A dynamic structural strength optimization method for a 400 km / h high-speed pantograph

Abstract

This paper discloses a method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph. By establishing a dynamic finite element analysis model for the pantograph, the dynamic structural strength of the pantograph at 400 km / h is studied. Based on the maximum stress and deformation of the pantograph at 400 km / h, a neural network-based optimization method is proposed to improve the dynamic structural strength of the pantograph at 400 km / h. This method can reduce the possibility of structural instability during high-speed operation of the pantograph and has reference significance for the structural design of new high-speed pantographs.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic structural strength optimization of high-speed railway pantographs, and in particular to a method for optimizing the dynamic structural strength of a high-speed pantograph with a speed of 400 kilometers per hour. Background Art

[0002] In the advancement of high-speed railways, stable contact between the pantograph and the catenary is crucial for the safe operation of high-speed trains. As a key current-collecting device, the stability of the pantograph's structure during operation directly impacts the power supply capacity of the pantograph-catenary system, and thus the safe operation of high-speed trains. As operating speeds increase, particularly at speeds of 400 km / h, the fluctuations in pantograph-catenary contact force significantly increase, increasing the likelihood of structural instability during operation. Damage to the pantograph structure not only disrupts current collection but can also damage the catenary system.

[0003] At present, a large number of scholars have conducted research on the performance analysis and optimization design of pantographs. Pombo et al. (Pombo J, J Ambrósio. Influence of pantograph suspension characteristics on the contact quality with the catenary for high-speed trains [J]. Computers & Structures, 2012, 110-111 (NOV.): 32-42.) studied the influence of pantograph mass, pantograph suspension stiffness and lower frame damping value on the pantograph-catenary contact force by establishing a collaborative simulation program of finite element and multi-body dynamics methods; Zhou et al. (Zhou N, Zhang W. Investigation on dynamic performance and parameter optimization design of pantograph and catenary system [J]. Finite Elements in Analysis and Design, 2011, 47 (3): 288-295.) optimized the pantograph reduction parameters using sensitivity analysis technology and conducted relevant tests; Wang et al. (Wang W, Liang Y, Zhang W, et al. Effect of the nonlinear displacement-dependent characteristics of a hydraulic damper on high-speed rail pantograph dynamics[J].Nonlinear Dynamics,2019.) proposed a new type of nonlinear damper that can better simulate the working conditions of the pantograph and analyzed the influence of damping parameters on the operating performance of the pantograph; Jia et al. (Jia F,Xu F,Zhou H,etal.Optimization and simulation of the operational motion of a pantograph:Uplift and retraction[J].Journal of Mechanical Science&Technology,2017,31(1):41-52.) constructed a multi-body mathematical model of the pantograph and optimized the rod parameters with the pantograph head motion trajectory and the balance bar deflection angle as the target; Kim et al. (Kim JW,Yu SN.Design variable optimization for pantograph systems of high-speed trains using robust design techniques [J]. International Journal of Precision Engineering & Manufacturing, 2013.) A robust design method was used to select optimal design variables, effectively reducing the vibration behavior of the pantograph system. In these studies, the optimized design of the pantograph was primarily performed using equivalent mass models or multi-rigid-body models for dynamic simulation analysis, without examining the dynamic structural strength of the pantograph's physical structure. Summary of the Invention

[0004] To address the above issues, the present invention aims to provide a method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph. By establishing a finite element dynamic analysis model for a pantograph, the dynamic structural strength of the pantograph at 400 km / h is studied. Based on the maximum stress and deformation of the pantograph at 400 km / h, a neural network-based optimization method is proposed to improve the dynamic structural strength of the pantograph at 400 km / h. The technical solution is as follows:

[0005] A dynamic structural strength optimization method for a 400 km / h high-speed pantograph.

[0006] The following steps are involved:

[0007] Step 1: Select the pantograph used in high-speed trains as the research object. Build a 3D solid model based on the mechanical parameters of the DSA380 pantograph. Use the Ansys Workbench platform to perform meshing and establish a finite element dynamic analysis model for the pantograph. Add boundary conditions and constraints to the finite element dynamic analysis model based on the actual operating conditions of the pantograph.

[0008] Step 2: Based on the pantograph equivalent model parameter identification method, the three-mass equivalent parameters of the established pantograph finite element dynamic analysis model at a standard working height are verified; the equivalent stiffness of the pantograph head and upper and lower frames is calculated according to the stiffness calculation formula, the equivalent mass of the pantograph head and upper and lower frames is calculated according to the single-degree-of-freedom system free vibration formula, and the equivalent damping of the lower frame is calculated according to the attenuation coefficient calculation formula and the damping coefficient calculation formula; then, simulation calculations are performed based on the calculated equivalent stiffness of the pantograph head and upper and lower frames, the equivalent mass of the pantograph head and upper and lower frames, and the equivalent damping parameters of the lower frame, and compared with the standard equivalent parameters to verify the accuracy of the pantograph finite element dynamic analysis model;

[0009] Step 3: Verify the lateral stiffness of the pantograph finite element dynamic analysis model according to the International Electrotechnical Commission standard IEC 60494-1. Perform modal analysis of the pantograph finite element dynamic analysis model using finite element calculations based on the vibration equations of rigid structures. Analyze the first six low-frequency modal shapes and compare them with experimental results.

[0010] Step 4: Establish a pantograph-catenary dynamic coupling model to simulate and analyze the load impact on the pantograph finite element dynamic analysis model under the working condition of 400 kilometers per hour. Based on the actual contact network structure, establish a dynamic coupling model of the contact network and the pantograph finite element dynamic analysis model under an anchor section length. Then, introduce the contact unit between the contact line and the bow head of the pantograph finite element dynamic analysis model into the dynamic coupling model to simulate the dynamic contact behavior of the pantograph-catenary during actual operation. Extract the pantograph-catenary contact force of a span length in the stable section during operation and the vertical acceleration of the pantograph finite element dynamic analysis model. Apply external excitation to the pantograph finite element dynamic analysis model based on the pantograph dynamic equilibrium equation. Analyze the overall stress and deformation of the pantograph finite element dynamic analysis model, and analyze the relationship between the load and mechanical parameters of the pantograph finite element dynamic analysis model components. Finally, analyze the stress of the pantograph finite element dynamic analysis model components and the stress of the hinge point to determine the structural danger point.

[0011] Step 5: Optimize the structural strength of the pantograph finite element dynamic analysis model by constructing a response surface to improve its operating strength at a speed of 400 km / h. Based on the pantograph equivalent structural parameters and the rod mechanical equations, determine the main structural parameters and variation ranges of the pantograph finite element dynamic analysis model, and construct a pantograph optimization model. Use the Latin hypercube experimental design method to sample the design variables of the pantograph finite element dynamic analysis model, and obtain simulation results for the dynamic structural strength analysis and static structural analysis of the pantograph finite element dynamic analysis model with different structural parameters. Parameter sensitivity analysis technology is used to study the correlation between the optimization objectives, constraints, and optimization variables, and analyze the influence of the structural parameters of the pantograph finite element dynamic analysis model on its dynamic and static structural strength at an operating speed of 400 km / h. Based on the experimental design data, a RBF neural network model is constructed, and the response relationship between the optimization variables and the optimization objectives is fitted to obtain the corresponding response surface results. A multi-objective genetic algorithm (MOGA) is used to optimize the structural strength of the pantograph finite element dynamic analysis model. Pareto optimal solutions are searched based on the response surface, and the optimization results are verified through simulation.

[0012] The dynamic structural strength of the pantograph includes the stress and deformation of the pantograph as a whole and the pantograph head, pantograph angle, upper arm, upper guide rod, lower arm and lower guide rod.

[0013] The specific method for identifying the pantograph equivalent model parameters in step 2 above is:

[0014] According to the stiffness calculation formula:

[0015]

[0016] Calculate the equivalent stiffness K of the bow head and upper and lower frames, where F is the applied load and Δx is the maximum displacement;

[0017] According to the free vibration formula of single degree of freedom system:

[0018]

[0019] Calculate the equivalent mass m of the bow head and upper and lower frames, where T is the system vibration period and K is the equivalent stiffness;

[0020] According to the calculation formula of attenuation coefficient and damping coefficient:

[0021]

[0022]

[0023] Calculate the equivalent damping c of the lower frame, where A0 is the reference point amplitude, A n is the amplitude that is n cycles apart from A0.

[0024] The pantograph dynamic balance equation in step 4 above is:

[0025] P(t)=F0+F a +ma

[0026] Where P(t) is the dynamic pantograph-catenary contact force, F0 is the static lifting force of the pantograph, and F a is the air lift force, ma is the transient impact force of the pantograph, m is the dynamic mass of the pantograph during operation, and a is the vertical acceleration;

[0027] The relationship between the load conditions of each member of the pantograph finite element dynamic analysis model and the structural parameters of the pantograph finite element dynamic analysis model should satisfy the Newton-Euler mechanics equation.

[0028] The learning equations are as follows:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] Where M t is the pantograph raising torque, F i and F i ' are the action and reaction forces at the hinge point i (i = A ~ G); m q 、a q They represent the mass and acceleration of the pantograph member p (p = a ~ e), J q Represents the moment of inertia around the hinge point q (q = A, B, C, E, G).

[0035] The pantograph optimization model in step 5 above is:

[0036] find X=(x1,x2,…,x 10 )

[0037] min f1(X)=Δx max

[0038] f2(X)=σ max

[0039] stΔx l ≤Δx l0

[0040] Δx r ≤Δx r0

[0041] ω≤ω0

[0042] Σm≤Σm0

[0043] X L ≤X≤X U

[0044] Where X represents the overall variable of pantograph optimization, Δx max and σ max They represent the maximum deformation and maximum stress of the pantograph during the dynamic simulation process of 400 km / h running speed, Δx l and Δx r They represent the maximum displacement on both sides of the pantograph in the lateral stiffness check, ω represents the first-order natural frequency of the pantograph, ∑m represents its overall mass, and X L and X U They represent the lower and upper limits of the overall variable X respectively;

[0045] In the sensitivity analysis technique, S(Y,x i ) is the objective function Y for variable parameter x i Sensitivity index:

[0046]

[0047] Where E(Y|x i ) is the variable parameter x i The average value of the objective function Y when it is a constant, Var(E(Y|x i )) is Y versus x i Var(Y) is the unconditional variance of the model output.

[0048] The beneficial effects of the present invention are as follows: under the condition that the high-speed railway pantograph runs at a speed of 400 kilometers per hour, the present invention uses the finite element method to explore the dynamic strength of the pantograph structure, and proposes an optimization method based on a neural network, which makes up for the shortcomings of the existing high-speed pantograph optimization method, thereby improving the structural strength of the pantograph without reducing the current-collecting quality of the pantograph network, and reducing the possibility of structural instability during high-speed operation of the pantograph. It is of great significance for the structural design of the new high-speed pantograph, and provides a reference for the structural strength index of the pantograph in the design of the future 400-kilometer-per-hour high-speed railway system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is the three-dimensional model of the DSA380 pantograph.

[0050] Figure 2 This is the equivalent model diagram of the three-mass pantograph.

[0051] Figure 3 These are the first six modal vibration shapes of the pantograph.

[0052] Figure 4 The diagram shows the simulation analysis results of the bow-catenary coupling model at different operating speeds.

[0053] Figure 5 This is the overall stress and deformation curve of the pantograph at a running speed of 400km / h.

[0054] Figure 6 The following is a graph showing the decomposed stress and deformation curves of the pantograph components at a running speed of 400 km / h.

[0055] Figure 7 This is the result diagram of sensitivity analysis of optimization parameters.

[0056] Figure 8 Optimized response surface model diagram.

[0057] Figure 9 Optimize sample result graph.

[0058] Figure 10 Optimize the overall flow chart for pantograph.

[0059] Icon: 001-slide plate, 002-bow angle, 003-upper arm, 004-upper guide rod, 005-lower arm, 006-lower guide rod, 007-base frame. DETAILED DESCRIPTION

[0060] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. The present invention establishes a pantograph dynamic analysis model based on the Ansys finite element simulation platform, studies the dynamic structural strength of the pantograph at a speed of 400 km / h, and proposes a neural network-based optimization method based on the maximum stress and deformation of the pantograph at a speed of 400 km / h. The sensitivity method is used to quantitatively analyze the influence of structural parameters on the pantograph structural strength, and a multi-objective genetic algorithm is used to obtain the optimal structural parameters of the pantograph. The method comprises the following steps:

[0061] Step 1: Select the DSA380 pantograph currently used in high-speed trains as the research object, and establish a three-dimensional solid model based on its mechanical structure parameters, such as Figure 1 The ANSYS Workbench platform is used to perform mesh division and establish the pantograph finite element dynamic analysis model.

[0062] In order to achieve the purpose of restoring the important mechanical properties of the actual structure and having high calculation accuracy and small calculation scale for the established pantograph finite element dynamic analysis model, the pantograph model is specially processed to simplify the small structures that are not the main load-bearing and remove the insulators. The main structure of the pantograph is composed of a number of hollow truss structures with variable cross-sections, so the fully flexible model uses the solid element Solid186 for meshing, which has strong adaptability to irregular structures. The unit sizes of the bow head rod unit, frame rod unit and hinged shaft unit are 15mm, 20mm and 5mm respectively. The pantograph suspension spring and hydraulic damper are simulated using the spring-damper element Combine14. Boundary conditions and constraints are added according to the actual operating conditions of the pantograph. The connection between each rod is realized by a rotating pair and a ball pair, and the pantograph base is fixedly constrained. The finite element model based on the actual DSA380 pantograph is as follows Figure 3 The main mechanical structure parameters of DSA380 pantograph are shown in Table 1:

[0063] Table 1 Mechanical structure parameters of DSA380 pantograph

[0064]

[0065] Step 2: Based on the pantograph equivalent model parameter identification method, the three-mass equivalent parameters of the established pantograph finite element dynamic analysis model at the standard working height are verified. In the pantograph finite element dynamic analysis model, the pantograph at a fixed working height is reduced to three reduced mass blocks connected by a spring damping system, namely the pantograph head (m1), the upper frame (m2) and the lower frame (m3). Figure 2 shown.

[0066] According to the stiffness calculation formula:

[0067]

[0068] Calculate the equivalent stiffness K of the bow head and the upper and lower frames, where F is the applied load and Δx is the maximum displacement.

[0069] According to the free vibration formula of single degree of freedom system, the equivalent mass parameters of the reduced system can be calculated.

[0070]

[0071] Where T is the vibration period of the system and K is the equivalent stiffness of the spring.

[0072] Calculate the equivalent damping of the lower frame according to the attenuation coefficient calculation formula and the damping coefficient calculation formula:

[0073]

[0074]

[0075] Where A0 is the reference point amplitude, A n is the amplitude that is n cycles apart from A0.

[0076] The comparison between the simulation results and the standard equivalent parameters of the DSA380 pantograph is shown in Table 2:

[0077] Table 2 Comparison results of equivalent parameters

[0078]

[0079] Step 3: According to the International Electrotechnical Commission standard IEC 60494-1, the lateral stiffness of the pantograph finite element dynamic analysis model was checked. The pantograph finite element dynamic analysis model was raised to the highest working position, and a lateral load of 300N was applied to the left and right ends of the frame supporting the pantograph. The maximum offsets were 19.09mm and 19.14mm, respectively, both within the 30mm displacement range specified by the standard.

[0080] Vibration equation based on rigid structure:

[0081]

[0082] Where [M] is the pantograph mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. {u} are acceleration, velocity, and displacement vectors, respectively, and F(t) is the external load on the pantograph. Since the damping ratio of common structures is less than 10%, the impact on the structure is small. The modal analysis finite element equation is written as follows without considering structural damping:

[0083]

[0084] When the pantograph vibrates freely, that is, performs simple harmonic motion, its motion displacement vector is:

[0085] {u}=φ i sin(ω i +θ i ) (6)

[0086] The corresponding motion acceleration vector can be obtained as:

[0087]

[0088] where φ i is the i-th order vibration mode vector of the pantograph, ω i is the i-th order natural frequency, θ i is the initial phase. Substituting equations (6) and (7) into equation (5), the finite element calculation equation for the natural frequency of the pantograph structure can be obtained:

[0089]

[0090] Use finite element calculation to perform pantograph finite element dynamic analysis model modal analysis such as Figure 3 As shown, the first six low-frequency modal vibration modes are analyzed and compared with the experimental results. The results are shown in Table 3:

[0091] Table 3 Pantograph modal analysis results

[0092]

[0093] Step 4: Establish a pantograph-catenary dynamic coupling model to simulate and analyze the load impact on the pantograph finite element dynamic analysis model under the working condition of 400 kilometers per hour. Based on the actual contact network structure of the Beijing-Guangzhou line, a dynamic coupling model of the contact network and the pantograph finite element dynamic analysis model under an anchor section length is established. Further, by introducing the contact unit between the contact wire and the bow head of the pantograph finite element dynamic analysis model into the dynamic coupling model, the dynamic contact behavior of the pantograph in actual operation is simulated. The pantograph-catenary dynamic coupling simulation is carried out using the pantograph three-mass equivalent model, and its dynamic equilibrium equations are as follows:

[0094]

[0095]

[0096]

[0097] where m i , k i , c i (i=1, 2, 3) are the equivalent mass, equivalent stiffness and equivalent damping of the pantograph head, upper frame and lower frame respectively, P(t) is the dynamic contact force between the pantograph and the catenary, F0 is the total lifting force on the pantograph, y1, y2 and y3 are the displacements of the pantograph head, upper frame and lower frame.

[0098] Compare and analyze the pantograph-catenary contact force and the response of the pantograph finite element dynamic analysis model at operating speeds of 200, 300, and 400 km / h, and extract the pantograph-catenary contact force of one span in the stable section during operation and the vertical acceleration of the pantograph finite element dynamic analysis model, such as Figure 4 shown.

[0099] Apply external excitation to the pantograph finite element dynamic analysis model based on the pantograph dynamic equilibrium equation

[0100] P(t)=F0+F a +ma (12)

[0101] Where P(t) is the dynamic pantograph-catenary contact force, F0 is the static lifting force of the pantograph, and F a is the air lift force, ma is the transient impact force on the pantograph, m is the dynamic mass of the pantograph during operation, and a is the vertical acceleration. Under the above loads, the pantograph finite element dynamic analysis model performs a single-degree-of-freedom lifting motion, at which point it is in dynamic equilibrium.

[0102] Analyze the overall stress and deformation of the pantograph finite element dynamic analysis model, such as Figure 5 As shown. The relationship between the load of each component and the mechanical parameters is analyzed. The relationship between the load conditions of each rod in the pantograph finite element dynamic analysis model and the structural parameters of the pantograph finite element dynamic analysis model should satisfy the Newton-Euler mechanical equation. The rod mechanical equation group of the pantograph finite element dynamic analysis model is listed as follows:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Further analysis of the component stress of the pantograph finite element dynamic analysis model shows that the largest deformation component of the pantograph finite element dynamic analysis model is the bow head, and the largest stress component in each rod is the bow angle, such as Figure 6 As shown. Combined with the stress cloud map analysis, stress concentration is prone to occur at the hinge positions of the components of the pantograph finite element dynamic analysis model. Analysis of the stress of each hinge shaft at a speed of 400km / h shows that the maximum dynamic stress position of the pantograph finite element dynamic analysis model is the hinge shaft of the bow head-balance rod connection, and its value is 248.59MPa. Combined with the hinge shaft material parameters in Table 2, it can be seen that the stress here is less than the yield limit value of the shaft material of 315MPa, but the difference is significantly reduced at low speed. In actual pantograph operation, due to the influence of external environmental factors, the maximum stress value may be close to or even greater than the yield limit, causing damage to the pantograph components.

[0109] Step 5: Since the relationship between the pantograph finite element analysis and structural parameters is highly nonlinear, the present invention optimizes the pantograph finite element dynamic analysis model structure by constructing a response surface to improve its dynamic structural strength at a speed of 400 km / h. Specifically:

[0110] In order to ensure the consistency of the equivalent model parameters of the pantograph finite element dynamic analysis model and the pantograph-catenary contact force remains unchanged, the main structural parameters and their variation ranges of the pantograph finite element dynamic analysis model are determined as shown in Table 4.

[0111] Table 4 Optimization variable value range

[0112]

[0113] The dynamic structural strength of the pantograph finite element dynamic analysis model at a running speed of 400 km / h is taken as the optimization target. At the same time, in order to ensure the structural lateral stiffness, dominant natural frequency and pantograph mass as constraints, a pantograph optimization model is established:

[0114]

[0115] Where X represents the overall variable of pantograph optimization, Δx max and σ max They represent the maximum deformation and maximum stress of the pantograph during the dynamic simulation process of 400 km / h running speed, Δx l and Δx r They represent the maximum displacement on both sides of the pantograph in the lateral stiffness check, ω represents the first-order natural frequency of the pantograph, ∑m represents its overall mass, and X L and X UThey represent the lower limit and upper limit of the population variable X respectively.

[0116] The Latin hypercube experimental design method is adopted to sample 150 groups of design variables of the pantograph finite element dynamic analysis model, and the simulation results of dynamic strength analysis and static structural analysis of the pantograph finite element dynamic analysis model with different structural parameters can be obtained.

[0117] The present invention studies the correlation degree among the optimization objectives, constraints and optimization variables through parameter sensitivity analysis technology to reflect the influence of the structural parameters of the pantograph finite element dynamic analysis model on its dynamic strength and static structural strength at a running speed of 400 km / h.

[0118] Define S(Y,x i ) is the objective function Y for the variable parameter x i Sensitivity index:

[0119]

[0120] Where E(Y|x i ) is the variable parameter x i The average value of the objective function Y when it is a constant, Var(E(Y|x i )) is Y versus x i Var(Y) is the unconditional variance of the model output. The sensitivity analysis results are as follows: Figure 7 shown.

[0121] Based on the experimental design data, the RBF neural network model is constructed, and the response relationship between the optimization variables and the optimization objectives is fitted to obtain the corresponding response surface results, such as Figure 8 shown.

[0122] In this paper, a multi-objective genetic algorithm (MOGA) is used to optimize the structure of the pantograph finite element dynamic analysis model. The Pareto optimal solution is searched based on the response surface, and the MOGA algorithm iteration parameters are set as shown in Table 5.

[0123] Table 5 MOGA iteration parameters

[0124]

[0125] After multiple iterative searches, the Pareto optimal solution is obtained, and the optimized pantograph structural parameters are shown in Table 6.

[0126] Table 6 Design parameter optimization results

[0127]

[0128] The maximum stress of the optimized pantograph model during operation at a speed of 400 km / h is 220.84 MPa, and the maximum deformation is 30.371 mm, which are 11.2% and 14.8% lower than those of the initial model, respectively. In addition, the lateral stiffness, natural frequency and mass are all better than the initial values. Figure 9 shown.

[0129] This paper takes the dynamic structural strength of the pantograph when running at 400km / h as the optimization target, establishes a pantograph-catenary system coupling model and a three-dimensional simulation model of the pantograph under dynamic load, analyzes the static structural characteristics of the pantograph and its stress and deformation during operation at 400km / h, obtains the optimal structural parameters through neural networks and optimization algorithms, and optimizes the overall process. Figure 10 shown.

Claims

1. A method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph, characterized in that: The following steps are involved: Step 1: Select the pantograph used in high-speed trains as the research object. Build a 3D solid model based on the mechanical parameters of the DSA380 pantograph. Use the Ansys Workbench platform to perform meshing and establish a finite element dynamic analysis model for the pantograph. Add boundary conditions and constraints to the finite element dynamic analysis model based on the actual operating conditions of the pantograph. Step 2: Based on the pantograph equivalent model parameter identification method, the three-mass equivalent parameters of the established pantograph finite element dynamic analysis model at a standard working height are verified; the equivalent stiffness of the pantograph head and upper and lower frames is calculated according to the stiffness calculation formula, the equivalent mass of the pantograph head and upper and lower frames is calculated according to the single-degree-of-freedom system free vibration formula, and the equivalent damping of the lower frame is calculated according to the attenuation coefficient calculation formula and the damping coefficient calculation formula; then, simulation calculations are performed based on the calculated equivalent stiffness of the pantograph head and upper and lower frames, the equivalent mass of the pantograph head and upper and lower frames, and the equivalent damping parameters of the lower frame, and compared with the standard equivalent parameters to verify the accuracy of the pantograph finite element dynamic analysis model; Step 3: Verify the lateral stiffness of the pantograph finite element dynamic analysis model according to the International Electrotechnical Commission standard IEC 60494-1. Perform modal analysis of the pantograph finite element dynamic analysis model using finite element calculations based on the vibration equations of rigid structures. Analyze the first six low-frequency modal shapes and compare them with experimental results. Step 4: Establish a pantograph-catenary dynamic coupling model to simulate and analyze the load impact on the pantograph finite element dynamic analysis model under the working condition of 400 kilometers per hour. Based on the actual contact network structure, establish a dynamic coupling model of the contact network and the pantograph finite element dynamic analysis model under an anchor section length. Then, introduce the contact unit between the contact line and the bow head of the pantograph finite element dynamic analysis model into the dynamic coupling model to simulate the dynamic contact behavior of the pantograph-catenary during actual operation. Extract the pantograph-catenary contact force of a span length in the stable section during operation and the vertical acceleration of the pantograph finite element dynamic analysis model. Apply external excitation to the pantograph finite element dynamic analysis model based on the pantograph dynamic equilibrium equation. Analyze the overall stress and deformation of the pantograph finite element dynamic analysis model, and analyze the relationship between the load and mechanical parameters of the pantograph finite element dynamic analysis model components. Finally, analyze the stress of the pantograph finite element dynamic analysis model components and the stress of the hinge point to determine the structural danger point. Step 5: Optimize the structural strength of the pantograph finite element dynamic analysis model by constructing a response surface to improve its operating strength at a speed of 400 km / h. Based on the pantograph equivalent structural parameters and the rod mechanical equations, determine the main structural parameters and variation ranges of the pantograph finite element dynamic analysis model, and construct a pantograph optimization model. Use the Latin hypercube experimental design method to sample the design variables of the pantograph finite element dynamic analysis model, and obtain simulation results for the dynamic structural strength analysis and static structural analysis of the pantograph finite element dynamic analysis model with different structural parameters. Parameter sensitivity analysis technology is used to study the correlation between the optimization objectives, constraints, and optimization variables, and analyze the influence of the structural parameters of the pantograph finite element dynamic analysis model on its dynamic and static structural strength at an operating speed of 400 km / h. Based on the experimental design data, a RBF neural network model is constructed, and the response relationship between the optimization variables and the optimization objectives is fitted to obtain the corresponding response surface results. A multi-objective genetic algorithm (MOGA) is used to optimize the structural strength of the pantograph finite element dynamic analysis model. Pareto optimal solutions are searched based on the response surface, and the optimization results are verified through simulation.

2. The method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph according to claim 1, characterized in that: The dynamic structural strength of the pantograph includes the stress and deformation of the pantograph as a whole and the pantograph head, pantograph angle, upper arm, upper guide rod, lower arm and lower guide rod.

3. The method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph according to claim 1, characterized in that: The method for identifying the pantograph equivalent model parameters in step 2 is specifically as follows: According to the stiffness calculation formula: Calculate the equivalent stiffness K of the bow head and upper and lower frames, where F is the external load, is the maximum displacement; According to the free vibration formula of single degree of freedom system: Calculate the equivalent mass m of the bow head and upper and lower frames, where T is the system vibration period and K is the equivalent stiffness; According to the calculation formula of attenuation coefficient and damping coefficient: Calculate the equivalent damping c of the lower frame, where A0 is the reference point amplitude, A n is the amplitude that is n cycles apart from A0.

4. The method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph according to claim 1, characterized in that: The pantograph dynamic balance equation in step 4 is: Where P(t) is the dynamic pantograph-catenary contact force, F0 is the static lifting force of the pantograph, and F a is the air lift force, ma is the transient impact force of the pantograph, m is the dynamic mass of the pantograph during operation, and a is the vertical acceleration; The relationship between the load conditions of each member of the pantograph finite element dynamic analysis model and the structural parameters of the pantograph finite element dynamic analysis model should satisfy the Newton-Euler mechanical equation. The member mechanical equations of the pantograph finite element dynamic analysis model are listed as follows: Where M t is the pantograph raising torque, F ix 、F ix’、 F iy 、F iy’ The hinge points i ， i = action and reaction forces at A~G; m p 、a px、 a py They represent the mass and acceleration of the pantograph member p, p=a~e, J q Represents the moment of inertia around the hinge point q, q=a, b, c, d, e.

5. The method for optimizing the dynamic structural strength of a 400 km / h high-speed pantograph according to claim 1, characterized in that: The pantograph optimization model in step 5 is: Where X represents the overall variable of pantograph optimization, Δx max and σ max They represent the maximum deformation and maximum stress of the pantograph during the dynamic simulation process of 400 km / h running speed, Δx l and Δx r They represent the maximum displacement on both sides of the pantograph in the lateral stiffness check, ω represents the first-order natural frequency of the pantograph, ∑m represents its overall mass, and X L and X U They represent the lower and upper limits of the overall variable X respectively; In sensitivity analysis, S(Y, x i ) is the objective function Y for the variable parameter x i Sensitivity index: In the formula For variable parameters When the objective function is a constant The average value of for right The unconditional variance of the change, is the unconditional variance of the model output.

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