Train collision energy absorption design method based on step-by-step constraint multi-objective optimization

Abstract

The invention discloses a step-by-step constraint multi-objective optimization-based train collision energy absorption design method, which comprises the following steps of: firstly, constructing a vehicle body structure deformation model based on a collision accident, an energy absorption model of energy generated in a collision process and a vehicle body damage model, and providing a basis for subsequent optimization; an objective function and constraint conditions are designed according to the constructed model. An improved constraint multi-objective optimization algorithm is combined with an adaptive correction infeasible solution and an adaptive parameter change, so that conflicts between targets are effectively processed, and an elite solution meeting a constraint condition can be found. The maximum deformation of the vehicle body is minimized, and deformation control of the vehicle body during collision is ensured; the kinetic energy absorbed by the vehicle body is maximized, and the residual energy which is not absorbed is reduced; the damage degree of the vehicle body is minimized, and the integrity of the vehicle body structure is kept.

Description

Technical Field

[0001] The present invention belongs to the technical field of train safety, and particularly relates to a train collision energy absorption design method based on stepwise constrained multi-objective optimization. Background Art

[0002] With the rapid development of train transportation, train safety issues have become increasingly important in the transportation industry. The kinetic energy generated by trains in collision accidents is huge. How to effectively absorb this energy and reduce the structural damage of trains after collisions has become an important topic for improving train safety and passenger protection. Currently, train collision energy absorption design mainly focuses on the energy absorption capacity of the car body in collisions, the control of car body deformation, and the minimization of damage degree. However, the existing technologies still have deficiencies in optimizing multiple objectives and meeting complex constraint conditions.

[0003] Traditional collision energy absorption design methods mainly absorb collision energy by enhancing the rigidity of the car body structure and the strength of materials, but these methods often have some problems. First, the increase in the rigidity of the car body may lead to ineffective energy absorption, resulting in a greater impact on passengers and the car body. Second, excessive deformation of the car body will cause structural damage, thereby affecting overall safety. Therefore, how to ensure that the train absorbs energy while avoiding excessive deformation or damage to the car body is an important challenge in train collision energy absorption design.

[0004] In recent years, the constrained multi-objective optimization algorithm, as an effective optimization tool, has been widely used in multiple engineering fields. By considering multiple objectives simultaneously during the optimization process and seeking the optimal solution according to the constraint conditions, it can effectively solve the multi-objective and multi-constraint problems existing in the design. In the design of train energy collision absorption, how to comprehensively consider the requirements of energy absorption, car body deformation control, and damage degree minimization through a multi-objective optimization algorithm has become a key issue in the optimization design. Summary of the Invention

[0005] The purpose of the present invention is to provide a train collision energy absorption design method based on stepwise constrained multi-objective optimization, which can improve the energy absorption effect of train collisions while minimizing car body deformation.

[0006] The technical solution adopted by the present invention is a train collision energy absorption design method based on stepwise constrained multi-objective optimization, which is specifically implemented according to the following steps: Step 1, establish a car body deformation model; Step 2, construct an energy absorption model; Step 3, construct a car body damage degree model; Step 4, construct a multi-objective optimization problem model and set corresponding constraint conditions; Step 5, execute the constrained multi-objective optimization algorithm to solve the constrained multi-objective optimization problem; Step 6: Optimize by combining constraint handling techniques. Through constraint handling techniques, combined with specific conditions of train energy collision, optimize to the constraint Pareto front; determine whether Step 7 can be executed, otherwise return to Step 5; Step 7: Finally output the automotive structure design solution that meets the constraint conditions.

[0007] The features of the present invention also lie in: In Step 1, establish a vehicle body deformation model. The goal is to reduce the maximum deformation of the vehicle body through design optimization, ensuring that the vehicle body does not undergo excessive deformation during a collision, specifically as follows: (1) Elastic deformation displacement: (2) Plastic deformation displacement: (3) Wherein, and respectively represent the acting forces in the elastic and plastic stages, is the length of the deformation region, is the cross-sectional area of the deformation region, and respectively represent the elastic modulus and plastic modulus of the material, and are further expressed as follows: (4) Wherein, represents stress, which depends on the vehicle body material and structural design, represents strain, which is calculated through the deformation amount of the material during the collision process.

[0008] (5) Wherein, represents the yield strain, which refers to the initial strain value at which the material undergoes plastic deformation.

[0009] In Step 2, construct an energy absorption model. The goal is to maximize the energy absorbed by the vehicle body, that is, to minimize the remaining energy , so that as much kinetic energy as possible is absorbed by the vehicle body, specifically: (6) (7) (8) Wherein, represents the initial kinetic energy of the train, which is affected by the train mass and speed of, Indicates the energy absorbed by the car body, which is the energy absorbed through elastic deformation and plastic deformation. Indicates the remaining energy that is not absorbed.

[0010] In step 3, a car body damage degree model is constructed. The goal is to reduce the maximum stress experienced by the car body during a collision, thereby minimizing the damage degree and maintaining the integrity of the car body structure, as follows: (9) (10) Among them, Indicates the maximum stress experienced by the car body during a collision. Is the yield stress of the material. The damage degree Reflects whether plastic deformation occurs in the car body material. A smaller Indicates that the car body remains in the elastic deformation stage, and a larger Indicates that plastic deformation occurs in the material, which may lead to structural damage.

[0011] In step 4, a constrained multi-objective optimization problem model for train collision is constructed. Constraint conditions such as material cost and manufacturing process are set, and at the same time, the objective function is optimized. The constraint conditions are as follows: Constraint condition 1: Material strength constraint The stress ratio of the car body material should be less than or equal to its yield stress to avoid material failure or excessive plastic deformation. (11) Constraint condition 2: Maximum deformation constraint The maximum deformation of the car body should be less than or equal to a safety threshold to ensure the safety of the structure. (12) Constraint condition 3: Damage degree constraint The damage degree D must be less than or equal to a preset safety threshold to avoid excessive damage to the car body. (13) Constraint condition 4: Energy absorption constraint The energy absorption capacity of the car body must meet the preset minimum energy absorption requirement. (14) In steps 1 - 4, the optimization problem can be summarized as: (15) (16)。

[0012] Step 5 is specifically implemented according to the following steps: Step 5.1: Initialize the individual of train collision parameters, and initialize to generate a population containing N random solutions. P Each individual in the population contains decision variables, objective function values, and constraint violation degrees; To store and save the elite solutions generated during the evolution process, construct an empty archive. A The elite solutions in the current population stored in this archive. P and the offspring O are generated. For the initialization of the population size N, the formula is as follows: (17) where, the decision vector of each individual is generated from the solution space by uniform random sampling: (18) where, represents the i th decision variable of the j th individual, and it is uniformly selected from the interval , and are the lower and upper bounds of the decision variable ; The archive is used to record the feasible solutions and potential infeasible solutions searched during the convergence process to the progressive constraint Pareto front, so as to ensure that the algorithm can store and track the optimal solution set in multi-objective optimization. When initialized, the archive is empty and its size is N: (19); Step 5.2: Population P Use differential evolution to generate offspring O. For each individual ( i = 1, 2, …, N ), randomly select three other different individuals from the population P and the archive A x r1 , x r2 , x r3 ; Step 5.3: The scaling factor F and the crossover probability CR both use adaptive parameters. By detecting the change of the average objective function value of the population in real time, dynamically adjust F and CR to achieve an adaptive balance between exploration and exploitation. When the average objective function value of the current generation population is better than that of the previous generation, it means that the algorithm has improved in optimizing the existing solutions. At this time, appropriately increase F and correspondingly reduce CR ​, thus enhancing the local search ability; Step 5.4: Objective function evaluation. For the parameter individuals in the population and the offspring, calculate their objective values under all objective functions, and perform constraint handling to evaluate whether the individuals meet the constraints in the problem. If an individual meets all the constraints, add it to the archive. When the archive is full, sort all the feasible solutions found and select the top N optimal individuals to add to the archive. When the archive is not full, introduce a potential infeasible solution correction strategy to correct the potential infeasible solutions to make them feasible solutions; Step 5.5: When the algorithm meets the termination condition, output the final population P , and finally obtain the parameters corresponding to train collisions from the population P .

[0013] The selection of individuals in Step 5.2 should ensure their diversity so as to be able to generate effective differences. A mutant vector is generated through differential mutation operation. The core of the mutation operation is to calculate the differences between three randomly selected individuals and weight these differences to the current individual. The specific mutation formula is as follows: (20) where x r1 , x r2 , x r3 are three different individuals randomly selected from the population, F is the mutation scaling factor, which controls the degree of difference amplification; To further enhance the search ability, differential evolution performs a crossover operation. The purpose of the crossover is to combine the mutant vector v i with the parent individual to generate a candidate offspring, which is achieved by independently selecting each dimension of the decision variable: (21) where o ij is the decision variable of the candidate offspring individual o i at the j th position, v ij is the decision variable of the mutant vector v i at the j th position, rand j is a number randomly generated in the interval [0, 1], CR is the crossover probability.

[0014] The correction of the infeasible solutions in Step 5.4 is specifically implemented as follows: For the solutions in the potential infeasible solution set, calculate the distance between them and the feasible solutions. The distance calculation formula is as follows: (22) Where, and represent the objective vectors of the feasible solution and the potential infeasible solution respectively, represents the distance. Move the infeasible solution in the direction of the nearest feasible solution to reduce the constraint violation degree of the infeasible solution. The formula is as follows: (23) Where, is the i th feasible solution, is the j th infeasible solution, is the moving step size, which is determined by the distance between the feasible solution and the potential infeasible solution . The greater the distance, the greater the moving distance of the potential infeasible solution . Therefore, the calculation method of is as follows: (24) By normalizing, is controlled within (0, 1), which can effectively adjust the moving amplitude of the solution, balance exploration and exploitation, avoid excessive adjustment, and contribute to improving the convergence and final performance of the algorithm.

[0015] The beneficial effects of the present invention are The train collision energy absorption design method based on step-by-step constrained multi-objective optimization of the present invention minimizes the maximum deformation of the car body to ensure the deformation control of the car body during collision; maximizes the kinetic energy absorbed by the car body to reduce the remaining energy not absorbed; minimizes the damage degree of the car body to maintain the integrity of the car body structure. By reasonably constraining and optimizing these objectives, the train collision energy absorption effect is improved, and the damage caused by the collision is effectively reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic flow chart of the train collision energy absorption design method based on step-by-step constrained multi-objective optimization of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0017] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0018] The present invention provides a train collision energy absorption design method based on step-by-step constrained multi-objective optimization. As Figure 1 shown, it is specifically implemented according to the following steps: Step 1, establish a vehicle body deformation model; Step 2, construct an energy absorption model; Step 3, construct a vehicle body damage degree model; Step 4, construct a multi-objective optimization problem model and set corresponding constraint conditions; Step 5, execute the constrained multi-objective optimization algorithm to solve the constrained multi-objective optimization problem; Step 6, perform optimization by combining constraint handling techniques. Through the constraint handling techniques, combined with the specific conditions of train energy collision, optimize to the constrained Pareto front; judge whether Step 7 can be executed, otherwise return to Step 5; Step 7, when the algorithm meets the termination condition, output the final population P , and finally obtain the parameters corresponding to the train collision from the population P .

[0019] Embodiment 1 A train collision energy absorption design method based on stepwise constrained multi-objective optimization. In Step 1, a vehicle body deformation model is established. The goal is to reduce the maximum deformation of the vehicle body through design optimization and ensure that the vehicle body does not undergo excessive deformation during a collision, specifically as follows: (1) Elastic deformation displacement: (2) Plastic deformation displacement: (3) Among them, , respectively represent the acting forces in the elastic and plastic stages, is the length of the deformation region, is the cross-sectional area of the deformation region, , respectively represent the elastic modulus and plastic modulus of the material, and are further expressed as follows: (4) Among them, represents the stress, which depends on the vehicle body material and structural design, represents the strain, which is calculated through the deformation amount of the material during the collision.

[0020] (5) Among them, represents the yield strain, which refers to the initial strain value at which the material undergoes plastic deformation, that is, the strain point at which the material enters the plastic stage from the elastic stage.

[0021] Embodiment 2 Train collision energy absorption design method based on step-by-step constrained multi-objective optimization. In step 2, an energy absorption model is constructed with the goal of maximizing the energy absorbed by the car body, that is, minimizing the remaining energy to the least amount, so that as much kinetic energy as possible is absorbed by the car body. Specifically: (6) (7) (8) Among them, represents the initial kinetic energy of the train, which is affected by the train mass and speed . represents the energy absorbed by the car body, which is the energy absorbed through elastic deformation and plastic deformation, represents the remaining energy that has not been absorbed.

[0022] Example 3 Train collision energy absorption design method based on step-by-step constrained multi-objective optimization. In step 3, a car body damage degree model is constructed with the goal of reducing the maximum stress experienced by the car body during the collision, thereby minimizing the damage degree and maintaining the integrity of the car body structure. Specifically as follows: (9) (10) Among them, represents the maximum stress experienced by the car body during the collision, is the yield stress of the material. The damage degree reflects whether the car body material undergoes plastic deformation. A smaller indicates that the car body remains in the elastic deformation stage, and a larger indicates that the material undergoes plastic deformation, which may lead to structural damage.

[0023] Example 4 Train collision energy absorption design method based on step-by-step constrained multi-objective optimization. In step 4, a constrained multi-objective optimization problem model for train collision is constructed, setting constraint conditions such as material cost and manufacturing process, and at the same time optimizing the objective function. The constraint conditions are as follows: Constraint condition 1: Material strength constraint The stress ratio of the car body material should be less than or equal to its yield stress to avoid material failure or excessive plastic deformation; (11) Constraint condition 2: Maximum deformation constraint The maximum deformation of the car body is less than or equal to a safety threshold to ensure the safety of the structure; (12) Constraint 3: Damage degree constraint The damage degree D must be less than or equal to a preset safety threshold to avoid excessive damage to the vehicle body; (13) Constraint 4: Energy absorption constraint The energy absorption capacity of the vehicle body must meet the preset minimum energy absorption requirement; (14) In steps 1 - 4, the optimization problem can be summarized as: (15) (16)。

[0024] Example 5 A train collision energy absorption design method based on step - by - step constrained multi - objective optimization. In step 5, the step - by - step constrained multi - objective optimization algorithm is executed to solve the constrained multi - objective optimization problem and optimize it to the unconstrained Pareto front. The pseudo - code framework of the algorithm is shown in Algorithm 1.

[0025]

[0026] Algorithm 1 gives the basic framework of the improved constrained multi - objective optimization algorithm. For the given CMOPs, the algorithm first generates an initial population containing N random solutions P and an initial archive A (lines 1 - 2 of Algorithm 1). In each generation, three individuals are selected into the mating pool (line 4 of Algorithm 1). Offspring are generated through the differential evolution operator, and an adaptive parameter mechanism is introduced into the differential evolution operator (line 5 of Algorithm 1). The infeasible solutions are corrected using the infeasible solution correction strategy, and then the feasible solutions are added to the archive A (line 6 of Algorithm 1). The first N individuals with high fitness are selected to form a new population P (line 7 of Algorithm 1). Finally, the population is updated P (line 9 of Algorithm 1). The above steps are continuously executed in the main loop (lines 4 - 7 of Algorithm 1) until the termination condition is met.

[0027] Example 6 A train collision energy absorption design method based on step - by - step constrained multi - objective optimization. In step 5, it is specifically implemented according to the following steps: Step 5.1: Initialize the individual of the train collision parameters, and initialize to generate a population containing N random solutions P, each individual in the population contains decision variables, objective function values, and constraint violation degrees; to store and preserve the elite solutions generated during the evolution process, an empty archive is constructed A , the current population stored in this archive P and the elite solutions in the generated offspring O; For the initialization of the population size N, the formula is as follows: (17) Among them, the decision vector of each individual is generated from the solution space through uniform random sampling: (18) Among them, represents the i -th decision variable of the j -th individual, and it is uniformly selected from the interval , and are the lower and upper bounds of the decision variable ; The archive is used to record the feasible solutions and potential infeasible solutions searched during the process of converging to the progressive constraint Pareto front, to ensure that the algorithm can store and track the optimal solution set in multi-objective optimization. At initialization, the archive is empty and its size is N: (19); Step 5.2: Population P Use differential evolution to generate offspring O. For each individual ( i = 1, 2,..., N), randomly select three other different individuals x P and the archive A from the population r1 , x r2 , x r3 ; The selection of individuals should ensure their diversity so as to be able to produce effective differences. The mutant vector is generated through the differential mutation operation. The core of the mutation operation is to calculate the differences between three random individuals and weight these differences to the current individual. The specific mutation formula is as follows: (20) Among them, x r1 , x r2 , x r3 are three different individuals randomly selected from the population, F is the mutation scaling factor, which controls the degree of difference amplification; To further enhance the search ability, differential evolution performs a crossover operation. The purpose of crossover is to combine the mutant vector v i with the parent individuals to generate a candidate offspring, which is achieved by independently selecting each dimension of the decision variables: (21) where, o ij is the \(i\)-th decision variable of the candidate offspring individual o i the \(j\)-th decision variable of the mutant vector j is the \(j\)-th decision variable of the mutant vector v ij is the \(j\)-th decision variable of the mutant vector v i the \(j\)-th decision variable of the mutant vector j is the \(j\)-th decision variable of the mutant vector rand j is a number randomly generated in the interval [0, 1], CR is the crossover probability; Step 5.3: The scaling factor F and the crossover probability CR both use adaptive parameters. By real-time detecting the change of the average objective function value of the population, F and CR are dynamically adjusted to achieve an adaptive balance between exploration and exploitation. When the average objective function value of the current generation population is better than that of the previous generation, it indicates that the algorithm has improved in optimizing the existing solutions. At this time, F is moderately increased, and CR, thus enhancing the local search ability; a larger scaling factor enables individuals to generate greater changes in the solution space, while a smaller crossover probability preserves more characteristics of the original solutions. This adjustment improves the algorithm's ability to finely optimize existing feasible solutions, helps it deeply explore local regions, and approach the global optimal solution. Conversely, if the average objective function value of the current population is not significantly better than that of the previous generation, it means that the exploration effect in the current solution space is limited, and the need to explore new regions increases. At this time, the algorithm will decrease the scaling factor and increase the crossover probability to promote the diversity of solutions and the global exploration ability of the population. A smaller scaling factor generates smaller mutations to avoid excessive perturbation of the solutions, while a larger crossover probability helps the population jump out of the local optimal region by introducing more new solutions, expands the search scope, and discovers new potential feasible solutions. This adaptive adjustment mechanism not only improves the flexibility of the algorithm in different optimization stages but also effectively avoids the problems of premature convergence or low search efficiency of the algorithm. By balancing the exploration and exploitation capabilities of the population in the solution space, the algorithm can fully explore a wide range of regions in the solution space at the initial stage of optimization, discover more potential high-quality solutions, and then concentrate on deeply developing these solutions in the later stage to make them approach the true Pareto front. Ultimately, this dynamic adjustment mechanism significantly improves the overall optimization effect of the algorithm, making it more robust and efficient in solving complex optimization problems. The formulas for the adaptive adjustment of the scaling factor and crossover probability are as follows: (22) (23) where sign(x) is the sign function, which takes 1 when x > 0, -1 when x < 0, and 0 when x = 0. and are the average objective function values of the current population and the previous generation population respectively.

[0028] The pseudo-code of the adaptive parameter dynamic adjustment strategy is shown in Algorithm 2:

[0029] Initially, the population is evolved using the given scaling factor (F0 = 0.5) and crossover probability (CR0 = 0.8) (lines 1 - 2 of Algorithm 2). In each generation of evolution, the differential evolution algorithm uses the current F and CR to optimize the population (lines 3 - 4 of Algorithm 2). The algorithm evaluates the average objective function value of the current population and compares it with that of the previous population (lines 5 - 6 of Algorithm 2). If the average objective function value of the current population is greater than that of the previous generation population, the scaling factor F is increased and the crossover probability CR, to enhance the exploration ability of the population (lines 7 - 9 of Algorithm 2); conversely, reduce the scaling factor F and increase the crossover probability CR , to improve the exploitation ability of the population (lines 10 - 12 of Algorithm 2). Through this mechanism, the algorithm can adaptively balance exploration and exploitation at different stages of the optimization process, thus improving the overall optimization effect.

[0030] Step 5.4: Objective function evaluation. For the parameter individuals in the population and offspring, calculate their objective values under all objective functions, and perform constraint handling to evaluate whether the individuals meet the constraints in the problem. If an individual meets all the constraints, add it to the archive. When the archive is full, sort all the searched feasible solutions and select the top N optimal individuals to add to the archive. When the archive is not full, introduce the potential infeasible solution correction strategy to correct the potential infeasible solutions to make them feasible solutions. The specific implementation of the correction of infeasible solutions is as follows: For the solutions in the set of potential infeasible solutions, calculate the distance between them and the feasible solutions. The distance calculation formula is as follows: (24) where and represent the objective vectors of the feasible solution and the potential infeasible solution respectively, represents the distance. Move the infeasible solution towards the direction of the nearest feasible solution to reduce the constraint violation degree of the infeasible solution. The formula is as follows: (25) where is the i th feasible solution, is the j th infeasible solution, is the moving step size, which is determined by the distance between the feasible solution and the potential infeasible solution . The greater the distance, the greater the distance that the potential infeasible solution moves. Therefore, is calculated as follows: (26) By normalizing, is controlled within (0, 1), which can effectively adjust the moving amplitude of the solution, balance exploration and exploitation, avoid excessive adjustment, and contribute to improving the convergence and final performance of the algorithm.

[0031] The adaptive infeasible solution correction strategy is shown in Algorithm 3:

[0032] Add all the feasible solutions in P1 to the archive A. If A = |N|, output A as the updated archive (lines 2 - 3 of Algorithm 3). If A < |N|, use the corrected feasible solutions to fill the archive. First, perform non - dominated sorting on the infeasible solutions, select the first |N - A| infeasible solutions, adjust them to the vicinity of the feasible solutions in the feasible region, and finally output the archive A (lines 4 - 10 of Algorithm 3). If A > |N|, use the fitness calculation method in SPEA2 - CDP to evaluate all the solutions in A, and select the first N solutions as the updated archive. (lines 11 - 16 of Algorithm 3). Finally, output the archive A (lines 4 - 17 of Algorithm 3). Step 5.5: When the algorithm meets the termination condition, output the final population P , and finally obtain the parameters corresponding to the train collision from the population P .

[0033] Based on the above, the present invention effectively solves the high - speed train collision problem through the step - by - step constrained multi - objective optimization algorithm and the adaptive correction of infeasible solutions technology. First, a body structure deformation model, an energy absorption model generated during the collision process, and a body damage model based on the collision accident are constructed, providing a basis for subsequent optimization. The objective function and constraint conditions are designed according to the constructed models. By using the improved constrained multi - objective optimization algorithm combined with the adaptive correction of infeasible solutions and the adaptive parameter change, not only can the conflicts between objectives be effectively handled, but also the elite solutions that meet the constraint conditions can be found.

[0034] During the optimization process of the present invention, by combining the infeasible solution handling technology and the parameter self - adaptation mechanism, it is ensured that the design scheme meets the time - collision safety requirements. Finally, through the iterative optimization of the evolutionary algorithm, an optimal design scheme of the high - speed train structure that meets both the safety requirements and has good performance is output.

Claims

1. A train collision energy absorption design method based on stepwise constrained multi-objective optimization, characterized in that The implementation is carried out according to the following steps: Step 1: Establish a vehicle body deformation model; Step 2: Construct an energy absorption model; Step 3: Construct a vehicle body damage degree model; Step 4: Construct a multi-objective optimization problem model and set corresponding constraint conditions; Step 5: Execute a constrained multi-objective optimization algorithm to solve the constrained multi-objective optimization problem; Step 6: Combine constraint handling techniques for optimization. Through constraint handling techniques, combined with specific conditions of train energy collision, optimize to the constrained Pareto front; judge whether Step 7 can be executed, otherwise return to Step 5; Step 7: Finally, output an automobile structure design scheme that meets the constraint conditions.

2. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 1, characterized in that In Step 1, when establishing the vehicle body deformation model, the goal is to reduce the maximum deformation of the vehicle body through design optimization, ensuring that the vehicle body does not undergo excessive deformation during a collision, specifically as follows: （1） Elastic deformation displacement: （2） Plastic deformation displacement: （3） Among them, and represent the acting forces in the elastic and plastic stages respectively, is the length of the deformation area, is the cross-sectional area of the deformation area, and represent the elastic modulus and plastic modulus of the material respectively, and are further expressed as follows: （4） Among them, represents stress, which depends on the vehicle body material and structural design, represents strain, which is calculated by the amount of deformation of the material during the collision; （5） Among them, represents the yield strain, which refers to the initial strain value at which the material undergoes plastic deformation.

3. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 1, characterized in that In step 2, an energy absorption model is constructed with the goal of maximizing the energy absorbed by the vehicle body, that is, minimizing the remaining energy to the least extent, so that as much kinetic energy as possible is absorbed by the vehicle body. Specifically: （6） （7） （8） Among them, represents the initial kinetic energy of the train, which is affected by the mass of the train and the speed . represents the energy absorbed by the car body, which is the energy absorbed through elastic deformation and plastic deformation. represents the remaining energy that is not absorbed.

4. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 1, characterized in that In Step 3, when constructing the vehicle body damage degree model, the goal is to reduce the maximum stress experienced by the vehicle body during a collision, thereby minimizing the damage degree and maintaining the integrity of the vehicle body structure, specifically as follows: （9） （10） Among them, represents the maximum stress experienced by the car body during the collision, is the yield stress of the material, and the damage degree reflects whether the plastic deformation of the car body material occurs. A smaller indicates that the car body remains in the elastic deformation stage, and a larger indicates that the material undergoes plastic deformation, which may lead to structural damage.

5. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 1, characterized in that In Step 4, when constructing a constrained multi-objective optimization problem model for train collision, set constraint conditions such as material cost and manufacturing process, and at the same time optimize the objective function. The constraint conditions are as follows: Constraint condition 1: Material strength constraint The stress ratio of the vehicle body material should be less than or equal to its yield stress to avoid material failure or excessive plastic deformation; （11） Constraint condition 2: Maximum deformation constraint The maximum deformation of the vehicle body should be less than or equal to a safety threshold to ensure the safety of the structure; （12） Constraint condition 3: Damage degree constraint The damage degree D must be less than or equal to a preset safety threshold to avoid excessive damage to the vehicle body; （13） Constraint condition 4: Energy absorption constraint The energy absorption capacity of the vehicle body must meet the preset minimum energy absorption requirement; （14） In Steps 1 - 4, the optimization problem can be summarized as: （15） （16）。 6. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 1, characterized in that, Step 5 is specifically implemented according to the following steps: Step 5.1: Initialize the individual of train collision parameters, and initialize to generate a population containing N random solutions. P Each individual in the population contains decision variables, objective function values, and the degree of constraint violation. To store and save the elite solutions generated during the evolution process, construct an empty archive. A The current population stored in this archive P and the elite solutions in the generated offspring O. For the initialization of the population size N, the formula is as follows: （17） Among them, the decision vector of each individual is generated from the solution space by uniform random sampling: （18） Among them, represents the i th decision variable of the j th individual, and it is uniformly selected from the interval , and are the lower and upper bounds of the decision variable ; The archive is used to record the feasible solutions and potential infeasible solutions searched during the convergence process to the progressive constraint Pareto front, to ensure that the algorithm can store and track the optimal solution set in multi-objective optimization. When initializing, the archive is empty and its size is N: （19）； Step 5.2: Population P Generate offspring O using differential evolution. For each individual ( i i = 1, 2, …, N), randomly select three other different individuals from the population P and the archive A ; x r1 , x r2 , x r3 ; Step 5.3: Scaling factor F and crossover probability CR both use adaptive parameters. By detecting the change of the average objective function value of the population in real time, they are dynamically adjusted F and CR . To achieve an adaptive balance between exploration and exploitation, when the average objective function value of the current generation population is better than that of the previous generation, it indicates that the algorithm has improved in optimizing the existing solution. At this time, appropriately increase F and correspondingly reduce CR to enhance the local search ability; Step 5.4: Objective function evaluation. For the parameter individuals in the population and offspring, calculate their objective values under all objective functions, and perform constraint handling to evaluate whether the individuals meet the constraint conditions in the problem. If an individual meets all constraint conditions, add it to the archive. When the archive is full, sort all the searched feasible solutions and select the top N optimal individuals to add to the archive. When the archive is not full, introduce a potential infeasible solution correction strategy to correct the potential infeasible solutions to make them feasible solutions; Step 5.5: When the algorithm meets the termination condition, output the final population P , and finally obtain the parameters corresponding to train collisions from the population P .

7. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 6, characterized in that The selection of individuals in Step 5.2 should ensure their diversity so as to be able to generate effective differences. Generate a mutation vector through differential mutation operation. The core of the mutation operation is to calculate the differences between three random individuals and weight these differences to the current individual. The specific mutation formula is as follows: （20） Among them, x r1 , x r2 , x r3 are three different individuals randomly selected from the population, and F is the mutation scaling factor that controls the degree of difference amplification; To further enhance the search ability, differential evolution performs a crossover operation. The purpose of crossover is to combine the mutant vector v i with the parent individuals to generate a candidate offspring, which is achieved by independently selecting each dimension of the decision variables: （21） Among them, o ij is the o i th decision variable of the candidate offspring individual j , v ij is the v i th decision variable of the mutation vector j , rand j is a number randomly generated in the interval [0, 1], CR and is the crossover probability.

8. The train collision energy absorption design method based on stepwise constrained multi-objective optimization according to claim 6, characterized in that The correction of the infeasible solutions in step 5.4 is specifically implemented as follows: For the solutions in the potential infeasible solution set, calculate the distance between them and the feasible solutions. The distance calculation formula is as follows: （22） Among them, and represent the objective vectors of the feasible solution and the potentially infeasible solution respectively, represents the distance. Move the infeasible solution in the direction of the nearest feasible solution to reduce the constraint violation degree of the infeasible solution. The formula is as follows: （23） Among them, is the i th feasible solution, is the j th infeasible solution, is the moving step size, which is determined by the distance between the feasible solution and the potential infeasible solution . The greater the distance, the greater the distance that the potential infeasible solution moves. Therefore, is calculated as follows: （24） By normalizing, being controlled within (0, 1) can effectively adjust the movement amplitude of the solution, balance exploration and exploitation, avoid excessive adjustment, and help improve the convergence and final performance of the algorithm.

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