Step-by-step collaborative design method for equivalent static and dynamic stiffness of rail vehicle crash response

Abstract

The invention discloses a step-by-step collaborative design method for equivalent static and dynamic stiffness of collision response of rail vehicles. In the process of parameter optimization of collision response equivalence, the correlation mechanism between collision response and static response equivalence can be determined through theoretical analysis and homogeneous flexible vehicle body simulation analysis, indicating that when designing a collision posture equivalent model, the number or range of variables can be reduced through collaborative design of static equivalence, and the amount of calculation for parameter optimization in collision conditions can be reduced, thereby solving the problem of low design efficiency caused by a large number of dependent variables, a wide range and a long calculation time of collision simulation models.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle simulation, and in particular to a step-by-step collaborative design method and system for equivalent static and dynamic stiffness of rail vehicle collision response. Background Art

[0002] Accidents such as rail vehicle collisions and derailments are major safety hazards in the field of rail transportation. Since these accidents may cause serious injuries to passengers, the passive safety of rail vehicles has become an urgent issue of safety protection in this field. In rail vehicle accidents, passengers are often in an unrestrained state, which makes them more susceptible to serious injuries. Therefore, protecting the lives of passengers has become an important direction and difficulty for research and development.

[0003] Traditional real vehicle collision is an effective means to study the crashworthiness of rail vehicles, but it has huge human, material and financial costs and takes a long time to complete. The cost and time of this real vehicle collision test limit its application in practice. Therefore, numerical simulation, especially finite element simulation, has become an important tool and means to study the collision dynamic response of rail vehicles. By establishing an accurate finite element model, the dynamic response of rail vehicles in collision accidents can be simulated, and the strength and crashworthiness of their structures can be evaluated. Finite element simulation is economical, fast and safe, providing researchers with an effective testing and evaluation platform, which helps to improve the passive safety performance of rail vehicles.

[0004] However, in order to design an equivalent model of rail vehicle collision posture under the framework of equivalent similarity model design that meets the gravity criterion, it is usually necessary to optimize the vehicle parameters so that its simulated response is as close to the target response as possible, thereby achieving the purpose of equivalence. However, in this optimization process, there are often challenges such as multiple dependent variables, a wide range of variables, and time-consuming collision model calculations, which lead to low optimization efficiency.

[0005] Therefore, there is an urgent need for a method that can analyze and determine the correlation mechanism between the static response and collision response of the vehicle body, so as to provide support for the step-by-step collaborative design method of equivalent static and dynamic stiffness for the collision response of rail vehicles. Summary of the invention

[0006] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a step-by-step collaborative design method for the equivalent static and dynamic stiffness of a rail vehicle collision response.

[0007] In order to solve the above technical problems, the present invention provides a step-by-step collaborative design method for equivalent static and dynamic stiffness of rail vehicle collision response, comprising:

[0008] Step S1: Establishing a vehicle body collision working condition simulation model, and then determining the calculation working conditions and boundary conditions of statics and modal simulation;

[0009] Step S2: According to the vehicle body collision condition simulation model, modal analysis is performed to obtain the natural frequency and modal vibration shape to ensure the vehicle body modal equivalence;

[0010] Step S3: analyzing the correlation between the static response of the vehicle body and the collision response, and then generating the correlation degree between the static response of the vehicle body and the collision response;

[0011] Step S4: According to the correlation degree, an equivalent analysis of the collision response of the rail vehicle is performed by using a step-by-step collaborative design method of static and dynamic stiffness.

[0012] As a preferred embodiment of the present invention, in step S1, the method comprises the following steps:

[0013] Step S10: establishing a static finite element model of a vehicle body prototype according to the collision energy management principle of the rail vehicle and the mechanical characteristics of the vehicle body during the collision of the rail vehicle;

[0014] Step S11: establishing a vehicle body statics simulation model using a homogeneous flexible vehicle body modeling method according to the vehicle body prototype statics finite element model;

[0015] Step S12: According to the vehicle body statics simulation model, a vehicle body collision condition simulation model is established by impact calculation using Ls-dyna construction and solution.

[0016] As a preferred embodiment of the present invention, in step S1, the method further comprises the following steps:

[0017] Step S13: determining the calculation conditions of statics and modal simulation according to the vehicle body statics simulation model;

[0018] Step S14: according to the determined calculation conditions, boundary conditions are set:

[0019] load1: applies a positive uniform force along the Z direction to the front node of the vehicle traction beam in the vehicle statics simulation model;

[0020] Load2: Use RBE3 unit to connect all nodes of the section at the front end of the elastic deformation area of ​​the cab of the vehicle body statics simulation model, and apply positive torque in the X direction at the center node;

[0021] Load3: Apply full constraints on the six degrees of freedom at the end wall nodes at the two ends of the vehicle statics simulation model;

[0022] Step S15: According to the boundary conditions, the bending calculation condition of the vehicle body is set:

[0023] Sub-condition 1: Apply a positive uniform force in the Z direction to the front node of the vehicle traction beam of the vehicle statics simulation model, and apply full constraints on the six degrees of freedom in the end wall nodes at the second end of the vehicle statics simulation model;

[0024] Car body torsion calculation condition - sub-condition 2: Apply positive torque in the X direction at the front center node of the cab elastic deformation zone of the car body statics simulation model, and apply full constraints on the six degrees of freedom in the direction at the end wall node of the second end of the car body statics simulation model;

[0025] Overall vibration calculation condition - Sub-condition 3: Normal mode calculation using the Lanczos method EIGRL, with the vehicle body in a free state.

[0026] As a preferred embodiment of the present invention, in step S2, the method comprises the following steps:

[0027] Step S20: According to the dynamic characteristics of the rail vehicle body of the vehicle body collision condition simulation model, the system is discretized and simplified into n degrees of freedom, each degree of freedom is represented by a second-order differential equation, and then the motion differential equation of the entire structural discrete system is:

[0028]

[0029] Where [M], [C], and [K] represent the mass matrix, damping matrix, and stiffness matrix of n degrees of freedom, respectively; {x t}、 and Respectively represent the displacement, velocity and acceleration vector of each node, and F is the excitation force vector;

[0030] Step S21: using the mode superposition method, the motion differential equation in physical coordinates is converted into an equation in modal coordinates, so that each equation is decoupled into an independent equation represented by natural modal frequency and modal vibration parameters, and the expression is:

[0031]

[0032] Step S22: Set the solution of each equation to:

[0033] x i (t) = X i T(t),i=1,2,…,n

[0034] Among them, X i is a constant; T(t) is a function of time. i Composed into {X} vectors, forming a mode, expressed as:

[0035]

[0036] Step S23: Convert the equation to:

[0037]

[0038] The solution becomes: det[[K]-ω 2 [M]]=0, thus we get n eigenvalues ​​ω i , i = 1, 2, ..., n; where ω i is the natural circular frequency, and 0≤ω 1 2 ≤ω 2 2 ≤……≤ω n 2 ,i=1,2,…,n;

[0039] Step S24: Calculate the natural frequency:

[0040]

[0041] Then by ω i The obtained eigenvector is the corresponding mode shape: {X (i)}, i=1,2,…,n.

[0042] As a preferred embodiment of the present invention, in step S3, the method comprises the following steps:

[0043] Step S30: obtaining a vehicle body static response and a collision response according to a vehicle body collision working condition simulation model;

[0044] Step S31: Use the Pearson correlation coefficient to describe the linear correlation between the vehicle body static response and the collision response:

[0045]

[0046] Where N is the number of samples, and are the means of the two responses a and b respectively. The range of r is [-1,1]. When r=1, it means that the two responses are completely correlated, that is, each point corresponding to the two responses can be represented by the same linear relationship. When r=0, it means that there is zero correlation between the two responses. When r=-1, it means that the linear relationship between the two responses is completely negatively correlated, and they are mirror images of each other in shape. As the absolute value of r increases, the positive and negative linear correlation between the two responses becomes stronger.

[0047] As a preferred embodiment of the present invention, in step S4, the method further comprises the following steps:

[0048] Step S40: According to the vehicle body collision condition simulation model, after satisfying the static parameter equivalence of the overall geometric profile size, mass, center of mass position and moment of inertia, adjusting the parameters of the vehicle body structure and materials through a preset optimization method to satisfy the static response equivalence;

[0049] Step S41: Based on the vehicle body collision working condition simulation model and on the basis of static equivalence, the vehicle body structure and material parameters are optimized to meet the vehicle body posture equivalence under vehicle collision.

[0050] As a preferred embodiment of the present invention, in step S40, the method further includes the following steps:

[0051] Step S400: setting the variable range of elastic modulus;

[0052] Step S401: Generate RAE index:

[0053]

[0054] Then, multiple response RAEs under multiple working conditions are comprehensively compared to generate the MRAE index:

[0055]

[0056] Among them, f i and are the actual output response and target response, respectively, and RAE is the absolute value of the relative difference between the two scalars;

[0057] Step S402: Calculate the modal vibration shape:

[0058]

[0059] in, is the i-th order natural vibration mode, is the j-th order natural vibration mode;

[0060] Step S403: Setting static optimization target:

[0061]

[0062] in, and are the RAE values ​​between the vertical displacements of the vehicle body sub-condition 1 and sub-condition 2 and the corresponding results of the vehicle body prototype, and are the RAE values ​​between the 7th and 8th order natural frequencies of the vehicle body and the corresponding results of the prototype, MAC 77 is the MAC value between the 7th modal natural frequency of the uniform vehicle body and the corresponding result of the vehicle body prototype, MAC 89The MAC value representing the 9th modal natural frequency of the homogeneous flexible body and the 8th modal natural frequency of the body prototype;

[0063] Step S404: Optimize the vehicle body collision condition simulation model until MRAE reaches the minimum optimal result to meet the static response equivalence.

[0064] As a preferred embodiment of the present invention, in step S403, when the static optimization objectives are separately set to and When the minimum, the mathematical expressions corresponding to the four groups of optimization problems are:

[0065]

[0066] By optimizing each optimization problem separately, each group of optimization converges smoothly and obtains four groups of optimal results.

[0067] As a preferred embodiment of the present invention, in step S41, the method further comprises the following steps:

[0068] Step S410: defining a variable range for collision response difference optimization;

[0069] Step S411: define the sum of the cross-section displacement response differences:

[0070]

[0071] Where Dx and Dz represent the longitudinal and vertical displacements respectively, s i represents the cross section, ΔDx is the sum of the displacement response differences of the cross section in the X direction, and ΔDz is the sum of the displacement response differences of the cross section in the Z direction;

[0072] Step S412: Setting the pose equivalent optimization target:

[0073]

[0074] Step S413: using a non-dominated sorting genetic algorithm II to optimize the vehicle body structure and material parameters for the vehicle body collision condition simulation model to meet the equivalent vehicle body posture under vehicle collision.

[0075] The present invention also provides a step-by-step collaborative design system for equivalent static and dynamic stiffness of rail vehicle collision response, comprising:

[0076] Model definition module, used to establish the vehicle body collision condition simulation model, and then determine the calculation conditions and boundary conditions of static and modal simulation;

[0077] The modal analysis module is used to perform modal analysis based on the vehicle body collision condition simulation model to obtain the natural frequency and modal vibration shape to ensure the modal equivalence of the vehicle body;

[0078] A correlation analysis module, used to analyze the correlation between the static response of the vehicle body and the collision response, and then generate the correlation degree between the static response of the vehicle body and the collision response;

[0079] The equivalent analysis module is used to perform an equivalent analysis of the collision response of the rail vehicle through a static and dynamic stiffness step-by-step collaborative design method according to the correlation degree.

[0080] The present invention also provides a computer medium, on which a computer program is stored, and the computer program is executed by a processor to implement the step-by-step collaborative design method for equivalent static and dynamic stiffness of a rail vehicle collision response.

[0081] The present invention also provides a computer, characterized in that it comprises the computer medium.

[0082] The above technical solution of the present invention has the following advantages compared with the prior art:

[0083] 1. In the process of parameter optimization of collision response equivalence, the correlation mechanism between collision response and static response equivalence was determined through theoretical analysis and homogeneous flexible vehicle body simulation analysis, indicating that when designing a collision posture equivalent model, the number or range of variables can be reduced through static equivalent collaborative design, thereby reducing the amount of calculation for parameter optimization in collision conditions. This solves the problem of low design efficiency caused by a large number of dependent variables, a wide range, and a long calculation time for collision simulation models.

[0084] 2. In order to verify the effectiveness of this technology, it is applied to the equivalent design of the collision posture of a homogeneous flexible vehicle body. Compared with the method of directly optimizing the equivalent parameters of the posture, the application of this design technology can reduce a lot of calculation time and improve the design efficiency while keeping the accuracy of the proxy model close to the optimization result. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0086] Figure 1 It is a schematic diagram of the curve area difference provided by an embodiment of the present invention.

[0087] Figure 2 It is a schematic diagram of a finite element model for static analysis of a lead vehicle body provided in an embodiment of the present invention.

[0088] Figure 3: is a schematic diagram of finite element modeling of the statics of a homogeneous flexible vehicle body and a head vehicle collision condition provided by an embodiment of the present invention; wherein, Figure 3 a is a schematic diagram of the static model of a homogeneous flexible vehicle body. Figure 3 b is a schematic diagram of the finite element model of the head-on collision of a homogeneous flexible vehicle body.

[0089] Figure 4 : is a schematic diagram of static loading of the original vehicle body and the homogeneous flexible vehicle body provided by an embodiment of the present invention; wherein, Figure 4 a is a schematic diagram of the original vehicle body loading model. Figure 4 b is a schematic diagram of the homogeneous flexible body loading model.

[0090] Figure 5 It is a cloud diagram of the calculation results of Subcase 1 and Subcase 2 of the statics of the head vehicle prototype provided by the embodiment of the present invention; Figure 5 a is the result cloud diagram of Subcase1, Figure 5 b is the result cloud diagram of Subcase2.

[0091] Figure 6 is a modal vibration shape cloud diagram of the prototype of the head vehicle body provided by an embodiment of the present invention; Figure 6 a is the first-order vertical bending mode vibration cloud diagram, Figure 6 b is the first-order torsional mode vibration cloud diagram.

[0092] Figure 7 is a target response curve diagram of each cross section of a collision condition provided by an embodiment of the present invention; Figure 7 a is the longitudinal target response curve of each section under collision conditions, Figure 7 b is the target vertical section target response curve diagram of the collision condition.

[0093] Figure 8 is a curve diagram showing the variation of the collision response difference values ​​of a homogeneous flexible vehicle body provided by an embodiment of the present invention; Figure 8 a is The curve of the change of elastic modulus is Figure 8 b is Curve diagram of the change of elastic modulus.

[0094] Fig. 9 is a curve diagram showing the variation of the difference values ​​of the static mechanical responses of the homogeneous flexible vehicle body provided by the embodiment of the present invention; Fig. 9 a is and The curve of the change of elastic modulus is Fig. 9 b is and Curve diagram of the change of elastic modulus.

[0095] Fig.10It is a schematic diagram of the correlation coefficient between the static and dynamic response differences provided by an embodiment of the present invention.

[0096] Fig.11 It is a curve diagram showing the variation of the difference values ​​of the collision responses of the homogeneous flexible vehicle body provided by the embodiment of the present invention in a narrowed variable range; Fig.11 a is The curve of the change of elastic modulus is Fig.11 b is Curve diagram of the change of elastic modulus.

[0097] Fig.12 It is a curve diagram showing the variation of the difference values ​​of the static mechanical responses of the homogeneous flexible vehicle body provided by the embodiment of the present invention in a narrowed variable range; Fig.12 a is and The curve of the change of elastic modulus is Fig.12 b is and Curve diagram of the change of elastic modulus.

[0098] Fig.13 is a schematic diagram of correlation coefficients between static and dynamic response differences of a homogeneous flexible vehicle body provided by an embodiment of the present invention in a narrowed variable range; Fig.13 a is a schematic diagram of the correlation coefficient of the variable range of 200MPa≤E≤4000MPa, Fig.13 b is a schematic diagram of the correlation coefficient in the variable range of 500MPa≤E≤2000MPa.

[0099] Fig.14 It is a schematic diagram of a step-by-step collaborative design route of equivalent static and dynamic stiffness of collision response provided by an embodiment of the present invention.

[0100] Fig.15 It is a variable and response iteration record in the three working condition target optimizations provided by the embodiment of the present invention; Fig.15 a is the iterative record of elastic modulus, Fig.15 b is the iterative record of the vertical displacement of the vehicle body, Fig.15 c is the iterative record of the modal natural frequency.

[0101] Fig.16 is the convergence value of the homogeneous flexible vehicle body variables and responses in various static optimization problems provided by the embodiment of the present invention, Fig.16 a is the convergence value of elastic modulus E in each optimization problem, Fig.16 b is the convergence value of the natural frequency in each optimization problem, Fig.16 c is The convergence value in each optimization problem, Fig.16 d is Convergence value in each optimization problem.

[0102] Fig.17 It is a flow chart of the NSGA-II optimization algorithm provided by an embodiment of the present invention.

[0103] Fig.18 It is a Pareto result diagram of equivalent vehicle body parameter optimization under collision conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0104] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0105] In order to make equivalent or similar vehicle bodies meet specific response equivalence in collision, researchers usually adjust parameters such as the vehicle body's mass, center of mass, moment of inertia, damping and stiffness. From the existing relevant research analysis, we can see that: (1) the current collision response equivalence mainly focuses on the longitudinal impact response; (2) constructing the vehicle body based on static stiffness equivalence is one of the ways to achieve the goal of vehicle collision response equivalence; (3) if the collision response equivalence is to be met, it is generally necessary to take a specific collision response as a benchmark object, adjust the parameters through optimization methods, reduce the difference with the collision response, and the optimal design obtained is the equivalent model.

[0106] This application focuses on the equivalence of the posture of the vehicle body in a three-dimensional collision. The posture response is more complex than the longitudinal collision response. Therefore, in the research process, an equivalent design is carried out based on the optimization method. The optimization method is essentially a design method that selects the best solution from multiple solutions to complex problems. It is based on optimization theory and usually uses computer research methods. The implementation methods include gradient method (sensitivity method), response surface method and global search algorithm. In the equivalent design of vehicle collision posture, the design variables are parameters such as vehicle structure, materials and performance. The final objective function is to minimize the difference between the collision posture response of the equivalent model and the prototype response. The constraints come from conditions such as spatial size, processing credibility and performance requirements. Since this type of problem is generally a constrained nonlinear optimization problem, it is difficult for traditional gradient-based optimization methods to find the correct optimization solution. In current engineering research, global search algorithms are often used for parameter optimization. At the same time, according to the objective function, it can be divided into single-objective and multi-objective optimization. In order to improve the optimization efficiency, when using the results of collision finite element simulation or test to carry out parameter optimization, it is often necessary to use the means of design of experiments (DOE) to sample within the variable range, use a proxy model to approximate the relationship between the input and output of each sample point, and use the optimization algorithm based on the proxy model to find the best. However, for the design of the equivalent model of the vehicle body posture in this paper, the number of variables is large and the range is large. It still requires more sample points and a longer collision finite element calculation to build a proxy model that meets the accuracy requirements. Therefore, it is necessary to propose a technology that can ensure design accuracy and improve design efficiency for the design of the equivalent model of the vehicle body collision posture.

[0107] When using the optimization method to adjust the vehicle body parameters to approximate the static response and collision posture response, the benchmark objects are scalar response and timing curve response. The scalar response uses the static response difference index RAE. The smaller the index is, the better the equivalence of the static response is. The goal of the timing curve response is to reduce the difference between the timing response curve of the equivalent vehicle body and the corresponding response curve of the lead vehicle prototype. The smaller the difference is, the better the equivalence is. Here, it is necessary to define the timing curve difference index.

[0108] When measuring the differences between different timing curves in engineering, relevant indicators such as shape difference, phase difference and distance difference between the curves can be defined for measurement. Shape difference can be described by correlation coefficient; phase difference can be described by mutual correlation coefficient, S&G criterion error and other indicators; distance difference description indicators include Minkowski distance, Euclidean distance, dynamic time normalization distance (DTW), Fletcher distance and Hausdorff distance. This application uses curve area difference to measure the differences between timing response curves according to the characteristics of the curves and the needs of subsequent optimization. Figure 1 As shown, its definition is close to the concept of Euclidean distance, and the calculation formula is:

[0109]

[0110] Among them, a and b represent two curves respectively; x 1 and x 2 Compare the lower and upper limits of the interval separately.

[0111] Generally, when comparing or calculating the differences between different curves horizontally, it is necessary to normalize the curve area difference. In this application, the normalized curve area difference is used as an indicator to measure the difference between the response of the homogeneous head-shaped vehicle body and the response of the head vehicle prototype. The calculation formula is:

[0112]

[0113] Therefore, this application determines the correlation mechanism between the static response and collision posture response of the vehicle body structure through theoretical and homogeneous flexible vehicle body simulation analysis, providing a basis for the step-by-step collaborative design method of the static and dynamic stiffness of the vehicle body.

[0114] 1. First, the equivalent correlation mechanism between the static response of the vehicle body and the collision response is modeled:

[0115] Since the rail vehicle body has a structure close to a cuboid and has a large aspect ratio, it is often assumed to be a homogeneous beam unit or a flexible rod unit for modeling and analysis in the early stage of collision research, which can quickly obtain the macroscopic mechanical response law in the collision. The purpose of homogeneous flexible body modeling is generally to preliminarily explore the collision law and verification method, without considering the actual processing and manufacturing, so it is an idealized modeling method. This application uses homogeneous flexible body modeling when analyzing the correlation mechanism between the collision response and static response of the body, and verifying the step-by-step collaborative design method of the equivalent static and dynamic stiffness of the collision.

[0116] According to the collision energy management principle of rail vehicles and the mechanical characteristics of the car body during rail vehicle collision, the car body structure of the head car of the rail vehicle can be divided from the first end to the second end into an energy absorption zone (including the anti-climbing energy absorption structure and the plastic deformation part of the front end of the driver's cab), an elastic deformation zone of the driver's cab and a passenger compartment zone. The latter two are collectively referred to as the head car elastic deformation zone in this application. In order to facilitate the static analysis and stiffness parameter optimization of the head car elastic deformation zone, for example, the body of a certain type of subway head car is separated from the vehicle, and a finite element model for static analysis is established based on Optistruct, with reference to Figure 2As shown. The elastic mechanical properties of the body material are characterized by MAT1 cards. Regarding the body counterweight, the CMASS2 mass unit is used to distribute it at the nodes of each load-bearing structure unit and the equipment position of the body, and the equipment counterweight is connected to the corresponding position of the body through RBE3. Ignoring the curved area and connection structure of the body, the geometric dimensions of the outer contour of the elastic zone load-bearing structure are 23200mm, 3000mm and 2500mm in length, width and height respectively. Based on this size, a rectangular block is established and meshed. The total weight of the body structure and counterweight is 30.42t.

[0117] In static calculation, Optistruct is used to construct and solve the finite element model of homogeneous flexible vehicle body, refer to Figure 3 As shown in a. Exemplarily, the entity unit type used is CHEXA octahedral unit, the unit attribute is PSOLD, the unit size is 300mm, the material card is MAT1, and only elastic deformation occurs; since the mass of the prototype of the lead vehicle body is distributed on the aluminum alloy plates and counterweight nodes on all sides, in order to make the mass distribution of the homogeneous flexible body close to that of the above-mentioned prototype of the lead vehicle body and meet the equivalence of relative mass, center of mass position and moment of inertia, the density of the entity unit material is set to 1×10-13t / m3, and the total mass of all entity units under this density is extremely small and can be ignored; then, counterweights are added to the nodes of each face of the cuboid structure, and the counterweight unit type is CMASS2, and the unit mass is distributed according to the actual mass of the face of the prototype of the lead vehicle body. For example, the total mass of the wall surfaces and counterweights on both sides of the lead vehicle prototype is 5.108t. The equivalent homogeneous vehicle body adds 676 CMASS2 mass units on the corresponding surfaces of the walls on both sides except for the doors and windows, and the mass of each unit is 5.108 / 676=0.0076t. At the same time, the equipment counterweight of the lead vehicle body prototype is also constructed using CMASS2 mass units and connected to the corresponding position of the vehicle body through RBE3 rigid body units.

[0118] In the impact calculation, Ls-dyna is used to construct and solve the finite element model of the head vehicle collision, referring to Figure 3 b. The unit form, size and material parameters of the car body are consistent with those used in the static simulation. The main difference is that the mass unit card used for the counterweight is "ELEMENT_MASS" and the equipment counterweight connection unit is a Rigid unit. In addition, in the collision calculation, the coupler, anti-climbing energy absorption structure and bogie of the above-mentioned head car prototype are connected to the corresponding positions of the car body.

[0119] Second, the target response of vehicle body statics and collision conditions is carried out:

[0120] When conducting static analysis conditions and target responses, determine the calculation conditions and boundary conditions for statics and modal simulation. The body of a rail vehicle is mainly subjected to compression, bending, and torsion loads during a collision. When the body is under pressure, the load mainly comes from the hook buffer, anti-climbing energy absorption transposition, and the driver's cab plastic deformation zone. The axial forces in these areas act on the body, which are basically loaded at the center of the body section in the form of eccentric loads. The bending moment generated by the axial force of the eccentric load causes the body to bend and twist. The displacements generated by these forms of motion are more significant than the displacements directly generated by axial compression. Therefore, for the static simulation of the body, the axial loading condition is not considered for the time being. For the bending and torsion of the body, three boundary conditions are set:

[0121] 1. Apply a positive uniform force along the Z direction at the front node of the traction beam, with a magnitude of 1×104N, which is load1;

[0122] 2. Use RBE3 unit to connect all nodes of the section at the front end of the elastic deformation zone of the cab, and apply a positive torque in the X direction at the center node, with a magnitude of 3×106N·mm, which is load2;

[0123] 3. Apply full constraints on the six degrees of freedom in the two end wall nodes, which is load3.

[0124] Therefore, for the three typical deformation conditions of the vehicle body, namely, vehicle body bending, torsion and overall vibration, the following static calculation conditions are established respectively:

[0125] 1. Subcase1, linear statics calculation condition: load1+load3;

[0126] 2. Subcase2, linear statics calculation condition: load2+load3;

[0127] 3. Subcase 3, normal mode calculation condition: Using the normal mode calculation of the Lanczos method EIGRL, the car body is in a free state. The rail vehicle is mainly subjected to medium and low frequency loads during operation and collision. According to TB / T3550.1-2019, the two main indicators for evaluating the modal stiffness of the car body are the first-order vertical bending frequency and the first-order torsional frequency of the chassis. Here, the 7th-order first-order torsional and the 8th-order first-order vertical bending natural frequencies and modal vibration shapes are taken as equivalent objects.

[0128] Therefore, in order to conveniently describe the deformation results in the static analysis and verify the equivalence of the static response, the section where the cab and the car body are connected is defined as S1, which intersects with the four side lines of the car body at four nodes N1-N4; the equivalence is judged based on whether the displacement changes of the four nodes are consistent:

[0129] (1) Whether the average z-direction displacements of the four nodes in Subcase 1 are consistent in the original vehicle body and the homogeneous flexible vehicle body;

[0130] (2) Whether the average z-direction displacement of nodes N1 and N3 (or N2 and N4) in Subcase 2 is consistent in the original car body and the homogeneous flexible car body;

[0131] The calculation results of the lead vehicle prototype under two working conditions are referenced Figure 5 The z-direction displacement cloud diagram shows that the average node displacement of the S1 section in the Subcase 1 condition is The average displacement of nodes N1 and N3 in Subcase 2 is

[0132]

[0133] To ensure the modal equivalence of the vehicle body, the natural frequency and modal vibration shape are mainly obtained through modal analysis. For the rail vehicle body of this application, the vibration characteristics of the elastic deformation area in the collision are linear. In order to characterize the dynamic characteristics of the continuous structure, the system of the original structure is first discretized and simplified into a system with n degrees of freedom. Each degree of freedom can be described by a second-order differential equation. The motion differential equation of the entire structural discrete system can be expressed as:

[0134]

[0135] Where [M], [C] and [K] represent the mass matrix, damping matrix and stiffness matrix of the multi-degree-of-freedom system respectively; {x t}、

[0136] and They represent the displacement, velocity and acceleration vectors of each node respectively, and F is the excitation force vector acting on the system.

[0137] When solving a system of differential equations of motion with multiple degrees of freedom, it is difficult to solve due to the coupling between the equations. In this case, the principle of mode superposition can be used to transform the original system of equations in physical coordinates into a system of equations in modal coordinates, so that each equation can be decoupled into an independent equation represented by natural modal frequency and modal vibration parameters. Since the modal parameters of the system are not affected by external forces, and the structure does not consider the influence of damping, the differential equation of motion can be formulated as a free and undamped vibration system, that is:

[0138]

[0139] Assume that the solution to each equation is of the form: x i (t) = X i T(t),i=1,2,…,n, where X iis a constant, T(t) is a function of time, and all X i The {X} vector is called the system configuration, or mode, and is expressed as:

[0140]

[0141] From this, the differential equation of motion can be formulated as:

[0142]

[0143] The equation solved becomes:

[0144] det[[K]-ω 2 [M]]=0

[0145] It can obtain n eigenvalues ​​ω i ,i=1,2,…,n,called ω i is the natural circular frequency of the system, satisfying:

[0146] 0≤ω 1 2 ≤ω 2 2 ≤……≤ω n 2 ,i=1,2,…,n

[0147]

[0148] Among them, f i That is the i-th order natural frequency of the system, given by ω i The obtained characteristic vector is the corresponding natural vibration mode {X (i)}, i=1,2,…,n.

[0149] Reference of vibration contour diagram of free normal mode of the prototype of the head car with counterweight Figure 6 As shown, the first six modes of the lead car are free rigid body modes, the 7th and 8th mode vibration modes are first-order vertical bending and first-order torsion modes, and the corresponding modal frequencies are ω7=7.84Hz and ω8=9.90Hz, respectively. The counterweights of the load-bearing structures of various parts of the car body and the equipment counterweights reduce the natural frequency value of the bare car body.

[0150] Collision response reference of homogeneous flexible vehicle body Figure 3 The simulation calculation shown in b shows that the target collision response is the longitudinal and vertical displacement time series curves of the three sections from front to back of the body of the lead vehicle prototype under the collision condition of 15km / h, reference Figure 7 As shown in the figure, Dx and Dz represent the longitudinal and vertical displacements respectively, and the subscript S i(i = 1, 2, 3) represents three cross-sections. Its variables are the elastic modulus E of the car body material and the initial collision velocity of 15 km / h. The same cross-sections as those of the prototype of the leading car are selected, and the cross-section displacements are obtained for equivalence.

[0151] When conducting the correlation analysis of the equivalence between the static response and the collision response of the car body, the DOE method is used to perform parametric analysis and correlation test on the equivalence between the collision response and the static response of a homogeneous flexible car body under the collision condition of 15 km / h and different variable ranges (design intervals).

[0152] To test the correlation between the static response and the collision response equivalence, the Pearson correlation coefficient is used to describe its degree of linear correlation. The expression is:

[0153]

[0154] Among them, and are the means of the two responses a and b respectively. The range of r is [-1, 1]. When r = 1, it means that the two responses are completely correlated, that is, each point corresponding to the two responses can be represented by the same linear relationship; when r = 0, it means that there is zero correlation between the two responses; when r = -1, it means that the linear relationship between the two responses is completely negatively correlated and is mirror images in shape. As the absolute value of r increases, it indicates that the positive (negative) linear correlation between the two responses is stronger. The corresponding correlation judgment rules are shown in the following table:

[0155] Pearson r Coefficient Judgment Rules Table

[0156] Absolute value range Relevance 0 Zero correlation (0,0.3] Micro-correlation (0.3，0.5] Real correlation (0.5，0.8] Significant correlation (0.8,1] Highly correlated

[0157] When conducting the parametric analysis and correlation test of the initial variable range, in order to cover a larger range as much as possible, the initial range is set to 200 MPa < E ≤ 20000 MPa, where E is the elastic modulus of the homogeneous flexible car body material. The full factor sampling method is used to generate 20 sample points within this variable range. The difference in the normalized curve area between the collision response curve of the homogeneous flexible car body and the response curve of the prototype car body of the leading car is referred to Figure 8 as shown. Dx and Dz represent the longitudinal and vertical displacements respectively. The subscript S i (i = 1, 2, 3) represents three cross-sections. For and The overall change trend of the normalized area difference of the response curve is relatively close. As the variable elastic modulus E increases from 200MPa to 20000MPa, the area difference first decreases, then increases, and finally tends to be stable, which means that there is a reasonable elastic modulus value or range that can make the four types of response differences reach a low level; and when the elastic modulus continues to increase, the vehicle body can gradually be regarded as a rigid body, and its dynamic response under collision tends to converge. The smaller the difference value of the response curve, the closer the corresponding response is to the prototype response of the lead vehicle, and the better the equivalence. Therefore, the elastic modulus can be optimized to minimize the comprehensive difference value of each response.

[0158] At the same time, the response differences of the four static working conditions are analyzed with the change of elastic modulus. Fig. 9 As shown. For the displacement response in static calculation and the natural frequency response of the specified mode, RAE (the relative absolute error) is defined to characterize the above scalar differences. This indicator is the absolute value of the relative difference between the two scalars, and the expression is:

[0159]

[0160] Among them, fi and are the actual output response and target response respectively.

[0161] and Respectively represent the RAE values ​​between the vertical displacement of the homogeneous flexible car body Subcase 1 and 2 and the corresponding results of the car body prototype. When E>200MPa, and The change trends are the same, both increase slowly with the increase of E and approach 1; and The definition of , when its value is closer to 1, it means that the vehicle body stiffness is greater and the actual displacement value Dz is closer to 0; and They represent the RAE values ​​between the 7th and 9th order natural frequencies of the homogeneous flexible body and the corresponding results of the prototype, which also increase rapidly with the increase of E, that is, the corresponding natural frequency values ​​increase accordingly, which is also caused by the increase in the body stiffness.

[0162] According to the similarity of the changing trends of the response difference values, the correlation coefficients between the response difference values ​​were calculated and compared according to the above correlation formula. Fig.10 As shown in the figure, the higher the blue saturation, the stronger the positive correlation; the higher the red saturation, the stronger the negative correlation; the variable's own comparative correlation coefficient value is 1, which is represented by a black block. As for the relationship between elastic modulus and response, it can be seen from the leftmost column or the bottom row that E is only related to and Highly positively correlated, but weakly linearly correlated with the other responses; for static responses, and There is a high positive correlation between and There is a high negative correlation between them. For collision response, and The correlations between the three cross-sections are significant, and the other responses are highly positively correlated. The correlation coefficient between them is greater than 0.998, that is, within this variable range, the responses of the three sections maintain a basically synchronous change trend. In addition, It can maintain a high positive correlation with other collision responses; except In addition, It maintains a high negative correlation with the other collision responses; and There is not much correlation with the collision response.

[0163] Since there are many variables in the actual equivalent vehicle body optimization design process, if the accuracy of the proxy model is improved by simply adding sampling points within a larger variable range, the amount of calculation required will be greatly increased, reducing the efficiency and accuracy of the equivalent vehicle body design. Therefore, a reasonable and effective approach is to reduce the design interval of the variables. From the heat map analysis, it can be seen that within the variable range of 200MPa≤E≤20000MPa, some static response differences and collision responses can maintain a high positive correlation; here, the variable range of the homogeneous flexible vehicle body is first reduced to 200MPa≤E≤4000MPa, resampled and analyzed, and then the parameter analysis and correlation analysis results of the static response and collision response differences are used to determine whether to further reduce the variable range.

[0164] In the variable range of 200MPa≤E≤4000MPa, the full factor sampling method is applied to regenerate 20 sample points, and the collision response and static response of the sample points are calculated to obtain the influence of the elastic modulus on the difference change of each response. Fig.11 As shown in Figure 2, within this variable range, the variation trend of the collision response differences is similar to that under 200MPa≤E≤20000MPa, which first decreases, then increases, and then tends to be stable. There is a common smaller variable range that can further reduce the difference value. Within the variable range of 200MPa≤E≤4000MPa, refer to Fig.12 As shown in Figure 2, the static response difference maintains a similar trend to that in the range of 200MPa≤E≤20000MPa. Fig.13As shown in a, the correlation coefficients between its variables, static and dynamic responses are also highly similar in the range of 200MPa≤E≤20000MPa.

[0165] According to the above results, the variable range is further narrowed to 500MPa≤E≤2000MPa. Within this range, the full factor sampling method is used to regenerate 20 sample points and calculate the changes in the corresponding responses. Fig.11 and Fig.12 In this range, the difference in collision response with the increase of elastic modulus has a completely different trend from the previous one: Keep fluctuating up and down, and there is a small difference in the response between the three sections; They all decrease first, then increase, and then decrease, and the changes between the three sections remain independent and the differences are obvious. Within 500MPa≤E≤2000MPa, there is no common change trend similar to the small interval for each collision response difference. At this time, the optimization needs to balance between the differences in each response. Static response difference and They all decrease first and then increase, but the trough positions are farther apart; and The correlation coefficient between the variables, static and dynamic responses within the range of 500MPa≤E≤2000MPa is shown in Table 1. Fig.13 As shown in b, the distribution trend is obviously different from the previous two larger ranges, mainly in the correlation coefficients between collision responses and between statics and collision responses: for collision response, and The correlation between them weakened or became negatively correlated; There is still a high positive correlation between them, but the degree is weakened; There is still a significant positive correlation between them, and the degree is also weakened; in the correlation between the static response and the collision response, there is a trend of weakening correlation and a positive-negative correlation conversion phenomenon. The above changes all show that: within this small variable range, the correlation between the response difference values ​​will be weakened, the independence will be stronger, there is no common change trend, and the equivalence of static response cannot represent the equivalence of collision response. This is also consistent with and Fig.11 and Fig.12 The changing characteristics of the small variable range response differences in the three variables confirm each other. Therefore, through the analysis of the changing trends and correlation coefficients of the response differences within the three variable ranges, it can be concluded that:

[0166] (1) When performing equivalent design of a vehicle body under collision response, if optimization is performed directly within a smaller range, the optimal solution may be missed; if optimization is performed within a larger range, there will be problems such as excessive calculation, low precision of the proxy model, and inaccurate optimization results.

[0167] (2) When the variable range is large, such as 200MPa≤E≤20000MPa and 200MPa≤E≤4000MPa, the collision response difference of the homogeneous flexible body generally maintains a relatively similar change trend, and there is a strong linear correlation between it and the static response difference;

[0168] (3) When the variable range is narrowed to a certain range, for example, 500MPa≤E≤2000MPa, the change trends of the collision response differences are different, the correlation coefficient is weakened, and the correlation coefficient with the static response difference is also weakened, and even the positive and negative correlation is reversed, indicating that there are different optimal solutions for each response in this range to minimize the difference. At this time, it is not suitable to continue to narrow the variable range, and parameter optimization should be performed directly within this range;

[0169] (4) The difference in collision response and the difference in static response maintain a strong correlation within a larger variable range, but show a weak correlation within a smaller variable range.

[0170] 3. Again, the technical verification of the step-by-step collaborative design method for equivalent static and dynamic stiffness of rail vehicle collision is carried out:

[0171] In order to improve the design efficiency of the flexible body equivalent model, according to the correlation mechanism of static and dynamic response equivalence obtained from theoretical analysis and simulation analysis of homogeneous flexible body, this application proposes a step-by-step collaborative design technology of static and dynamic stiffness, and uses a homogeneous flexible body finite element model to verify the feasibility of this method.

[0172] When the collision response is equivalent, it is necessary to determine the number of variables and the range of variables in parameter optimization. From the above technical analysis, it can be seen that a large range of variables will lead to problems such as low accuracy of the proxy model, large errors, and difficulty in finding the best solution. This problem can be solved by appropriately narrowing the range of variables. When the number of variables is small, the equivalence of the equivalent vehicle body collision response changes with the variables more regularly. At this time, the range can be gradually narrowed through parameter analysis. However, when the number of variables is large and the change trends of the equivalence of each response are inconsistent, it is difficult to directly narrow the range of variables using the parameter analysis method.

[0173] Therefore, a step-by-step collaborative design method for equivalent static and dynamic stiffness of collision response is proposed, that is, in response to the design requirements of the equivalent model of vehicle body collision posture: on the premise of satisfying the equivalence of static parameters such as overall geometric contour size, mass, center of mass position and moment of inertia, the parameters of the vehicle body structure and materials are first adjusted by optimization methods to meet the equivalence of static response. Since the static solution is relatively time-consuming and the number and range of variables can be reduced according to the static optimization results, this method can reduce the number of collision model solutions; finally, on the basis of static equivalence, the vehicle body structure and material parameters are further optimized to meet the equivalence of vehicle body posture under vehicle collision and realize the improvement of design efficiency. Its design ideas refer to Fig.14 shown.

[0174] When performing the static equivalent optimization process, for a homogeneous flexible body, its stiffness can only be adjusted by changing the elastic modulus E, so the optimization is mainly carried out for the elastic modulus E. Because the static calculation speed is fast, it is possible to directly seek the best solution within a larger variable range to avoid missing the optimal solution outside the variable range. The variable range of this optimization E is set at 20MPa≤E≤20000MPa, and E is the elastic modulus of the homogeneous flexible body material; the goal of this optimization problem is to minimize the error between the Z-direction displacement of the homogeneous flexible body and the displacement of the prototype body in the two working conditions, and to minimize the difference between the modal natural frequency and the original body frequency, and measure the response difference through the RAE indicator of the RAE or MRAE formula. When performing optimization analysis in Hyperstudy, the "System Identification" tool can be used to define the optimization target to approximate the target value under a single working condition or multiple working conditions, that is, to minimize the RAE or MRAE. RAE is the absolute value of the relative difference between two scalars, and the expression is:

[0175]

[0176] Among them, f i and are the actual output response and the target response respectively; the comprehensive comparison of multiple response RAEs under multiple working conditions is defined as the MRAE index (the multiple relative absolute error):

[0177]

[0178] It is also necessary to verify the low-order natural frequencies ω of the model and prototype i Whether the difference is within the acceptable error range and its corresponding mode vibration MAC ij Is it ≥ 0.9? If all are satisfied, the equivalence of the vehicle body natural frequency and modal vibration mode can be proved. Among them, the modal assurance criterion MAC (Modal Assurance Criteria, MAC) is defined as:

[0179]

[0180] in, is the i-th order natural vibration mode of a system, is the jth natural vibration mode of the system or another system; MAC ij It changes between 0 and 1. When the two vibration modes are in the same system, MAC ij Represents the distinction between natural vibration modes of each order, MAC ij The closer it is to 0, the higher the distinction between the two vibration modes. When the two vibration modes are in different systems and i=j, if MAC ij The closer it is to 1, the more similar the natural vibration modes of the two systems at this order of natural frequency are; in this application, MAC ij When ≥0.9, the natural vibration modes of the two systems at the i-th order are equivalent.

[0181] After establishing the static parameter optimization model of the homogeneous flexible vehicle body with different objectives, the solution is carried out according to the following process:

[0182] (1) Convert the original finite element calculation file into a Templex parameterized file, where the variable is the elastic modulus E;

[0183] (2) Set goals and constraints in Hyperstudy;

[0184] (3) Select optimization algorithm and set algorithm parameters;

[0185] (4) Directly call the Optistruct solver to perform each optimization iteration and finally obtain the optimal solution.

[0186] Here we choose the most common genetic algorithm (GA), and its genetic algorithm parameters are set as follows: population size 50, mutation probability 0.01, crossover rate 0.7, maximum and minimum evolutionary generations are 200 and 25 respectively.

[0187] Therefore, the static equivalent optimization result is:

[0188] (1) When the static optimization target of the homogeneous flexible vehicle body is set to satisfy all three working conditions, the mathematical expression of the optimization problem is:

[0189]

[0190] in, and They represent the RAE values ​​between the vertical displacements of the homogeneous flexible car bodies Subcase 1 and 2 and the corresponding results of the car body prototype; and Respectively represent the RAE values ​​between the 7th and 9th order natural frequencies of the homogeneous flexible body and the corresponding results of the prototype; MAC77 represents the MAC value between the 7th order modal natural frequency of the homogeneous flexible body and the corresponding results of the body prototype; MAC89 represents the MAC value between the 9th order modal natural frequency of the homogeneous flexible body and the 8th order modal natural frequency of the body prototype;

[0191] For a homogeneous flexible car body of this size, the 7th-order modal vibration type is a first-order vertical bending mode, the 8th-order modal vibration type is a first-order lateral bending mode, and the 9th-order modal vibration type is a first-order torsion mode, which is different from the original car body. Therefore, when extracting the first-order vertical bending and first-order torsion modes of the homogeneous flexible car body, the 7th and 9th-order modes are selected; after 25 generations of evolution, the optimal result with the minimum target value of all working conditions is obtained, which is referenced Fig.15 As shown in the figure, it is the iterative record of variables and responses. In the early stage of optimization, the variables and responses basically reach convergence, and the corresponding final specific convergence values ​​and the errors between them and the target values ​​are shown in the following table:

[0192] Equivalent vehicle body static working condition comprehensive optimization error table

[0193]

[0194] In the calculation, although the optimization result minimizes the MRAE in the optimization problem formula, when it comes to each variable or response: the minimum error value is 24.70% of the first-order vertical bending frequency, and the maximum error is 104.77% of the first-order torsional frequency; this shows that for this homogeneous body structure, even if the body stiffness can be adjusted by changing the elastic modulus, it is difficult to meet the stiffness requirements of multiple working conditions at the same time.

[0195] (2) When the static optimization objectives of the homogeneous flexible vehicle body are set separately and When it is the smallest, there are four sets of optimization problems, referred to as Subcase1, Subcase2, first-order vertical bending and first-order torsion, and their corresponding mathematical expressions are:

[0196]

[0197] Each optimization problem is optimized separately, and each group of optimization converges smoothly, obtaining four groups of optimal results. Fig.16 As shown in the figure, the final convergence values ​​of variables and responses in the above four groups of optimizations; for the optimal parameters obtained, in the four groups of optimizations, to satisfy Subcase 1 The elastic modulus is the largest, which is 1602MPa, and the torsional force of Subcase 2 is The elastic moduli obtained by equivalent and first-order torsional mode equivalent are relatively close, which are 180MPa and 215MPa respectively; the convergence value of the elastic modulus obtained by the first-order vertical bending mode equivalent is 559MPa; the final convergence values ​​of the target responses of the four groups of optimizations are basically consistent with the responses of the original vehicle body, indicating that when a single response is used as the target of the homogeneous flexible vehicle body optimization problem, it can be optimized to the precise target value; in addition, the elastic moduli obtained by the four groups of optimizations are relatively concentrated relative to the entire variable range, distributed between 180-1600MPa, and the deformation mode of Subcase2 torsional stress is relatively close to the first-order torsional mode vibration mode, and the optimal variable values ​​obtained are also relatively close.

[0198] When the collision response of a homogeneous flexible vehicle body is equivalent, since the optimal elastic modulus obtained by static optimization in multiple static working conditions and a single static working condition is maintained between 180-1600MPa, the variable range of the new collision response difference optimization is set to 150-2000MPa according to the convergence characteristics of the variables of each working condition.

[0199] Depend on Fig.13 b Analysis shows that the collision response difference value and There is an overall negative correlation between the three sections. The positive correlation is strong but there are differences. Therefore, the equivalent problem of collision response of homogeneous flexible car body is suitable for multi-objective optimization to find parameters. The sum of the displacement response differences of the three sections is defined as:

[0200]

[0201] Where Dx and Dz represent the longitudinal and vertical displacements respectively, s i represents the cross section, ΔDx is the sum of the displacement response differences of the cross section in the X direction, and ΔDz is the sum of the displacement response differences of the cross section in the Z direction. Minimizing the above two comprehensive response differences is taken as the two objectives of the optimization problem.

[0202] Therefore, the equivalent optimization definition expression of the collision response of the homogeneous flexible vehicle body is:

[0203]

[0204] In order to compare the optimization efficiency of this method, the collision posture is directly used as the target response for parameter optimization. The variable range is 20MPa≤E≤20000MPa. The expression of the optimization problem is:

[0205]

[0206] For multi-objective optimization problems, the non-dominated sorting genetic algorithm II (NSGA-II) is used for optimization. NSGA-II is developed for multi-objective optimization problems based on genetic algorithms, Pareto concepts, and fast non-dominated sorting algorithms. It has good results in engineering applications of multi-objective optimization. The core ideas and steps of the algorithm are briefly described as follows: the initial population is subjected to fast non-dominated sorting with the introduction of an elite strategy, thereby increasing the probability that excellent individuals are retained; then the population is subjected to selection, crossover, and mutation operations in the genetic algorithm; finally, the method of crowding calculation is used to select suitable excellent individuals, ensuring the positivity of individuals in the population, facilitating selection, crossover, and mutation of individuals throughout the entire interval, and forming a new population. NSGA-II can take into account both convergence and diversity in optimization. The corresponding flowchart can be referenced. Fig.17 As shown in the figure, the NSGA-II algorithm parameter settings are as follows: population size 120, evolutionary generations 200, and crossover probability 0.9.

[0207] Set up a posture response difference proxy model, and build a proxy model between the variables of the optimization problem and the two objectives based on the results of the finite element calculation; in engineering parameter analysis and optimization research, common proxy models include polynomial model (Response surface method, RSM), Kriging model, support vector machine (SVM) model and radial basis function (RBF) model. This application uses the RBF model for fitting. This model is a type of function that fits multivariate discrete data. It uses the Euclidean distance between the test point and the sample point as the independent variable, selects a suitable radial function as the kernel function (basis function), adds polynomial functions as needed, and then linearly superimposes each function to obtain the final radial basis function. The total function expression is:

[0208]

[0209] Where N and n are the number of sampling points and the order of fitting sampling points respectively; x and x n represent the design variables of the function and the design variables at the nth sampling point, respectively, and ||xx n || represents the Euclidean distance between two points; φ(||xx n ||) represents the basis function with Euclidean distance as the variable, λ n is the unknown function weight coefficient; the linear superposition function in the second part of the formula is the linear superposition of K polynomials, which generally exists when the radial basis function fitting in the first part is incomplete, where p j (x) and c jThey are polynomial functions and corresponding coefficients respectively. For the selection of basis functions in the first part, common ones are: Cubic cubic function, Liner linear function, Gaussian Gaussian distribution function, Multi-quadric function and TPS thin plate spline function, etc. Different basis functions have obvious differences in performance, and it is necessary to select the appropriate basis function according to the fitting conditions.

[0210] The radial basis function proxy model has the following characteristics:

[0211] (1) It is suitable for complex nonlinear problems. It has good fitting effects for models with many parameters and scattered data, and is not limited to grid data.

[0212] (2) The interpolation accuracy is high, and accurate fitting is performed at the sampling points;

[0213] (3) If the basis function is positive definite, then the entire radial basis function can approximate any continuous function;

[0214] (4) The sample size does not need to be too large.

[0215] Generally, when constructing a proxy model based on sample data, it is necessary to judge the accuracy of model fitting and prediction. In order to measure the accuracy of the prediction target of the RBF proxy model constructed in this application, the definitions of three evaluation indicators are introduced here, namely, the coefficient of determination (R2), the average relative error (ARE) and the maximum relative error (MRE). The definitions of the three indicators are as follows:

[0216]

[0217] Where n is the number of samples used for the model fitting or the number of additional samples added to verify the model. and i Represent the predicted value and true value of the i-th sample respectively, is the average value of the true value of the sample; R2 is also called goodness of fit, which represents a measure of the goodness of fit of the surrogate model. The closer its value is to 1, the better the model fitting quality. In engineering, if R2 exceeds 0.9, it can be considered that the fitting accuracy meets the requirements; the indicators ARE and MRE are the average and maximum values ​​of the sample relative errors, respectively, representing the overall error of the sample and the local maximum error. The smaller their values ​​are, the better.

[0218] In order to construct an RBF proxy model, this application uses the static and dynamic stiffness step-by-step collaborative design and applies the full factor sampling method to generate 25 sample points within the corresponding variable range. For the method of directly using the collision posture as the target response for parameter optimization, 250 sample points are generated within the corresponding variable range. Subsequently, the cross validation method is used to verify the error, that is, for a data set of N sample points, a certain number of verification points are randomly selected before the verification begins. Each time, N-1 sample points are selected to train the data, and one sample is left out to verify the quality of the model prediction, which is also called leave-one-out cross validation.

[0219] After testing the fitting accuracy of the RBF models constructed by the two methods, the results are shown in the table of accuracy of the proxy model predicting the collision response of a homogeneous flexible vehicle body. All error indicators meet the accuracy requirements. Therefore, multi-objective optimization can be performed based on the two proxy models. The accuracy of the proxy model of method No. 2 is slightly higher than that of method No. 1, and both are within the error requirement range.

[0220] Accuracy table of surrogate model predicting collision response of homogeneous flexible vehicle body

[0221]

[0222] Reference to Pareto results obtained by two methods of multi-objective optimization Fig.18 As shown in the figure, the amplitudes and trends of the two scatter curves are relatively close, and the changing trends of the two response differences ΔDx and ΔDz are opposite, which is consistent with the results of the correlation analysis in the previous article. The appropriate optimal solution can be selected in the Pareto solution set according to the demand for the difference in the two target responses in actual engineering. At the same time, the resources used for calculation of the two methods are shown in the statistical table of computing resources for optimizing the two methods. The static equivalent and collision equivalent calculation times of method No. 1 are 12h and 75h respectively, totaling 87h; the collision equivalent time of method No. 2 is 750h. When the model and result accuracy are relatively close, the static and dynamic stiffness step-by-step collaborative design technology is used to reduce the calculation time by 88.4%, thereby improving the design efficiency.

[0223] Computing resource statistics of two optimization methods

[0224]

[0225] Therefore, the present application proposes a step-by-step collaborative design technology for equivalent static and dynamic stiffness of collision response. First, the design concept of adjusting parameters based on optimization methods to approximate the prototype response when designing an equivalent model is introduced, and an indicator for measuring equivalence is introduced. In the process of parameter optimization of collision response equivalence, there are problems of low design efficiency caused by the large number and wide range of dependent variables and the long calculation time of collision simulation models. To solve this problem, the correlation mechanism between the equivalence of collision response and static response is determined through theoretical analysis and homogeneous flexible body simulation analysis, which shows that when designing an equivalent model of collision posture, the number or range of variables can be reduced through collaborative design of static equivalence, and the calculation amount of parameter optimization in collision conditions can be reduced. The whole process is the step-by-step collaborative design technology for equivalent static and dynamic stiffness of collision response. Subsequently, in order to verify the effectiveness of this technology, it was applied to the equivalent design of the collision posture of a homogeneous flexible vehicle body. Compared with the method of directly optimizing the equivalent parameters of the posture, the application of this design technology can reduce the calculation time by 88.4% while keeping the accuracy of the proxy model close to the optimization result, thereby improving the design efficiency. Therefore, this design technology can be applied to the equivalent analysis and design of the collision response of rail vehicles.

[0226] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0227] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A step-by-step collaborative design method for equivalent static and dynamic stiffness of rail vehicle collision response, characterized in that: The following steps are involved: Step S1: Establishing a vehicle body collision working condition simulation model, and then determining the calculation working conditions and boundary conditions of statics and modal simulation; Step S2: According to the vehicle body collision condition simulation model, modal analysis is performed to obtain the natural frequency and modal vibration shape to ensure the vehicle body modal equivalence; Step S3: analyzing the correlation between the static response of the vehicle body and the collision response, and then generating the correlation degree between the static response of the vehicle body and the collision response; The following steps are involved: Step S30: obtaining a vehicle body static response and a collision response according to a vehicle body collision working condition simulation model; Step S31: Use the Pearson correlation coefficient to describe the linear correlation between the vehicle body static response and the collision response: Where N is the number of samples, and are the means of the two responses a and b, respectively. i and b i are the i-th values ​​of responses a and b respectively, and the range of r is [-1,1]. When r=1, it means that the two responses are completely correlated, that is, each point corresponding to the two responses can be represented by the same linear relationship. When r=0, it means that there is zero correlation between the two responses. When r=-1, it means that the linear relationship between the two responses is completely negatively correlated, and they are mirror images of each other in shape. As the absolute value of r increases, the positive and negative linear correlation between the two responses becomes stronger. Step S4: According to the correlation degree, performing rail vehicle collision response equivalent analysis by using a static and dynamic stiffness step-by-step collaborative design method; comprising the following steps: Step S40: According to the vehicle body collision condition simulation model, after satisfying the static parameter equivalence of the overall geometric profile size, mass, center of mass position and moment of inertia, adjusting the parameters of the vehicle body structure and materials through a preset optimization method to satisfy the static response equivalence; The following steps are involved: Step S400: setting the variable range of elastic modulus; Step S401: Generate RAE index: Then, multiple response RAEs under multiple working conditions are comprehensively compared to generate the MRAE index: Among them, f i and are the actual output response and target response, respectively, and RAE is the absolute value of the relative difference between the two scalars; Step S402: Calculate the modal vibration shape: in, is the i-th order natural vibration mode, is the j-th order natural vibration mode; Step S403: Setting static optimization target: Where, E is the elastic modulus of the body material, and are the RAE values ​​between the vertical displacements of the vehicle body sub-condition 1 and sub-condition 2 and the corresponding results of the vehicle body prototype, and are the RAE values ​​between the 7th and 8th order natural frequencies of the vehicle body and the corresponding results of the prototype, MAC 77 is the MAC value between the 7th modal natural frequency of the homogeneous flexible body and the corresponding result of the body prototype, MAC 89 The MAC value representing the 9th modal natural frequency of the homogeneous flexible body and the 8th modal natural frequency of the body prototype; Step S404: Optimizing the vehicle body collision condition simulation model until MRAE reaches the minimum optimal result to meet the static response equivalence; Step S41: Based on the vehicle body collision working condition simulation model and on the basis of static equivalence, the vehicle body structure and material parameters are optimized to meet the vehicle body posture equivalence under vehicle collision.

2. The method for step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to claim 1, characterized in that: In step S1, the method comprises the following steps: Step S10: establishing a static finite element model of a vehicle body prototype according to the collision energy management principle of the rail vehicle and the mechanical characteristics of the vehicle body during the collision of the rail vehicle; Step S11: establishing a vehicle body statics simulation model using a homogeneous flexible vehicle body modeling method according to the vehicle body prototype statics finite element model; Step S12: constructing a vehicle body collision condition simulation model based on Ls-dyna solution according to the vehicle body statics simulation model.

3. The method for step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to claim 2, characterized in that: In step S1, the method further comprises the following steps: Step S13: determining the calculation conditions of statics and modal simulation according to the vehicle body statics simulation model; Step S14: according to the determined calculation conditions, boundary conditions are set: load1: applies a positive uniform force along the Z direction to the front node of the vehicle traction beam in the vehicle statics simulation model; Load2: Use RBE3 unit to connect all nodes of the selected section at the front end of the elastic deformation area of ​​the cab of the vehicle body static simulation model, and apply positive torque in the X direction at the center node; Load3: Apply full constraints on the six degrees of freedom at the end wall nodes at the two ends of the vehicle statics simulation model; Step S15: According to the boundary conditions, the bending calculation condition of the vehicle body is set: Sub-condition 1: Apply a positive uniform force in the Z direction to the front node of the vehicle traction beam of the vehicle statics simulation model, and apply full constraints on the six degrees of freedom in the end wall nodes at the second end of the vehicle statics simulation model; Car body torsion calculation condition - sub-condition 2: Apply positive torque in the X direction at the front center node of the cab elastic deformation zone of the car body statics simulation model, and apply full constraints on the six degrees of freedom in the direction at the end wall node of the second end of the car body statics simulation model; Overall vibration calculation condition - Sub-condition 3: Normal mode calculation using the Lanczos method EIGRL, with the vehicle body in a free state.

4. The method for step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to claim 1, characterized in that: In step S2, the method comprises the following steps: Step S20: According to the dynamic characteristics of the rail vehicle body of the vehicle body collision condition simulation model, the system is discretized and simplified into n degrees of freedom, each degree of freedom is represented by a second-order differential equation, and then the motion differential equation of the entire structural discrete system is: Where [M], [C], and [K] represent the mass matrix, damping matrix, and stiffness matrix of n degrees of freedom, respectively; {x t }、 and They represent the displacement, velocity and acceleration vectors of each node respectively, and F is the excitation force vector; Step S21: using the mode superposition method, the motion differential equation in physical coordinates is converted into an equation in modal coordinates, so that each equation is decoupled into an independent equation represented by natural modal frequency and modal vibration parameters, and the expression is: Step S22: Set the solution of each equation to: x i (t)=X i T(t),i=1,2,…,n Among them, X i is a constant; T(t) is a function of time. i Composed into {X} vectors, forming a mode, expressed as: Step S23: Convert the equation to: The solution becomes: det[[K]-ω 2 [M]] = 0, where det represents the determinant, ω is the natural circular frequency to be determined, and thus n eigenvalues ​​ω are obtained. i , i = 1, 2, ..., n; where ω i is the i-th natural circular frequency, and 0≤ω1 2 ≤ω2 2 ≤……≤ω n 2 ,i=1,2,…,n; Step S24: Calculate the natural frequency: Then by ω i The obtained eigenvector is the corresponding mode shape: {X (i) }, i=1,2,…,n.

5. The method for step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to claim 1, characterized in that: In step S403, when the static optimization objectives are set to and When the minimum, the mathematical expressions corresponding to the four groups of optimization problems are: By optimizing each optimization problem separately, each group of optimization converges smoothly and obtains four groups of optimal results.

6. The method for step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to claim 1, characterized in that: In step S41, the method further comprises the following steps: Step S410: defining a variable range for collision response difference optimization; Step S411: define the sum of the cross-section displacement response differences: Where Dx and Dz represent the longitudinal and vertical displacements respectively, s i represents the cross section, ΔDx is the sum of the displacement response differences in the X direction of the cross section, and ΔDz is the sum of the displacement response differences in the Z direction of the cross section. is the displacement response difference in the X direction of the i-th section, is the displacement response difference in the Z direction of the i-th section; Step S412: Setting the pose equivalent optimization target: Step S413: using a non-dominated sorting genetic algorithm II to optimize the vehicle body structure and material parameters for the vehicle body collision condition simulation model to meet the equivalent vehicle body posture under vehicle collision.

7. A step-by-step collaborative design system for equivalent static and dynamic stiffness of rail vehicle collision response, characterized in that: The method for implementing the step-by-step collaborative design of equivalent static and dynamic stiffness of rail vehicle collision response according to any one of claims 1 to 6 comprises: Model definition module, used to establish the vehicle body collision condition simulation model, and then determine the calculation conditions and boundary conditions of static and modal simulation; The modal analysis module is used to perform modal analysis based on the vehicle body collision condition simulation model to obtain the natural frequency and modal vibration shape to ensure the modal equivalence of the vehicle body; A correlation analysis module, used to analyze the correlation between the static response of the vehicle body and the collision response, and then generate the correlation degree between the static response of the vehicle body and the collision response; The equivalent analysis module is used to perform an equivalent analysis of the collision response of the rail vehicle through a static and dynamic stiffness step-by-step collaborative design method according to the correlation degree.

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