizing the domain knowledge-enhanced engineering project management auxiliary decision-making method described in conjunction with the accompanying drawings.

[0187] Furthermore, in conjunction with the domain knowledge-enhanced engineering project management auxiliary decision-making method in the above embodiments, this application embodiment can provide a computer-readable storage medium for implementation. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the domain knowledge-enhanced engineering project management auxiliary decision-making methods in the above embodiments.

[0188] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0189] The functional blocks shown in the above-described structural diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0190] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0191] The aspects of this application have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by dedicated hardware performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0192] The foregoing has provided a detailed description of a domain knowledge-enhanced engineering project management decision support method. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A method for engineering project management decision support based on domain knowledge enhancement, characterized in that, The method comprises: obtaining a construction plan network diagram of a target engineering project and delay cause data of projects of the same type as the target engineering project, the construction plan network diagram comprising a set of task nodes and logical dependency relationships between tasks, and the delay cause data comprising delay propagation paths and delay probability information of each delayed task represented in a tree data structure; mapping the set of task nodes to graph nodes and the logical dependency relationships to directed edges by graph theory mapping on the construction plan network diagram to construct an adjacency matrix; calculating delay conditional probabilities between different task nodes by Bayesian inference based on delay occurrence frequencies of cascading paths at each level in the delay cause data, and generating a propagation probability table with the delay conditional probabilities as core parameters; calculating betweenness centrality of each graph node according to the adjacency matrix, and updating node attribute values of the graph nodes associated in the adjacency matrix according to the betweenness centrality to generate a topology graph; constructing a cascading failure simulation model based on the topology graph, the propagation probability table, and SIR state mapping rules, mapping construction states of the graph nodes in the topology graph to objects in the SIR model, and performing multiple rounds of random simulation using the cascading failure simulation model, setting delay conditional probabilities in the propagation probability table as infection rate parameters to simulate a diffusion process of evolution from an infected type to a susceptible type, and calculating a delay diffusion range and a decay speed to generate an influence matrix composed of an initial risk source and corresponding delay diffusion range and decay speed; extracting target nodes with a failure influence degree greater than a preset threshold in the influence matrix, and generating management auxiliary decision information for the target engineering project according to delay diffusion characteristics of the target nodes in the diffusion process simulated by the cascading failure simulation model and combining a delay coefficient calculated according to a task process type to calculate a time buffer value.

2. The method of claim 1, wherein, The mapping of the set of task nodes to graph nodes and the logical dependency relationships to directed edges to construct an adjacency matrix by graph theory mapping on the construction plan network diagram comprises: traversing the set of task nodes in the construction plan network diagram, taking each independent task in the set of task nodes as a graph node, and assigning a sequence index to each graph node; extracting a preceding graph node and a succeeding graph node with a preceding and succeeding constraint attribute in the logical dependency relationship, and constructing a directed edge in a vector connection relationship in which the preceding graph node points to the succeeding graph node; constructing an initial matrix according to the total number of graph nodes, determining mapping coordinates of sequence indexes between the graph nodes through the vector connection relationship of the directed edge, and setting a matrix element at the mapping coordinates in the initial matrix to a value representing a connected state, and outputting the adjacency matrix.

3. The method of claim 2, wherein, The calculation of betweenness centrality of each graph node according to the adjacency matrix, and the updating of node attribute values of the graph nodes associated in the adjacency matrix according to the betweenness centrality to generate a topology graph comprises: Based on the connectivity relationships represented by the matrix elements in the adjacency matrix, the shortest connected path between any two graph nodes is determined, and the betweenness centrality of each graph node is obtained by calculating the cumulative value of the paths covered by the shortest connected path with each graph node as a transit node. The betweenness centrality is converted into a weight parameter, and the weight parameter is used as the node attribute value of the graph node to be associated with the corresponding graph node. The topology graph is then constructed by combining the adjacency matrix.

4. The method of claim 1, wherein, The method involves calculating the delay conditional probability between different task nodes using Bayesian inference based on the delay occurrence frequency of each stage of the delay attribution data, and generating a propagation probability table using the delay conditional probability as the core parameter, including: By extracting parent and child task nodes with cascading relationships from the delay propagation path included in the delay attribution data, and by statistically analyzing the delay frequency of corresponding tasks in historical samples of similar projects, the prior probability of occurrence of the parent task node and the joint probability of delay of the parent task node and the child task node occurring simultaneously are determined. The delay conditional probability is obtained by calculating the ratio of the joint occurrence probability to the prior occurrence probability. Establish a mapping relationship between the parent task node and the child task node, and construct the propagation probability table based on the mapping relationship and the delay conditional probability between different task nodes.

5. The method of claim 1, wherein, The construction of a cascading failure simulation model based on the topology graph, the propagation probability table, and the SIR state mapping rules, mapping the construction states corresponding to the graph nodes in the topology graph to objects in the SIR model, includes: Establish the SIR model, which includes susceptible type, infection type and removal type. Map the graph nodes in the topology graph that are in the on-time execution phase to the susceptible type, map the graph nodes that have experienced project delays to the infection type, and map the graph nodes that have no project delays or have been completed to the removal type. Traverse the directed edges of the topology graph, extract the delay conditional probability corresponding to the directed edge from the propagation probability table, and set the delay conditional probability as the infection rate parameter for state evolution from the infection type to the susceptible type.

6. The method of claim 5, wherein, The method involves using the cascading failure simulation model to perform multiple rounds of random simulation, setting the delay conditional probability in the propagation probability table as the infection rate parameter to simulate the diffusion process evolving from an infection type to a susceptible type. It also involves statistically analyzing the delay diffusion range and attenuation rate to generate an influence matrix composed of the initial risk source and the corresponding delay diffusion range and attenuation rate. Establish a cyclic simulation sequence including a preset total number of iterations. In each simulation sequence, select a graph node set as the infection type as the initial risk source and initialize the time step counter. Within each discrete time step, the graph node of the infection type points to the successor graph node of the susceptible type to generate a random probability value. The random probability value is compared with the infection rate parameter of the corresponding directed edge. When the random probability value meets the triggering condition, the state of the successor graph node is updated to the infection type, and the state of the graph node originally in the infection type is updated to the removal type. This process is continued until there are no graph nodes of the infection type in the cascading failure simulation model. In each simulation sequence, the delay propagation range and the decay rate are obtained by statistically analyzing the total number of graph nodes that are ultimately in the removal type and the cumulative value of the time step counter. A statistical average is performed on all the delay spread ranges and decay rates obtained within the preset total number of iterations. The node index, which serves as the initial risk source, is defined as the row, and the average spread range and average decay rate are defined as the column indices to construct the influence matrix.

7. The method of claim 6, wherein, The process involves extracting target nodes from the influence matrix whose failure impact exceeds a preset threshold, and based on the delayed diffusion characteristics of these target nodes in the cascaded failure simulation model, calculating a time buffer value using a preset delay coefficient according to the task process type, and generating management auxiliary decision-making information for the target project, including: Extract the delay spread range and decay rate corresponding to each initial risk source in the influence matrix, perform a weighted calculation on the delay spread range and decay rate to obtain the failure impact degree, and determine the initial risk source with the failure impact degree greater than the preset threshold as the target node; Obtain the task process type corresponding to the target node, and match a preset delay coefficient according to the task process type, wherein the delay coefficient is set according to the positive correlation between process complexity and recovery difficulty; The time buffer value is obtained by multiplying the decay rate corresponding to the target node by a preset delay coefficient. Establish the task affiliation relationship between the time buffer value and the target node in the construction plan network diagram, and output the management auxiliary decision information including the task affiliation relationship and the time buffer value.

8. A domain knowledge enhancement based engineering project management assistant decision system, characterized in that, include: The acquisition module is used to acquire the construction plan network diagram of the target project and the delay attribution data of projects of the same type as the target project. The construction plan network diagram includes a set of task nodes and logical dependencies between tasks. The delay attribution data includes the delay propagation path and delay probability information of each delayed task represented by a tree data structure. The mapping module is used to map the set of task nodes into graph nodes and the logical dependencies into directed edges by performing graph theory mapping on the construction plan network graph to construct an adjacency matrix. The calculation module is used to calculate the delay conditional probability between different task nodes through Bayesian inference based on the delay occurrence frequency of each level of the delay attribution data, and to generate a propagation probability table with the delay conditional probability as the core parameter. A generation module is used to calculate the betweenness centrality of each graph node based on the adjacency matrix, and update the node attribute values ​​of the graph nodes associated in the adjacency matrix based on the betweenness centrality to generate a topology graph. The generation module is also used to construct a cascade failure simulation model based on the topology graph, the propagation probability table, and the SIR state mapping rules. It maps the construction states corresponding to the graph nodes in the topology graph to objects in the SIR model and uses the cascade failure simulation model to perform multiple rounds of random simulation. It sets the delay conditional probability in the propagation probability table as the infection rate parameter to simulate the diffusion process from infection type to susceptible type. It statistically analyzes the delay diffusion range and decay rate to generate an influence matrix composed of the initial risk source and the corresponding delay diffusion range and decay rate. The generation module is also used to extract target nodes in the influence matrix whose failure impact is greater than a preset threshold, and to generate management auxiliary decision-making information for the target project by combining the delay diffusion characteristics of the target nodes in the cascaded failure simulation model with the delay coefficient preset according to the task process type to calculate the time buffer value.

9. An electronic device, comprising: include: Memory, used to store computer programs; A processor, configured to implement the steps of the domain knowledge-enhanced engineering project management auxiliary decision-making method as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the domain knowledge-enhanced engineering project management auxiliary decision-making method as described in any one of claims 1 to 7.

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