A method for predicting construction time and monitoring progress of maintenance of ballastless track based on improved critical chain theory
Patent Information
- Application Number
- CN202611174574.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-04
- Publication Date
- 2026-09-11
AI Technical Summary
[0005]针对现有技术中的上述不足，本发明提供的基于改进关键链理论的无砟轨道维修施工时间预测及进度监管方法解决了现有技术难以预测无砟轨道维修施工的理论总时长，进而无法适时监管无砟轨道维修施工进度的问题
1、本发明采用改进关键链理论对无砟轨道维修施工进度进行优化，综合考虑了无砟轨道维修施工中多种不确定性因素，并采用多种应用数学方法量化这些因素的影响效果，所优化后的维修施工工序的时间紧凑、风险易辨，使得本方法预测的各工序完工时的理论施工总时长为现场施工人员构建了统一标准，为有序、安全施工提供基础支撑。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of ballastless track maintenance and construction management, specifically to a method for predicting the construction time and monitoring the progress of ballastless track maintenance based on an improved critical chain theory. Background Technology
[0002] Under the long-term combined effects of train load, service environment, construction errors, and material properties, all types of ballastless track structures will experience various damages such as cracking, spalling, and interlayer separation. Ballastless tracks operating with these defects should be repaired promptly; otherwise, it can lead to exceeding track geometry limits, increased wheel-rail dynamic impact, and even threaten safe train operation. The longitudinally long, strip-shaped, and vertically multi-layered anisotropic structural characteristics of ballastless track make maintenance and construction complex and involve numerous procedures. Under these circumstances, sufficient, even extra, maintenance time is essential to ensure the smoothness and stability of the track and achieve high-quality maintenance.
[0003] Currently, the comprehensive maintenance window for each railway bureau is typically 240 minutes (0:00-4:00 AM), while for some high-traffic lines, the shortest window is only 180 minutes. During the comprehensive maintenance window, the actual available time for ballastless track maintenance is dynamically compressed due to the overlapping construction work such as electrical debugging and power supply maintenance.
[0004] Therefore, using advanced construction project management theories to predict the theoretical total time of ballastless track maintenance construction, and identifying the deviation between the actual total construction time and the theoretical total construction time at the completion of each process, is of great significance for timely monitoring of the progress of ballastless track maintenance construction and ensuring that the maintenance work can be completed on time within the limited maintenance window. Summary of the Invention
[0005] To address the aforementioned shortcomings in existing technologies, the present invention provides a method for predicting the construction time and monitoring the progress of ballastless track maintenance based on an improved critical chain theory. This method solves the problem that existing technologies struggle to predict the theoretical total duration of ballastless track maintenance construction, thus hindering timely monitoring of the construction progress.
[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A method for predicting the construction time of ballastless track maintenance based on improved critical chain theory is provided, which includes the following steps: Obtain the three times for each process of the target ballastless track; where the three times are the most optimistic time, the most likely time, and the most pessimistic time. Based on the most pessimistic time for each process, and with the principle of no time conflict, the critical path, non-critical path, and transition path in the maintenance and construction are determined. Based on the three times of each process, the planned time and safety time of each process are calculated using the consistency index transformation formula of triangular fuzzy numbers; The factors influencing personnel's subjective judgment and resource uncertainty during maintenance and construction were selected and quantified, and the optimal weight of each influencing factor was calculated. Based on the quantitative results and optimal weights of each influencing factor, the correlation coefficient of each process is calculated, and then the project buffer time on the critical path is calculated and allocated. Based on the planned time, safety time, and project buffer time of each process on the critical path, calculate the theoretical total construction time when each process on the critical path is completed.
[0007] A method for monitoring the construction progress of ballastless track maintenance based on an improved critical chain theory is provided, which includes the following steps: By comparing the actual construction time of each process on the critical path with its corresponding theoretical total construction time, the time domain of the actual construction time of each process on the critical path is determined; the time domain includes the ideal domain, the warning domain, and the danger domain. Based on the time domain of the actual construction time of each process on the critical path, adjust the resource allocation and / or construction organization in subsequent construction to ensure efficient execution of the construction schedule.
[0008] The beneficial effects of this invention are as follows: 1. This invention uses an improved critical chain theory to optimize the construction progress of ballastless track maintenance. It comprehensively considers various uncertainties in ballastless track maintenance and uses multiple applied mathematical methods to quantify the impact of these factors. The optimized maintenance and construction procedures are compact in time and the risks are easy to identify. This method provides a unified standard for the theoretical total construction time when each procedure is completed, thus providing a basic support for orderly and safe construction.
[0009] 2. This invention uses three time domains, which are divided according to the theoretical total construction time corresponding to each process in the maintenance and construction of ballastless track, as a quantitative basis for whether the construction progress of a single process is smooth or not. This allows construction personnel to quickly judge whether the construction efficiency of each process is normal and ensures the efficient execution of the construction progress. Attached Figure Description
[0010] Figure 1 This is a complete flowchart illustrating the maintenance time prediction method and maintenance construction progress monitoring method. Figure 2 This is a construction network diagram illustrating an example of the present invention; Figure 3 Three path diagrams illustrating the construction of this invention; Figure 4 Two types of buffer location diagrams are provided as examples of construction methods for this invention; Figure 5The first example of construction of the present invention i A graph showing the relationship between the actual total construction time at the completion of each process and the theoretical total construction time at the completion of each process. Figure 6 This is a schematic diagram of the time domain division in this invention; Figure 7 This is a completion time control chart for each process on the critical path in this invention. Detailed Implementation
[0011] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0012] like Figure 1 As shown, the method for predicting the maintenance construction time of ballastless track based on the improved critical chain theory includes the following steps: S1. Obtain the three times for each process of the target ballastless track; where the three times are the most optimistic time, the most likely time, and the most pessimistic time. In this embodiment, the three-times of each process in the target ballastless track construction can be obtained through expert analysis and on-site construction management. Furthermore, the types and quantities of resources required for each process can also be obtained. Based on the obtained logical sequence of processes and the three-times of each process, according to... Figure 2 The examples listed herein are used to create construction network diagrams. The letters and numbers in parentheses in the diagrams represent the process number and the most optimistic, most likely, and most pessimistic times for that process, respectively.
[0013] S2. Based on the most pessimistic time for each process, and with the principle of no time conflict, determine the critical path, non-critical path, and transition path in the maintenance and construction. In this embodiment, as Figure 3 As shown, the most pessimistic time of each process on each path is summed, and the path with the largest sum is taken as the critical path, while the remaining paths are taken as non-critical paths. A transition line is set at the point where the non-critical path merges into the critical path to form a transition line path.
[0014] S3. Based on the three times of each process, calculate the planned time and safety time of each process using the consistency index transformation formula of triangular fuzzy numbers; In this embodiment, this step includes the following sub-steps: S3-1. Substitute the three times of each process into the consistency index transformation formula of the triangular fuzzy number, taking a truth value of 0.5, and then calculate the planned time of each process. The expression is as follows:
[0015] in Indicates the first i The fuzzy time value of the process with a fidelity of 0.5, i.e., the fuzzy time value of the process. i Planned time for each process; , and The first i The most optimistic time, the most likely time, and the most pessimistic time for each process; S3-2. The difference between the fuzzy time of sampling accuracy 0.95 and accuracy 0.5 for the same process is taken as the safety time for that process, and its expression is:
[0016] in For the first i Safety time for each process; For the first i The fuzzy time value for each process with a fidelity of 0.95.
[0017] S4. Select and quantify the influencing factors of personnel's subjective judgment and resource uncertainty in maintenance and construction, and calculate the optimal weight of each influencing factor; In this embodiment, the influencing factors include resource constraints, process constraints, risk elasticity coefficient, and construction difficulty; The specific method for calculating the optimal weights of each influencing factor includes the following sub-steps: S4-1. Quantify the selected resource constraints, process constraints, risk elasticity coefficient, and construction difficulty; For example, the quantitative expression for resource constraint is:
[0018] in Indicates the first i The quantitative results of resource constraints for each process; Indicates the first i The quantity of different types of resources required for each process; Indicates the first i The required first step in the process k The quantity of species resources; Indicates the first i The required first step in the process k The total supply of the species; The quantitative expression for process constraint degree is:
[0019] in For the first iThe quantitative results of the process constraints of each process; Indicates the first i The position of each process in the longest path; This represents the number of processes along the longest path in a process; The quantitative expression for the risk elasticity coefficient is:
[0020] in For the first i The quantitative results of the risk elasticity coefficient of each process; , and The first i The most optimistic time, the most likely time, and the most pessimistic time for each process; The construction difficulty was quantified by expert evaluation, and different levels of construction difficulty were characterized by difficulty coefficients, as shown in Table 1.
[0021] Table 1: Construction Difficulty Coefficient Table
[0022] S4-2. Calculate the weights of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty based on the entropy weight method; For example, this sub-step includes the following operations: S4-2-1, Quantifying the target involved in ballastless track maintenance construction n The values of the four influencing factors for each process are arranged with the process as the row and the quantified values of the four influencing factors as the column, thus constructing a... n A decision matrix of ×4, denoted as X; S4-2-2. Transform the decision matrix X into a standardized decision matrix, denoted as V, using a mathematical formula. The mathematical transformation formula is as follows:
[0023] in The standardized decision matrix V represents the first... i OK j Column elements; Represents the decision matrix X, i.e., the first... i OK j Column elements; S4-2-3, Calculate the first j Under the influence factor, the first i The ratio of each process : ; S4-2-4, Calculate the... j Entropy value of each influencing factor :
[0024] in For natural index; S4-2-5, Definition of the first j The coefficient of difference of each influencing factor Thus determining the first j Entropy weight of each influencing factor This gives the weight of the influencing factor:
[0025] in Indicates the first h The coefficient of difference of each influencing factor.
[0026] S4-3. Calculate the weights of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty based on fuzzy hierarchical analysis. For example, this sub-step includes the following operations: S4-3-1. Using a fuzzy complementary scale of 0.1 to 0.9, a 4×4 fuzzy complementary judgment matrix R is constructed based on the results of pairwise comparisons by experts on four influencing factors: resource constraints, process constraints, risk elasticity coefficient, and construction difficulty. 4×4 ; S4-3-2. The fuzzy complementary judgment matrix is tested for consistency using both additive and multiplicative consistency indices. If the test fails, the four influencing factors are re-compared until the consistency test passes. If the test passes, the rows of the passed fuzzy complementary matrix are summed to obtain matrix S. 4×1 ; S4-3-3, Regarding matrix S 4×1 Perform mathematical transformations to obtain the fuzzy consistency matrix. R´ The conversion process is as follows:
[0027] in For fuzzy consistency matrix R´ The Middle i OK j Column elements; and They are matrices S 4×1 The Middle i row and number j row element; S4-3-4, Based on the fuzzy consistency matrix R´ The weight value of each influencing factor is calculated using the following expression:
[0028] in For the first j The weights of the influencing factors are calculated based on the fuzzy hierarchical analysis method. This is for adjusting the coefficient.
[0029] S4-4. Based on the entropy weight method and fuzzy hierarchical analysis method, the weights of resource constraint degree, process constraint degree, risk elasticity coefficient and construction difficulty are calculated respectively, and the deviation maximization criterion is used to calculate the optimal weights of the corresponding influencing factors.
[0030] For example, for two evaluation methods and four technical indicators, let the evaluation method y be denoted as y and y'. (Each value can be 1 or 2) The evaluation value for technical indicator j (j=1,2,3,4) is Then, the deviation maximization criterion calculates the optimal weights of the corresponding influencing factors. The expression is: .
[0031] S5. Calculate the correlation coefficient of each process based on the quantitative results and optimal weights of each influencing factor, and then calculate and allocate the project buffer time on the critical path. In this embodiment, this step includes the following sub-steps: S5-1. Based on the quantitative results of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty, construct an ideal object matrix. X 0=( x 01 , x 02 , x 03 , x 04 ),in x 0j ( j =1,2,3,4) represents the quantitative results of each influencing factor; S5-2. Construct a decision matrix X with the process as the row and the quantitative results of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty as the column. S5-3. The value of each element in the dimensionless matrix R is obtained using the extreme value method. Its expression is:
[0032] in The dimensionless matrix R is the nth i Line 1 j The value of the column; For the decision matrix X, the first... i Line 1 j The value of the column; For the ideal object matrixX 0th j The value of the column; S5-4. Improved resolution coefficient based on the dimensionless matrix R and the optimal weights of each influencing factor. Its expression is:
[0033] in For the first j The optimal weights of each influencing factor; S5-5, Based on resolution coefficient Ideal object matrix X Calculate the incidence matrix using 0 and the dimensionless matrix R; where the nth element in the incidence matrix... i Line 1 j The expression for calculating the correlation coefficient of a column is:
[0034] in Indicates the first i The first process and the first j The correlation coefficients of the influencing factors; Represents the dimensionless matrix R in which the th j The maximum value in the column; Indicates traversal i , j All possible combinations of values and take The minimum value; Indicates traversal i , j All possible combinations of values and take The maximum value; S5-6, Calculate the first i Grey relational degree corresponding to each process Its expression is ; S5-7. Improve the calculation formula for the buffer based on the root variance method to obtain the project buffer on the critical path. Inbound buffers on non-critical paths Its expression is:
[0035]
[0036] in For the first i Safety time for each process; G This represents the total number of processes on the critical path; F This represents the total number of processes on non-critical paths; It should be noted that when seeking hour, and These all correspond to the processes on the critical path; when calculating... hour, and These all correspond to processes on non-critical paths; S5-8. Based on the risk elasticity coefficient and construction difficulty, calculate the project buffer allocation weight for each process. The expression is as follows:
[0037] in For the first i Project buffer allocation weights for each process; For the first i The construction difficulty of each process; For the first k Risk elasticity coefficient for each process; For the first k The construction difficulty of each process; n This represents the total number of processes. S5-9, Calculate the project buffer allocation to the critical path. i The buffer time for each process is expressed as follows:
[0038] in For the first critical path i The buffer time for each process.
[0039] like Figure 5 As shown, the first i The actual total construction time of each process and all preceding processes is consistent with its theoretical total construction time, but the first process... i The actual construction time of each process changes dynamically with the difference Δt between the theoretical total time of the preceding processes and the actual total time.
[0040] from Figure 5 From this, we can know that: In actual case 1, Δt is negative, and the first... i The actual workable time for each process has been compressed, indicating that i The overall progress of the previous process was severely delayed. i Subsequent processes cannot be guaranteed to be completed on time; In actual case 2, Δt is 0, the first... i The actual workable time for each process is equal to the theoretical workable time, indicating that... i The buffer time for each preceding process has been completely consumed. i The actual working time, apart from the theoretically available working time, has no other time buffer, unless it is occupied. iThe buffer time for subsequent processes will further compress the actual operation time of subsequent processes; In actual case 3, Δt is less than , No. i The actual workable time for each process is greater than the theoretical workable time, indicating that... i Previously, only a portion of the buffer time for each process was utilized. i The process has ample actual operating time, reducing the uncertainty and risk it faces, and providing room for maneuver in the face of unexpected situations. At this point, managers can allocate some resources (manpower, equipment) from... i The process is temporarily reassigned to more critical processes, thereby achieving dynamic optimization of resource utilization; In actual case 4, Δt is greater than , No. i The actual workable time for each process is significantly longer than its theoretical workable time, not only i Some processes were completed ahead of schedule, and i The buffer time of each previous process was not consumed, indicating that i Previously, each process progressed efficiently, the first i Each process has ample actual working time, and the construction progress is optimal under such circumstances.
[0041] It should be noted that the buffer time on the critical path is called the project buffer (PB), and the buffer time on the non-critical path is called the inflow buffer (FB). The project buffer is located at the end of the critical path, while the inflow buffer is located on the transition line.
[0042] S6. Based on the planned time, safety time, and project buffer time of each process on the critical path, calculate the theoretical total construction time when each process on the critical path is completed.
[0043] In this embodiment, to facilitate on-site construction personnel in quickly determining the actual operation time of a real-time process based on a unified standard, Figure 5 In the context of the actual situation described, this embodiment suggests dividing the ballastless track maintenance construction progress into three time periods: an ideal region, a warning region, and a danger region. Figure 6 As shown.
[0044] Specifically, this step includes the following sub-steps: S6-1. For each process on the critical path, based on the preceding... i The sum of the planned times for each process Determine the first i The right-hand time node of the ideal domain interval for each process, i.e., the time node when construction has progressed to the [number]th [stage]. i For each process, the corresponding ideal domain is: ;in Indicates the first kThe fuzzy time value of the process with a fidelity of 0.5, i.e., the fuzzy time value of the process. k Planned time for each process; S6-12, according to Determine the first i The right-hand time node of each process warning zone, i.e., the time node when construction has progressed to the [number]th [stage]. i For each process step, the corresponding warning field is: ;in Indicates the first [item] on the critical path k The buffer time for each process; S6-3, according to Determine the first i The right-hand time node of the hazardous area interval of each process, that is, the time node when construction has progressed to the [number]th [stage]. i For each process, the corresponding danger zone is: ; S6-4, such as Figure 7 As shown, based on the ideal domain boundary values, warning domain boundary values, and danger domain boundary values of each process on the critical path, a completion time control chart for each process on the critical path is drawn, thus obtaining the theoretical total construction time when each process on the critical path is completed.
[0045] Specifically, this embodiment, based on the ballastless track maintenance construction time prediction method based on the improved critical chain theory, also discloses a construction progress monitoring method, which further includes the following step after the aforementioned step S6: S7. By comparing the actual construction time of each process on the critical path with its corresponding theoretical total construction time, the time domain of the actual construction time of each process on the critical path is determined; the time domain includes the ideal domain, the warning domain, and the danger domain. S8. Based on the time domain of the actual construction time of each process on the critical path, adjust the resource allocation and / or construction organization in subsequent construction to ensure efficient execution of the construction schedule.
[0046] It should be noted that, such as Figure 4 As shown, the non-critical paths to which the inflow buffer belongs have fewer procedures and simpler links, so the calculated inflow buffer value can be placed on the connection line of its path. According to the principle that the total buffer time actually consumed by the non-critical path should not exceed its inflow buffer time, the construction personnel can flexibly allocate it during construction.
[0047] In this embodiment, a ballastless track maintenance construction time prediction and progress monitoring system based on improved critical chain theory is also provided. This system is used to implement a ballastless track maintenance construction time prediction method and / or progress monitoring method based on improved critical chain theory, comprising: The three-time input module responds to external input and acquires the three times of each process of the target ballastless track; The path determination module determines the critical path, non-critical path, and transition path in maintenance and construction based on the most pessimistic time for each process and with the principle of no time conflict. The first time calculation module calculates the planned time and safety time of each process based on the three times of each process and through the consistency index transformation formula of triangular fuzzy numbers. The influencing factor calculation module responds to external input factors such as personnel's subjective judgment and resource uncertainty in maintenance and construction, calculates and quantifies the influencing factor, and calculates the optimal weight of each influencing factor. The second time calculation module calculates the correlation coefficient of each process based on the quantification results and optimal weights of each influencing factor, and then calculates and allocates the project buffer time on the critical path. The maintenance and construction time prediction module calculates the theoretical total construction time when each process on the critical path is completed, based on the planned time, safety time, and project buffer time of each process on the critical path. The time domain determination module determines the time domain of each process on the critical path by comparing the actual construction time of each process with its corresponding theoretical total construction time; the time domain includes the ideal domain, the warning domain, and the danger domain. The progress monitoring module adjusts resource allocation and / or construction organization plans in subsequent construction based on the actual construction time of each process on the critical path, in order to ensure efficient execution of the construction schedule.
Claims
1. A method for predicting the construction time of ballastless track maintenance based on improved critical chain theory, characterized in that, Includes the following steps: Obtain the three times for each process of the target ballastless track; where the three times are the most optimistic time, the most likely time, and the most pessimistic time. Based on the most pessimistic time for each process, and with the principle of no time conflict, the critical path, non-critical path, and transition path in the maintenance and construction are determined. Based on the three times of each process, the planned time and safety time of each process are calculated using the consistency index transformation formula of triangular fuzzy numbers; The factors influencing personnel's subjective judgment and resource uncertainty during maintenance and construction were selected and quantified, and the optimal weight of each influencing factor was calculated. Based on the quantitative results and optimal weights of each influencing factor, the correlation coefficient of each process is calculated, and then the project buffer time on the critical path is calculated and allocated. Based on the planned time, safety time, and project buffer time of each process on the critical path, calculate the theoretical total construction time when each process on the critical path is completed.
2. The method for predicting the construction time of ballastless track maintenance based on improved critical chain theory according to claim 1, characterized in that, Specific methods for determining the critical path, non-critical path, and transition path during maintenance work include: The most pessimistic time for each process on each path is summed, and the path with the largest sum is designated as the critical path. The remaining paths are designated as non-critical paths, and a transition line is set at the point where the non-critical path merges into the critical path to form a transition path.
3. The method for predicting the construction time of ballastless track maintenance based on improved critical chain theory according to claim 1, characterized in that, The specific methods for calculating the planned time and safety time of each process using the consistency index transformation formula of triangular fuzzy numbers include: Substituting the three times of each process into the consistency index transformation formula of the triangular fuzzy number, and taking a truth value of 0.5, the planned time of each process is calculated, and its expression is: in Indicates the first i The fuzzy time value of the process with a fidelity of 0.5, i.e., the fuzzy time value of the process. i Planned time for each process; , and The first i The most optimistic time, the most likely time, and the most pessimistic time for each process; The difference between the fuzzy time of sampling accuracy 0.95 and accuracy 0.5 for the same process is taken as the safety time for that process, and its expression is: in For the first i Safety time for each process; For the first i The fuzzy time value for each process with a fidelity of 0.
95.
4. The method for predicting the construction time of ballastless track maintenance based on improved critical chain theory according to claim 1, characterized in that, Influencing factors include resource constraints, process constraints, risk elasticity coefficient, and construction difficulty; Specific methods for calculating the optimal weights of each influencing factor include: Quantify the selected resource constraints, process constraints, risk elasticity coefficient, and construction difficulty; The weights of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty are calculated based on the entropy weight method. The weights of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty are calculated based on the fuzzy hierarchical analysis method. Based on the weights of resource constraints, process constraints, risk elasticity coefficients, and construction difficulty calculated by the entropy weight method and fuzzy hierarchical analysis method respectively, the optimal weights of the corresponding influencing factors are obtained by using the deviation maximization criterion.
5. The method for predicting the maintenance construction time of ballastless track based on the improved critical chain theory according to claim 4, characterized in that, The quantitative expression for resource constraints is: in Indicates the first i The quantitative results of resource constraints for each process; Indicates the first i The quantity of different types of resources required for each process; Indicates the first i The required first step in the process k The quantity of species resources; Indicates the first i The required first step in the process k The total supply of the species; The quantitative expression for process constraint degree is: in For the first i The quantitative results of the process constraints of each process; Indicates the first i The position of each process in the longest path; This represents the number of processes along the longest path in a process; The quantitative expression for the risk elasticity coefficient is: in For the first i The quantitative results of the risk elasticity coefficient of each process; , and The first i The most optimistic time, the most likely time, and the most pessimistic time for each process; The difficulty of construction was quantified by expert assessment.
6. The method for predicting the maintenance construction time of ballastless track based on the improved critical chain theory according to claim 5, characterized in that, The specific methods for calculating and allocating project buffer time on the critical path based on the quantitative results and optimal weights of each influencing factor to determine the correlation coefficient of each process include: Based on the quantitative results of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty, an ideal object matrix is constructed. X 0=( x 01 , x 02 , x 03 , x 04 ),in x 0j ( j =1,2,3,4) represents the quantitative results of each influencing factor; Construct a decision matrix X with the process as the row and the quantitative results of resource constraints, process constraints, risk elasticity coefficient, and construction difficulty as the column; The value of each element in the dimensionless matrix R is obtained using the extremum method, and its expression is as follows: in The dimensionless matrix R is the nth i Line number j The value of the column; For the decision matrix X, the first... i Line number j The value of the column; For the ideal object matrix X 0th j The value of the column; Improved resolution coefficient based on dimensionless matrix R and optimal weights of influencing factors Its expression is: in For the first j The optimal weights of each influencing factor; Based on resolution coefficient Ideal object matrix X Calculate the incidence matrix using 0 and the dimensionless matrix R; where the nth element in the incidence matrix... i Line number j The expression for calculating the correlation coefficient of a column is: in Indicates the first i The first process and the first j The correlation coefficients of the influencing factors; Represents the dimensionless matrix R in which the th j The maximum value in the column; Indicates traversal i , j All possible combinations of values and take The minimum value; Indicates traversal i , j All possible combinations of values and take The maximum value; Calculate the first i Grey relational degree corresponding to each process Its expression is ; Based on the root variance method, the calculation formula for the buffer is improved to obtain the project buffer on the critical path. Its expression is: in Provide a buffer for projects on the critical path; For the first i Safety time for each process; The project buffer allocation weight for each process is calculated based on the risk elasticity coefficient and construction difficulty, and its expression is as follows: in For the first i Project buffer allocation weights for each process; For the first i The construction difficulty of each process; For the first k Risk elasticity coefficient for each process; For the first k The construction difficulty of each process; n This represents the total number of processes. Calculate the project buffer allocation to the critical path. i The buffer time for each process is expressed as follows: in For the first critical path i The buffer time for each process.
7. The method for predicting the construction time of ballastless track maintenance based on improved critical chain theory according to claim 6, characterized in that, Based on the planned time, safety time, and project buffer time of each process on the critical path, the specific methods for calculating the theoretical total construction time when each process is completed on the critical path include: For each process on the critical path, based on the preceding... i The sum of the planned times for each process Determine the first i The right-hand time node of the ideal domain interval for each process, i.e., the time node when construction has progressed to the [number]th [stage]. i For each process, the corresponding ideal domain is: ;in Indicates the first k The fuzzy time value of the process with a fidelity of 0.5, i.e., the fuzzy time value of the process. k Planned time for each process; according to Determine the first i The right-hand time node of each process warning zone, i.e., the time node when construction has progressed to the [number]th [stage]. i For each process step, the corresponding warning field is: ;in Indicates the first [item] on the critical path k The buffer time for each process; according to Determine the first i The right-hand time node of the hazardous area interval of each process, that is, the time node when construction has progressed to the [number]th [stage]. i For each process, the corresponding danger zone is: ; Based on the ideal domain boundary values, warning domain boundary values, and danger domain boundary values of each process on the critical path, a completion time control chart for each process on the critical path is drawn, thus obtaining the theoretical total construction time for the completion of each process on the critical path.
8. A progress monitoring method based on the improved critical chain theory-based method for predicting the construction time of ballastless track maintenance as described in any one of claims 1 to 7, characterized in that, Includes the following steps: By comparing the actual construction time of each process on the critical path with its corresponding theoretical total construction time, the time domain of the actual construction time of each process on the critical path is determined; the time domain includes the ideal domain, the warning domain, and the danger domain. Based on the time domain of the actual construction time of each process on the critical path, adjust the resource allocation and / or construction organization in subsequent construction to ensure efficient execution of the construction schedule.
9. The progress monitoring method according to claim 8, characterized in that, Based on the principle that the total buffer time actually consumed by non-critical paths should not exceed their merging buffer time, the construction personnel shall flexibly allocate the buffer time during construction; among which, the merging buffer time of non-critical paths shall be placed on the transition path.