Wattle damage equipment maintenance scheduling method based on digital twinning and robustness optimization

Abstract

The invention discloses a war damaged equipment maintenance scheduling method based on digital twinning and robustness optimization, and aims to solve the problems that a traditional optimization model is insufficient in adaptability to a battlefield dynamic scene and is incomplete in consideration of risk factors. The method is realized through the following steps: firstly, acquiring a battle damage equipment state, a maintenance unit state and environmental factor data in real time by using a digital twin technology, and constructing a task importance degree, battle damage equipment maintenance time and maintenance unit maneuvering time evaluation model; secondly, a multi-objective optimization function with the maximum comprehensive importance degree and the minimum maximum maintenance time as objectives is established, an uncertainty set of team confrontation intensity, capacity matching coefficients, threat coefficients and fatigue coefficients is constructed, and robustness buffer capacity is introduced for robustness optimization modeling; example verification shows that the method can effectively fuse dynamic data, quantitatively process multiple risks, improve the anti-interference capability and battlefield adaptability of a scheduling scheme, and provide scientific decision support for wartime equipment maintenance support.

Description

Technical Field

[0001] The present invention relates to the field of battle-damaged equipment maintenance scheduling, and specifically to a battle-damaged equipment maintenance scheduling method based on digital twins and robustness optimization. Background Art

[0002] The battlefield situation is ever-changing, and the maintenance and scheduling of damaged equipment must closely follow these changes. Based on real-time combat needs, high-importance equipment must be quickly repaired. Through batch repairs, damaged equipment can gradually recover its performance and enhance overall combat capabilities. Faced with the high demand for wartime equipment maintenance and the limited resources available for equipment maintenance, optimizing the scheduling of repair tasks, utilizing maintenance resources rationally, and allocating repair tasks scientifically, with the goal of maximizing the importance of damaged equipment and minimizing repair time, is crucial for command and decision-making regarding the maintenance and support of damaged equipment.

[0003] Current research on optimizing the scheduling of repair tasks for battle-damaged equipment suffers from the following major shortcomings: First, traditional optimization models lack adaptability to dynamic battlefield scenarios, resulting in insufficient integration of factors influencing the optimal scheduling of equipment maintenance tasks. Second, fluctuations in maintenance time and dynamic changes in importance have not been analyzed based on battlefield dynamics, resulting in incomplete consideration of risk factors in optimizing maintenance tasks. Therefore, a maintenance scheduling method for battle-damaged equipment based on digital twins and robust optimization is proposed to address these issues. Summary of the Invention

[0004] The purpose of the present invention is to provide a maintenance scheduling method for damaged equipment based on digital twins and robust optimization, focusing on solving the problems of insufficient integration of influencing factors and incomplete consideration of risk factors in the optimization scheduling of the above-mentioned equipment maintenance tasks. By integrating multi-source dynamic data and constructing a robust optimization model, efficient scheduling of damage equipment maintenance tasks can be achieved, and the response speed and reliability of battlefield maintenance support can be improved. Through the rapid repair of damage equipment and the optimal allocation of resources, it can better adapt to the dynamically changing equipment maintenance and support needs.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a maintenance scheduling method for damaged equipment based on digital twins and robustness optimization, comprising the following steps:

[0006] S1. Digital twin-driven data collection and modeling: Using digital twin technology, real-time data on damaged equipment status, maintenance unit status, and environmental factors are collected. Mission importance assessment models, collaboration importance assessment models, capability importance assessment models, damaged equipment repair time models, and maintenance unit mobility time models are constructed. The outputs are the importance of damaged equipment, repair time for damaged equipment, and mobility time for maintenance units.

[0007] S2. Multi-objective robustness optimization modeling: A dual-objective optimization function is established. Objective 1 is to maximize the comprehensive importance of damaged equipment, and Objective 2 is to minimize the maximum maintenance unit maintenance time. Hard constraints and soft constraints with penalty terms are set. Hard constraints include maintenance skill matching constraints and unique allocation constraints, and soft constraints include spare parts inventory constraints and threat threshold constraints. An uncertainty set of team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient is constructed, and robust constraints are introduced to cope with parameter fluctuations.

[0008] S3, Discrete Particle Swarm Optimization Solution: Integer coding is used to represent the maintenance allocation plan, the particle swarm is initialized and hard constraints are met, a dual-objective weighted sum is converted into a single-objective fitness function, soft constraint penalty terms are incorporated, particle speed and position are iteratively updated, and the optimal allocation plan is searched based on individual optimality and global optimality;

[0009] S4. Dynamic scheduling and re-optimization: When spare parts inventory falls below the safety threshold, the threat coefficient fluctuates, or new combat-damaged equipment is added, the re-optimization process is triggered to update data, reconstruct the model, and solve a new allocation plan.

[0010] Based on the above, in step S1, the battle damaged equipment status data includes: il is the lth fault type of the i-th battle-damaged equipment. According to the equipment's composition structure and common fault types, the wartime equipment damage types are classified into four categories: D il = {1, 2, 3, 4}, 1 is power failure, 2 is electronic failure, 3 is communication failure, 4 is navigation failure; r il The minimum skill required to repair the lth type of failure of the i-th battle-damaged equipment; u il The number of spare parts of type l required to repair the i-th damaged equipment; P i is the geographical location of the i-th damaged equipment after the damage, N i The number of equipment in the team where the i-th damaged equipment is performing the task; γ i The intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the task γ i ∈[0,1], the value increases from low to high, and the intensity of the confrontation gradually increases; θ i is the threat coefficient when repairing the i-th damaged equipment, θ i ∈[0,1];

[0011] The maintenance unit status data includes: jl is the skill level of the jth maintenance unit in repairing the lth fault type, S jl ∈[0,1],S jl is a matrix. The larger the value, the higher the skill level of the maintenance unit and the more mature the technology.j is the current position of the jth maintenance unit V j is the moving speed of the jth maintenance unit; f j is the fatigue influence coefficient of the jth maintenance unit, which is determined by the comprehensive time used by the maintenance unit. The longer the comprehensive time, the greater the fatigue influence coefficient of the maintenance unit; is the safety stock of the sth type of spare parts;

[0012] The environmental factor data include: TR is the threat level, TR = {1, 2, 3}, 1 is low threat, 2 is medium threat, 3 is threat;

[0013] The task importance evaluation model is:

[0014]

[0015] in, is the mission importance of the i-th damaged equipment, N i is the number of equipment in the group where the i-th damaged equipment is located, γ i is the intensity of the confrontation of the group where the i-th damaged equipment belongs;

[0016] The collaborative importance evaluation model is a collaborative importance matrix C obtained by training historical data. ik =[c ik ] m×m , c ik represents the synergy importance of damaged equipment i and k, c ik ∈[0,1];

[0017] The capability importance evaluation model is:

[0018]

[0019] in, is the capability importance of the i-th damaged equipment; η i is the capability level of the i-th damaged equipment; δ i The matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities;

[0020] The repair time model of damaged equipment is: according to the acquired damage type D il , output fault detection time T i detection =f(D il ), Output spare parts disassembly time T i disassemble =f(D il ), output spare parts replacement time T i replace=f(D il );

[0021] The maintenance unit maneuvering time model is: according to the maintenance unit position information Damaged equipment location information Maintenance unit maneuvering speed V j , calculate the maintenance unit maneuvering time dist(P i ,P j ) is the distance from the maintenance unit to the damaged equipment.

[0022] Based on the above, in step S2, the objective function 1 is to maximize the comprehensive importance:

[0023]

[0024] 1≤i≤m,1≤j≤n

[0025]

[0026] φ1+φ2+φ3=1

[0027] Where: m is the total number of damaged equipment; n is the total number of repair units; x ij is a decision variable, indicating whether the j-th maintenance unit repairs the i-th damaged equipment, 1 for repair and 0 for no repair; is the comprehensive importance of the i-th damaged equipment; The importance of the task performed by the team of the i-th damaged equipment in the overall task; is the comprehensive coordination importance of the i-th damaged equipment; is the capability importance of the i-th damaged equipment; the weights of the three importances φ1, φ2, and φ3 are 0.3, 0.3, and 0.4 respectively; σ I is the standard deviation of the importance of damaged equipment, λ is the adjustment coefficient of the standard deviation of the importance of damaged equipment, usually 0.5;

[0028] The objective function 2 is to minimize the maintenance time of the largest maintenance unit:

[0029]

[0030] 1≤i≤m,1≤j≤n

[0031]

[0032] Where: m is the total number of battle-damaged equipment; n is the total number of repair units; The total time it takes for the jth maintenance unit to repair the ith damaged equipment; T idetection is the inspection time required for the i-th damaged equipment; T i disassemble T is the time required to disassemble the spare parts of the i-th damaged equipment; i assemble The time required to replace spare parts for the i-th damaged equipment; f is the total maneuvering time required by the jth maintenance unit to repair the damaged equipment it is responsible for; j is the fatigue influence coefficient of the jth maintenance unit during maintenance; θ i is the threat coefficient when repairing the i-th damaged equipment; the time is in minutes;

[0033] The hard constraints include: the maintenance skill of the maintenance unit should be greater than the minimum skill requirement for damaged equipment:

[0034]

[0035] Where: S jl The skill level of the jth maintenance unit in repairing the lth fault type, r il The minimum skill requirement for repairing the lth type of failure of the i-th battle-damaged equipment, r il ∈[0,1];

[0036] Each damaged equipment can only be repaired by one repair unit:

[0037]

[0038] The soft constraints include: the total number of spare parts required for all damaged equipment cannot exceed the spare parts inventory:

[0039]

[0040] Where: u il The number of spare parts of type l required to repair the i-th battle-damaged equipment; is the safety stock of the sth type of spare parts; s is the excess quantity allowed for the sth type of spare parts, ξ s ≥0, the penalty term is O1, which is included in the objective function;

[0041] The total threat level of all maintenance units during maintenance cannot exceed the tolerable threat threshold:

[0042]

[0043] in: is the security threat threshold that the j-th maintenance unit can bear, ζ jis the safety threat limit allowed for the jth maintenance unit, ζ j ≥0, the penalty term is O2, which is included in the objective function;

[0044] The robustness optimization constructs an uncertainty set to describe the fluctuation range of the team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient:

[0045]

[0046] in: The fluctuation range of the intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the mission; The lowest confrontation intensity; The highest confrontation intensity; The fluctuation range of the matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; is the minimum matching coefficient; is the highest matching coefficient; is the fluctuation range of the threat coefficient when repairing the i-th damaged equipment; The lowest threat factor; The highest threat factor; The fluctuation range of fatigue coefficient of the jth maintenance unit; is the lowest fatigue coefficient; is the highest fatigue coefficient;

[0047] Robustness constraints:

[0048]

[0049] Where: Z4 is the completion time of the optimal solution; is the baseline completion time of the optimized solution; Δz is the robustness buffer, determined by digital twin simulation, such as the worst case calculated by 100 Monte Carlo simulations.

[0050] Based on the above, in step S3, the discrete particle swarm algorithm process includes: discrete particle encoding: integer encoding is used, each particle represents a maintenance allocation plan, the length is the number of damaged equipment m, and each element is the maintenance unit number j∈{1,2,…,n};

[0051] Initialize the particle swarm: Generate S initial particles, each particle must meet the hard constraint maintenance skill matching: If the randomly generated allocation does not satisfy the constraint, the maintenance units are reallocated until the condition is satisfied;

[0052] The weighted summation of the two objectives is transformed into a single objective: Fit = ω1·Max Z1+ω2·Min Z2. When the spare parts inventory exceeds the limit or the total threat exceeds the limit, the excess part needs to be penalized, which are O1 and O2 respectively. The total fitness is Fit1 = ω1·Max Z1+ω2·Min Z2-O1-O2.

[0053] Particle speed and position update: For each particle, if the current fitness is better than the historical optimal fitness, then update pbest; for the entire population, if a particle's fitness is better than the global optimal, then update gbest;

[0054] After reaching the maximum number of iterations, the iteration stops and the allocation scheme corresponding to gbest is output as the optimal solution.

[0055] Based on the above, in step S4, the dynamic scheduling and re-optimization process includes: when the spare parts inventory is lower than the safety threshold, the threat coefficient fluctuates, and new damaged equipment is added, the re-optimization process is started; the re-optimization process is: collecting the parameters of the damaged equipment and the status of the maintenance unit under the new situation; recalculating the importance and maintenance time, adjusting the soft constraint threshold; introducing a new uncertainty set, and solving the mixed integer programming problem.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The present invention provides a method for scheduling maintenance of damaged equipment based on digital twins and robust optimization, which can achieve the following three effects: First, it uses digital twins to map battlefield uncertainties in real time, re-optimizes allocation plans according to combat scenario requirements, and solves the problem of insufficient adaptability of traditional optimization models to dynamic scenarios; second, the robust optimization framework can quantify and process multiple risks such as dynamic changes in importance and fluctuations in maintenance time, making the scheduling of maintenance of damaged equipment more in line with battlefield reality; third, it combines the real-time simulation capabilities of digital twins with the global optimization capabilities of PSO, incorporates robust constraints, and improves the anti-interference ability of the scheduling plan. Based on the dynamic changes in the battlefield situation, the present invention anticipates possible new situations and dynamically adjusts and optimizes the allocation plan, so that maintenance scheduling and resource allocation are closely aligned with battlefield reality, making them more reasonable and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is the overall flow chart of the battle-damaged equipment maintenance and scheduling of the present invention;

[0059] Figure 2 The particle swarm algorithm flow chart of the present invention;

[0060] Figure 3 This is a re-optimization flow chart of the present invention. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0062] like Figure 1 As shown in FIG, a maintenance scheduling method for damaged equipment based on digital twins and robustness optimization includes the following steps:

[0063] S1. Digital Twin-Driven Data Collection and Modeling: Digital twin technology is used to collect real-time data on damaged equipment status, maintenance unit status, and environmental factors. Models are constructed for task importance assessment, collaboration importance assessment, capability importance assessment, damaged equipment repair time, and maintenance unit maneuver time. Outputs are generated for damaged equipment importance, damaged equipment repair time, and maintenance unit maneuver time.

[0064] S2. Multi-Objective Robust Optimization Modeling: A dual-objective optimization function is established. Objective 1 is to maximize the comprehensive importance of damaged equipment, and Objective 2 is to minimize the maximum repair unit repair time. Hard constraints and soft constraints with penalty terms are set. Hard constraints include maintenance skill matching constraints and unique allocation constraints, while soft constraints include spare parts inventory constraints and threat threshold constraints. An uncertainty set is constructed for team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient, and robust constraints are introduced to address parameter fluctuations.

[0065] S3. Discrete Particle Swarm Optimization Solution: Integer encoding is used to represent the maintenance allocation plan. The particle swarm is initialized and ensures that hard constraints are met. A weighted sum of two objectives is converted into a single-objective fitness function, incorporating soft constraint penalty terms. Particle velocities and positions are iteratively updated, and the optimal allocation plan is searched for based on individual and global optima.

[0066] S4. Dynamic Scheduling and Re-Optimization: When spare parts inventory falls below the safety threshold, the threat coefficient fluctuates, or new combat-damaged equipment is added, the re-optimization process is triggered to update data, reconstruct the model, and solve a new allocation plan.

[0067] In S1, the digital twin-driven data collection and modeling methods include:

[0068] Battle damaged equipment status data includes: D il is the lth fault type of the i-th battle-damaged equipment. According to the equipment's composition structure and common fault types, the wartime equipment damage types are classified into four categories: D il = {1, 2, 3, 4}, 1 is power failure, 2 is electronic failure, 3 is communication failure, 4 is navigation failure; r il The minimum skill required to repair the lth type of failure of the i-th battle-damaged equipment; u ilThe number of spare parts of type l required to repair the i-th battle-damaged equipment; P i is the geographical location of the i-th damaged equipment after the damage, N i The number of equipment in the team where the i-th damaged equipment is performing the task; γ i The intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the task γ i ∈[0,1], the value increases from low to high, and the intensity of the confrontation gradually increases; θ i is the threat coefficient when repairing the i-th damaged equipment, θ i ∈[0,1].

[0069] Maintenance unit status data includes: S jl S is the skill level of the jth maintenance unit in repairing the lth fault type, jl ∈[0,1],S jl is a matrix. The larger the value, the higher the skill level of the maintenance unit and the more mature the technology. j is the current position of the jth maintenance unit V j is the moving speed of the jth maintenance unit; f j is the fatigue influence coefficient of the jth maintenance unit, which is determined by the comprehensive time used by the maintenance unit. The longer the comprehensive time, the greater the fatigue influence coefficient of the maintenance unit; is the safety stock of the sth spare part type.

[0070] Environmental factor data include: θ i is the threat coefficient when repairing the i-th battle-damaged equipment, TR is the threat level, TR = {1, 2, 3}, 1 is low threat, 2 is medium threat, and 3 is threat.

[0071] The task importance evaluation model is:

[0072]

[0073] in, is the mission importance of the i-th damaged equipment, N i is the number of equipment in the group where the i-th damaged equipment is located, γ i is the intensity of the confrontation of the team where the i-th damaged equipment belongs.

[0074] The collaborative importance evaluation model is: the collaborative importance matrix C obtained through historical data training ik =[c ik ] m×m , c ik represents the synergy importance of damaged equipment i and k, c ik ∈[0,1].

[0075] The capability importance evaluation model is:

[0076]

[0077] in, is the capability importance of the i-th damaged equipment; η i is the capability level of the i-th damaged equipment; δ i The matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities.

[0078] The repair time model of damaged equipment is: According to the acquired damage type D il , output fault detection time T i detection =f(D il ), Output spare parts disassembly time T i disassemble =f(D il ), output spare parts replacement time T i replace =f(D il );

[0079] The maintenance unit maneuvering time model is: according to the maintenance unit location information Damaged equipment location information Maintenance unit maneuvering speed V j , calculate the maintenance unit maneuvering time dist(P i ,P j ) is the distance from the maintenance unit to the damaged equipment.

[0080] In S2, the methods for multi-objective robustness optimization modeling include:

[0081] Objective function 1 is to maximize the comprehensive importance:

[0082]

[0083] 1≤i≤m,1≤j≤n

[0084]

[0085] φ1+φ2+φ3=1

[0086]

[0087] Where: x ij is a decision variable, indicating whether the j-th maintenance unit repairs the i-th damaged equipment, 1 for repair and 0 for no repair; is the comprehensive importance of the i-th damaged equipment; The importance of the task performed by the team of the i-th damaged equipment in the overall task; N i is the number of equipment in the group where the i-th damaged equipment belongs; γ i is the intensity of the confrontation of the group where the i-th damaged equipment belongs; is the comprehensive coordination importance of the i-th damaged equipment, C ik is the synergy importance between the kth damaged equipment and the ith damaged equipment, which is effective only when the damaged equipment k is assigned to the maintenance unit j; is the capability importance of the i-th damaged equipment; η i is the capability level of the i-th damaged equipment; δ i is the matching coefficient between the mission performed by the i-th damaged equipment and its own capability. The combat capability of the equipment must match the capability requirements of the current combat mission. The higher the matching degree, the higher the capability level of the equipment itself and the higher the capability importance of the equipment. φ1, φ2, and φ3 are the weights of the three importances, which are 0.3, 0.3, and 0.4 respectively. σ I is the standard deviation of importance of battle-damaged equipment, is the average importance of damaged equipment, which is used to control the distribution balance; λ is the standard deviation adjustment coefficient of the importance of damaged equipment, which is usually 0.5.

[0088] Objective function 2 is to minimize the maintenance time of the largest maintenance unit:

[0089]

[0090] 1≤i≤m,1≤j≤n

[0091]

[0092]

[0093] Wherein: time is in minutes; The total time it takes for the jth maintenance unit to repair the ith damaged equipment; T i detection is the inspection time required for the i-th damaged equipment; t d,il T is the time required to detect the lth type of fault of the i-th damaged equipment; i disassemble is the time required to disassemble spare parts of the i-th damaged equipment; t da,il The time required to disassemble a single spare part for the lth type of failure of the i-th battle-damaged equipment; u il The number of spare parts of type l required to repair the i-th damaged equipment; T i assemble is the spare parts replacement time required for the i-th damaged equipment; t r,ilThe replacement time of a single spare part for the lth type of failure of the i-th battle-damaged equipment; The total maneuvering time required for the jth maintenance unit to repair the damaged equipment it is responsible for; is the geographical location of the i-th damaged equipment, in kilometers; is the geographical location of the jth maintenance unit, in kilometers; v j f is the maneuvering speed of the jth maintenance unit during maintenance, in minutes / kilometers; j is the fatigue influence coefficient of the jth maintenance unit during maintenance; θ i is the threat coefficient when repairing the i-th battle-damaged equipment, TR is the threat level, TR = {1, 2, 3}, 1 is low threat, 2 is medium threat, and 3 is threat.

[0094] Hard constraints include:

[0095] The repair skill of the repair unit should be greater than the minimum skill required for damaged equipment:

[0096]

[0097] Where: S jl The skill level of the jth maintenance unit in repairing the lth fault type, r il The minimum skill requirement for repairing the lth type of failure of the i-th battle-damaged equipment, r il ∈[0,1].

[0098] Each damaged equipment can only be repaired by one repair unit:

[0099]

[0100] Soft constraints include:

[0101] The total number of spare parts required for all battle-damaged equipment cannot exceed the spare parts inventory:

[0102]

[0103] Where: u il The number of spare parts of type l required to repair the i-th battle-damaged equipment; is the safety stock of the sth type of spare parts; s is the excess quantity allowed for the sth type of spare parts, ξ s ≥0, the penalty term is O1, which is included in the objective function.

[0104] The total threat level of all maintenance units during maintenance cannot exceed the tolerable threat threshold:

[0105]

[0106] in: is the security threat threshold that the j-th maintenance unit can bear, ζ j is the safety threat limit allowed for the jth maintenance unit, ζ j ≥0, the penalty term is O2, which is included in the objective function.

[0107] Robustness optimization:

[0108] Construct an uncertainty set to describe the fluctuation range of team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient:

[0109]

[0110] in: The fluctuation range of the intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the mission; The lowest intensity of confrontation between the team and the enemy when the i-th damaged equipment is performing the mission; The highest intensity of confrontation between the team and the enemy when the i-th damaged equipment is performing the mission; The fluctuation range of the matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; The minimum matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; The highest matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; is the fluctuation range of the threat coefficient when repairing the i-th damaged equipment; is the minimum threat coefficient of the i-th battle-damaged equipment; is the highest threat coefficient of the i-th battle-damaged equipment; The fluctuation range of fatigue coefficient of the jth maintenance unit; is the minimum fatigue coefficient of the jth maintenance unit; is the highest fatigue coefficient of the jth maintenance unit.

[0111] Robustness constraints:

[0112]

[0113] Where: Z4 is the completion time of the optimal solution; is the baseline completion time of the optimized solution; Δz is the robustness buffer, determined by digital twin simulation, such as the worst case calculated by 100 Monte Carlo simulations.

[0114] In S3, such as Figure 2 , the discrete particle swarm optimization solution methods include:

[0115] Discrete particle encoding: Integer encoding is used. Each particle represents a maintenance allocation scheme. The length is the number of damaged equipment m. Each element is the maintenance unit number j∈{1,2,…,n}. For example, particle X=[1,2,1,3,…] means that the first damaged equipment is assigned to maintenance unit 1, the second to maintenance unit 2, and so on.

[0116] Initialize the particle swarm: Generate S initial particles, where S is the population size, usually 100. Each particle must meet hard constraint 1 and maintenance skill matching: If the randomly generated allocation does not satisfy the constraint, the maintenance units are reallocated until the condition is satisfied.

[0117] Objective function and fitness calculation: transform the weighted sum of the two objectives into a single objective

[0118] Fit=ω1·MaxZ1+ω2·MinZ2

[0119] Where: weight coefficient, ω1+ω2=1, set according to actual needs, ω1=0.5, ω2=0.5.

[0120] Soft constraint penalty:

[0121] When the spare parts inventory exceeds the limit, the penalty for excess is:

[0122]

[0123] Where: u il The number of spare parts of type l required to repair the i-th battle-damaged equipment; is the safety stock of the sth type of spare parts; s is the excess quantity allowed for the sth type of spare parts, ξ s ≥0, the penalty term is O1, which is included in the objective function.

[0124] When the total threat exceeds the limit, the penalty for the excess amount is:

[0125]

[0126] Where: θ i is the threat coefficient when repairing the i-th damaged equipment, θ i ∈[0,1]; is the security threat threshold that the j-th maintenance unit can bear, ζ j is the safety threat limit allowed for the jth maintenance unit, ζ j ≥0, the penalty term is O2, which is included in the objective function.

[0127] Total fitness:

[0128] Fit1=ω1·MaxZ1+ω2·MinZ2-O1-O2

[0129] Iterative optimization: Binary PSO or integer PSO is used for speed update. The speed formula is:

[0130]

[0131] Where: ω is the inertia weight, c1 and c2 are learning factors, and r1, r2∈[0,1] are random numbers.

[0132] Position update: Map the speed to probability through the sigmoid function to decide whether to change the maintenance unit allocation.

[0133]

[0134] Where: r3∈[0,1] is a random number that ensures that the allocation always satisfies the maintenance skill constraint.

[0135] Individual best (pbest) and global best (gbest): For each particle, if the current fitness is better than the historical best fitness, pbest is updated; for the entire population, if the fitness of a particle is better than the global best, gbest is updated.

[0136] Iteration termination conditions: reaching the maximum number of iterations, such as 200, or gbest has not been updated for several consecutive generations, or the fitness of all particles converges to the preset threshold.

[0137] Output result: The allocation plan corresponding to gbest is the optimal solution. Verify the soft constraints. If the soft constraints exceed the limit, adjust the penalty item and optimize again.

[0138] In S4, as Figure 3 , dynamic scheduling and re-optimization methods include:

[0139] When spare parts inventory falls below the safety threshold, the threat coefficient fluctuates, or new equipment is damaged in combat, the re-optimization process is initiated. The re-optimization steps are as follows:

[0140] Data update: Digital twin collects new battle damage equipment parameters in real time (D il ,r il ,μ il ,P i ,N i ,γ i ,θ i ); Update the maintenance unit status, fatigue f i , number of spare parts used, current task progress, etc.

[0141] Model Reconstruction: Recalculate all equipment and Adjust soft constraint thresholds, such as the allowable value for excess spare parts ξ j Increase or decrease, etc.

[0142] Robust reoptimization: Based on the current battlefield environment, a new uncertainty set Γ′ is introduced. A mixed integer programming problem is solved based on the information to balance the importance of damaged equipment with the repair time. A new allocation matrix is ​​output based on hard constraints, soft constraints, and robustness constraints.

[0143] Example 2: A preferred embodiment:

[0144] In a certain local confrontation, 10 of our equipment were damaged. Assuming that each damaged equipment had only one type of fault, 3 maintenance units were arranged to carry out emergency repairs. It was required to use digital twins and robust optimization models to optimize the scheduling of maintenance support tasks for the damaged equipment. The digital twins of the damaged equipment and the maintenance unit have been generated, and the collaborative importance matrix between the damaged equipment has been constructed through the digital twin model. Now it is necessary to solve the model using a particle swarm algorithm to generate an initial plan. Based on the constraints and scenario requirements, the initial maintenance task plan is optimized and adjusted to achieve efficient maintenance of the damaged equipment. Assuming that the threat safety threshold of the maintenance unit is 1.0, ζ s is 0, ζ j is 0.

[0145] (1) Initial data

[0146] Battle-damaged equipment parameters (10 items)

[0147]

[0148] Maintenance unit parameters (3)

[0149]

[0150] Added 3 parameters for battle-damaged equipment

[0151]

[0152] Battle-damaged equipment coordination importance matrix

[0153] E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E1 0 0.4 0.2 0 0.7 0 0.1 0 0 0 0 0 0 E2 0.4 0 0.3 0 0.3 0 0 0 0 0.8 0 0 0.3 E3 0.2 0.3 0 0 0 0 0.6 0 0 0 0 0 0 E4 0 0 0 0 0.5 0 0 0 0.8 0 0 0.6 0 E5 0.7 0.3 0 0 0 0 0.3 0 0 0 0 0 0 E6 0 0 0 0.5 0 0 0 0.4 0.4 0 0.4 0 0 E7 0.1 0 0.6 0 0.3 0 0 0 0 0 0 0 0 E8 0 0 0 0 0 0.4 0 0 0.7 0 0 0 0 E9 0 0 0 0.8 0 0.4 0 0.7 0 0 0.3 0 0 E10 0 0.8 0 0 0 0 0 0 0 0 0 0 0 E11 0 0 0 0 0 0.4 0 0 0.3 0 0 0.2 0 E12 0 0 0 0.6 0 0 0 0 0 0 0.2 0 0.2 E13 0 0.3 0 0 0 0 0 0 0 0 0 0.2 0

[0154] (2) Initial distribution plan:

[0155] Allocation strategy: prioritize equipment with high overall importance, ensure that maintenance unit skills meet hard constraints, and allow soft constraints to exceed but record penalties. The allocation results are shown in the table below:

[0156]

[0157] (3) Re-optimization allocation schemes under three scenarios

[0158] Scenario 1: Spare parts over-adjustment

[0159] Emergency: Maintenance units A and B were hit while performing their tasks, and their spare parts safety stocks were reduced to [2,3,0,0] and [2,6,0,0] respectively. After spare parts replenishment, they became [4,5,0,0] and [3,7,7,0].

[0160] Adjustment strategy: Prioritize retaining high-importance equipment, abandon low-importance equipment with serious excess spare parts, such as E5 and E8, and reallocate some equipment to other units to balance inventory. The allocation results are shown in the table below:

[0161]

[0162] Scenario 2: Threat Over-Value Adjustment

[0163] Emergency: The maintenance unit is suddenly attacked by the enemy, and the threat to the overall maintenance operation increases. The safety thresholds of the three maintenance units are adjusted to 0.4, 0.7, and 0.7 respectively. Maintenance unit B is a backbone member of the maintenance force and the security threat needs to be given special consideration.

[0164] Adjustment strategy: Prioritize allocating low-threat equipment to repair unit B to meet the threat threshold. Equipment with high threat coefficients, such as E9 with a threat coefficient of 0.4, can be removed from the repair order without B and reallocated to units with lower threat coefficients or abandoned. The allocation results are shown in the table below:

[0165]

[0166] Scene 3: New Equipment

[0167] Emergency: Three new pieces of important damaged equipment have suddenly appeared, numbered E11-E13. The relevant parameters have been given. These three new pieces of damaged equipment need to be repaired first.

[0168] Adjustment strategy: Rebalance spare parts inventory and threat thresholds, allowing some old equipment to remain unrepaired. The allocation results are shown in the table below:

[0169]

[0170] (4) Comparison of final results

[0171] Scenario Total importance Maximum maintenance time (minutes) Total excess spare parts Total Threat Excess Initial distribution 13.20 233.16 5 0 Spare parts excess adjustment 10.08 186.34 1 0 Threat Overvalue Adjustment 10.91 201.12 4 0.1 New equipment adjustments 14.52 245.54 11 0

[0172] (5) Conclusion: First, spare parts excess adjustment: by abandoning low-importance equipment E5 and E8, spare parts excess is reduced by 80%, the maximum maintenance time is reduced by 20.1%, but the total importance is slightly reduced. Second, threat excess adjustment: remove the equipment E9 with a high threat coefficient from the maintenance order B and reallocate it to the maintenance unit with lower threat, but some maintenance units still have threat excess, and further adjustment or abandonment of some damaged equipment maintenance is required according to actual conditions. Third, new equipment adjustment: the total importance is increased by 10%, but the maintenance time and spare parts excess increase, indicating that the newly added important damaged equipment requires more maintenance resources. Fourth, the impact of standard deviation: the total importance decreases after adjustment, reflecting the impact of distribution balance on comprehensive effectiveness. The larger the standard deviation in the scenario, the greater the decrease in total importance after adjustment, indicating that the importance distribution of damaged equipment in the scenario is more unbalanced. Fifth, comprehensive trade-off: the adjustment of spare parts and threat constraints comes at the expense of some importance, while the new equipment scenario needs to prioritize high-importance tasks and allow moderate excess to maintain combat effectiveness.

Claims

1. A maintenance scheduling method for damaged equipment based on digital twins and robustness optimization, characterized in that: The following steps are involved: S1. Digital twin-driven data collection and modeling: Using digital twin technology, real-time data on damaged equipment status, maintenance unit status, and environmental factors are collected. Mission importance assessment models, collaboration importance assessment models, capability importance assessment models, damaged equipment repair time models, and maintenance unit mobility time models are constructed. The outputs are the importance of damaged equipment, repair time for damaged equipment, and mobility time for maintenance units. S2. Multi-objective robustness optimization modeling: A dual-objective optimization function is established. Objective 1 is to maximize the comprehensive importance of damaged equipment, and Objective 2 is to minimize the maximum maintenance unit maintenance time. Hard constraints and soft constraints with penalty terms are set. Hard constraints include maintenance skill matching constraints and unique allocation constraints, and soft constraints include spare parts inventory constraints and threat threshold constraints. An uncertainty set of team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient is constructed, and robust constraints are introduced to cope with parameter fluctuations. S3, Discrete Particle Swarm Optimization Solution: Integer coding is used to represent the maintenance allocation plan, the particle swarm is initialized and hard constraints are met, a dual-objective weighted sum is converted into a single-objective fitness function, soft constraint penalty terms are incorporated, particle speed and position are iteratively updated, and the optimal allocation plan is searched based on individual optimality and global optimality; S4. Dynamic scheduling and re-optimization: When spare parts inventory falls below the safety threshold, the threat coefficient fluctuates, or new combat-damaged equipment is added, the re-optimization process is triggered to update data, reconstruct the model, and solve a new allocation plan.

2. The method for maintenance scheduling of battle-damaged equipment based on digital twins and robustness optimization according to claim 1 is characterized by: In step S1, the battle damaged equipment status data includes: il is the lth fault type of the i-th battle-damaged equipment. According to the equipment's composition structure and common fault types, the wartime equipment damage types are classified into four categories: D il = {1, 2, 3, 4}, 1 is power failure, 2 is electronic failure, 3 is communication failure, 4 is navigation failure; r il The minimum skill required to repair the lth type of failure of the i-th battle-damaged equipment; u il The number of spare parts of type l required to repair the i-th damaged equipment; P i is the geographical location of the i-th damaged equipment after the damage, N i The number of equipment in the team where the i-th damaged equipment is performing the task; γ i The intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the task γ i ∈[0,1], the value increases from low to high, and the intensity of the confrontation gradually increases; θ i is the threat coefficient when repairing the i-th damaged equipment, θ i ∈[0,1]; The maintenance unit status data includes: jl S is the skill level of the jth maintenance unit in repairing the lth fault type, jl ∈[0,1],S jl is a matrix. The larger the value, the higher the skill level of the maintenance unit and the more mature the technology. j is the current position of the jth maintenance unit V j is the moving speed of the jth maintenance unit; f j is the fatigue influence coefficient of the jth maintenance unit, which is determined by the comprehensive time used by the maintenance unit. The longer the comprehensive time, the greater the fatigue influence coefficient of the maintenance unit; is the safety stock of the sth type of spare parts; The environmental factor data include: TR is the threat level, TR = {1, 2, 3}, 1 is low threat, 2 is medium threat, 3 is threat; The task importance evaluation model is: in, is the mission importance of the i-th damaged equipment, N i is the number of equipment in the group where the i-th damaged equipment is located, γ i is the intensity of the confrontation of the group where the i-th damaged equipment belongs; The collaborative importance evaluation model is a collaborative importance matrix C obtained by training historical data. ik =[c ik ] m×m , c ik represents the synergy importance of damaged equipment i and k, c ik ∈[0,1]; The capability importance evaluation model is: in, is the capability importance of the i-th damaged equipment; η i is the capability level of the i-th damaged equipment; δ i The matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; The repair time model of damaged equipment is: according to the acquired damage type D il , output fault detection time Output spare parts removal time Output spare parts replacement time The maintenance unit maneuvering time model is: according to the maintenance unit position information Battle-damaged equipment location information Maintenance unit maneuvering speed V j , calculate the maintenance unit maneuvering time dist(P i ,P j ) is the distance from the maintenance unit to the damaged equipment.

3. The method for maintenance scheduling of battle-damaged equipment based on digital twin and robustness optimization according to claim 1 is characterized by: In step S2, the objective function 1 is to maximize the comprehensive importance: Where: m is the total number of damaged equipment; n is the total number of repair units; x ij is a decision variable, indicating whether the j-th maintenance unit repairs the i-th damaged equipment, 1 for repair and 0 for no repair; is the comprehensive importance of the i-th damaged equipment; The importance of the task performed by the team of the i-th damaged equipment in the overall task; is the comprehensive coordination importance of the i-th damaged equipment; is the capability importance of the i-th damaged equipment; the weights of the three importances φ1, φ2, and φ3 are 0.3, 0.3, and 0.4 respectively; σ I is the standard deviation of the importance of damaged equipment, λ is the adjustment coefficient of the standard deviation of the importance of damaged equipment, usually 0.5; The objective function 2 is to minimize the maintenance time of the largest maintenance unit: Where: m is the total number of battle-damaged equipment; n is the total number of repair units; The total time taken by the jth maintenance unit to repair the ith battle-damaged equipment; is the inspection time required for the i-th damaged equipment; The time required to remove spare parts from the i-th damaged equipment; The time required to replace spare parts for the i-th damaged equipment; f is the total maneuvering time required by the jth maintenance unit to repair the damaged equipment it is responsible for; j is the fatigue influence coefficient of the jth maintenance unit during maintenance; θ i is the threat coefficient when repairing the i-th damaged equipment; the time is in minutes; The hard constraints include: the maintenance skill of the maintenance unit should be greater than the minimum skill requirement for damaged equipment: Where: S jl The skill level of the jth maintenance unit in repairing the lth fault type, r il The minimum skill requirement for repairing the lth type of failure of the i-th battle-damaged equipment, r il ∈[0,1]; Each damaged equipment can only be repaired by one repair unit: The soft constraints include: the total number of spare parts required for all damaged equipment cannot exceed the spare parts inventory: Where: u il The number of spare parts of type l required to repair the i-th battle-damaged equipment; is the safety stock of the sth type of spare parts; s is the excess quantity allowed for the sth type of spare parts, ξ s ≥0, the penalty term is O1, which is included in the objective function; The total threat level of all maintenance units during maintenance cannot exceed the tolerable threat threshold: in: is the security threat threshold that the j-th maintenance unit can bear, ζ j is the safety threat limit allowed for the jth maintenance unit, ζ j ≥0, the penalty term is O2, which is included in the objective function; The robustness optimization constructs an uncertainty set to describe the fluctuation range of the team confrontation intensity, capability matching coefficient, threat coefficient, and fatigue coefficient: in: The fluctuation range of the intensity of the confrontation between the team and the enemy when the i-th damaged equipment is performing the mission; The lowest confrontation intensity; The highest confrontation intensity; The fluctuation range of the matching coefficient between the task performed by the i-th damaged equipment and the equipment's own capabilities; is the minimum matching coefficient; is the highest matching coefficient; is the fluctuation range of the threat coefficient when repairing the i-th damaged equipment; The lowest threat factor; The highest threat factor; The fluctuation range of fatigue coefficient of the jth maintenance unit; is the lowest fatigue coefficient; is the highest fatigue coefficient; Robustness constraints: Where: Z4 is the completion time of the optimal solution; is the baseline completion time of the optimized solution; Δz is the robustness buffer, determined by digital twin simulation, such as the worst case calculated by 100 Monte Carlo simulations.

4. The method for maintenance scheduling of battle-damaged equipment based on digital twin and robustness optimization according to claim 1 is characterized in that: In step S3, the discrete particle swarm algorithm process includes: discrete particle encoding: integer encoding is used, each particle represents a maintenance allocation plan, the length is the number of damaged equipment m, and each element is the maintenance unit number j∈{1,2,…,n}; Initialize particle swarm: Generate S initial particles, each particle must meet the hard constraint maintenance skill matching: S jl ≥r il ·x ij , If the randomly generated allocation does not satisfy the constraint, the maintenance units are reallocated until the condition is satisfied; The weighted summation of the two objectives is transformed into a single objective: Fit = ω1·MaxZ1 + ω2·MinZ2. When the spare parts inventory exceeds the limit or the total threat exceeds the limit, the excess part needs to be penalized, which are O1 and O2 respectively. The total fitness is Fit1 = ω1·MaxZ1 + ω2·MinZ2 - O1 - O2. Particle speed and position update: For each particle, if the current fitness is better than the historical optimal fitness, then update pbest; for the entire population, if a particle's fitness is better than the global optimal, then update gbest; After reaching the maximum number of iterations, the iteration stops and the allocation scheme corresponding to gbest is output as the optimal solution.

5. The method for maintenance scheduling of battle-damaged equipment based on digital twin and robustness optimization according to claim 1 is characterized by: In step S4, the dynamic scheduling and re-optimization process includes: when the spare parts inventory is lower than the safety threshold, the threat coefficient fluctuates, and new damaged equipment is added, the re-optimization process is started; the re-optimization process is: collecting the parameters of the damaged equipment and the status of the maintenance unit under the new situation; recalculating the importance and maintenance time, adjusting the soft constraint threshold; introducing a new uncertainty set, and solving the mixed integer programming problem.

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