A Bi-objective Optimization Design Method for Contact Suspension Based on Hierarchical Constraints and Mixed Variables

Abstract

This invention discloses a dual-objective optimization design method for contact suspension based on hierarchical constraints and mixed variables, comprising: determining the optimization design parameters of the contact suspension system, including continuous and discrete variables; establishing a pantograph-catenary dynamic simulation model and a pantograph-catenary electrical simulation model, obtaining mechanical current collection performance indicators and electrical current collection performance indicators based on the models, and synthesizing current collection performance evaluation indicators through weighted aggregation; taking the contact wire, catenary, droppers, and electrical connection as key components of the contact suspension affecting pantograph-catenary current collection and system lifespan, performing transient thermo-structural coupling analysis, and taking the minimum component lifespan as the contact suspension system lifespan; establishing a dual-objective optimization model for current collection performance and lifespan, and solving the optimization model using an improved NSGA-II type multi-objective evolutionary algorithm; the calculation results of this invention are more in line with engineering practice, ensuring the effectiveness of the contact suspension parameter optimization results.

Description

Technical Field

[0001] This invention relates to the field of contact suspension system optimization design technology, and more specifically, to a contact suspension dual-objective optimization design method based on hierarchical constraints and mixed variables. Background Technology

[0002] The contact suspension system is a key component of the traction power supply system in electrified railways, mainly comprising components such as the contact wire, catenary, droppers, and electrical connections. Its function is to continuously provide high-quality electrical energy to electric locomotives via the pantograph. The geometry, mechanical parameters, and electrical characteristics of the contact suspension system directly affect the pantograph-catenary dynamic current collection performance and the system's service life. With the continuous increase in train operating speeds and traffic density, the contact suspension system faces the dual requirements of high current collection quality and long service life, making its design increasingly challenging.

[0003] The existing contact suspension system design technology has the following shortcomings: (1) The current collection performance evaluation only focuses on mechanical indicators and does not include electrical current collection characteristics, and lacks a scientific weighting mechanism that integrates mechanical and electrical indicators; (2) The component life evaluation does not take into account the electromechanical-thermal multi-field coupling effect, and the prediction model is not accurate enough; (3) A dual-objective optimization model and corresponding solution algorithm that balances current collection performance and component life have not yet been established, making it difficult to obtain the optimal design scheme that takes into account both current collection quality and service life. Therefore, it is urgent to propose a contact suspension system design method that can comprehensively evaluate electromechanical current collection performance, accurately predict component life under the action of multiple physical fields, and achieve the best balance between the two objectives through multi-objective optimization, so as to make up for the shortcomings of the existing technology. Summary of the Invention

[0004] This invention addresses the challenges of narrow feasible domains in contact suspension optimization, design parameters containing a mixture of continuous and discrete variables, existing optimization methods that struggle to balance pantograph-catenary current collection electrical performance with the lifespan of multiple components, and the tendency for the population to generate numerous individuals violating hard safety constraints. The invention constructs a dual-objective framework for current collection performance and system bottleneck lifespan; it hierarchically assigns constraints and dynamically switches constraint dominance modes based on the proportion of feasible solutions in the population; it employs an evolutionary operator adapted to the mixed variables and introduces constraint-aware local search in the later stages of iteration, outputting a set of Pareto solutions that satisfy both soft and hard constraints, thus achieving an optimized design that balances current collection performance and the overall lifespan of the contact suspension system.

[0005] Specifically, this invention provides a bi-objective optimization design method for contact suspension based on hierarchical constraints and mixed variables, comprising the following steps:

[0006] S1. Determine the optimal design parameters of the contact suspension system, including continuous variables and discrete variables;

[0007] S2. Establish pantograph-catenary dynamics simulation model and pantograph-catenary electrical simulation model, and obtain mechanical current collection performance indicators based on the models. Electrical current collection performance indicators And by weighted synthesis of current collection performance evaluation index ;

[0008] S3. The contact wire, catenary, droppers and electrical connection are regarded as key components of the contact suspension that affect the pantograph-catenary current collection and system life. The mechanical load and electrical load time history of the key components are extracted, and transient thermal-structural coupling analysis is performed to obtain the life of different components. The minimum value among them is taken as the life of the contact suspension system L.

[0009] S4. A dual-objective optimization model for current collection performance and contact suspension life is established, with the dual objectives of maximizing the current collection performance evaluation index Q and maximizing the contact suspension life L. The improved NSGA-II type multi-objective evolutionary algorithm is then used to solve the optimization model. The solution method includes the following steps:

[0010] Set the population size, maximum number of generations, crossover probability, mutation probability, crossover distribution index, and mutation distribution index for different combinations of contact suspension system design parameters, and randomly generate the initial parent population P0.

[0011] Calculate the proportion of individuals in the current population that satisfy all safety hard constraints. If this proportion is less than a threshold... If the target value is selected, the safety-first domination mode is activated; otherwise, the full-constraint domination mode is activated. The population is then sorted into non-dominated groups according to the selected domination mode. For individuals within the same non-dominated frontier, the crowding distance after sorting based on the target value is calculated.

[0012] Construct a mating pool. Each time, randomly select two individuals from the parent population with replacement, prioritizing individuals with lower non-dominant rank; if the ranks are the same, select individuals with larger crowding distance; repeat the selection until a mating pool of size N is obtained.

[0013] Mixed crossover and mixed mutation are performed on individuals in the mating pool to generate offspring populations; among them, the continuous variable part adopts simulated binary crossover and multinomial mutation, and the discrete variable part adopts integer difference crossover and integer value neighborhood reset mutation based on binomial distribution.

[0014] Merge the parent and offspring populations, sort them according to non-dominance level and crowding distance, and truncate and retain N individuals to form a new generation population;

[0015] When the proportion of individuals in the population that satisfy the hard safety constraints meets the threshold At that time, a constraint-aware local search is performed on the 2-3 feasible individuals with the smallest crowding distance in the non-dominated front. The new individuals that satisfy all constraints and are not dominated by the original individuals are then put back into the population to replace the original individuals.

[0016] When the maximum number of generations is reached, the set of non-dominated individuals in the final population that satisfy all constraints is output as the Pareto optimal design set that takes into account both flow performance and system lifetime.

[0017] Furthermore, the optimization model also includes multiple constraints, which are divided into hard safety constraints and soft performance constraints. The hard safety constraints include maximum contact force ≤ 400N, maximum contact line stress ≤ 500Mpa, and maximum positioning point lifting amount ≤ 200mm. The soft performance constraints include current collection performance evaluation index ≥ 0.7 and contact suspension life ≥ 10 years.

[0018] When the proportion of individuals in the population that can satisfy the safety hard constraint does not exceed the threshold When the population enters a safety-first dominance mode, individual dominance analysis is not performed using soft performance constraints. Through population iteration, the number of individuals meeting the hard safety constraints gradually increases. When the proportion of individuals in the population that meet the hard safety constraints reaches a threshold... Then, it enters the full-constraint mode, activating all constraints to perform individual dominance analysis.

[0019] Furthermore, when performing non-dominated sorting of the population according to the selected dominance pattern, the dominance rule is as follows:

[0020] Under the safety-first domination mode, the domination rules are as follows:

[0021] Individual p dominates individual q if and only if (1) p satisfies all hard safety constraints while q does not; or (2) neither satisfies hard safety constraints and p violates the hard safety constraints less than q; or (3) both satisfy all hard safety constraints and p achieves Pareto domination over q based on target index Q and index L.

[0022] Under the fully constrained domination mode, the domination rule is as follows:

[0023] Individual p dominates individual q if and only if (1) p satisfies all constraints while q does not; or (2) neither satisfies all constraints, and p's violation of all constraints is less than q's; or (3) both satisfy all constraints and p achieves Pareto domination of q based on target index Q and index L.

[0024] Furthermore, the degree of violation of individual safety hard constraints Defined as ,like If the condition is met, the individual is a safe and feasible individual; otherwise, the individual is a safe and infeasible individual.

[0025] Total constraint violation rate of individuals Defined as ,like If the condition is met, the individual is a feasible individual; otherwise, the individual is an infeasible individual.

[0026] in , , , , These represent the normalized constraint forms for contact force, contact line stress, positioning point lift, current collection performance evaluation index, and contact suspension life, respectively.

[0027] Furthermore, the constraint-aware local search is defined as follows: when the proportion of individuals in the population that satisfy the safety hard constraints meets a threshold... At that time, select 2-3 feasible individuals with the smallest crowding distance from the first-level non-dominated frontier as local search targets, and apply a small perturbation of 2% of the variable range to the j-th continuous variable one by one. The gradients of Q and L with respect to continuous variables are calculated by finite difference. The search is performed along the weighted synthesis direction of the two. The compensation search step size is set to 5% of the corresponding continuous variable value range. If the new individual satisfies all constraints and is not dominated by the original individual Pareto, then the original individual is replaced.

[0028] Furthermore, the optimization model is as follows:

[0029] ;

[0030] In the formula, Find(x) represents the 7-dimensional decision vector to be solved; Maximize represents multi-objective maximization; Subject represents the 5 inequality constraints that must be strictly satisfied. represent ;T con For the contact line tension, T mes Where S is the tension of the load-bearing cable, S is the contact suspension span, and d is the tension of the load- dro For the spacing of the dropper arrangement, A con Let A be the cross-sectional area of ​​the contact wire. mes d is the cross-sectional area of ​​the load-bearing cable. ele For electrical connection installation location; Q min As the minimum permissible current collection performance evaluation index, L min For the minimum permissible contact suspension life, and These are the maximum contact force for an individual and the maximum contact force allowed by the circuit design, respectively. and These are the maximum individual contact wire stress and the maximum allowable stress of the contact wire in the circuit design, respectively. and These are the maximum individual positioning point elevation and the maximum positioning point elevation allowed by the line design, respectively. and These represent the lower and upper limits of the optimal design parameter variation for the contact suspension system, respectively.

[0031] Furthermore, step S3 includes:

[0032] Obtain the equivalent stress that changes over time. ,temperature and current density amplitude Where k=1 refers to the contact wire, k=2 refers to the catenary wire, k=3 refers to the dropper, and k=4 refers to the electrical connection.

[0033] The fatigue life N of contact wires, catenary wires, droppers, and electrical connections under different load cycles is calculated using material fatigue life formulas that consider the effects of temperature and current. k,f :

[0034] ;

[0035] Where, N k,0 , m represents the material fatigue parameter under normal temperature and no current conditions;

[0036] Temperature correction function In the formula, T k,0 For laboratory reference temperature, K k,t This refers to the temperature influence coefficient of the material.

[0037] Current density correction function In the formula, J k,0 The nominal current density, It is an accelerating factor for electrical damage;

[0038] Using rainflow counting method to statistically analyze different equivalent stresses With temperature T k Current density amplitude J k The number of load cycles n under the combination k,i Calculate the total damage D according to Miner's rule. k :

[0039]

[0040] in, Represents a specific equivalent force With temperature T k Current amplitude J k The number of life cycles of components in a combination;

[0041] Based on the number of trains passing through N annually train Obtain annual cumulative damage D k,year =D k ×N train Calculate the lifespan of components ;

[0042] The lifespan L of the contact suspension system is taken as the shortest lifespan of the critical component in the contact suspension system.

[0043] ;

[0044] In the formula, L1 is the contact wire life, L2 is the catenary wire life, L3 is the dropper life, and L4 is the electrical connection life.

[0045] Furthermore, step S2 includes:

[0046] S201. Build a pantograph-catenary dynamics simulation model. Obtain dynamic contact force, pantograph head displacement, positioning point lift, and pantograph-catenary decoupling rate through pantograph-catenary dynamics simulation. Based on the obtained parameters, calculate the mechanical current collection performance index Q. mech calculate;

[0047] ;

[0048] in, For average contact force, For the standard deviation of contact force, and These are the maximum and minimum contact forces, respectively. For bow and fire net offline rate, This represents the range of vertical displacement of the bow head. The maximum lifting amount of the contact wire positioning point; g1, g2, g3, g4, g5, and g6 are the normalization functions of each parameter; All are weighting coefficients;

[0049] S202. Construct a pantograph-catenary electrical simulation model. Utilize the pantograph-catenary electrical simulation data and combine it with the dynamic contact resistance influenced by dynamic contact force, current, and temperature to obtain the electrical current collection performance index Q. elec ;

[0050] ;

[0051] Among them, the coefficient of variation of dynamic contact resistance , The standard deviation of dynamic contact resistance. Average dynamic contact resistance; current collection efficiency , where P train P is the active power received by the pantograph. subThe active power output by the traction substation;

[0052] S203, Based on the obtained mechanical current collection performance index Q mech and electrical current collection performance index Q elec Weighted composite current collection performance evaluation index ,in, These are the weighting coefficients, and .

[0053] Furthermore, in step S4, the method for calculating the crowding distance based on the target value ranking for individuals within the same non-dominated frontier is as follows:

[0054] In the same non-dominated frontier Fr k Within the k-th level non-dominated frontier, after sorting each individual in descending order according to the target values ​​Q and L, the crowding distance d of the i-th individual is calculated. ki :

[0055] ;

[0056] In the formula, and These are the values ​​of the i-th individual after sorting according to the target value Q, and the values ​​of the previous and next individuals. and These are the values ​​of the i-th individual after sorting according to the target value L, and the values ​​of the i-th individual before and after it. and The maximum and minimum values ​​of target Q within the current non-dominant frontier level. and The maximum and minimum values ​​of target L within the current non-dominated frontier level are given, and the crowding distance of boundary individuals after sorting according to target values ​​Q and L is set to infinity.

[0057] Furthermore, the optimized design parameters of the contact suspension system in step S1 include continuous variables such as contact wire tension, catenary tension, contact suspension span, and dropper arrangement spacing, as well as discrete variables such as contact wire cross-sectional area, catenary cross-sectional area, and electrical connection installation position.

[0058] The beneficial technical effects of this invention are as follows:

[0059] (1) This invention addresses the problem that traditional constrained multi-objective algorithms have fixed dominance rules throughout the process and do not adaptively switch. It adopts a hierarchical constraint processing strategy, which focuses on satisfying safety hard constraints in the early stage of evolution to quickly enter the engineering feasible region, and then activates performance soft constraints in the later stage. This conforms to the design logic of prioritizing safety and taking performance into account, which significantly improves the search efficiency of feasible solutions and the engineering rationality of the optimization process. It can balance constraint satisfaction and objective optimization, avoid a large number of infeasible individuals crowding out the population in the early stage, and also avoid excessive conservatism and loss of optimal solutions in the later stage.

[0060] (2) This invention addresses the issue that the contact suspension parameters contain both continuous and discrete variables. The common non-dominated sorting genetic algorithm-II (NSGA-II) with elitist strategy only adapts to continuous variables by default. In engineering, discrete variables are often treated as continuous, resulting in invalid solutions. This invention designs special integer difference crossover and neighborhood mutation for discrete variables, which fundamentally solves the problem of invalid solutions and search oscillation caused by real number rounding, and ensures the stable transmission of genetic information.

[0061] (3) The constraint-aware local search of the present invention uses gradient information to fine-tune the Pareto front in the later stage of evolution, which accelerates convergence and improves the accuracy of the front.

[0062] (4) Compared with the traditional fatigue life model that only considers mechanical stress, the temperature-current dual correction life model of the present invention introduces both temperature correction function and current density correction function, taking into account the weakening effect of temperature rise on material performance and the current-induced electric fatigue acceleration effect. It is more in line with the service characteristics of mechanical-thermal-electric multi-field coupling of the pantograph-catenary system, and can realize the synergistic consideration of electrical current collection performance and component fatigue life, identify the weak links of the system under thermal-electric coupling, and provide quantitative support for the design and operation and maintenance of contact suspension.

[0063] (5) Unlike the fixed contact resistance processing method commonly used in pantograph-catenary simulation, the dynamic contact resistance model of the present invention, which is a force-electric-thermal coupling model, fully considers the mechanical-electrical-thermal multi-physics field coupling effect of the pantograph-catenary system. It can reflect the influence of dynamic contact force fluctuation, traction current magnitude and contact point temperature rise on contact resistance in real time. It can reproduce the contact resistance degradation behavior under poor current collection conditions, making the calculation results of electrical current collection performance evaluation index more in line with engineering reality and ensuring the effectiveness of the contact suspension parameter optimization results. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating the contact suspension dual-objective optimization design method based on hierarchical constraints and mixed variables provided in an embodiment of the present invention. Detailed Implementation

[0065] Example 1

[0066] Figure 1 This is a flowchart illustrating the bi-objective optimization design method for contact suspension based on hierarchical constraints and mixed variables provided in this embodiment of the invention; as shown below. Figure 1 As shown, this embodiment discloses a bi-objective optimization design method for contact suspension based on hierarchical constraints and mixed variables, including the following steps:

[0067] S1. Determine the optimal design parameters of the contact suspension system, including contact wire tension, catenary tension, contact suspension span, dropper arrangement spacing, contact wire cross-sectional area, catenary cross-sectional area, and electrical connection installation position.

[0068] It should be noted that, in this application, the optimized design parameters of the contact suspension system include continuous variables such as contact wire tension, catenary tension, contact suspension span, and dropper arrangement spacing, as well as discrete variables such as contact wire cross-sectional area, catenary cross-sectional area, and electrical connection installation position. Among these seven design parameters, contact wire tension, catenary tension, contact suspension span, contact wire cross-sectional area, and catenary cross-sectional area directly affect the wave propagation speed of the contact suspension, thereby affecting the current draw and vibration state when the pantograph contacts the overhead contact line, and consequently affecting the lifespan of components and the system. The dropper arrangement spacing affects the current draw and vibration state when the pantograph contacts the overhead contact line by influencing the elasticity within the span, thereby affecting the lifespan of the dropper itself. The electrical connection installation position mainly affects the state of the pantograph when it passes its installation position and the lifespan of the electrical connection itself. Furthermore, contact wire tension, catenary tension, contact suspension span, dropper arrangement spacing, contact wire cross-sectional area, catenary cross-sectional area, and electrical connection installation position are also key components of the contact suspension system; therefore, they are determined to be the optimized design parameters of the contact suspension system.

[0069] S2. Establish pantograph-catenary dynamics simulation model and pantograph-catenary electrical simulation model, and obtain mechanical current collection performance indicators based on the models. Electrical current collection performance indicators And by weighted synthesis of current collection performance evaluation index ,in These are the weighting coefficients, and ;

[0070] S201. Build a pantograph-catenary dynamics simulation model. The simulation model is verified by EN50318. The dynamic contact force, pantograph head displacement, positioning point lift, and pantograph-catenary disconnection rate are obtained through pantograph-catenary dynamics simulation. Based on the obtained parameters, the mechanical current collection performance index is calculated.

[0071] Mechanical current collection performance index Q mech The following calculations were performed:

[0072] ;

[0073] in, For average contact force, For the standard deviation of contact force, and These are the maximum and minimum contact forces, respectively. For bow and fire net offline rate, This represents the range of vertical displacement of the bow head. This represents the maximum lifting amount of the overhead contact line positioning point;

[0074] In this embodiment, the sampling time period is divided according to the pantograph passing through a whole anchor section at the line running speed; a whole anchor section is generally 1400m, and the current running speed of high-speed rail pantographs is generally 250~400km / h, so the time period is 12.6~20.16s; the average contact force is the statistical average of the dynamic contact force within the sampling time period; the maximum and minimum contact forces are the statistical maximum and minimum values ​​within the sampling time period; the pantograph-catenary disconnection rate is the proportion of time during which the dynamic contact force is zero within the sampling time period to the total time; the vertical displacement range of the pantograph head is the maximum vertical displacement of the pantograph head minus the minimum vertical displacement within the time period, and both the maximum and minimum displacements are obtained by statistically analyzing the vertical displacement time history data of the pantograph head obtained through simulation; the maximum lifting amount of the contact wire positioning point is the maximum lifting amount of all positioning points within the entire anchor section, which is obtained by statistically analyzing the lifting amount data of all positioning points within the entire anchor section after simulation.

[0075] g1, g2, g3, g4, g5, and g6 are the normalization functions for each parameter, taking values ​​in the range [0, 1].

[0076] ;

[0077] in, This represents the maximum allowable dynamic average contact force for a specific circuit design, typically expressed as 0.00097 × V. 2 +70 is calculated, where V is the maximum designed operating speed of the line, in km / h; , These represent the maximum and minimum dynamic contact force allowed for a specific line design, respectively. The minimum value is generally required to be >0, while the maximum value is related to the maximum operating speed. This represents the pantograph-catenary disconnection rate allowed for a specific line design. This represents the allowable vertical displacement of the bow head for a specific line design. This represents the maximum allowable lifting of the contact wire positioning points for a specific railway line. , , All are related to the maximum operating speed of the line;

[0078] All are weight coefficients, obtained through the analytic hierarchy process (AHP), and ;

[0079] S202. Build a pantograph-catenary electrical simulation model in MATLAB / Simulink, and use the pantograph-catenary electrical simulation data and dynamic contact resistance affected by dynamic contact force, current and temperature to obtain electrical current collection performance indicators.

[0080] Electrical current collection performance index Q elec Calculated using the dynamic contact resistance variation coefficient and current collection efficiency:

[0081] ;

[0082] Among them, the coefficient of variation of dynamic contact resistance , The standard deviation of dynamic contact resistance. The average dynamic contact resistance; current collection efficiency. , where P train P is the active power received by the pantograph. sub The active power output of the traction substation is obtained through pantograph-catenary electrical simulation;

[0083] The detailed calculation method for dynamic contact resistance, which is affected by dynamic contact force, current, and temperature, is as follows:

[0084] ;

[0085] In the formula, For dynamic contact resistance, The dynamic contact force of the pantograph and the contact wire is represented by K and n, which are contact constants related to the current taking in between the pantograph slide and the contact wire. The values ​​are different for different pantograph slides and contact wires and can be calibrated by experiments. In this embodiment, K is 0.08 and n is 0.5. This is a correction factor for the current effect. Temperature effect correction factor:

[0086] ;

[0087] ;

[0088] In the formula, I(t) is the real-time current value. The current effect correction factor is set to 0.0025, I0 is the reference current (500A), and T(t) is the real-time temperature value. The temperature effect correction factor is set to 0.004, and T0 is the reference temperature, set to 20℃.

[0089] The real-time temperature value is obtained by iteratively solving the heat balance equation using the lumped heat capacity method:

[0090] ;

[0091] In the formula, The equivalent heat capacity at the pantograph-catenary contact point is taken as 50 J / ℃. Let V be the coefficient of friction between the bow-head slide plate and the contact wire, taken as 0.3; V represent the maximum designed operating speed of the track; and h be the air convection heat dissipation coefficient, taken as 25 W / (m²).2 ·℃), A s To achieve effective heat dissipation area, T amb The ambient temperature;

[0092] S203, Based on the obtained mechanical current collection performance index Q mech and electrical current collection performance index Q elec Weighted composite current collection performance evaluation index ,in, The weighting coefficients and Since the mechanical vibration between the pantograph and the contact suspension directly affects operational safety, the weight of mechanical current collection performance needs to be higher than that of electrical current collection performance. This can be considered. The value is 0.7. The value is 0.3;

[0093] S3. The contact wire, catenary, droppers and electrical connection are regarded as key components of the contact suspension that affect the pantograph-catenary current collection and system life. The mechanical load and electrical load time history of the key components are extracted, and transient thermal-structural coupling analysis is performed to obtain the life of different components. The minimum value among them is taken as the life of the contact suspension system L.

[0094] Based on the simulation results of the pantograph-catenary dynamics simulation model and the pantograph-catenary electrical simulation model, mechanical and electrical load data of the contact wire, catenary, droppers, and electrical connections are extracted. Transient thermo-structural coupling analysis is performed, using the current-induced thermal effects of the mechanical and electrical loads as boundaries, to obtain the equivalent stress that varies with time. ,temperature and current density amplitude Where k=1 refers to the contact wire, k=2 refers to the catenary wire, k=3 refers to the dropper, and k=4 refers to the electrical connection.

[0095] The fatigue life N of contact wires, catenary wires, droppers, and electrical connections under different load cycles is calculated using material fatigue life formulas that consider the effects of temperature and current. k,f :

[0096]

[0097] Where, N k,0 , m represents the material fatigue parameter under normal temperature and no current conditions;

[0098] Temperature correction function In the formula, T k,0 For laboratory reference temperature, K k,t This refers to the temperature influence coefficient of the material.

[0099] Current density correction function In the formula, Jk,0 The nominal current density, It is an accelerating factor for electrical damage;

[0100] Using rainflow counting method to statistically analyze different equivalent stresses With temperature T k Current density amplitude J k The number of load cycles n under the combination k,i Calculate the total damage D according to Miner's rule. k :

[0101]

[0102] in, Represents a specific equivalent force With temperature T k Current amplitude J k The number of life cycles of components in a combination;

[0103] According to the design documents, the estimated annual train throughput N train Obtain annual cumulative damage D k,year =D k ×N train Calculate the lifespan of components ;

[0104] The lifespan L of the contact suspension system is taken as the lifespan of the shortest critical component in the contact suspension system, that is:

[0105] ;

[0106] In the formula, L1 is the contact wire life, L2 is the catenary wire life, L3 is the dropper life, and L4 is the electrical connection life.

[0107] S4. A dual-objective optimization model is established, with the maximization of the current collection performance evaluation index Q and the maximization of the contact suspension life L as the two objectives. An improved NSGA-II type multi-objective evolutionary algorithm is then used to solve the optimization model, obtaining a set of Pareto optimal design schemes that balance current collection performance and system life. Detailed steps are as follows:

[0108] S401. Establish a dual-objective optimization model for current collection performance and lifespan. The optimization model takes maximizing the current collection performance evaluation index Q and maximizing the contact suspension lifespan L as its dual objectives, and also includes multiple constraints. Specifically, the optimization model is as follows:

[0109] ;

[0110] In the formula, Find(x) represents the 7-dimensional decision vector to be solved, and the optimal combination of these 7 design parameters is found through optimization algorithm; Maximize represents multi-objective maximization, which pursues the maximization of two core performance indicators while satisfying constraints; Subject represents the 5 inequality constraints that must be strictly satisfied to ensure the safety and feasibility of the design scheme. represent ;T con For the contact line tension, T mes Where S is the tension of the load-bearing cable, S is the contact suspension span, and d is the tension of the load-bearing cable. dro For the spacing of the dropper arrangement, A con Let A be the cross-sectional area of ​​the contact wire. mes d is the cross-sectional area of ​​the load-bearing cable. ele For electrical connection installation location; Q min As the minimum permissible current collection performance evaluation index, L min For the minimum permissible contact suspension life, and These are the maximum contact force for an individual and the maximum contact force allowed by the circuit design, respectively. and These are the maximum individual contact wire stress and the maximum allowable stress of the contact wire in the circuit design, respectively. and These are the maximum individual positioning point elevation and the maximum positioning point elevation allowed by the line design, respectively. and These represent the lower and upper limits of the optimal design parameter variation for the contact suspension system, respectively.

[0111] Furthermore, in this application, the multiple constraints of the optimization model are divided into safety hard constraints and performance soft constraints. Specifically, the safety hard constraints include maximum contact force ≤ 400N, maximum contact line stress ≤ 500Mpa, and maximum positioning point lifting amount ≤ 200mm. The performance soft constraints include current collection performance evaluation index ≥ 0.7 and contact suspension system life ≥ 10 years.

[0112] The normalized form of each index in the hard safety constraints is as follows:

[0113] ;

[0114] in, , , These represent the normalized constraint forms for contact force, contact line stress, and positioning point lift in a hard safety constraint, respectively.

[0115] The normalized form of each index in the soft performance constraint is as follows:

[0116] ;

[0117] in, , These represent the normalized constraint forms for the current-collecting performance evaluation index and the lifespan of the contact suspension system, respectively, in the soft constraint of performance.

[0118] Individual safety hard constraint violation Defined as ,like If the constraint violation is met, the individual is considered safe and feasible; otherwise, the individual is considered unsafe and infeasible. The total constraint violation rate of an individual... Defined as ,like If the condition is met, the individual is a feasible individual; otherwise, the individual is an infeasible individual.

[0119] Set a safe and feasible ratio threshold The value is 0.8. When the proportion of individuals in the population that can satisfy the hard safety constraints does not exceed the safe and feasible proportion threshold, the population enters the safety priority domination mode and does not include the performance soft constraints for individual domination analysis. Through population iteration, the number of individuals that meet the hard safety constraints gradually increases. When the proportion of individuals in the population that can satisfy the hard safety constraints reaches the safe and feasible proportion threshold, the population enters the full constraint mode and activates all 5 constraint indicators to conduct individual domination analysis.

[0120] S402. Set the population size N=30, maximum number of generations G=15, and crossover probability p for different combinations of contact suspension system design parameters. c =0.9, mutation probability p m =0.1, Cross-distribution index Variation distribution index Within the parameter boundary range of the design parameter combination of the contact suspension system, 30 individuals are randomly generated to form the initial parent population P0;

[0121] In the safety-first domination mode, non-dominated sorting is performed. First, all individuals that meet the safety hard constraints are assigned to the better frontier. Individuals that do not meet the safety hard constraints are assigned to the subsequent frontier based on the number of feasible individuals they are dominated by. The goal of this stage is to rapidly increase the proportion of feasible hard constraints.

[0122] Under the safety-first domination model, the rule for individual p to dominate individual q is that one of the following conditions is met:

[0123] ;

[0124] Identify all individuals in the current population that are not dominated by any other individual, classify them as the first-level non-dominated frontier Fr1, and assign them the rank i. rank =1;

[0125] Temporarily remove individuals from the first-level non-dominated front from the population, update the constraint dominance relationships of the remaining individuals, and find all individuals that are not dominated by any other individuals to form the second-level non-dominated front Fr2, assigning it the level i. rank =2;

[0126] Repeat the above process until all individuals in the population have been assigned to the non-dominated frontier Fr. k Assign level i rank =k;

[0127] In the same non-dominated frontier Fr k Within the k-th level non-dominated frontier, after sorting each individual in descending order according to the target values ​​Q and L, the crowding distance d of the i-th individual is calculated. ki :

[0128] ;

[0129] In the formula, and These are the values ​​of the i-th individual after sorting according to the target value Q, and the values ​​of the previous and next individuals. and These are the values ​​of the i-th individual after sorting according to the target value L, and the values ​​of the i-th individual before and after it. and The maximum and minimum values ​​of target Q within the current non-dominant frontier level. and The maximum and minimum values ​​of target L within the current non-dominant frontier level are set to the maximum and minimum values, and the crowding distance of boundary individuals after sorting according to the target values ​​Q and L is set to infinity.

[0130] From the current parent generation P t In each step, two random individuals p and q are randomly selected and replaced. The selection is then performed according to the following rules to increase the probability of selecting a feasible solution that satisfies the safety hard constraints:

[0131] ;

[0132] In the formula, p.rank and q.rank represent the non-dominated frontier ranks of random individuals p and q, respectively; p.crowding and q.crowding represent the crowding distances of random individuals p and q, respectively.

[0133] Repeat the above process, prioritizing individuals that meet all safety hard constraints to enter the mating pool, until 30 individuals are selected to form the mating pool;

[0134] Two random individuals were selected from the mating pool as parent variables. and Generate a random number r in the interval [0, 1].c If r c ≤p c If r c >p c Directly set the child variable and equal to parent variable and , ;

[0135] When performing hybrid crossover, the continuous variable design parameters of the contact suspension system are generated using simulated binary crossover (SBX) and polynomial mutation. The simulated binary crossover is based on the parent variables of two random individuals. and Generate offspring variables using the following formula :

[0136] ;

[0137] In the formula, the offspring variable Offspring variables including 2 random individuals and ; , These are the expansion factors of two random individuals of a continuous variable, consisting of a random number u in the interval [0, 1] and a crossover index. If u ≤ 0.5, then ,otherwise j takes the values ​​1, 2, 3, and 4, which represent the four continuous variable optimization design parameters of the contact suspension system, respectively.

[0138] Using polynomial mutation to mutate the offspring variable Generate a random number r in the interval [0, 1]. m If r m ≤p m Then, executing the following formula will include the variable... Mutation into mutated offspring variables If r m >p m offspring variables Invariable:

[0139]

[0140] In the formula, The variation amplitude parameter is generated by random numbers. and variation distribution index If r < 0.5, then ,otherwise, ;

[0141] After the design parameters of each continuous variable for an individual are variated, the parameters are checked and truncated using constraint boundaries to obtain the final continuous variable design parameters for the individual. :

[0142] ;

[0143] Here, fix means to truncate and round the value within the parentheses;

[0144] For discrete variable optimization design parameters of the contact suspension system: for parent variables and ,like offspring variables and The following formula is used to generate the parameters, where j takes values ​​of 5, 6, and 7, representing the three discrete-variable optimization design parameters of the contact suspension system:

[0145] ;

[0146] In the formula, , These are the expansion factors of two random individuals of the discrete variable, respectively, and are determined by a binomial distribution. Sampling determination; This indicates that the value in parentheses is rounded to the nearest integer.

[0147] For the generated child discrete variables and Determine if it belongs to discrete variables The range in which it is located Generate a random number r in the interval [0, 1]. m If r m ≤p m Then the discrete variables of the offspring are reset to Otherwise, the discrete variables of the offspring are reset to If the size of the discrete variable of the offspring is exactly equal to Then reset to If the size of the discrete variable of the offspring is exactly equal to Then reset to ;in, This represents the kth available value within the range of values ​​for the j-th discrete variable;

[0148] Repeat the above process until 30 child variables are generated;

[0149] Merge parent generation P t With offspring C t A temporary population R of size 2N is formed. t , for R tThe safety priority ranking and crowding degree calculation are performed again, and the top N individuals are selected in order of level and crowding distance to form the new generation parent P. t+1 ;

[0150] S403. When the proportion of individuals in the population that can meet the safety hard constraints reaches the safety feasible proportion threshold of 0.8, the population enters the full constraint mode and activates all 5 constraint indicators to jointly perform individual dominance analysis.

[0151] Under full constraint mode, the constraint dominance relationship between individuals is defined for any two individuals p and q:

[0152] ;

[0153] If neither exists It does not exist. If p and q are mutually exclusive, then p and q are said to be mutually exclusive; where, Symbols representing dominance;

[0154] Identify all individuals in the current population that are not dominated by any other individual, classify them as the first-level non-dominated frontier Fr1, and assign them the rank i. rank =1;

[0155] Temporarily remove individuals from the first-level non-dominated front from the population, update the constraint dominance relationships of the remaining individuals, and find all individuals that are not dominated by any other individuals to form the second-level non-dominated front Fr2, assigning it the level i. rank =2;

[0156] Repeat the above process until all individuals in the population have been assigned to the non-dominated frontier Fr. k Assign level i rank =k;

[0157] In the same non-dominated frontier Fr k Within the k-th level non-dominated frontier, after sorting each individual in descending order according to the target values ​​Q and L, the crowding distance d of the i-th individual is calculated. ki :

[0158] ;

[0159] In the formula, and These are the values ​​of the i-th individual after sorting according to the target value Q, and the values ​​of the previous and next individuals. and These are the values ​​of the i-th individual after sorting according to the target value L, and the values ​​of the i-th individual before and after it. and The maximum and minimum values ​​of target Q within the current non-dominant frontier level. and The maximum and minimum values ​​of target L within the current non-dominant frontier level are set to the maximum and minimum values, and the crowding distance of boundary individuals after sorting according to the target values ​​Q and L is set to infinity.

[0160] From the current parent generation P t In each step, two random individuals p and q are randomly selected and replaced. The selection is then performed according to the following rules to increase the probability of selecting a feasible solution that satisfies all constraints:

[0161] ;

[0162] In the formula, p.rank and q.rank represent the non-dominated frontier ranks of random individuals p and q, respectively; p.crowding and q.crowding represent the crowding distances of random individuals p and q, respectively.

[0163] Repeat the above process until 30 individuals are selected to form a mating pool;

[0164] Two random individuals were selected from the mating pool as parent variables. and Generate a random number r in the interval [0, 1]. c If r c ≤p c If r c >p c Directly set the child variable and equal to parent variable and , ;

[0165] When performing hybrid crossover, the continuous variable design parameters of the contact suspension system are generated using simulated binary crossover (SBX) and polynomial mutation. The simulated binary crossover is based on the parent variables of two random individuals. and Generate offspring variables using the following formula :

[0166] ;

[0167] In the formula, the offspring variable Offspring variables including 2 random individuals and ; , These are the expansion factors of two random individuals of a continuous variable, consisting of a random number u in the interval [0, 1] and a crossover index. If u ≤ 0.5, then ,otherwise j takes the values ​​1, 2, 3, and 4, which represent the four continuous variable optimization design parameters of the contact suspension system, respectively.

[0168] Using polynomial mutation to mutate the offspring variable Generate a random number r in the interval [0, 1]. m If r m ≤p m Then, executing the following formula will include the variable... Mutation into mutated offspring variables If r m >p m offspring variables Invariable:

[0169] ;

[0170] In the formula, The variation amplitude parameter is generated by random numbers. and variation distribution index If r < 0.5, then ,otherwise, ;

[0171] After the design parameters of each continuous variable for an individual are variated, the parameters are checked and truncated using constraint boundaries to obtain the final continuous variable design parameters for the individual. :

[0172] ;

[0173] Here, fix means to truncate and round the value within the parentheses;

[0174] For discrete variable optimization design parameters of the contact suspension system: for parent variables and ,like offspring variables and The following formula is used to generate the parameters, where j takes values ​​of 5, 6, and 7, representing the three discrete-variable optimization design parameters of the contact suspension system:

[0175] ;

[0176] In the formula, , These are the expansion factors of two random individuals of the discrete variable, respectively, and are determined by a binomial distribution. Sampling determination; This indicates that the value in parentheses is rounded to the nearest integer.

[0177] For the generated child discrete variables and Determine if it belongs to discrete variables The range in which it is located Generate a random number r in the interval [0, 1]. m If r m ≤p m Then the discrete variables of the offspring are reset to Otherwise, the discrete variables of the offspring are reset to... If the size of the discrete variable of the offspring is exactly equal to Then reset to If the size of the discrete variable of the offspring is exactly equal to Then reset to ;in, This represents the kth available value within the range of values ​​for the j-th discrete variable;

[0178] Repeat the above process until 30 child variables are generated;

[0179] Merge parent generation P t With offspring C t A temporary population R of size 2N is formed. t , for R t The non-dominated sorting and crowding degree calculations were performed again, and the top N individuals were selected in order of rank and crowding distance to form the new generation parent P. t+1 ;

[0180] For the N1 individuals constituting the first-level non-dominated frontier Fr1, select the 2-3 individuals with the lowest crowding as local search targets, and apply a small perturbation of 2% of the variable range to the j-th continuous variable one by one. The gradients of Q and L with respect to continuous variables are calculated by finite difference, and the search is performed along the weighted synthesis direction of the two. The compensation search step size is set to 5% of the corresponding continuous variable value range. If the new individual found satisfies all constraints and is not dominated by the original individual Pareto, the new individual replaces the original individual.

[0181] S404. When the maximum number of generations G is reached, output the final population P of the G-th generation. G The optimal set of individuals in the China-Africa dominance front serves as the Pareto optimal solution set, which designers can select based on engineering priorities; otherwise, the evolution continues by returning to the steps under the fully constrained dominance mode.

[0182] Example 2

[0183] A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements the contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables as described in Example 1.

[0184] Furthermore, the present invention adopts the following technical solution:

[0185] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables as described in Example 1.

[0186] From the above description of the embodiments, those skilled in the art will clearly understand that the facilities of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Embodiments of the present invention can be implemented using existing processors, or by dedicated processors used for this or other purposes for suitable systems, or by hardwired systems. Embodiments of the present invention also include non-transitory computer-readable storage media, comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and is accessible by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hardwired, wireless, or a combination of hardwired and wireless), that connection is also considered a machine-readable medium.

[0187] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A dual-objective optimization design method for contact suspension based on hierarchical constraints and mixed variables, characterized in that, Includes the following steps: S1. Determine the optimal design parameters of the contact suspension system, including continuous variables and discrete variables; S2. Establish pantograph-catenary dynamics simulation model and pantograph-catenary electrical simulation model, and obtain mechanical current collection performance indicators based on the models. Electrical current collection performance indicators And by weighted synthesis of current collection performance evaluation index ; S3. The contact wire, catenary, droppers and electrical connection are regarded as key components of the contact suspension that affect the pantograph-catenary current collection and system life. The mechanical load and electrical load time history of the key components are extracted, and transient thermal-structural coupling analysis is performed to obtain the life of different components. The minimum value among them is taken as the life of the contact suspension system L. S4. A dual-objective optimization model for current collection performance and contact suspension life is established, with the dual objectives of maximizing the current collection performance evaluation index Q and maximizing the contact suspension life L. The improved NSGA-II type multi-objective evolutionary algorithm is then used to solve the optimization model. The solution method includes the following steps: Set the population size, maximum number of generations, crossover probability, mutation probability, crossover distribution index, and mutation distribution index for different combinations of contact suspension system design parameters, and randomly generate the initial parent population P0. Calculate the proportion of individuals in the current population that satisfy all safety hard constraints. If this proportion is less than a threshold... If the target value is selected, the safety-first domination mode is activated; otherwise, the full-constraint domination mode is activated. The population is then sorted into non-dominated groups according to the selected domination mode. For individuals within the same non-dominated frontier, the crowding distance after sorting based on the target value is calculated. Construct a mating pool. Each time, randomly select two individuals from the parent population with replacement, prioritizing individuals with lower non-dominant rank; if the ranks are the same, select individuals with larger crowding distance; repeat the selection until a mating pool of size N is obtained. Mixed crossover and mixed mutation are performed on individuals in the mating pool to generate offspring populations; among them, the continuous variable part adopts simulated binary crossover and multinomial mutation, and the discrete variable part adopts integer difference crossover and integer value neighborhood reset mutation based on binomial distribution. Merge the parent and offspring populations, sort them according to non-dominance level and crowding distance, and truncate and retain N individuals to form a new generation population; When the proportion of individuals in the population that satisfy the hard safety constraints meets the threshold At that time, a constraint-aware local search is performed on the 2-3 feasible individuals with the smallest crowding distance in the non-dominated front. The new individuals that satisfy all constraints and are not dominated by the original individuals are then put back into the population to replace the original individuals. When the maximum number of generations is reached, the set of non-dominated individuals in the final population that satisfy all constraints is output as the Pareto optimal design set that takes into account both flow performance and system lifetime.

2. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: The optimization model also includes multiple constraints, which are divided into hard safety constraints and soft performance constraints. Hard safety constraints include maximum contact force ≤ 400N, maximum contact line stress ≤ 500Mpa, and maximum positioning point lifting ≤ 200mm. Soft performance constraints include current collection performance evaluation index ≥ 0.7 and contact suspension life ≥ 10 years. When the proportion of individuals in the population that can satisfy the safety hard constraint does not exceed the threshold When the population enters a safety-first dominance mode, individual dominance analysis is not performed using soft performance constraints. Through population iteration, the number of individuals meeting the hard safety constraints gradually increases. When the proportion of individuals in the population that meet the hard safety constraints reaches a threshold... Then, it enters the full-constraint mode, activating all constraints to perform individual dominance analysis.

3. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 2, characterized in that: When performing non-dominated sorting of the population according to the selected dominance pattern, the dominance rule is as follows: Under the safety-first domination mode, the domination rules are as follows: Individual p dominates individual q if and only if (1) p satisfies all hard safety constraints while q does not; or (2) neither satisfies hard safety constraints and p violates the hard safety constraints less than q; or (3) both satisfy all hard safety constraints and p achieves Pareto domination over q based on target index Q and index L. Under the fully constrained domination mode, the domination rule is as follows: Individual p dominates individual q if and only if (1) p satisfies all constraints while q does not; or (2) neither satisfies all constraints, and p's violation of all constraints is less than q's; or (3) both satisfy all constraints and p achieves Pareto domination of q based on target index Q and index L.

4. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 3, characterized in that: Individual safety hard constraint violation Defined as ,like If the condition is met, the individual is a safe and feasible individual; otherwise, the individual is a safe and infeasible individual. Total constraint violation rate of individuals Defined as ,like If the condition is met, the individual is a feasible individual; otherwise, the individual is an infeasible individual. in , , , , These represent the normalized constraint forms for contact force, contact line stress, positioning point lift, current collection performance evaluation index, and contact suspension life, respectively.

5. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 4, characterized in that: The constraint-aware local search is defined as follows: when the proportion of individuals in the population that satisfy the safety hard constraints meets a threshold... At that time, select 2-3 feasible individuals with the smallest crowding distance from the first-level non-dominated frontier as local search targets, and apply a small perturbation of 2% of the variable range to the j-th continuous variable one by one. The gradients of Q and L with respect to continuous variables are calculated by finite difference. The search is performed along the weighted synthesis direction of the two. The compensation search step size is set to 5% of the corresponding continuous variable value range. If the new individual satisfies all constraints and is not dominated by the original individual Pareto, then the original individual is replaced.

6. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: The optimization model is shown below: ； In the formula, Find(x) represents the 7-dimensional decision vector to be solved; Maximize represents multi-objective maximization; Subject represents the 5 inequality constraints that must be strictly satisfied. represent ;T con For the contact line tension, T mes Where S is the tension of the load-bearing cable, S is the contact suspension span, and d is the tension of the load- dro For the spacing of the dropper arrangement, A con Let A be the cross-sectional area of ​​the contact wire. mes d is the cross-sectional area of ​​the load-bearing cable. ele For electrical connection installation location; Q min As the minimum permissible current collection performance evaluation index, L min For the minimum permissible contact suspension life, and These are the maximum contact force for an individual and the maximum contact force allowed by the circuit design, respectively. and These are the maximum individual contact wire stress and the maximum allowable stress of the contact wire in the circuit design, respectively. and These are the maximum individual positioning point elevation and the maximum positioning point elevation allowed by the line design, respectively. and These represent the lower and upper limits of the optimal design parameter variation for the contact suspension system, respectively.

7. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: Step S3 includes: Obtain the equivalent stress that changes over time. ,temperature and current density amplitude Where k=1 refers to the contact wire, k=2 refers to the catenary wire, k=3 refers to the dropper, and k=4 refers to the electrical connection. The fatigue life N of contact wires, catenary wires, droppers, and electrical connections under different load cycles is calculated using material fatigue life formulas that consider the effects of temperature and current. k,f : ； Where, N k,0 , m represents the material fatigue parameter under normal temperature and no current conditions; Temperature correction function In the formula, T k,0 For laboratory reference temperature, K k,t This refers to the temperature influence coefficient of the material. Current density correction function In the formula, J k,0 The nominal current density, It is an accelerating factor for electrical damage; Statistical analysis of different equivalent stresses using rainflow counting method With temperature T k Current density amplitude J k The number of load cycles n under the combination k,i Calculate the total damage D according to Miner's rule. k : ； in, Represents a specific equivalent force With temperature T k Current amplitude J k The number of life cycles of components in a combination; Based on the number of trains passing through N annually train Obtain annual cumulative damage D k,year =D k ×N train Calculate the lifespan of components ; The lifespan L of the contact suspension system is taken as the shortest lifespan of the critical component in the contact suspension system. ； In the formula, L1 is the contact wire life, L2 is the catenary wire life, L3 is the dropper life, and L4 is the electrical connection life.

8. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: Step S2 includes: S201. Build a pantograph-catenary dynamics simulation model. Obtain dynamic contact force, pantograph head displacement, positioning point lift, and pantograph-catenary decoupling rate through pantograph-catenary dynamics simulation. Based on the obtained parameters, calculate the mechanical current collection performance index Q. mech calculate; ； in, For average contact force, For the standard deviation of contact force, and These are the maximum and minimum contact forces, respectively. For bow and fire net offline rate, This represents the range of vertical displacement of the bow head. The maximum lifting amount of the contact wire positioning point; g1, g2, g3, g4, g5, and g6 are the normalization functions of each parameter; All are weighting coefficients; S202. Construct a pantograph-catenary electrical simulation model. Utilize the pantograph-catenary electrical simulation data and combine it with the dynamic contact resistance influenced by dynamic contact force, current, and temperature to obtain the electrical current collection performance index Q. elec ; ； Among them, the coefficient of variation of dynamic contact resistance , The standard deviation of dynamic contact resistance. The average dynamic contact resistance; current collection efficiency. , where P train P is the active power received by the pantograph. sub The active power output by the traction substation; S203, Based on the obtained mechanical current collection performance index Q mech and electrical current collection performance index Q elec Weighted composite current collection performance evaluation index ,in, These are the weighting coefficients, and .

9. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: In step S4, the method for calculating the crowding distance based on the target value ranking for individuals within the same non-dominated frontier is as follows: In the same non-dominated frontier Fr k Within the k-th level non-dominated frontier, after sorting each individual in descending order according to the target values ​​Q and L, the crowding distance d of the i-th individual is calculated. ki : ； In the formula, and These are the values ​​of the i-th individual after sorting according to the target value Q, and the values ​​of the previous and next individuals. and These are the values ​​of the i-th individual after sorting according to the target value L, and the values ​​of the i-th individual before and after it. and The maximum and minimum values ​​of target Q within the current non-dominant frontier level. and The maximum and minimum values ​​of target L within the current non-dominated frontier level are given, and the crowding distance of boundary individuals after sorting according to target values ​​Q and L is set to infinity.

10. The contact suspension bi-objective optimization design method based on hierarchical constraints and mixed variables according to claim 1, characterized in that: The optimized design parameters of the contact suspension system in step S1 include continuous variables such as contact wire tension, catenary tension, contact suspension span, and dropper arrangement spacing, as well as discrete variables such as contact wire cross-sectional area, catenary cross-sectional area, and electrical connection installation position.

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