Project full life cycle progress visualization method and system

Abstract

The invention relates to the technical field of project management, and discloses a project full life cycle progress visualization method and system.The method comprises the steps that multi-project task dependency data and real-time execution data are collected to construct a weighted key partial order lattice; extracting a conduction path between tasks based on the weighted key partial order lattice, calculating a conduction coefficient to generate a deviation conduction matrix, receiving the deviation conduction matrix, collecting real-time deviation data to construct a deviation vector, calculating an accumulated influence value through matrix operation, and combining with a key metric value to generate a risk layering quantification quasi-matrix; a differential early warning strategy is configured based on the risk layering quantitative quasi-matrix, and a visual early warning identifier is rendered in the global progress view; according to the method, the weighted key partial order lattice and the deviation conduction matrix are constructed, so that the problems of key path dynamic identification, deviation conduction modeling and risk layering in multi-project parallel management are solved, and accurate early warning and visual visualization of project full-life-cycle progress abnormity are realized.

Description

Technical Field

[0001] This invention relates to the field of project management technology, and in particular to a method and system for visualizing the progress of a project throughout its entire lifecycle. Background Technology

[0002] In scenarios involving the parallel management of multiple types of projects, a project lifecycle progress visualization system is typically used for progress tracking and anomaly alerts. This type of system collects data on planned and actual task completion times, compares the time differences to trigger alerts, and assists managers in monitoring project progress. It features real-time data collection and unified threshold alerts.

[0003] In actual project management, engineers often face a situation where the system pushes a large number of warning messages, requiring them to spend a lot of time checking each one, yet they may still miss potential delays in critical tasks. This is because existing systems trigger warnings only based on the time difference of individual tasks, without distinguishing between critical and non-critical path tasks, nor considering the propagation characteristics of schedule deviations along task dependencies. Non-critical path tasks, due to their buffer time, usually do not affect the overall schedule in the short term due to delays, but are consumed by frequent warnings, consuming management effort; while potential risks in critical path tasks that have not reached the time threshold but have shown a tendency for deviation propagation cannot be captured in time due to the lack of a dynamic identification mechanism, which may lead to the continuous accumulation of deviations and cause delays in the overall project schedule. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, the present invention provides the following technical solution:

[0005] A method for visualizing the entire project lifecycle progress includes:

[0006] Collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metrics of each task based on the partial order lattice structure, and generate a weighted key partial order lattice.

[0007] Based on the weighted key partial order lattice, the transmission path between tasks is extracted along the partial order relation, and the transmission coefficient is calculated by combining resource redundancy and buffer time to generate the deviation transmission matrix;

[0008] Receive the deviation propagation matrix, collect real-time deviation data of each task to construct a deviation vector, calculate the cumulative impact value of each task through matrix operations, and combine the key metric values ​​in the weighted key partial order lattice to generate a risk stratification quantification matroid.

[0009] Based on risk-stratified quantitative matroid, differentiated early warning strategies are configured according to the priority of each risk level. Real-time early warnings are generated for high-risk level tasks and the scope of their impact is marked. For low-risk level tasks, only observation logs are recorded. Visual early warning indicators are rendered hierarchically in the global progress view.

[0010] Furthermore, the process of constructing a weighted key partial order lattice includes:

[0011] Collect task dependency data and real-time execution data from multiple projects to construct a raw dataset for multiple projects;

[0012] Based on the original dataset of multiple projects, the dependencies between tasks are analyzed, and a partially ordered lattice structure is constructed.

[0013] Based on the partial order lattice structure, calculate the time margin parameters of each task node;

[0014] Based on the time margin parameter and the partial order lattice structure, the key metrics of each task are calculated, and a weighted key partial order lattice is generated.

[0015] Furthermore, the construction process of the partially ordered lattice structure is as follows:

[0016] Extract all task nodes and their dependencies from the original dataset of multiple projects, treat each task node as an element of a partial order lattice, and transform the predecessor and successor dependencies between tasks into partial order relations.

[0017] All task nodes are hierarchically divided according to their dependencies, and the hierarchical position of each task node in the partial order lattice is determined.

[0018] Construct rules for upper and lower bound operations on partially ordered lattices;

[0019] The hierarchical partitioning results and lattice operation rules are encapsulated into a partial order lattice structure, where each node stores a unique task identifier, hierarchical code, a set of predecessor nodes, a set of successor nodes, and a node attribute dictionary.

[0020] Furthermore, the calculation process for the time margin parameter is as follows:

[0021] Perform a forward traversal on the partially ordered lattice structure, calculating the earliest start time and earliest finish time of each task node layer by layer starting from the first level;

[0022] Perform a reverse traversal on the partially ordered lattice structure, calculating the latest completion time and latest start time of each task node layer by layer starting from the highest level;

[0023] Calculate the total float time for each task node, whereby the total float time is defined as the difference between the latest start time and the earliest start time of the task.

[0024] Furthermore, the calculation method for the key metric is as follows:

[0025] For each task node, obtain its total floating time and the number of subsequent tasks;

[0026] Calculate the critical metric. The calculation rule for the critical metric is as follows: when the total float time is greater than zero, the critical metric is equal to the product of the reciprocal of the total float time and the number of subsequent tasks plus one; when the total float time is equal to zero, the critical metric is set to the maximum value constant allowed by the system, and the task is marked as an absolutely critical task.

[0027] The key metrics are added as weight attributes to the node attribute dictionary of the corresponding task node in the partial order lattice structure to form a weighted key partial order lattice.

[0028] Furthermore, the process of generating the deviation transmission matrix includes:

[0029] Based on weighted key partial order lattices, resource configuration data for each task is collected, and resource redundancy index is calculated.

[0030] Based on the weighted key partial order lattice, extract all task pairs with reachability relations and their propagation path sets;

[0031] Based on the set of conduction paths, calculate the single-hop conduction coefficient and the total conduction coefficient of each conduction path.

[0032] Based on the total path transmission coefficient, construct the deviation transmission matrix.

[0033] Furthermore, the calculation process for the conduction coefficient is as follows:

[0034] For each pair of adjacent task nodes in the transmission path, calculate the single-hop transmission coefficient from the predecessor task to the successor task;

[0035] The three factors of buffer time ratio, resource redundancy, and dependency intensity are standardized.

[0036] The single-hop conduction coefficient was calculated using the weighted geometric mean method.

[0037] For each propagation path, the single-hop propagation coefficients of all adjacent task pairs on the path are multiplied together to obtain the total propagation coefficient of the path.

[0038] Furthermore, the process for generating the risk stratified quantitative matroid includes:

[0039] Collect real-time deviation data for each task and construct a deviation vector;

[0040] Based on the deviation transmission matrix and deviation vector, the cumulative transmission influence value vector is calculated through matrix operations.

[0041] By combining the deviation vector, the cumulative transmitted impact value vector, and the key metric values, the risk score for each task is calculated.

[0042] Based on the dependency relationship between the risk score vector and the weighted key partial order lattice, a risk hierarchical quantitative matroid is constructed.

[0043] Furthermore, the construction process of the risk stratification quantization matrix is ​​as follows:

[0044] Define the base set of matroid as the set of all task nodes in the weighted critical partial order lattice;

[0045] Define the rules for determining independent sets;

[0046] A greedy algorithm is used to solve the maximal independent set decomposition of matroids;

[0047] All maximal independent sets are sorted in descending order of the average risk score of the tasks within the set, and a hierarchical priority label is assigned to each maximal independent set.

[0048] The base set, independent set family, hierarchical partitioning results, and matroid operation interface are encapsulated into a risk-stratified quantitative matroid.

[0049] A project lifecycle progress visualization system is provided to implement the aforementioned project lifecycle progress visualization method. The system includes:

[0050] Weighted Key Partial Order Lattice Construction Module: Used to collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metric value of each task based on the partial order lattice structure, and generate a weighted key partial order lattice.

[0051] Deviation Transmission Matrix Generation Module: This module is used to extract the transmission paths between tasks based on the weighted key partial order lattice and the partial order relationship, and to calculate the transmission coefficients by combining resource redundancy and buffer time to generate the deviation transmission matrix.

[0052] Risk stratification quantization matte generation module: It is used to receive the deviation transmission matrix, collect real-time deviation data of each task to construct the deviation vector, calculate the cumulative impact value of each task through matrix operations, and generate the risk stratification quantization matte by combining the key metric values ​​in the weighted key partial order lattice.

[0053] Differentiated Early Warning and Visualization Module: This module is used to configure differentiated early warning strategies based on the priority of each risk level by using a risk-stratified quantitative matrix. It generates real-time early warnings for high-risk level tasks and marks the scope of their impact, while only recording observation logs for low-risk level tasks. Visualized early warning indicators are rendered hierarchically in the global progress view.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] This invention effectively addresses the challenges of dynamic identification of critical paths, inaccurate assessment of deviation transmission effects, unreasonable risk stratification, and limited early warning strategies in multi-project parallel management scenarios by constructing a weighted critical partial-order lattice, a deviation transmission matrix, and a risk stratification quantification matroid. The weighted critical partial-order lattice introduces minimum upper bound and maximum lower bound operations, elevating task-dependent network topology analysis from path traversal to algebraic operations. This enables constant-time complexity identification of multi-project dependency intersections, overcoming the limitation of traditional directed acyclic graphs that can only output a single critical path. By using critical metrics, the dichotomy between critical and non-critical tasks is transformed into a continuous numerical spectrum, accurately identifying secondary critical tasks. The deviation transmission matrix integrates buffer time proportion, resource redundancy, and dependency strength, employing a weighted geometric average to calculate the single-hop transmission coefficient. This reduces the exponential complexity of deviation impact analysis from path-by-path traversal to polynomial complexity using matrix-vector multiplication, supporting real-time transmission impact calculation for thousands of tasks. The risk-stratified quantitative matroid achieves adaptive risk level division through risk score difference constraints and dependency constraints in the definition of independent sets. This avoids the failure of level differentiation and the problem of duplicate classification of dependent tasks caused by fixed thresholds. The heritability and commutativity of the matroid ensure the stability of the hierarchical structure. Based on the differentiated early warning strategy of the risk-stratified quantitative matroid, early warnings with the scope of propagation impact are pushed in real time for high-risk level tasks, while only observation logs are recorded for low-risk level tasks. Combined with the hierarchical visualization rendering of the global progress view, accurate push and intuitive display of progress anomaly early warnings are achieved, significantly improving the efficiency of progress risk identification and response in multi-project parallel management. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart of a method for visualizing the entire lifecycle progress of a project in this invention;

[0058] Figure 2 This is a schematic diagram of a weighted key partial order lattice structure in an embodiment of the present invention;

[0059] Figure 3 This is a schematic diagram of the deviation transmission path and coefficient calculation in an embodiment of the present invention;

[0060] Figure 4 This is a schematic diagram illustrating the construction of a risk-stratified quantization matroid in an embodiment of the present invention;

[0061] Figure 5This is a schematic diagram illustrating differentiated early warning and visualization rendering in an embodiment of the present invention;

[0062] Figure 6 This is a schematic diagram of deviation transmission matrix and vector operations in an embodiment of the present invention;

[0063] Figure 7 This is a functional module diagram of a project lifecycle progress visualization system according to the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Example 1:

[0066] Please see Figure 1 As shown, this embodiment provides a method for visualizing the entire lifecycle progress of a project, including:

[0067] S1: Collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metrics of each task based on the partial order lattice structure, and generate a weighted key partial order lattice.

[0068] This step addresses the issue of project lifecycle progress visualization systems failing to dynamically identify critical paths in scenarios involving parallel management of multiple project types. By collecting task dependency data and real-time execution data from multiple projects, a partially ordered lattice structure capable of expressing the hierarchical nesting and intersection characteristics between tasks is constructed. Based on this, critical metrics for each task are calculated, ultimately generating a weighted critical partially ordered lattice. This weighted critical partially ordered lattice, as the final output of S1, will be used in S2 to extract the propagation paths between tasks along the partially ordered relationships and calculate propagation coefficients.

[0069] Specifically, the process of constructing a weighted key partial order lattice includes:

[0070] S11: Collect multi-project task dependency data and real-time execution data to construct a multi-project raw data set.

[0071] In this step, task definition data, inter-task dependency data, planned time data, and real-time execution progress data for all parallel projects are obtained from the database interface of the project management system. The task definition data includes a unique task identifier, task name, project identifier, task hierarchy code, and task type label. The inter-task dependency data includes a predecessor task identifier, a successor task identifier, dependency type, and dependency strength coefficient. Dependency types are categorized into four types: finish-to-start, start-to-start, finish-to-finish, and start-to-finish. The dependency strength coefficient is a value between zero and one, representing the degree of constraint imposed by the predecessor task on the successor task. The planned time data includes the planned start time, planned finish time, planned duration, and baseline milestone time. The real-time execution progress data includes the actual start time, current percentage of completion, elapsed duration, estimated remaining duration, and the most recent update timestamp. These data types are then linked and organized according to project identifiers and task identifiers to construct a multi-project raw data set with the unique task identifier as the primary key, providing a complete data foundation for the subsequent construction of a partially ordered lattice structure.

[0072] S12: Based on the original dataset of multiple projects, analyze the dependencies between tasks and construct a partially ordered lattice structure.

[0073] Specifically, the construction process of the partially ordered lattice structure is as follows:

[0074] S121: Extract all task nodes and their dependencies from the original multi-project dataset. Treat each task node as an element of a partial order lattice, and transform the predecessor-successor dependencies between tasks into partial order relations. The partial order relations must satisfy three basic properties: reflexivity (each task has a partial order relation with itself); antisymmetry (if task A is a predecessor of task B and task B is a predecessor of task A, then task A and task B are the same task); and transitivity (if task A is a predecessor of task B and task B is a predecessor of task C, then task A is a predecessor of task C).

[0075] S122: All task nodes are hierarchically partitioned according to their dependencies, determining the hierarchical position of each task node in the partial order lattice. The hierarchical partitioning method is as follows: nodes without predecessor tasks are assigned to the first level; nodes that depend only on tasks of the first level are assigned to the second level, and so on, until all task nodes are assigned a level. For task nodes with cross-level dependencies, the maximum level value among all its predecessor tasks plus one is taken as the level of that node.

[0076] S123: Constructing upper and lower bound operations for partially ordered lattices. For any two task nodes, the lowest upper bound is defined as the set of task nodes with the lowest level among all task nodes that depend on both tasks; the highest lower bound is defined as the set of task nodes with the highest level among all predecessor tasks that both tasks depend on. Upper bound operations can quickly locate the convergence node of multiple execution paths, while lower bound operations can trace the common predecessor tasks of multiple tasks. This lattice operation capability is the core characteristic that distinguishes partially ordered lattices from ordinary directed acyclic graphs.

[0077] S124: The hierarchical partitioning results and lattice operation rules are encapsulated into a partially ordered lattice structure, where each node stores a unique task identifier, hierarchical code, a set of predecessor nodes, a set of successor nodes, and a node attribute dictionary. The node attribute dictionary is used to store time attributes such as planned duration, actual duration, planned start time, and planned completion time extracted from the original data set of multiple projects.

[0078] S13: Calculate the time margin parameters of each task node based on the partial order lattice structure.

[0079] Specifically, the calculation process for the time margin parameter is as follows:

[0080] S131: Perform a forward traversal of the partially ordered lattice structure, calculating the earliest start time and earliest finish time for each task node, starting from the first level and working layer by layer. The earliest start time for first-level tasks is set as the project baseline start time, and the earliest finish time is the earliest start time plus the planned duration. For task nodes not in the first level, their earliest start time is the maximum of the earliest finish times of all predecessor tasks, and their earliest finish time is the earliest start time plus the planned duration.

[0081] S132: Perform a reverse traversal of the partially ordered lattice structure, calculating the latest completion time and latest start time for each task node, starting from the highest level and working layer by layer. The latest completion time for the highest-level task is set to the project target completion time, and the latest start time is the latest completion time minus the planned duration. For task nodes not at the highest level, their latest completion time is the minimum of the latest start times of all subsequent tasks, and the latest start time is the latest completion time minus the planned duration.

[0082] S133: Calculate the total float time for each task node. The total float time is defined as the difference between the latest start time and the earliest start time of the task. The total float time represents the maximum amount of time that the task can be delayed without affecting the overall project completion time. Tasks with a total float time of zero are located on the critical path.

[0083] S14: Based on the time margin parameter and the partial order lattice structure, calculate the key metrics for each task and generate a weighted key partial order lattice.

[0084] Specifically, the calculation method for the key metric is as follows:

[0085] S141: For each task node, obtain its total float time and the number of successor tasks. The number of successor tasks is obtained by counting the number of elements in the set of direct successor nodes of that node in the partial order lattice structure.

[0086] S142: Calculate the critical metric. The calculation rule for the critical metric is as follows: when the total float time is greater than zero, the critical metric is equal to the product of the reciprocal of the total float time and the number of successor tasks plus one; when the total float time is equal to zero, the critical metric is set to the maximum allowed value constant of the system, and the task is marked as an absolutely critical task. The purpose of adding one to the number of successor tasks is to avoid the critical metric value of a leaf node being zero due to the number of successor tasks being zero, and to ensure that the criticality of the leaf node is reasonably evaluated.

[0087] S143: Key metrics are appended as weight attributes to the node attribute dictionary of the corresponding task node in the partial order lattice structure, forming a weighted key partial order lattice. The data structure of the weighted key partial order lattice includes: a node set, where each node contains a unique task identifier, hierarchical code, a set of predecessor nodes, a set of successor nodes, total float time, key metrics, and other time attributes; a partial order relation set, recording all valid predecessor-successor relation pairs; and a lattice operation interface, providing methods for calculating minimum upper bound queries and maximum lower bound queries. See also Figure 2 This is a schematic diagram of a weighted key partial order lattice structure provided in an embodiment of this application. For example... Figure 2 As shown, the overall structure is divided into four levels according to task dependencies, progressing upwards from the bottom level. The gray nodes in the first level (task A, task B, task C) represent ordinary tasks with relatively large total float times and low critical metrics; the orange nodes in the second level (task D, task E, task F) represent secondary critical tasks with relatively small but non-zero total float times; the red nodes in the third and fourth levels (task G, task H, task I) represent absolutely critical tasks with zero total float times, located on the critical path. Figure 2The labeled "Minimum Upper Bound" node (Task G) demonstrates the core algebraic characteristic of the partial-order lattice: multiple execution paths converge here, and the common successor convergence point of Tasks D, E, and F can be quickly located through the minimum upper bound operation. The "Maximum Lower Bound Region" labeled at the bottom represents the query results of multiple first-level tasks as common predecessors. In multi-project parallel management scenarios, tasks in different projects may share resources or have overlapping time windows, forming a complex intertwined dependency network. The partial-order lattice structure, by introducing minimum upper bound and maximum lower bound operations, elevates the topological analysis of the task dependency network from path-by-path traversal to algebraic operations, enabling the identification of dependency intersection points between multiple projects to be completed in constant time complexity. At the same time, the key metrics transform the traditional critical and non-critical dichotomy into a continuous numerical spectrum, providing a quantitative evaluation basis for subsequent deviation propagation analysis.

[0088] Specifically, traditional project management systems use directed acyclic graphs (DAGs) combined with the longest path algorithm to identify critical paths. This method can only output a single critical path sequence, simply dividing tasks into critical and non-critical categories. In multi-project parallel management scenarios, tasks from different projects may share resources or have overlapping time windows, forming complex intertwined dependency networks. The DAG structure cannot directly express the hierarchical nesting characteristics of multiple paths converging and then branching at a certain node, nor can it support the query requirement of quickly locating the common convergence point or common predecessor of any subset of tasks. The partial-order lattice structure, by introducing minimum upper bound and maximum lower bound operations, elevates the topological analysis of task dependency networks from path traversal to algebraic operations, enabling the identification of dependency intersection points between multiple projects to be completed in constant time complexity. At the same time, the critical metric transforms the traditional critical-non-critical dichotomy into a continuous numerical spectrum. Tasks with smaller but non-zero total float times will receive higher critical metric values ​​and be identified as secondary critical tasks. Although these tasks are not on the traditional critical path, their delay risk still needs to be considered. By embedding key metrics as weights into a partial order lattice structure, the weighted key partial order lattice retains complete topological information dependent on the task and provides key quantitative evaluation criteria, laying a data foundation for subsequent deviation transmission analysis and risk stratification assessment.

[0089] S2: Based on the weighted key partial order lattice, extract the transmission path between tasks along the partial order relation, and calculate the transmission coefficient by combining resource redundancy and buffer time to generate the deviation transmission matrix;

[0090] This step addresses the issue of the existing system lacking a model for the propagation of task progress deviations along dependencies. Based on the weighted key partial order lattice output by S1, it extracts all propagation paths between tasks along the partial order relationship. Combining the resource redundancy and buffer time of each task, it calculates the propagation coefficients on the paths, ultimately generating a deviation propagation matrix. This deviation propagation matrix, as the final output of S2, will be used in S3 to calculate the cumulative propagation impact value of each task.

[0091] Specifically, the process for generating the deviation transmission matrix includes:

[0092] S21: Based on a weighted key partial order lattice, collect resource configuration data for each task and calculate the resource redundancy index.

[0093] In this step, resource configuration data for each task is obtained from the resource management module of the project management system. This data includes a list of resource types required by the task, the required quantity of each resource type, the currently available resource quantity, and the quantity of alternative resources. The resource redundancy index is calculated as follows: for each task, the ratio of the number of alternative resources to the required quantity for each resource type is calculated, and the minimum value of this ratio among all resource types is taken as the resource redundancy index for that task. The resource redundancy index ranges from zero to positive infinity. When the resource redundancy index is greater than one, it indicates that the task has sufficient alternative resources, and schedule deviations can be mitigated through resource allocation. When the resource redundancy index is less than one, it indicates that the task is resource-constrained, and schedule deviations are difficult to resolve through resource allocation. The resource redundancy index for each task is stored in the node attribute dictionary of the corresponding node in the weighted key partial order lattice.

[0094] S22: Based on the weighted key partial order lattice, extract all task pairs with reachability relations and their propagation path sets.

[0095] Specifically, the transmission path extraction process is as follows:

[0096] S221: Traverse all task nodes in the weighted key partial order lattice. For each task node, use a breadth-first search algorithm to obtain the set of all reachable successor task nodes. The reachability relation refers to the path from the source task node along the partial order relation, through one or more intermediate nodes, to the target task node.

[0097] S222: For each pair of source and target tasks with reachability, record all propagation paths from the source task to the target task. Each propagation path consists of an ordered sequence of task nodes, where adjacent nodes in the sequence have direct predecessor-successor relationships. When there are multiple propagation paths between the source and target tasks, include all paths in the propagation path set.

[0098] S223: Organize all task pairs and their corresponding transmission path sets into a transmission path index structure. This structure uses the combination of source task identifier and target task identifier as the key and the transmission path set as the value, supporting fast retrieval of all transmission paths between any task pairs.

[0099] S23: Based on the set of conduction paths, calculate the single-hop conduction coefficient and the total conduction coefficient of each conduction path.

[0100] Specifically, the calculation process for the conduction coefficient is as follows:

[0101] S231: For each pair of adjacent task nodes in the propagation path, calculate the single-hop propagation coefficient from the predecessor task to the successor task. The single-hop propagation coefficient is determined by three factors: the buffer time proportion of the successor task, the resource redundancy of the successor task, and the dependency strength of the dependency relationship. The buffer time proportion is defined as the ratio of the total float time of the successor task to the planned duration, and is read from the node attribute dictionary of the weighted critical partial order lattice. When the buffer time proportion is larger, the successor task has a stronger ability to absorb the deviation of the predecessor task, and the propagation attenuation is more significant.

[0102] S232: Standardize the three factors: buffer time percentage, resource redundancy, and dependency strength. The standardization method is as follows: for the buffer time percentage, truncate it to one when it is greater than one, and set it to zero when it is less than zero; for resource redundancy, use the hyperbolic tangent function to map it to the interval between zero and one; for dependency strength, directly use the original values ​​stored in the original dataset of multiple projects.

[0103] S233: The single-hop transmission coefficient is calculated using the weighted geometric mean method. Let the standardized value of buffer time percentage be the first factor, the standardized value of resource redundancy be the second factor, and dependency intensity be the third factor. The weights of the three factors are determined according to the characteristics of the project type, and the sum of the weights equals one. The single-hop transmission coefficient is equal to the product of the first factor raised to the first power, the second factor raised to the second power, and the third factor raised to the third power. The advantage of the weighted geometric mean over the arithmetic mean is that when any factor approaches zero, the overall transmission coefficient also approaches zero, which conforms to the physical meaning of the weakest link effect.

[0104] S234: For each propagation path, multiply the single-hop propagation coefficients of all adjacent task pairs along the path to obtain the total path propagation coefficient. The total path propagation coefficient represents the proportion of the progress deviation of the source task retained when propagated to the target task through this path; a larger coefficient indicates weaker attenuation and stronger propagation impact. See also Figure 3 This is a schematic diagram of a deviation transmission path and coefficient calculation provided in an embodiment of this application. Figure 3 As shown, starting from Task 1, which is marked as "delayed" on the left, the deviation propagates sequentially along the dependency relationship to Task 2, Task 3, and finally affects Task 4. The values ​​marked between each pair of adjacent tasks (0.7, 0.8, 0.6) represent the single-hop propagation coefficient, which is calculated by weighted geometric average of three factors: the proportion of buffer time of subsequent tasks, resource redundancy, and dependency strength. Figure 3The formula area below illustrates the calculation process of the total path transmission coefficient: multiplying the coefficients of each single hop (0.7 × 0.8 × 0.6 = 0.336) yields the total path transmission coefficient from task one to task four. In actual project execution, existing systems typically employ a simple transmission assumption, assuming that any delay in the preceding task will be fully transmitted to the subsequent task. This assumption ignores various buffering mechanisms, such as the total float time allowing tasks to be delayed within a certain range without affecting the overall schedule, and resource redundancy enabling tasks to compress their duration by allocating alternative resources. The calculation of the deviation transmission coefficient incorporates these factors into the transmission model for the first time. A larger coefficient indicates weaker attenuation and stronger transmission impact, thus accurately quantifying the physical process of deviation attenuation at each level in the dependency chain.

[0105] S24: Construct the deviation transmission matrix based on the total path transmission coefficient.

[0106] Specifically, the method for constructing the deviation transmission matrix is ​​as follows:

[0107] S241: Determine the matrix dimensions, where the number of rows and columns equals the total number of task nodes in the weighted key partial order lattice. Row indices correspond to source task nodes, and column indices correspond to target task nodes.

[0108] S242: Initialize matrix elements by setting all matrix elements to zero, indicating that by default there is no deviation propagation relationship between any two tasks.

[0109] S243: Traverse all task pairs in the transmission path index structure. For each source task and target task pair with a reachability relationship, obtain the total transmission coefficient of all paths from its transmission path set, and take the maximum value as the final transmission coefficient of the task pair. The design intention of taking the maximum value is to select the path with the strongest transmission effect as a representative, ensuring that the assessment of potential risks is not overlooked due to path selection.

[0110] S244: Fill the final transmission coefficients into the corresponding elements of the deviation transmission matrix. Since not all task pairs are reachable, this matrix is ​​sparse, with non-zero values ​​only at the positions of task pairs with transmission paths.

[0111] S245: The deviation transmission matrix is ​​stored in a structured manner, using a compressed sparse row format to record the position and value of non-zero elements, reducing storage space usage and supporting efficient matrix operations. The data structure of the deviation transmission matrix includes: an array of non-zero element values, an array of column indices, an array of row offsets, and matrix dimension information.

[0112] Specifically, existing project schedule management systems typically employ a simple propagation assumption when assessing the impact of task delays, assuming that any delay in a preceding task will be fully transmitted to subsequent tasks. This assumption overlooks various buffering mechanisms present in actual project execution: total float time allows tasks to be delayed within a certain range without affecting the overall schedule; resource redundancy allows tasks to compress their duration by allocating alternative resources; and differences in dependency types lead to varying degrees of propagation of deviations across different dependencies. The deviation propagation matrix is ​​the first to incorporate these three factors into the propagation model, comprehensively quantifying the physical process of deviation decaying step-by-step in the dependency chain using a weighted geometric average method. The introduction of the matrix structure transforms deviation impact analysis from path-by-path traversal to vectorized computation. When a task experiences a schedule deviation, simply multiplying the deviation value by the corresponding row of the matrix yields the impact on all downstream tasks at once. The computational complexity is reduced from exponential (related to the number of paths) to polynomial (related to the matrix dimension), meeting the real-time requirements of multi-project parallel scenarios. Simultaneously, the compressed storage format of the sparse matrix significantly reduces memory usage while maintaining computational efficiency, enabling the method to be extended to large-scale project management scenarios involving thousands of task nodes.

[0113] S3: Receive the deviation propagation matrix, collect real-time deviation data of each task to construct a deviation vector, calculate the cumulative impact value of each task through matrix operations, and generate a risk stratification quantification matroid by combining the key metric values ​​in the weighted key partial order lattice.

[0114] This step addresses the problem that existing systems cannot distinguish the actual impact weights of deviations from different types of tasks. It receives the deviation propagation matrix output from S2, collects real-time deviation data for each task to construct a deviation vector, calculates the cumulative propagation impact value for each task through matrix operations, and combines this with the key metric values ​​in the weighted key partial-order lattice output from S1 to calculate risk scores. Finally, a risk-stratified quantitative matel is constructed based on these risk scores. This risk-stratified quantitative matel, as the final output of S3, will be called in S4 to configure differentiated early warning strategies and render visual early warning indicators.

[0115] Specifically, the process of generating the risk stratification quantization matrix includes:

[0116] S31: Collect real-time deviation data for each task and construct a deviation vector.

[0117] In this step, the current execution status data of each task is obtained in real time from the progress monitoring module of the project management system. The collected real-time deviation data includes: a unique task identifier, the current actual completion percentage, the planned completion percentage, and a data update timestamp. The planned completion percentage is calculated based on the current time point's position relative to the planned start and completion times, reflecting the degree of completion the task should achieve according to plan. The deviation vector is constructed as follows: for each task node in the weighted key partial order grid, the difference between its actual completion percentage and the planned completion percentage is calculated, and this difference is used as the element at the corresponding position in the deviation vector. The number of elements in the deviation vector equals the total number of task nodes, and the element order is consistent with the row and column index order of the deviation propagation matrix. A negative deviation value indicates that the task progress is lagging behind the plan, and a positive deviation value indicates that the task progress is ahead of the plan.

[0118] S32: Based on the deviation transmission matrix and deviation vector, calculate the cumulative transmission influence value vector through matrix operations.

[0119] Specifically, the matrix operation process is as follows:

[0120] S321: Set all positive elements in the deviation vector to zero, retaining only negative elements to obtain the lag deviation vector. The purpose of this process is to consider only the negative impact of delayed tasks on downstream tasks; tasks ahead of schedule do not pose a transmission risk.

[0121] S322: Perform a transpose operation on the deviation propagation matrix to obtain the transposed deviation propagation matrix. The row indices of the original matrix represent the source task and the column indices represent the target task. After transpose, the row indices represent the target task and the column indices represent the source task, which facilitates the calculation of the cumulative propagation effect on each task when it is the target task.

[0122] S323: Perform matrix-vector multiplication on the transposed bias propagation matrix and the lag bias vector to obtain the cumulative propagation influence vector. Each element in the cumulative propagation influence vector represents the sum of the propagated influence of all upstream lag task biases on the corresponding task. Due to the sparsity of the bias propagation matrix, a sparse matrix-vector multiplication algorithm is used, calculating only non-zero elements to ensure computational efficiency. See also Figure 6 This is a schematic diagram of deviation transmission matrix and vector operations provided in an embodiment of this application. For example... Figure 6As shown, in the vertically arranged lag deviation vector on the left, red cells (values ​​-0.2, -0.3, -0.1) represent tasks with schedule lags, while gray cells (value 0) represent tasks with no deviations or those ahead of schedule. The six rows and six columns in the middle represent the transposed deviation propagation matrix, where blue-filled cells are marked with non-zero propagation coefficients (such as 0.3, 0.4, 0.8, etc.), and white cells represent zero-value elements, reflecting the sparse nature of the matrix. The cumulative propagation impact vector on the right is the result of matrix-vector multiplication. Red and orange cells represent the degree of influence from upstream lag task deviation propagation; larger values ​​indicate stronger cumulative impact, with the cell containing the value 0.28 being the most significantly affected. In multi-project parallel management scenarios, when a task experiences a schedule deviation, traditional methods require traversing each path to calculate the impact range, and the computational complexity increases exponentially with the number of paths. The introduction of the matrix structure transforms the deviation impact analysis into a vectorized computation. By simply multiplying the deviation value by the corresponding row of the matrix, the impact of the deviation on all downstream tasks can be obtained at once. The computational complexity is reduced to the polynomial level related to the matrix dimension. At the same time, the compressed storage format of sparse matrices significantly reduces memory usage, meeting the real-time requirements of multi-project parallel scenarios.

[0123] S33: Combine the deviation vector, the cumulative transmission impact value vector, and the key metric value to calculate the risk score for each task.

[0124] Specifically, the risk score is calculated as follows:

[0125] S331: Read the key metrics of each task node from the weighted key partial order lattice, and construct the key metric vector according to the same index order as the deviation vector.

[0126] S332: Take the absolute value of the deviation vector and add it element-by-element to the cumulative transmission influence vector to obtain the comprehensive deviation vector. Each element in the comprehensive deviation vector represents the superposition of the corresponding task's own deviation degree and the degree of influence from upstream transmission.

[0127] S333: Multiply the overall deviation value vector element-by-element with the key metric value vector to obtain the risk score vector. Each element in the risk score vector represents the quantitative assessment result of the schedule risk of the corresponding task. The higher the risk score, the greater the threat that the schedule abnormality of the task poses to the overall project completion time.

[0128] S34: Construct a risk-stratified quantitative matroid based on the dependency relationship between the risk score vector and the weighted key partial order lattice.

[0129] Specifically, the construction process of the risk stratification quantization matrix is ​​as follows:

[0130] S341: Define the base set of a matroid as the set of all task nodes in a weighted key partial order lattice. The matroid is a combinatorial algebraic structure composed of the base set and a family of independent sets, satisfying the axioms of heredity and commutativity. The axiom of heredity requires that any subset of an independent set remains an independent set. The axiom of commutativity requires that for any two independent sets, if one independent set has fewer elements, an element not belonging to the smaller independent set can be selected from the larger independent set and added to the smaller independent set to maintain its independence.

[0131] S342: Define the rules for determining independent sets. A task subset is considered independent if it simultaneously meets two conditions: Condition 1, the difference in risk scores between any two tasks in the subset does not exceed a preset hierarchical division threshold; Condition 2, no two tasks in the subset have a direct predecessor-successor relationship in the weighted key partial order lattice. The hierarchical division threshold is determined by: calculating the standard deviation of all elements in the risk score vector, multiplying the standard deviation by a preset hierarchical coefficient, and using this coefficient as the hierarchical division threshold. The hierarchical coefficient is configured based on project complexity and user preferences. See also... Figure 4 This is a schematic diagram of a risk stratification quantization matroid construction provided in an embodiment of this application. Figure 4 As shown, the vertical axis represents the distribution of risk scores from low to high, and the three horizontal bands correspond to the immediate warning level (red background), the attention warning level (orange background), and the observation and recording level (blue background), respectively. Each square node represents a task, and the lines between nodes represent the direct dependencies between tasks. Figure 4 This paper demonstrates two core constraints in the matroid independent set definition: Constraint 1 is the risk score difference constraint, ensuring that tasks within the same level have similar risk scores, thus guaranteeing the effectiveness of risk clustering; Constraint 2 is the dependency constraint, requiring all connections to span different levels, meaning tasks with direct dependencies must be located at different levels to avoid duplicate reporting of the same issue in warning messages. Traditional risk stratification methods use fixed thresholds to classify tasks into high, medium, and low levels, which cannot adapt to the differences in risk distribution across different projects and execution stages, and do not consider the dependencies between tasks. The matroid structure solves these problems simultaneously through the dual constraints embedded in the independent set definition: the level boundaries are adaptively determined based on the actual risk score distribution, and the dependency constraint ensures that tasks with direct sequential relationships are assigned to different levels, preventing causal redundancy in warning messages within levels, significantly improving the rationality of risk stratification and the accuracy of warnings.

[0132] S343: A greedy algorithm is used to solve the maximal independent set decomposition of matroids. First, all tasks are sorted in descending order of risk score. The first maximal independent set is initialized as an empty set. Starting with the task with the highest risk score, each task is checked sequentially to see if it can be added to the current maximal independent set. If adding it still satisfies the independence set determination rule, the task is added to the current maximal independent set; otherwise, if adding it violates the independence set determination rule, the current maximal independent set is marked as completed, a new empty maximal independent set is created, and the task is set as the first element of the new maximal independent set. This process is repeated until all tasks are assigned to a maximal independent set.

[0133] S344: Sort all maximal independent sets in descending order of average risk score of tasks within the set, and assign a hierarchical priority label to each maximal independent set. The maximal independent set with the highest average risk score is assigned the highest priority label, and so on down. Each level records its list of task members, level risk threshold range, and level priority label.

[0134] S345: The base set, independent set family, hierarchical partitioning results, and matroid operation interface are encapsulated into a risk-stratified quantization matroid. The data structure of the risk-stratified quantization matroid includes: a task base set array, storing the unique identifier and risk score of all tasks; a hierarchical grouping mapping table, using hierarchical priority labels as keys and task member lists as values; a hierarchical threshold table, recording the upper and lower bounds of the risk score for each level; and a matroid verification interface, providing methods for determining independent sets and querying maximal independent sets.

[0135] Specifically, traditional risk stratification methods use fixed thresholds to classify tasks into high, medium, and low risk levels. This method has two significant drawbacks: fixed thresholds cannot adapt to the differences in risk distribution across different projects and execution stages, potentially leading to most tasks in some projects being classified into the same level and losing their distinguishing significance; simple threshold classification does not consider the dependencies between tasks, potentially classifying directly dependent tasks into the same risk level, resulting in duplicate reporting of the same issue in warning messages. The matroid structure addresses both of these problems simultaneously through two constraints embedded in the definition of independent sets. The risk score difference constraint ensures that tasks within the same level have similar risk levels, and the level boundary is adaptively determined based on the actual risk score distribution rather than relying on a preset threshold. The dependency constraint ensures that tasks with direct sequential relationships are assigned to different levels, preventing causal redundancy in warning messages within levels. The heritability of matroids guarantees that a subset of tasks in a high-risk level remains in the high-risk category, and the risk characterization is not altered by subset selection; commutativity ensures the stability of the stratification results, preventing drastic restructuring of the stratification structure due to small changes in risk scores. The time complexity of the greedy algorithm is on the order of the square of the number of tasks, and it can still maintain a response time in the order of seconds even with thousands of tasks, thus meeting the real-time requirements of progress monitoring.

[0136] S4: Based on risk-stratified quantitative matroid, differentiated early warning strategies are configured according to the priority of each risk level. Real-time early warnings are generated for high-risk level tasks and the scope of the transmission impact is marked. For low-risk level tasks, only observation logs are recorded. Visual early warning indicators are rendered in the global progress view according to the level.

[0137] This step addresses the problem of existing systems' simplistic early warning strategies leading to the omission of high-value warnings and the proliferation of low-value warnings. Based on the risk-layered quantitative matroid output by S3, differentiated early warning response strategies are configured according to the priority of each risk level. Real-time early warning messages are generated for high-risk level tasks, and the impact range of their deviation propagation is marked. For low-risk level tasks, only observation logs are recorded without pushing intrusive notifications. Finally, differentiated visual early warning icons are rendered in the global progress view according to the risk level, achieving accurate push and intuitive display of progress anomaly warnings.

[0138] Specifically, the process of differentiated early warning and visualization rendering includes:

[0139] S41: Read the hierarchical structure of the risk stratification quantization matrix and configure the early warning response strategy corresponding to each level.

[0140] In this step, a hierarchical grouping mapping table and a hierarchical threshold table are obtained from the risk stratification quantification matrix to determine the number of existing risk levels and the task member list for each level. The configuration rules for the early warning response strategy are as follows: the level with the highest priority label is marked as the immediate early warning level; any abnormal task progress within this level will trigger an immediate message push. The level with the second highest priority label is marked as the attention early warning level; any abnormal task progress within this level will generate an early warning record, but will only be displayed when the user actively accesses the progress view. The remaining levels are marked as observation record levels; any task progress deviations within this level are only written to the system log for subsequent analysis and will not generate any form of early warning display. The early warning response strategy allows users to customize and adjust the correspondence between levels and response methods according to project management needs.

[0141] S42: Generate warning messages for tasks at the real-time warning level and indicate the scope of their impact.

[0142] Specifically, the real-time early warning generation process is as follows:

[0143] S421: Traverse the task member list of the real-time warning level. For each task, read its current deviation value from the deviation vector and its risk score from the risk score vector.

[0144] S422: Determine the transmission influence range of this task based on the deviation transmission matrix. Read the row vectors from the deviation transmission matrix that contain the task as the source task, filter the target tasks corresponding to the non-zero elements in the row vectors, and sort them according to the transmission coefficient from largest to smallest; the larger the coefficient, the stronger the transmission influence. Include target tasks with transmission coefficients greater than a preset transmission significance threshold in the influence range task list. The transmission significance threshold is determined by taking the median of all non-zero elements in the deviation transmission matrix as the transmission significance threshold.

[0145] S423: Construct a warning message data structure containing the following fields: source task identifier, source task name, current deviation value, risk score, deviation direction identifier, list of tasks within the affected area, list of expected impact levels, and warning generation timestamp. The deviation direction identifier is determined based on the sign of the deviation value; negative values ​​indicate delayed progress, and positive values ​​indicate advanced progress. Each element in the expected impact level list is a combination of the identifier of the tasks within the affected area and the expected impact amount, where the expected impact amount is equal to the product of the source task deviation value and the corresponding transmission coefficient.

[0146] S424: Push the warning message to the messaging terminals of the project manager and relevant stakeholders. The push method can be selected from instant messaging, email, mobile push notifications, etc., depending on the system configuration. Simultaneously, the warning message is written to the warning history table for subsequent tracing and statistical analysis.

[0147] S43: Generate warning records for tasks at the warning level and write observation logs for tasks at the observation record level.

[0148] Specifically, the hierarchical recording process is as follows:

[0149] S431: Iterate through the list of task members at the monitored alert level. For each task, construct the alert message data structure using the same method as in S422 and S423, but do not perform message push operations; instead, write the alert message to the alert queue to be displayed. The alert queue to be displayed uses a first-in, first-out queue structure for storage. When the user accesses the global progress view, the alert message is read from the queue and displayed.

[0150] S432: Iterate through the task member list at the observation record level. For each task, construct an observation log record, including the task identifier, current deviation value, risk score, level label, and record timestamp. Write the observation log record to the progress observation section of the system operation log, without generating any warning display content.

[0151] S44: Render differentiated visual warning indicators by risk level in the global progress view. See also Figure 5 This is a schematic diagram illustrating a differentiated early warning and visualization rendering provided in an embodiment of this application. For example... Figure 5As shown, the overall progress view is a Gantt chart in the form of a horizontal timeline, with five task time bars arranged vertically. Task A is filled in red and has an alarm icon at the end, indicating an immediate warning level task whose progress lag requires immediate notification to relevant personnel; Task D is marked with a bold orange border, indicating a task at the attention warning level, with warning records only displayed when the user actively accesses the progress view; Tasks B, C, and E are marked in a normal blue style, indicating tasks at the observation and recording level, with deviations only written to the system log. Figure 5 The curve extending downstream from Task A visually illustrates the extent of the transmission impact: a solid red line connecting to Task B indicates a strong transmission impact, while a dashed orange line connecting to Task C indicates a weak transmission impact; the line thickness is proportional to the transmission coefficient. In practical applications, existing progress warning systems use a uniform time deviation threshold to trigger warnings, leading to frequent warnings from short-term, controllable delays in non-critical path tasks, causing user fatigue, while potential risks in critical path tasks are overlooked. This solution, based on a risk-layered quantitative matroid, implements a differentiated warning strategy, transforming abstract risk scores into intuitive graphical representations. Users can quickly locate high-risk tasks and critical transmission paths from a global view without needing to read detailed data.

[0152] Specifically, the visualization rendering process is as follows:

[0153] S441: Loads the base canvas for the global progress view. This canvas uses the timeline as the horizontal axis and tasks or projects as the vertical axis, and displays the planned time bar and actual progress bar for each task in the form of a Gantt chart.

[0154] S442: Traverse all levels in the risk stratification quantification matrix and determine the visualization style based on the level priority label. Tasks at the immediate warning level are filled with red task bars with a pulse flashing animation effect, tasks at the monitoring warning level are filled with orange task bars with a thickened border effect, and tasks at the observation and recording level retain the default gray or blue fill style.

[0155] S443: For tasks at the immediate warning level, draw a transmission influence line above their task bar. The starting point of the line is the end of the task bar, and the ending point is the beginning of each task bar in the influence range task list. The line is drawn using a Bézier curve to avoid overlapping with other primitives. The line width is inversely proportional to the transmission coefficient; the larger the coefficient, the thicker the line, indicating a stronger transmission influence. The line color uses a gradient from red to yellow to represent the transition from strong to weak influence.

[0156] S444: Add risk level descriptions to the legend area of ​​the global progress view, indicating the meaning of the risk level corresponding to each color and style, so that users can quickly understand the warning indicators in the view.

[0157] S445: Add interactive functionality to the visual warning indicator. When a user clicks on a task bar with a warning indicator, a details pop-up will display the complete warning message for that task, including the deviation value, risk score, list of affected areas, and suggested response measures.

[0158] S45: Provides a user-defined configuration interface for early warning strategies.

[0159] Specifically, the configuration interface functions include:

[0160] S451: Allows users to adjust the level coefficient of the level division threshold. Increasing the level coefficient will reduce the number of levels, allowing each level to contain more tasks. Decreasing the level coefficient will increase the number of levels, allowing for more refined risk division.

[0161] S452: Allows users to customize the correspondence between each level and the early warning response method. Tasks that originally belong to the attention and early warning level can be upgraded to the immediate early warning level, or tasks that belong to the observation and recording level can be upgraded to the attention and early warning level.

[0162] S453: Allows users to configure the significance threshold for propagation, adjusting the strictness of the filtering of the task list of the scope of influence in the warning message.

[0163] S454: Allows users to configure preferred push channels and push time windows for alert messages, avoiding receiving intrusive notifications outside of working hours.

[0164] Specifically, existing progress warning systems use a uniform time deviation threshold to trigger warnings. All tasks exceeding the threshold receive warning messages in the same way, leading to two problems: frequent short-term, controllable delays in non-critical path tasks trigger warnings, causing information overload and user fatigue, with users gradually ignoring the warning content; and potential risks in critical path tasks that have not yet reached the time threshold but show a deviation propagation trend cannot be identified, resulting in the omission of truly high-risk hazards. This step fundamentally solves these problems with a differentiated warning strategy based on risk-layered quantitative matroids. The immediate warning level corresponds to tasks with high critical metrics and large overall deviation values. Progress anomalies in these tasks will significantly impact the overall project completion time, requiring immediate notification of relevant personnel to take action. The observation and recording level corresponds to tasks on non-critical paths with smaller deviation values. These tasks have sufficient float time to absorb deviations and do not require user intervention. The labeling of the propagation impact range transforms warning information from isolated task deviation reports into a panoramic view of the risk propagation chain, helping users understand the causes of deviations and potential propagation directions, and supporting the development of targeted progress adjustment strategies. Color coding and line drawing in visualization rendering transform abstract risk scores into intuitive graphical representations. Users can quickly locate high-risk tasks and key transmission paths from a global view without reading detailed data, significantly improving the efficiency of schedule risk identification.

[0165] For example, suppose a project portfolio contains three parallel projects with a total of fifty task nodes. The system executes progress anomaly warnings according to the process from S1 to S4. In S1, dependency and planned time data for each task are collected, a weighted critical partial order lattice is constructed, and eight absolutely critical tasks with a total float of zero and twelve secondary critical tasks with a total float of less than two days are identified. In S2, the deviation propagation coefficient between tasks is calculated, generating a 50x50 sparse deviation propagation matrix, where non-zero elements account for approximately 15%. In S3, real-time progress data is collected, and seven tasks are found to be lagging. The cumulative propagation impact value is calculated through matrix operations and multiplied by the critical metric to obtain a risk score. Based on the matroid independent set rule, the fifty tasks are divided into four risk levels, with the highest level containing three tasks. In S4, immediate warning messages are generated for the three tasks at the highest level and pushed to the project manager. The warning messages indicate the list of downstream tasks affected by each lagging task and the expected degree of impact. Warning records to be displayed are generated for the eight tasks at the next lower level; the remaining tasks are only written to the observation log. In the global progress view, the highest-level tasks are highlighted in a flashing red light, with lines pointing downstream to affected tasks. The project manager quickly identified three high-risk tasks through the view. Clicking to view details revealed that a delay in one of these tasks would propagate to a project milestone without intervention, prompting the manager to initiate resource reallocation and time-compression measures. The entire warning identification and display process was completed within three seconds of the progress data update, meeting the response requirements for real-time monitoring.

[0166] Example 2:

[0167] This embodiment, based on Embodiment 1, provides a project lifecycle progress visualization system, such as... Figure 7 As shown, it includes:

[0168] Weighted Key Partial Order Lattice Construction Module: Used to collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metric value of each task based on the partial order lattice structure, and generate a weighted key partial order lattice.

[0169] Deviation Transmission Matrix Generation Module: This module is used to extract the transmission paths between tasks based on the weighted key partial order lattice and the partial order relationship, and to calculate the transmission coefficients by combining resource redundancy and buffer time to generate the deviation transmission matrix.

[0170] Risk stratification quantization matte generation module: It is used to receive the deviation transmission matrix, collect real-time deviation data of each task to construct the deviation vector, calculate the cumulative impact value of each task through matrix operations, and generate the risk stratification quantization matte by combining the key metric values ​​in the weighted key partial order lattice.

[0171] Differentiated Early Warning and Visualization Module: This module is used to configure differentiated early warning strategies based on the priority of each risk level by using a risk-stratified quantitative matrix. It generates real-time early warnings for high-risk level tasks and marks the scope of their impact, while only recording observation logs for low-risk level tasks. Visualized early warning indicators are rendered hierarchically in the global progress view.

Claims

1. A method for visualizing the entire lifecycle progress of a project, characterized in that, The method includes: Collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metrics of each task based on the partial order lattice structure, and generate a weighted key partial order lattice. Based on the weighted key partial order lattice, the transmission path between tasks is extracted along the partial order relation, and the transmission coefficient is calculated by combining resource redundancy and buffer time to generate the deviation transmission matrix; Receive the deviation propagation matrix, collect real-time deviation data of each task to construct a deviation vector, calculate the cumulative impact value of each task through matrix operations, and combine the key metric values ​​in the weighted key partial order lattice to generate a risk stratification quantification matroid. Based on risk-stratified quantitative matroid, differentiated early warning strategies are configured according to the priority of each risk level. Real-time early warnings are generated for high-risk level tasks and the scope of their impact is marked. For low-risk level tasks, only observation logs are recorded. Visual early warning indicators are rendered hierarchically in the global progress view.

2. The method for visualizing the entire lifecycle progress of a project according to claim 1, characterized in that, The process of constructing a weighted key partial order lattice includes: Collect task dependency data and real-time execution data from multiple projects to construct a raw dataset for multiple projects; Based on the original dataset of multiple projects, the dependencies between tasks are analyzed, and a partially ordered lattice structure is constructed. Based on the partial order lattice structure, calculate the time margin parameters of each task node; Based on the time margin parameter and the partial order lattice structure, the key metrics of each task are calculated, and a weighted key partial order lattice is generated.

3. The method for visualizing the entire lifecycle progress of a project according to claim 2, characterized in that, The construction process of the partially ordered lattice structure is as follows: Extract all task nodes and their dependencies from the original dataset of multiple projects, treat each task node as an element of a partial order lattice, and transform the predecessor and successor dependencies between tasks into partial order relations. All task nodes are hierarchically divided according to their dependencies, and the hierarchical position of each task node in the partial order lattice is determined. Construct rules for upper and lower bound operations on partially ordered lattices; The hierarchical partitioning results and lattice operation rules are encapsulated into a partial order lattice structure, where each node stores a unique task identifier, hierarchical code, a set of predecessor nodes, a set of successor nodes, and a node attribute dictionary.

4. The method for visualizing the entire lifecycle progress of a project according to claim 2, characterized in that, The calculation process for the time margin parameter is as follows: Perform a forward traversal on the partially ordered lattice structure, calculating the earliest start time and earliest finish time of each task node layer by layer starting from the first level; Perform a reverse traversal on the partially ordered lattice structure, calculating the latest completion time and latest start time of each task node layer by layer starting from the highest level; Calculate the total float time for each task node, whereby the total float time is defined as the difference between the latest start time and the earliest start time of the task.

5. The method for visualizing the entire lifecycle progress of a project according to claim 2, characterized in that, The calculation method for the key metric is as follows: For each task node, obtain its total floating time and the number of subsequent tasks; Calculate the critical metric, and the calculation rule for the critical metric is as follows: when the total float time is greater than zero, the critical metric is equal to the product of the reciprocal of the total float time and the number of subsequent tasks plus one; when the total float time is equal to zero, the critical metric is set to the maximum value constant allowed by the system, and the current task is marked as an absolutely critical task. The key metrics are added as weight attributes to the node attribute dictionary of the corresponding task node in the partial order lattice structure to form a weighted key partial order lattice.

6. The method for visualizing the entire lifecycle progress of a project according to claim 1, characterized in that, The process for generating the deviation transmission matrix includes: Based on weighted key partial order lattices, resource configuration data for each task is collected, and resource redundancy index is calculated. Based on the weighted key partial order lattice, extract all task pairs with reachability relations and their propagation path sets; Based on the set of conduction paths, calculate the single-hop conduction coefficient and the total conduction coefficient of each conduction path. Based on the total path transmission coefficient, construct the deviation transmission matrix.

7. The method for visualizing the entire lifecycle progress of a project according to claim 6, characterized in that, The calculation process for the conductivity coefficient is as follows: For each pair of adjacent task nodes in the transmission path, calculate the single-hop transmission coefficient from the predecessor task to the successor task; The three factors of buffer time ratio, resource redundancy, and dependency intensity are standardized. The single-hop conduction coefficient was calculated using the weighted geometric mean method. For each propagation path, the single-hop propagation coefficients of all adjacent task pairs on the path are multiplied together to obtain the total propagation coefficient of the path.

8. The method for visualizing the entire lifecycle progress of a project according to claim 1, characterized in that, The process for generating the risk stratified quantitative matroid includes: Collect real-time deviation data for each task and construct a deviation vector; Based on the deviation transmission matrix and deviation vector, the cumulative transmission influence value vector is calculated through matrix operations. By combining the deviation vector, the cumulative transmitted impact value vector, and the key metric values, the risk score for each task is calculated. Based on the dependency relationship between the risk score vector and the weighted key partial order lattice, a risk hierarchical quantitative matroid is constructed.

9. A method for visualizing the entire lifecycle progress of a project according to claim 8, characterized in that, The construction process of the risk stratification quantitative matroid is as follows: Define the base set of matroid as the set of all task nodes in the weighted critical partial order lattice; Define the rules for determining independent sets; A greedy algorithm is used to solve the maximal independent set decomposition of matroids; All maximal independent sets are sorted in descending order of the average risk score of the tasks within the set, and a hierarchical priority label is assigned to each maximal independent set. The base set, independent set family, hierarchical partitioning results, and matroid operation interface are encapsulated into a risk-stratified quantitative matroid.

10. A project lifecycle progress visualization system, used to implement the project lifecycle progress visualization method according to any one of claims 1-9, characterized in that, The system includes: Weighted Key Partial Order Lattice Construction Module: Used to collect multi-project task dependency data and real-time execution data, construct a partial order lattice structure of task dependencies, calculate the key metric value of each task based on the partial order lattice structure, and generate a weighted key partial order lattice. Deviation Transmission Matrix Generation Module: This module is used to extract the transmission paths between tasks based on the weighted key partial order lattice and the partial order relationship, and to calculate the transmission coefficients by combining resource redundancy and buffer time to generate the deviation transmission matrix. Risk stratification quantization matte generation module: It is used to receive the deviation transmission matrix, collect real-time deviation data of each task to construct the deviation vector, calculate the cumulative impact value of each task through matrix operations, and generate the risk stratification quantization matte by combining the key metric values ​​in the weighted key partial order lattice. Differentiated Early Warning and Visualization Module: This module is used to configure differentiated early warning strategies based on the priority of each risk level by using a risk-stratified quantitative matrix. It generates real-time early warnings for high-risk level tasks and marks the scope of their impact, while only recording observation logs for low-risk level tasks. Visualized early warning indicators are rendered hierarchically in the global progress view.

Images