Urban rail transit vehicle depot maintenance resource sharing optimization method

Abstract

The application provides a kind of urban rail transit vehicle base maintenance resource sharing optimization method, comprising the following steps: step S1, analysis urban rail transit vehicle base maintenance resource sharing problem, it is inducted as multi-facility location-distribution problem;Step S2, based on line network topological structure, under the condition of feasibility, with minimum transfer distance as target to find optimal transfer path;Step S3, based on p-media model, with the value of weighted sum of all maintenance resources round trip transfer mileage as objective function, establish general constraint model for all maintenance resources;Step S4, for the operation characteristics of four kinds of vehicle base maintenance resources, establish its respective specific constraint model;Step S5, the solver is used to solve the constraint model established, to determine the final maintenance resource supply point and the configuration scheme of maintenance resource.The application improves the rationality and effectiveness of vehicle base maintenance resource sharing optimization scheme formulation and implementation.

Description

Technical Field

[0001] This invention belongs to the field of rail transit depot maintenance technology, specifically relating to a method for optimizing resource sharing in urban rail transit vehicle depot maintenance. Background Technology

[0002] The planning of urban rail transit networks is of paramount importance to the development of modern cities. Currently, many cities in my country face problems in their urban rail transit network planning, such as unreasonable network scale and inadequate integration with other urban transportation systems. Therefore, it is crucial to grasp the key points of network planning, including resource sharing planning, depot planning, and route planning. With the rapid development of urban rail transit, the number of operating lines and mileage is increasing significantly, and the number of depots and yards is also growing. my country's urban rail transit has entered a stage of large-scale, networked development and operation. Networked conditions provide opportunities for resource sharing in urban rail transit vehicle depot maintenance. Simultaneously, the continuous development and improvement of the network places higher demands on the planning of network vehicle depots. The shift from single-line vehicle depot planning to network-based vehicle depot planning and resource sharing, along with the increasing requirements for maintenance resource sharing and allocation due to the growing variety of vehicle types, makes further research on resource sharing in network vehicle depot maintenance particularly important. Current research on resource sharing in urban rail transit maintenance, such as "Research on Resource Sharing Scheme for Large-scale Inspection and Maintenance Vehicles in Urban Rail Transit" (Wang Yongyuan, Urban Rapid Rail Transit, Vol. 33, No. 6, October 2020), mainly focuses on qualitative analysis of specific rail networks. Other studies, such as the intelligent maintenance analysis method and system for rail transit vehicles disclosed in Chinese Patent CN 113392991 A, which formulates maintenance plans based on component reliability assessments, require quantitative optimization through model building to scientifically and effectively realize the formulation and implementation of resource sharing schemes for urban rail transit maintenance. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing an optimization method for sharing maintenance resources at urban rail transit vehicle depots. This method aims to achieve rational planning of urban rail transit maintenance resource sharing schemes and optimize maintenance strategies at urban rail transit vehicle depots.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for optimizing resource sharing in urban rail transit vehicle depot maintenance includes the following steps:

[0006] Step S1: Analyze the problem of sharing maintenance resources in urban rail transit vehicle depots, and summarize it as a multi-facility site selection-allocation problem;

[0007] Step S2: Based on the network topology, and taking into account the line system, vehicle type, and connectivity conditions, find the optimal transfer path with the goal of minimizing the transfer distance under feasible conditions.

[0008] Step S3: Based on the p-media model, and with the objective function of minimizing the weighted sum of the round-trip mileage of all maintenance resources, establish a general constraint model for all maintenance resources;

[0009] Step S4: Establish unique constraint models for the four types of vehicle base maintenance resources: overhaul resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources, based on their respective operational characteristics.

[0010] Step S5: Use the solver to solve the constraint model established in steps S3 and S4 to determine the final maintenance resource supply point and maintenance resource allocation scheme.

[0011] Furthermore, in step S1, the problem of sharing maintenance resources at urban rail transit vehicle depots, namely the selection of maintenance supply points and the matching of maintenance supply points with maintenance demand points, includes the following situations: in the urban rail transit network, all depots are considered maintenance supply points; for overhaul resources and engineering vehicle resources, each line is considered a maintenance resource demand point; for rail welding base resources, the inter-station lines are considered maintenance resource demand points; for line systems and equipment, stations are considered maintenance resource demand points.

[0012] Furthermore, the specific steps of step S2 are as follows:

[0013] Step S201, Input Adjacency Matrix: When calculating the transfer distance, the network is abstracted into a topology graph, denoted as G={V,E}, where G represents the topology network, V represents the points in the network, E represents the arcs in the network, and E is the subway line connecting two stations. The length of the arc is represented by the distance between stations.

[0014] Establish an adjacency matrix based on the adjacency relationships between points;

[0015] Step S202: Input the specified vehicle base numbered m and the route numbered i, and search for the vehicle section numbered mm on the route i.

[0016] Step S203: Determine whether the number of turns p from vehicle section mm to vehicle base m is greater than a pre-set upper limit M; if it is greater than the upper limit M, the path search result is empty, and proceed to step 206; if it is less than or equal to the upper limit M, proceed to step 204.

[0017] Step S204: Perform the classic k-short path algorithm search; calculate the k-th shortest path between vehicle base numbered m and vehicle segment numbered mm.

[0018] Step S205, delete redundant points in the path: When the searched path passes through a certain connecting line without changing lines, the connecting line is redundant in the path and is deleted.

[0019] Step S206: Determine whether the path satisfies the constraints of the number of turns and the transfer distance. If not, let k = k + 1 and go to step S203. If it satisfies, retain the path search results from the vehicle base m to the vehicle section mm. The path search results include the numbering and order of the points and arcs in the network.

[0020] Step S207: Determine whether the route type allows the vehicle type assigned to the depot numbered mm to pass through. If not, let k = k + 1 and go to step S203; if so, retain the route type result.

[0021] Step S208: Determine whether all vehicle segments on line i have been traversed. If yes, proceed to step S202. If no, select the shortest path from the retained path results as the transfer path between vehicle base m and line i, and the length of this path is used as the transfer distance.

[0022] Step S209: Output the transfer route selection results and distance calculation results.

[0023] Further, in step S201, the points in the network include connecting lines and depots, wherein the connecting line is represented by the station where it is located, and the depot is represented by the station connected by the depot access line; the weight in the adjacency matrix represents the length of the arc between each point, and if two points are not directly connected, the weight in the adjacency matrix is ​​∞.

[0024] Furthermore, the specific steps for establishing a universal constraint model for all maintenance resources in step S3 are as follows:

[0025] Step S301: Let I = {i} represent the set of lines, B = {b} represent the set of maintenance resource supply points, M = {m} represent the set of connecting lines, S = {s} represent the set of stations, and E = {e} represent the set of arcs. Let F = {f} represent the set of the smallest units of demand for a certain maintenance resource. Depending on the maintenance resource, it can be the set of lines, the set of stations, or the set of inter-station lines.

[0026] Step S302: The objective function is to minimize the weighted sum of the round-trip mileage of all maintenance resources. The specific expression is as follows:

[0027]

[0028] In the formula: Z—the weighted sum of the round-trip transfer distances between the maintenance resource supply point b and the maintenance resource demand point f;

[0029] w b —The weight of the fixed costs invested in upgrading each depot to a vehicle base is determined by taking 1 if maintenance resource supply point b is a depot and the larger value if maintenance resource supply point b is a parking lot.

[0030] y b,f —A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand at the maintenance resource demand point f, and 0 otherwise;

[0031] q f —Maintenance resource demand points f Maintenance resource demand scale;

[0032] D b,f —The distance between maintenance resource supply point b and maintenance resource demand point f;

[0033] Step S303: Establish constraint one for the correspondence between resource demand points and resource supply points, which respectively represent: the point selected for a demand point must be a maintenance resource supply point; one demand point corresponds to a unique supply point; and a maintenance resource supply point must be responsible for the demand point it belongs to. The expression of constraint one is as follows:

[0034]

[0035]

[0036]

[0037] In the formula: x b —A 0-1 variable, which takes the value 1 when the depot at point b is set as a maintenance resource supply point, and 0 otherwise;

[0038] O b,f — A 0-1 variable representing the locational relationship between maintenance resource supply points and maintenance resource demand points; when the location of maintenance resource supply point b is the same as that of maintenance resource demand point f, it is set to 1, otherwise it is set to 0;

[0039] Step S304: To ensure that the transfer distance between the maintenance resource demand point and the selected maintenance resource supply point does not exceed a certain upper limit, constraint two is established, which is expressed as follows:

[0040]

[0041] In the formula: D max —Maximum transfer distance for a single transit;

[0042] Step S305: Set a quantity limit for maintenance resource supply points and establish constraint three. The specific expression of constraint three is as follows:

[0043]

[0044] In the formula: N — the number of maintenance resource supply points.

[0045] Furthermore, the specific steps for establishing the unique constraints for each of the overhaul resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources in step S4 are as follows:

[0046] Step S401, establish a specific constraint model for overhaul resources: the smallest unit of overhaul resource demand is the line, and the expression for calculating the overhaul demand on line i is as follows:

[0047]

[0048] In the formula: q i —Scale of maintenance resource requirements for line i;

[0049] Q i —Number of trains assigned to line i (units);

[0050] T1, T2 — Overhaul and maintenance cycle;

[0051]

[0052] In the formula: l i —Line i main frame repair needs / position;

[0053] α1, α2 — Imbalance coefficients during major overhauls and maintenance;

[0054] t1, t2 — Downtime for major overhauls, overhauls, and maintenance.

[0055] The column size of maintenance resource supply point b must not exceed a certain upper limit, as shown below:

[0056]

[0057] In the formula: y b,f —A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand of line i, and 0 otherwise;

[0058] l max —Maximum size of a single maintenance resource supply point;

[0059] Step S402, establish a resource-specific constraint model for engineering vehicles: the smallest unit of engineering vehicle resource requirements is the route, and the expression for calculating the number of days for a single inspection on route i is as follows:

[0060]

[0061]

[0062] In the formula: T i J —Single inspection time for engineering vehicle on line i;

[0063] L i —Line i length;

[0064] v — Operating speed of the engineering vehicle;

[0065] Δt — Duration of nighttime operation window;

[0066] β—Work duration reduction factor;

[0067] The average monthly occupancy time of the engineering vehicles at maintenance resource supply point b must not exceed a certain upper limit, typically set at 30 days. This constraint is expressed as follows:

[0068]

[0069] In the formula: y b,f —A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand of line i, and 0 otherwise;

[0070] —Duration of a single line transfer between maintenance resource supply point b and line i;

[0071] n—average number of tests per month;

[0072] T b —Average monthly repair time for engineering vehicles;

[0073] T max —The upper limit of the average monthly occupancy time of construction vehicles;

[0074] Step S403, establish a resource-specific constraint model for rail welding bases: For rail welding base resources, the smallest unit of demand is the inter-station track. To facilitate statistics, multiple adjacent inter-station tracks on a line can be merged into arcs, and the rail replacement demand on the arc segment can be calculated:

[0075]

[0076] In the formula: q e — Track changing requirements on arc segment e;

[0077] H e —Large-scale track replacement cycle on the line where arc segment e is located;

[0078] Le ′——Length of arc segment e;

[0079] h e —Cyclic track changing cycle on small radius curves on arc segment e;

[0080] l e ′——Length of the small-radius curve on line e;

[0081] The constraint on the length of the track covered by a single rail welding base is established, as shown in the following expression:

[0082]

[0083] In the formula: y b,e —A 0-1 variable, which takes the value 1 when the welding rail base at point b covers the arc segment v, and 0 otherwise;

[0084] L max —The length of track that a single rail welding base is responsible for;

[0085] Step S404: Establish a resource-specific constraint model for the integrated maintenance base: For integrated maintenance base resources, the maintenance tasks of the equipment are mainly offline maintenance tasks of various line professional systems and equipment, including professional inspection and measurement, professional maintenance, improvement maintenance (intermediate and major repairs) and fault maintenance of systems and equipment.

[0086] Equipment maintenance needs under preventative maintenance:

[0087]

[0088]

[0089]

[0090]

[0091] In the formula: T1, T2, T3, T4 — major overhaul, intermediate overhaul, and minor overhaul professional maintenance and inspection cycle;

[0092] L1, L2, L3, L4 — Average number of major overhauls, intermediate overhauls, minor overhauls, and inspections per year;

[0093] P t —t∈T represents the type of equipment, P t Indicates the quantity of equipment of type t (equipment configuration varies by site). Equipment maintenance requirements under fault-based maintenance:

[0094] L(u)=P t ×χ t (u)

[0095] Where: χt (u) — Failure rate of equipment type t in year u;

[0096] L(u) — The number of repairs required for equipment type t in year u;

[0097] P t —t∈T represents the type of equipment, P t This represents the quantity of the t-th type of equipment;

[0098] Furthermore, the steps in step S5 for determining the final maintenance resource supply point and the maintenance resource allocation scheme are as follows:

[0099] Step S501, optimize resource sharing for overhaul: Using the overhaul resource sharing optimization model established in steps S3 and S4, input the transfer distance obtained in step S2 and perform quantitative solution.

[0100] Step S502, optimize the resource sharing of engineering vehicles: use the optimization model for resource sharing of engineering vehicles established in steps S3 and S4 to perform quantitative solution;

[0101] Step S503: Optimize the resource sharing of the rail welding base: Quantitatively solve the resource sharing optimization model of the rail welding base established in steps S3 and S4.

[0102] Step S504: Optimize resource sharing in the comprehensive maintenance base: Quantitatively solve the resource sharing optimization model established in steps S3 and S4.

[0103] Compared with the prior art, the beneficial effects of the present invention are as follows: the problem of vehicle depot maintenance resource optimization is accurately analyzed through constraint model, and optimization is carried out by quantitative modeling method, which further improves the rationality and effectiveness of the formulation and implementation of vehicle depot maintenance resource sharing optimization scheme, and realizes the rational planning of urban rail transit maintenance resource sharing scheme. Attached Figure Description

[0104] Figure 1 Flowchart for optimizing resource sharing in urban rail transit maintenance;

[0105] Figure 2 A flowchart for calculating the optimal transfer path between vehicle base m and line i that satisfies the constraints;

[0106] Figure 3 This is a schematic diagram of the topology of the subway network. Detailed Implementation

[0107] To more clearly illustrate the present invention, the following description, in conjunction with preferred embodiments and accompanying drawings, further clarifies the invention. Those skilled in the art should understand that the specific description below is illustrative rather than restrictive and should not be construed as limiting the scope of protection of the present invention.

[0108] like Figure 1 As shown, a method for optimizing resource sharing in urban rail transit vehicle depot maintenance includes the following steps:

[0109] Step S1: Analyze the problem of sharing maintenance resources in urban rail transit vehicle depots, and summarize the problem of sharing maintenance resources in urban rail transit vehicle depots as a multi-facility site selection-allocation problem;

[0110] The problem of optimizing maintenance resource sharing in urban rail transit vehicle depots is essentially about selecting maintenance supply points and matching them with maintenance resource demand points. Therefore, in an urban rail transit network, all depots can be considered maintenance supply points; for overhaul and engineering vehicle resources, each line can be considered a maintenance resource demand point; for rail welding depot resources, inter-station lines can be considered maintenance resource demand points; and for line systems and equipment, stations can be considered maintenance resource demand points. Allocating each maintenance resource demand point to a unique corresponding maintenance resource supply point is the process of optimizing maintenance resource sharing, which can be summarized as a multi-facility site selection and allocation problem.

[0111] Step S2: Based on the network topology, and taking into account the line system, vehicle type, connectivity, etc., find the optimal transfer path with the goal of minimizing the transfer distance under feasible conditions.

[0112] For resources related to overhaul, engineering vehicles, and rail welding bases, since transfers via subway lines are required, it is necessary to search for the optimal transfer path between the vehicle depot and different sections of the service line. This involves transforming the distance calculation from "point-to-line" to "point-to-point" distance calculation, and selecting the shortest path as the optimal transfer path between the vehicle depot and the service line. The specific calculation process is as follows: Figure 2 As shown, it mainly includes the following steps:

[0113] Step S201, Input Adjacency Matrix: When calculating the transit distance, the wire network is abstracted into a topology graph, such as... Figure 3As shown, let G = {V, E}, where G represents the topology network, V represents a point in the network, including connecting lines (represented by the station where the point is located) and depots (represented by stations connected by depot access lines), and E represents an arc in the network, which is the subway line connecting two stations. The length of the arc is represented by the distance between stations. An adjacency matrix is ​​established based on the adjacency relationships between points. The weights in the adjacency matrix represent the lengths of the arcs between points. If two points are not directly connected, the weights in the adjacency matrix are ∞.

[0114] Step S202: Input the specified vehicle depot numbered m and the route numbered i, and search for the vehicle section numbered mm on route i.

[0115] Step S203: Determine whether the number of turns p from vehicle section mm to vehicle base m is greater than a pre-set upper limit M; if it is greater than the upper limit M, the path search result is empty, and proceed to step 206; if it is less than or equal to the upper limit M, proceed to step 204.

[0116] Step S204: Perform the classic k-short path algorithm search; calculate the k-th shortest path between vehicle base numbered m and vehicle segment numbered mm.

[0117] Step S205, delete redundant points in the path: When the searched path passes through a certain connecting line without changing lines, the connecting line is redundant in the path and is deleted.

[0118] Assuming the path is: Vehicle Base m - Connecting Line C1 - Connecting Line C2 - Connecting Line C3 - Vehicle Depot mm; Read the route of each point sequentially, assuming it is: 2→2 / 3→3 / 4→3 / 5→5. The route changes as follows: 2→3→3→5. There is no change when passing the second connecting line, so we delete connecting line C2, resulting in the final path: Vehicle Base m - Connecting Line C1 - Connecting Line C3 - Vehicle Depot mm.

[0119] Step S206: Determine whether the path satisfies the constraints of the number of turns and the transfer distance. If not, let k = k + 1 and go to step S203. If it satisfies, retain the path search results from the vehicle base m to the vehicle section mm (the numbering and order of the points and arcs in the network).

[0120] Step S207: Determine whether the route type allows the vehicle type assigned to the depot numbered mm to pass through. If not, let k = k + 1 and go to step S203; if so, retain the route type result.

[0121] Step S208: Determine whether all vehicle segments on line i have been traversed. If yes, proceed to step S202. If no, select the shortest path from the retained path results as the transfer path between vehicle base m and line i, and the length of this path is used as the transfer distance.

[0122] Step S209: Output the transfer route selection results and distance calculation results.

[0123] Step S3: Based on the p-media model, and with the objective function of minimizing the weighted sum of the round-trip mileage of all maintenance resources, establish a general constraint model for all maintenance resources. The specific steps are as follows:

[0124] Step S301: Let I = {i} represent the set of lines, B = {b} represent the set of maintenance resource supply points, M = {m} represent the set of connecting lines, S = {s} represent the set of stations, and E = {e} represent the set of arcs. Let F = {f} represent the set of the smallest units of demand for a certain maintenance resource. Depending on the maintenance resource, it can be the set of lines, the set of stations, or the set of inter-station lines.

[0125] Step S302: The objective function is to minimize the weighted sum of the round-trip mileage of all maintenance resources. The specific expression is as follows:

[0126]

[0127] In the formula: Z—the weighted sum of the round-trip transfer mileage between the maintenance resource supply point b and the maintenance resource demand point f;

[0128] w b —The weight of the fixed costs invested in upgrading each depot to a vehicle base is determined by taking 1 if maintenance resource supply point b is a depot and the larger value if maintenance resource supply point b is a parking lot.

[0129] y b,f —A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand at the maintenance resource demand point f, and 0 otherwise;

[0130] q f —Maintenance resource demand points f Maintenance resource demand scale;

[0131] D b,f — The distance between maintenance resource supply point b and maintenance resource demand point f.

[0132] Step S303: Establish constraint one for the correspondence between resource demand points and resource supply points, which respectively represent: the point selected for a demand point must be a maintenance resource supply point; one demand point corresponds to a unique supply point; and a maintenance resource supply point must be responsible for the demand point it belongs to. The expression of constraint one is as follows:

[0133]

[0134]

[0135]

[0136] In the formula: x b —A 0-1 variable, which takes the value 1 when the depot at point b is set as a maintenance resource supply point, and 0 otherwise;

[0137] O b,f — A 0-1 variable representing the locational relationship between maintenance resource supply points and maintenance resource demand points; when the location of maintenance resource supply point b is the same as that of maintenance resource demand point f, it is set to 1, otherwise it is set to 0;

[0138] Step S304: To ensure that the transfer distance between the maintenance resource demand point and the selected maintenance resource supply point does not exceed a certain upper limit, constraint two is established, which is expressed as follows:

[0139]

[0140] In the formula: D max —Maximum transfer distance for a single transit;

[0141] Step S305: Set a quantity limit for maintenance resource supply points and establish constraint three. The specific expression of constraint three is as follows:

[0142]

[0143] In the formula: N — the number of maintenance resource supply points.

[0144] Step S4: Based on the operational characteristics of the four types of vehicle base maintenance resources—overhead repair resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources—establish their respective unique constraints. The specific steps are as follows:

[0145] Step S401, establish specific constraints for overhaul resources: the smallest unit of overhaul resource demand is the line, and the expression for calculating the overhaul demand on line i is as follows:

[0146]

[0147] In the formula: q i —Scale of maintenance resource requirements for line i;

[0148] Q i —Number of trains assigned to line i (units);

[0149] T1 and T2 represent overhaul and maintenance cycles.

[0150]

[0151] In the formula: l i —Line i main frame repair needs / column;

[0152] α1, α2 — Imbalance coefficients during major overhauls and maintenance;

[0153] t1, t2 — Overhaul, overhaul, and maintenance shutdown time.

[0154] The column size of maintenance resource supply point b must not exceed a certain upper limit, as shown below:

[0155]

[0156] In the formula: y b,f —A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand of line i, and 0 otherwise;

[0157] l max —Maximum size of a single maintenance resource supply point;

[0158] Step S402, establish specific constraints for engineering vehicle resources: the smallest unit of engineering vehicle resource requirements is the line, and the expression for calculating the number of days for a single inspection on line i is as follows:

[0159]

[0160]

[0161] In the formula: T i J —Single inspection time for engineering vehicle on line i;

[0162] L i —Line i length;

[0163] v — Operating speed of the engineering vehicle;

[0164] Δt — Duration of nighttime operation window;

[0165] β — Work time reduction factor.

[0166] The average monthly occupancy time of the engineering vehicles at maintenance resource supply point b must not exceed a certain upper limit, typically set at 30 days. This constraint is expressed as follows:

[0167]

[0168] In the formula: y b,f—A 0-1 variable, which takes the value 1 when the maintenance resource supply point at point b covers the demand of line i, and 0 otherwise;

[0169] —Duration of a single line transfer between maintenance resource supply point b and line i;

[0170] n—average number of tests per month;

[0171] T b —Average monthly repair time for engineering vehicles;

[0172] T max —The upper limit of the average monthly occupation time of engineering vehicles.

[0173] Step S403, establish resource-specific constraints for rail welding bases: For rail welding base resources, the smallest unit of demand is the inter-station track. To facilitate statistics, multiple adjacent inter-station tracks on a line can be merged into arcs, and the rail replacement demand on the arc segment can be calculated:

[0174]

[0175] In the formula: q e — Track changing requirements on arc segment e;

[0176] H e —Large-scale track replacement cycle on the line where arc segment e is located;

[0177] L e ′——Length of arc segment e;

[0178] h e —Cyclic track changing cycle on small radius curves on arc segment e;

[0179] l e ′——Length of the small radius curve on line e.

[0180] The constraint on the length of the track covered by a single rail welding base is established, as shown in the following expression:

[0181]

[0182] In the formula: y b,e —A 0-1 variable, which takes the value 1 when the welding rail base at point b covers the arc segment v, and 0 otherwise;

[0183] L max —The maximum length of track that a single rail welding base can handle;

[0184] Step S404, establish resource-specific constraints for integrated maintenance bases: For integrated maintenance base resources, the maintenance tasks of equipment mainly involve offline maintenance tasks of various line professional systems and equipment, including professional inspection and measurement of systems and equipment, professional maintenance, improvement maintenance (intermediate and major repairs) and fault repair.

[0185] Equipment maintenance needs under preventative maintenance:

[0186]

[0187]

[0188]

[0189]

[0190] In the formula: T1, T2, T3, T4 — major overhaul, intermediate overhaul, and minor overhaul professional maintenance and inspection cycle;

[0191] L1, L2, L3, L4 — Average number of major overhauls, intermediate overhauls, minor overhauls, and inspections per year;

[0192] P t —t∈T represents the type of equipment, P t Indicates the quantity of equipment of type t (equipment configuration varies by site). Equipment maintenance requirements under fault-based maintenance:

[0193] L(u)=P t ×χ t (u)

[0194] Where: χ t (u) — Failure rate of equipment type t in year u;

[0195] L(u) — The number of repairs required for equipment type t in year u;

[0196] P t —t∈T represents the type of equipment, P t This represents the number of devices of type t (devices are configured according to the site).

[0197] Step S5: Use the solver to solve the constraint model established in steps S3 and S4 to determine the final maintenance resource supply points and maintenance resource allocation scheme.

[0198] Step S501, optimize resource sharing for overhaul: Using the overhaul resource sharing optimization model established in steps S3 and S4, input the transfer distance obtained in step S2 and perform quantitative solution.

[0199] To more intuitively illustrate the optimization of overhaul maintenance resource sharing, this invention uses the Guangzhou Metro Phase III Plan Type A train network as a case study. The established topology includes 7 lines, 12 depots, and 7 existing connecting lines. Using the overhaul maintenance resource sharing optimization model established in steps S3 and S4, and inputting the transfer distance obtained in step S2, a quantitative solution is performed. The resulting overhaul maintenance resource sharing configuration schemes based on different numbers of vehicle depots for existing connecting lines are shown in Table 2 below.

[0200] Table 2 shows that as the number of depots increases, the number of trains required for the network increases slightly, while the total round-trip transfer distance decreases significantly. Compared to the scheme with 2 depots, the total transfer distance is reduced by 44% and 64% for schemes with 3 and 4 depots, respectively. In terms of the overall layout of the depots, the locations of the depots become more balanced and dispersed as the number of depots increases. All three schemes select the Chatou Depot to handle the major overhaul of trains on lines 12, 13, and 24. The difference lies in the allocation for lines 1, 2, 8, and 11: with 2 depots, the Chisha Depot is responsible; with 3 depots, the Hualong Depot is added; and with 4 depots, the Jiahe Depot is added.

[0201] Table 2 Resource Sharing Allocation Scheme for Major Overhaul

[0202]

[0203] Step S502, optimize the resource sharing of engineering vehicles: use the optimization model for resource sharing of engineering vehicles established in steps S3 and S4 to perform quantitative solution;

[0204] To more intuitively illustrate the optimization of engineering vehicle resource sharing, this invention uses the track inspection vehicle of the Guangzhou Metro Phase III planned line as a case study. The established topology map includes 19 lines, 17 depots, and 11 existing connecting lines. The engineering vehicle resource sharing optimization model established in previous steps S3 and S4 is used for quantitative solution. Since the third-rail power supply lines need to be configured separately, the number of configured track inspection vehicles is shown in Table 3 below, the configuration scheme of the DC motor lines is shown in Table 4 below, and the configuration scheme of the contact power supply lines is shown in Table 5 below.

[0205] The table shows that the linear motor track inspection vehicle is located at Yuzhu Depot, responsible for the inspection of lines 4, 5, and 6, with an average monthly occupation of 28 days, which meets the constraints of the number of working days. Five track inspection vehicles are configured for the contact power supply lines, located at Jiahe Depot, Chisha Depot, Zhenlong Depot, Longzhen Parking Lot, and Chatou Depot. The track inspection vehicle at Jiahe Depot is responsible for the inspection of lines 1, 2, 3, and 9; at Chisha Depot, lines 7, 8, 10, and 11; at Zhenlong Depot, lines 14, 27 (14 branches), and 21; at Chatou Depot, lines 12, 13, and 24; and at Longzhen Parking Lot, lines 22 and 18.

[0206] Table 3: Number of Track Inspection Vehicles

[0207]

[0208] Table 4. Configuration Scheme of DC Motor Circuit

[0209]

[0210] Table 5. Configuration Scheme of Contact Power Supply Line

[0211]

[0212]

[0213]

[0214] Step S503: Optimize the resource sharing of the rail welding base: Quantitatively solve the resource sharing optimization model of the rail welding base established in steps S3 and S4.

[0215] To more intuitively illustrate the resource sharing optimization of rail welding bases, this invention uses the rail welding bases of the Guangzhou Metro Phase III planned network as a case study. The established topology map includes 19 lines, 17 depots, and 11 existing connecting lines. The resource sharing optimization model for rail welding bases established in previous steps S3 and S4 is used for quantitative solution. The resulting resource sharing configuration scheme for rail welding bases based on existing connecting lines is shown in Table 6 below. From the table, we can see that 5 rail welding bases are selected, located at Jiahe Depot, Yuzhu Depot, Chisha Depot, Zhenlong Depot, and Longzhen Parking Lot.

[0216] Table 6. Resource Sharing Allocation Scheme for Rail Welding Base

[0217]

[0218]

[0219] Step S504: Optimize resource sharing in the comprehensive maintenance base: Quantitatively solve the resource sharing optimization model established in steps S3 and S4.

[0220] To more intuitively illustrate the optimization of integrated maintenance base resource sharing, this invention uses the existing stations of the entire Guangzhou Metro network as an example. The established topology map includes 13 lines and 223 stations. The transfer distance is referenced from the optimal vehicle travel distance recommended by Baidu Maps, and the integrated maintenance base resource sharing optimization model established in previous steps S3 and S4 is used for quantitative solution. The resulting integrated maintenance base resource sharing configuration schemes based on different numbers of existing connecting lines are shown in Table 7 below. Two integrated maintenance bases are selected, located at Jiahe Depot and Chisha Depot respectively.

[0221] Table 7

[0222]

[0223]

[0224] This invention, based on the essential analysis of resource sharing optimization in vehicle depots, employs mathematical modeling principles, using the p-media model as a foundation. Considering the network topology and comprehensively taking into account factors such as line type, vehicle type, and connectivity, it establishes a model method that minimizes the total distance for maintenance pickup and delivery. This method satisfies both general constraints for various maintenance resources and specific constraints for four types of resources: overhaul resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources. The final maintenance resource supply points and resource allocation schemes are then determined. This invention effectively analyzes the commonalities and characteristics of different maintenance resources and can serve as a basis for formulating and implementing resource sharing optimization schemes for urban rail transit vehicle depots.

[0225] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for optimizing resource sharing in urban rail transit vehicle depot maintenance, characterized in that, Includes the following steps: Step S1: Analyze the problem of sharing maintenance resources in urban rail transit vehicle depots, and summarize it as a multi-facility site selection-allocation problem; Step S2: Based on the network topology, and taking into account the line system, vehicle type, and connectivity conditions, find the optimal transfer path with the goal of minimizing the transfer distance under feasible conditions. Step S3: Based on the p-media model, and with the objective function of minimizing the weighted sum of the round-trip mileage of all maintenance resources, establish a general constraint model for all maintenance resources; Step S4: Establish unique constraint models for the four types of vehicle base maintenance resources: overhaul resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources, based on their respective operational characteristics. Step S5: Use the solver to solve the constraint model established in steps S3 and S4 to determine the final maintenance resource supply point and maintenance resource allocation scheme. The specific steps for establishing a general constraint model for all maintenance resources in step S3 are as follows: Step S301, setting Represents a set of routes. This represents a set of maintenance resource supply points. Indicates a set of connecting lines. Indicates meeting at the station. Let the set of arcs be represented; This represents the smallest set of demand for a certain maintenance resource. Depending on the type of maintenance resource, it can be a set of lines, a set of stations, or a set of lines between stations. Step S302: The objective function is to minimize the weighted sum of the round-trip mileage of all maintenance resources. The specific expression is as follows: In the formula: ——Maintenance Resource Supply Point b Points of demand for maintenance resources f Weighted sum of round-trip transit distances between the two locations; —The weighting of fixed costs invested in upgrading each depot to a vehicle base, if maintenance resource supply points b For the vehicle depot, take 1; if the maintenance resource supply point... b For parking lots, take the larger value; —0-1 variables, when b The maintenance resource supply points cover the maintenance resource demand points. f When there is a demand, take 1; otherwise, take 0. —Maintenance resource demand points f Scale of maintenance resource demand; ——Maintenance Resource Supply Point b Repair resource demand points f The distance between them; Step S303: Establish constraint one for the correspondence between resource demand points and resource supply points, which respectively represent: the point selected for a demand point must be a maintenance resource supply point; one demand point corresponds to a unique supply point; and a maintenance resource supply point must be responsible for the demand point it belongs to. The expression of constraint one is as follows: In the formula: ——0-1 variables, when b When a vehicle depot is set as a maintenance resource supply point, take 1; otherwise, take 0. —A 0-1 variable, representing the locational relationship between maintenance resource supply points and maintenance resource demand points; when b Location of maintenance resource supply points and maintenance resource demand points f If they match, take 1; otherwise, take 0. Step S304: To ensure that the transfer distance between the maintenance resource demand point and the selected maintenance resource supply point does not exceed a certain upper limit, constraint two is established, which is expressed as follows: In the formula: —Maximum transfer distance for a single transit; Step S305: Set a quantity limit for maintenance resource supply points and establish constraint three. The specific expression of constraint three is as follows: In the formula: —Number of maintenance resource supply points; The specific steps for establishing the unique constraint models for each of the major overhaul resources, engineering vehicle resources, rail welding base resources, and comprehensive maintenance base resources in step S4 are as follows: Step S401, establish a resource-specific constraint model for mainframe repair: the smallest unit of mainframe repair resource demand is the line, and the line... i The expression for calculating the demand for overhaul is shown below: In the formula: --line i Scale of maintenance resource demand; --line i Number of trains assigned; , —Overhaul and maintenance cycle; In the formula: --line i Main frame repair needs / Employees; , —Unbalance coefficient during major overhauls and maintenance; , —Downtime for major overhauls, overhauls, and maintenance; Repair resource supply points b The column size must not exceed a certain upper limit, as shown below: In the formula: ——0-1 variables, when b Maintenance resource supply points cover the lines i When there is a demand, take 1; otherwise, take 0. —Maximum size of a single maintenance resource supply point; Step S402, establish a resource-specific constraint model for engineering vehicles: the smallest unit of engineering vehicle resource demand is the route, and the route... i The expression for calculating the number of days for a single test is shown below: In the formula: --line i Duration of a single engineering vehicle inspection; --line i length; —Working speed of engineering vehicles; —Duration of nighttime operation windows; —Work time reduction factor; Repair resource supply points b The average monthly occupancy time of the engineering vehicles configured at the site must not exceed a certain upper limit, generally taken as 30 days. This constraint is established and expressed as follows: In the formula: —0-1 variables, when b Maintenance resource supply points cover the lines i The value is 1 when there is a need, and 0 otherwise. ——Maintenance Resource Supply Point b line i Duration of a single line switch; —Average number of tests per month; —Average monthly repair time for engineering vehicles; —The upper limit of the average monthly occupancy time of construction vehicles; Step S403, establish a resource-specific constraint model for rail welding bases: For rail welding base resources, the smallest unit of demand is the inter-station track. To facilitate statistics, multiple adjacent inter-station tracks on a line can be merged into arcs, and the rail replacement demand on the arc segment can be calculated: In the formula: —arc segment e The need for track replacement; —arc segment e Large-scale track replacement cycle on the line in question; —arc segment e length; —arc segment e Track changing cycle for small radius curves; --line e Length of the curve with the smaller radius; The constraint on the length of the track covered by a single rail welding base is established, as shown in the following expression: In the formula: ——0-1 variables, when b The arc section of the rail welding base v The value is 1 when there is a need, and 0 otherwise. —The length of track that a single rail welding base is responsible for; Step S404: Establish a resource-specific constraint model for the integrated maintenance base: For integrated maintenance base resources, the maintenance tasks of the equipment are mainly offline maintenance tasks of various line professional systems and equipment, including professional inspection and measurement, professional maintenance, improvement maintenance and fault maintenance of systems and equipment. Equipment maintenance needs under preventative maintenance: In the formula: , , , —The cycle of professional maintenance and inspection for major, medium and minor repairs; , , , —The average number of major overhauls, intermediate overhauls, minor overhauls, and inspections per year; —— Indicates the type of equipment. Indicates the first t The number of devices (devices are configured according to the site); Equipment maintenance needs under fault-based repair: In the formula: ——No. t The equipment in the first u Annual failure rate; ——No. t The equipment in the first u Annual repair volume; —— Indicates the type of equipment. Indicates the first t The number of such devices.

2. The method for optimizing resource sharing in urban rail transit vehicle depot maintenance as described in claim 1, characterized in that, In step S1, the problem of sharing maintenance resources at urban rail transit vehicle depots, namely the selection of maintenance resource supply points and the matching of maintenance resource supply points with maintenance resource demand points, includes the following situations: In the urban rail transit network, all depots are considered maintenance resource supply points; for overhaul resources and engineering vehicle resources, each line is considered a maintenance resource demand point; for rail welding base resources, the inter-station lines are considered maintenance resource demand points; and for line systems and equipment, stations are considered maintenance resource demand points.

3. The method for optimizing resource sharing in urban rail transit vehicle depot maintenance as described in claim 1, characterized in that, The specific steps of step S2 are as follows: Step S201, Input Adjacency Matrix: When calculating the transit distance, the wire network is abstracted into a topological network, denoted as... , where G represents the topology network; V represents a point in the network; E represents an arc in the network, which is a subway line connecting two stations, and the length of the arc is represented by the distance between stations; Establish an adjacency matrix based on the adjacency relationships between points; Step S202: Input the specified vehicle base numbered m and the route numbered i, and search for the vehicle section numbered mm on the route i. Step S203: Determine whether the number of turns p from vehicle section mm to vehicle base m is greater than a pre-set upper limit value M; if it is greater than the upper limit value M, the path search result is empty, and proceed to step 206; if it is less than or equal to the upper limit value M, proceed to step 204. Step S204: Perform the classic k-short path algorithm search; calculate the k-th shortest path between vehicle base numbered m and vehicle segment numbered mm. Step S205, delete redundant points in the path: When the searched path passes through a certain connecting line without changing lines, the connecting line is redundant in the path and is deleted. Step S206: Determine whether the path satisfies the constraints of the number of turns and the transfer distance. If not, let k = k + 1 and go to step S203. If it satisfies, retain the path search result from the vehicle base m to the vehicle section mm. The path search result is the number and order of the points and arcs in the network. Step S207: Determine whether the route type allows the vehicle type assigned to the depot numbered mm to pass through. If not, set k=k+1 and go to step S203; if so, retain the route type result. Step S208: Determine whether all vehicle segments on line i have been traversed. If yes, proceed to step S202. If no, select the shortest path from the retained path results as the transfer path between vehicle base m and line i, and the length of this path is used as the transfer distance. Step S209: Output the transfer route selection results and distance calculation results.

4. The method for optimizing resource sharing in urban rail transit vehicle depot maintenance as described in claim 3, characterized in that, In step S201, the points in the network include connecting lines and depots, wherein the connecting line is represented by the station where it is located, and the depot is represented by the station connected by the depot access line; the weight in the adjacency matrix represents the length of the arc between each point, and if two points are not directly connected, the weight in the adjacency matrix is ​​∞.

5. The method for optimizing resource sharing in urban rail transit vehicle depot maintenance as described in claim 1, characterized in that, The steps in step S5 for determining the final maintenance resource supply point and the maintenance resource allocation plan are as follows: Step S501, optimize resource sharing for overhaul: Using the overhaul resource sharing optimization model established in steps S3 and S4, input the transfer distance obtained in step S2 and perform quantitative solution. Step S502, optimize the resource sharing of engineering vehicles: use the optimization model for resource sharing of engineering vehicles established in steps S3 and S4 to perform quantitative solution; Step S503: Optimize the resource sharing of the rail welding base: Quantitatively solve the resource sharing optimization model of the rail welding base established in steps S3 and S4. Step S504: Optimize resource sharing in the comprehensive maintenance base: Quantitatively solve the resource sharing optimization model established in steps S3 and S4.

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