Response surface method-based steel spring floating slab track parameter design method and system

Abstract

The invention discloses a steel spring floating slab track parameter design method and system based on a response surface method. The method comprises the following steps: constructing a vertical coupling dynamic model of a vehicle-steel spring floating slab track; obtaining at least one parametric variable, inputting the at least one parametric variable into the vertical coupling kinetic model to obtain a response value corresponding to the at least one parametric variable, and performing polynomial fitting regression on the at least one parametric variable and the response value to obtain a target function of the response value; determining a response surface function between the target function and the at least one parameter variable according to a response surface method; and according to the response surface function, solving to obtain the value of the parameter variable which enables the target function to be optimal and meets the constraint condition requirement. And multi-objective optimization of dynamic characteristics of various steel spring floating slab track structures such as steel rail acceleration and floating slab acceleration is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of urban rail parameter design, and in particular relates to a steel spring floating plate rail parameter design method and system based on a response surface method. Background Art

[0002] Since subway lines usually pass through downtown areas with large passenger flow, commercial centers with dense buildings, scenic spots or ancient buildings, scientific research institutes and hospitals with precision instruments, and areas with special regulations on vibration and noise, when subway trains are running, the buildings and people above them will inevitably be affected by the vibration and noise of the foundation or surface caused by the subway operation, and the people and instruments in the buildings will also be affected by secondary vibration and secondary noise. Especially after the construction of a subway network that extends in all directions, the impact of vibration and noise generated by subway operation on the environment will increase and become a public nuisance that cannot be ignored.

[0003] The steel spring floating plate track structure is a common vibration reduction measure in modern rail transit. The reasonable design of its structural parameters is of great significance to ensure the stability of the track structure and improve driving safety. Different structural parameters will have a great impact on the dynamic characteristics of the system, such as the stiffness of the steel spring, the thickness of the floating plate, the size of the track structure, etc. If these parameters are not designed reasonably, it will have an adverse effect on the dynamic characteristics and vibration reduction performance of the track structure. Under the action of train loads, unreasonable structural parameter design will aggravate the deterioration of the line and cause problems such as diseases in the track structure. These diseases will not only affect the normal use of the track structure, but may also cause safety accidents. For example, the insufficient stiffness of the steel spring floating plate track structure will cause excessive deformation of the track structure, thereby affecting the smoothness and safety of the train. Summary of the invention

[0004] The present invention provides a steel spring floating plate track parameter design method and system based on response surface method, which are used to solve the technical problem that unreasonable structural parameter design of steel spring floating plate track will have adverse effects on the dynamic characteristics and vibration reduction performance of the track structure.

[0005] In a first aspect, the present invention provides a method for designing track parameters of a steel spring floating plate based on a response surface method, comprising:

[0006] Construct a vertical coupling dynamic model of vehicle-steel spring floating plate track;

[0007] Acquire at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamics model to obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value;

[0008] determining a response surface function between the objective function and the at least one parameter variable according to a response surface methodology;

[0009] According to the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the requirements of the constraint conditions are solved.

[0010] In a second aspect, the present invention provides a steel spring floating plate track parameter design system based on a response surface method, comprising:

[0011] A construction module configured to construct a vertical coupled dynamic model of a vehicle-steel spring floating plate track;

[0012] a fitting module, configured to obtain at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamics model, obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value;

[0013] a determination module configured to determine a response surface function between the objective function and the at least one parameter variable according to a response surface method;

[0014] The solution module is configured to solve, based on the response surface function, the parameter variable value that makes the objective function optimal and meets the constraint requirements.

[0015] According to a third aspect, an electronic device is provided, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the steps of the method for designing steel spring floating plate track parameters based on the response surface method according to any embodiment of the present invention.

[0016] In a fourth aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor executes the steps of the steel spring floating plate track parameter design method based on the response surface method of any embodiment of the present invention.

[0017] The steel spring floating plate track parameter design method and system based on response surface methodology of the present application realize multi-objective optimization of the dynamic characteristics of various steel spring floating plate track structures such as rail acceleration and floating plate acceleration by adjusting the steel spring stiffness, steel spring damping and floating plate density based on response surface methodology, providing technical method support for the dynamic characteristics analysis and vibration reduction and noise reduction optimization design of urban rail transit. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0019] Figure 1 A flow chart of a method for designing track parameters of a steel spring floating plate based on a response surface method according to an embodiment of the present invention;

[0020] Figure 2 A structural block diagram of a steel spring floating plate track parameter design system based on response surface methodology provided by one embodiment of the present invention;

[0021] Figure 3 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0023] See also Figure 1 , which shows a flow chart of a steel spring floating plate track parameter design method based on response surface methodology of the present application.

[0024] like Figure 1 As shown in FIG. 1 , the parameter design method of the steel spring floating plate track based on the response surface method specifically includes the following steps:

[0025] Step S101, constructing a vertical coupling dynamic model of a vehicle-steel spring floating plate track.

[0026] In this step, the vehicle-track coupling system is decomposed into a vehicle system and a steel spring floating plate track system, and the vehicle system and the steel spring floating plate track system are coupled vertically by the wheel-rail contact relationship, wherein the vehicle system includes a vehicle body, a secondary suspension system, a bogie, a primary suspension system and a wheelset from top to bottom, and the steel spring floating plate track system includes rails, fasteners, a floating plate, a steel spring and a foundation under the rail from top to bottom;

[0027] The vehicle system takes into account the heave and nodding motion of the vehicle body, the heave and nodding motion of the front and rear frames, and the vertical vibration of the four wheel sets, a total of 10 degrees of freedom. The expression of the vibration differential equation of the vehicle system is:

[0028]

[0029] In the formula, [M v ]、[C v ]、[K v ] are the mass matrix, stiffness matrix and damping matrix of the vehicle system, {Z v} are the displacement vector, velocity vector and acceleration vector of the vehicle system respectively, {P v} is the generalized force vector of the vehicle system;

[0030] The rail is regarded as a discrete point supported Euler beam, and the Ritz method is used to solve it. The canonical vibration mode coordinates of the rail are introduced to obtain the second-order ordinary differential equations of the vibration mode coordinates of the rail, which are expressed as follows:

[0031]

[0032] In the formula, is the vibration coordinate of the rail, p j (t) is the wheel-rail force of the jth wheelset, Z k (x i ) is the vibration mode of the sleeper support, Z k (x wj ) is the wheel vibration mode, E r ,I r are the elastic modulus and section inertia moment of the rail, m r , L r are the mass per unit length of the rail and the total length of the rail, k is a positive integer, π is the circumference of a circle, and q k (t) is the generalized coordinate of rail vibration, F rsi (t) is the support reaction force at the i-th fastener position, x i 、x wj are the coordinates of the ith fastener and the jth wheelset along the train, nr is the number of fasteners, and Nr is the rail modal order;

[0033] The floating slab is regarded as a discrete point supported Euler beam, and the Ritz method is used to solve the vertical vibration differential equation of the track slab, which is expressed as:

[0034]

[0035] In the formula, E s ,I s are the elastic modulus and section inertia moment of the track plate, Z s (x, t) is the vibration displacement of the track plate, M s is the mass of the track slab, L s is the length of the track plate, Cs , k s are the distributed damping and distributed stiffness of the filling layer under the track slab along the length direction, t is the train running time, x is the train running coordinate, x i is the coordinate of the ith fastener when running along the train;

[0036] The Hertz nonlinear elastic contact model is applied to determine the vertical force between the wheel and the rail through the vertical elastic compression between the wheel and the rail. The vibration of the vehicle system and the vibration of the steel spring floating plate track system are coupled through the wheel-rail force to obtain the vibration model, which is expressed as follows:

[0037]

[0038] δZ(t)=Z wj (t)-Z r (x wj , t)-Z0(t),

[0039] G=3.86R -0.115× 10 -8 ,

[0040] Where P(t) is the wheel-rail force, G is the wheel-rail contact constant, δZ(t) is the elastic compression between the wheel and rail, and Z wj (t) is the vertical displacement of the jth wheel at time t, Z r (x wj , t) is the vertical displacement of the rail under the jth wheel at time t, Z0(t) is the vertical irregularity of the track, and R is the wheel radius;

[0041] For the vehicle-track coupled dynamic system, the explicit integration method is used to obtain the system dynamic response generated by the train operation through iterative calculation, and the time history curve of the train vibration load is determined. The expression is:

[0042] {X n+1}={X n}+{V n}Δt+(1 / 2+ψ){A} n Δt 2 -ψ{A} n-1 Δt 2 ,

[0043]

[0044] {A n+1}=[M] -1 ({F} n+1 -[K] n+1 {X} n+1 -[C] n+1 {V} n+1 ),

[0045] In the formula, ψ is the integration constant, Δt is the integration time step, {X n+1} is the system displacement at time n+1, {X n} is the displacement of the system at time n, {V n} is the system speed at time n, {A} n is the system acceleration at time n, {A} n-1 is the system acceleration at time n-1, [M] is the system mass, {F} n+1 is the system force at time n+1, [K] n+1 is the system stiffness at time n+1, [C] n+1 The system damping at time n+1, the initial condition is {X}0={V}0={A}0=0.

[0046] Step S102, obtaining at least one parameter variable, and inputting the at least one parameter variable into the vertical coupling dynamic model, obtaining a response value corresponding to the at least one parameter variable, and performing polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value.

[0047] In this step, multiple single-factor variation tests are carried out on the steel spring floating plate track structure with steel spring stiffness, steel spring damping and floating plate density as influencing factors; with rail acceleration and floating plate acceleration as judgment criteria, the influence of each factor on the dynamic characteristics of the steel spring floating plate track structure is obtained according to the single-factor test; on the basis of the single-factor test, the steel spring stiffness, steel spring damping and floating plate density are selected as investigation factors, and the rail acceleration and floating plate acceleration are used as response values, and a three-factor two-level test scheme is designed to experimentally design the parameters of the steel spring floating plate track structure; the polynomial fitting regression of the experimental data in the experimental design is carried out to obtain the objective function of the response value.

[0048] Specifically, the expression of the objective function is:

[0049]

[0050] In the formula, y1 is the first objective function, y2 is the second objective function, α2 is the unknown coefficient of the constant term in the first objective function, α2 is the unknown coefficient of the constant term in the second objective function, and α ij is the unknown coefficient of the target term in the quadratic function, α i is the coefficient of the first-order term in the objective function, n is the number of parameter variables, x i is the i-th parameter variable, x j is the jth parameter variable.

[0051] In order to determine the unknown coefficients of the target term in the quadratic function, m independent tests are required, where m ≥ k = (n + 1) (n + 2) / 2. Each test obtains the response value y(i) (i = 0, 1, ..., m-1) of the target function corresponding to m samples according to the different values ​​of the design variables. The least squares principle can be used to obtain:

[0052] β=(X T X) -1 X T y

[0053] In the formula, γ is the unknown coefficient of the target item, X is the design variable of m independent experiments, and y is the response value of the objective function of m independent experiments;

[0054] in,

[0055] In the formula, is the first variable value of the initial test, is the kth variable value of the initial trial, is the first variable value of m-1 trials, is the kth variable value of m-1 trials;

[0056]

[0057] In the formula, y (0) is the initial objective function response value, y (1) is the objective function response value of the first trial, y (m-1) is the objective function response value of m-1 trials;

[0058]

[0059] In the formula, β0 is the coefficient of the initial target item to be determined, β1 is the coefficient of the target item to be determined, and β k-1 is the undetermined coefficient of the m-1th objective term;

[0060]

[0061] In the formula, x n-1 is the value of the n-1th variable, x n is the nth variable value;

[0062]

[0063] In the formula, α (n-1)n is the interaction coefficient between the n-1th variable and the nth variable;

[0064] Substitute the experimental design variable x and the corresponding response value y into β=(X T X) -1 XT y, the unknown coefficients in the polynomial function can be found, and thus the fitted polynomial function can be obtained.

[0065] Step S103: determining a response surface function between the objective function and the at least one parameter variable according to a response surface method.

[0066] In this step, the range and initial value of steel spring stiffness, steel spring damping, and floating plate density are determined according to the relevant requirements of the steel spring floating plate track technical specifications and actual engineering values. The expression of the response surface function is:

[0067]

[0068] Where y1 is the rail acceleration, y2 is the floating plate acceleration, x1 is the steel spring stiffness, x2 is the steel spring damping, x3 is the floating plate density, a is the design minimum value of the steel spring stiffness, b is the design maximum value of the steel spring stiffness, c is the design minimum value of the steel spring damping, d is the design maximum value of the steel spring damping, e is the design minimum value of the floating plate density, and f is the design maximum value of the floating plate density.

[0069] The design requirements in the technical specifications for steel spring floating slab tracks are compared with the dynamic characteristics calculated from multiple single factor variation tests;

[0070] If the calculation results differ from the design requirements, the design requirements shall be set as the design target;

[0071] If the calculation results meet the design requirements, then the design requirements are set as constraints;

[0072] Among them, the design requirements include rail acceleration and floating plate acceleration.

[0073] Step S104, according to the response surface function, solving to obtain the values ​​of the parameter variables that make the objective function optimal and meet the requirements of the constraint conditions.

[0074] In this step, based on the response surface function, a constrained optimization problem solving method is used to obtain the values ​​of the parameter variables that make the objective function optimal and meet the constraints.

[0075] In summary, the method of the present application is based on the response surface methodology and realizes multi-objective optimization of the dynamic characteristics of various steel spring floating plate track structures such as rail acceleration and floating plate acceleration by adjusting the steel spring stiffness, steel spring damping, and floating plate density, providing technical method support for the dynamic characteristics analysis and vibration and noise reduction optimization design of urban rail transit.

[0076] In a specific embodiment, a vehicle-steel spring floating plate track vertical coupling dynamic model is established, and the relevant vehicle and steel spring floating plate structural parameters are shown in Tables 1 and 2 below.

[0077] Table 1 Related parameters of metro type B vehicle

[0078]

[0079] Table 2 Parameters of steel spring floating plate track structure

[0080]

[0081] The parameter gradients of steel spring stiffness, steel spring damping, and floating plate density are set as shown in Table 3 below, and the influence of each factor on the dynamic characteristics of the steel spring floating plate track structure is calculated.

[0082] Table 3 Gradient table of parameters

[0083]

[0084] Result analysis:

[0085] 1) Influence of steel spring stiffness on rail acceleration

[0086] From the perspective of time domain, the rail acceleration fluctuates within the stiffness range of 5-20kN / mm, and shows an overall downward trend; from the perspective of frequency domain, within 0-40Hz, the rail acceleration vibration level decreases with the increase of stiffness, and the opposite rule occurs after exceeding 40Hz.

[0087] 2) Influence of steel spring stiffness on floating plate acceleration

[0088] From the perspective of time domain, the acceleration of the floating plate fluctuates within the stiffness range of 5-20kN / mm, and shows an overall upward trend. From the perspective of frequency domain, within 0-40Hz, the acceleration level of the floating plate decreases with the increase of stiffness, and the opposite rule occurs after exceeding 40Hz.

[0089] 3) Influence of steel spring damping on rail acceleration

[0090] From the perspective of time domain, the rail acceleration is 6.57-6.58m / s 2 From the frequency domain perspective, the rail acceleration level decreases with the increase of damping within 8-40Hz, but the overall change is not significant.

[0091] 4) Effect of steel spring damping on the acceleration of floating plate

[0092] From the perspective of time domain, the acceleration of the floating plate decreases with the increase of damping; from the perspective of frequency domain, the acceleration of the floating plate decreases with the increase of damping after 8 Hz.

[0093] 5) Influence of floating plate density on rail acceleration

[0094] From the perspective of time domain, the rail acceleration is 2500-3200kg / m 3 It increases within the range and decreases beyond the range; from the frequency domain perspective, the acceleration level of the rail does not change much with density.

[0095] 6) The influence of floating plate density on the acceleration of floating plate

[0096] From the perspective of time domain, the acceleration of the floating plate decreases with the increase of density; from the perspective of frequency domain, the acceleration level of the floating plate decreases with the increase of density after 40Hz.

[0097] Response Surface Experimental Design:

[0098] On the basis of single factor test, steel spring stiffness (A), steel spring damping (B) and floating plate density (C) were selected as investigation factors, rail acceleration (y1) and floating plate acceleration (y2) were used as response values, and the Box-Benhnken method was used to design a three-factor three-level test scheme to optimize the experimental design of steel spring floating plate track structure parameters. The experimental factors and level settings are shown in Table 4, and the response surface test design and results are shown in Table 5.

[0099] Table 4 Experimental factors and level settings

[0100]

[0101] Table 5 Response surface experimental design and results

[0102]

[0103] Objective function establishment:

[0104] The experimental results were regressed by polynomial fitting using Design-Expert software, and the quadratic polynomials of rail acceleration (y1), floating plate acceleration (y2), spring stiffness (A), spring damping (B), and floating plate density (C) were obtained:

[0105] y1=6.2731-0.0107*A+3.1703e-3*B+1.7162e-4*C+8.005e-5*A*B+3.0938e-7*A*C-1.5064e-6*B*C,

[0106] y2=13.5943+0.2169*A-0.0481*B-5.32e-3*C-6.9213e-4*A*B-8.8813e-6*A*C+7.35e-6*B*C-2.2969e-3*A 2 +1.2028e-4*B 2 +6.2552e-7*C 2 ,

[0107] Regression model statistical analysis:

[0108] The model variance analysis was performed using the binary regression equation, and the results are shown in Tables 6 and 7.

[0109] Table 6 Results of variance analysis of rail acceleration regression model

[0110]

[0111] Table 7 Analysis of variance results of floating slab acceleration regression model

[0112]

[0113] The results in Table 6 show that the significance level of the regression model is P = 0.0002, indicating that the established regression model is significant; the determination coefficient R 2 =0.9552, indicating that the model can explain 95.52% of the changes in the response value; R Adj 2 =0.9104, indicating that the regression equation has a good fitting condition, indicating that the regression model established in the present invention can better describe the relationship between each factor and the response value, can fit the actual test results, and can be used to guide the optimization of the structural parameters of the steel spring floating plate.

[0114] The results in Table 7 show that the significance level of the regression model is P<0.0001, indicating that the established regression model is significant; the determination coefficient R 2 =0.9917, indicating that the model can explain 99.17% of the changes in the response value; R Adj 2 =0.9810, indicating that the regression equation has a good fitting condition, indicating that the regression model established in the present invention can better describe the relationship between each factor and the response value, can fit the actual test results, and can be used to guide the optimization of the structural parameters of the steel spring floating plate.

[0115] Establishment of response surface function:

[0116] According to the technical specifications of steel spring floating plate track, the selectable value ranges of A, B, and C are as follows:

[0117] A∈[10,30], B∈[40,120], C∈[2800,3600];

[0118] Substituting the value range of A, B, and C into the response surface function, we get:

[0119]

[0120] After analysis, the optimal design parameters of the steel spring floating plate track structure are: steel spring stiffness (A) is 15kN / mm, steel spring damping (B) is 100kN*s / m, floating plate density (C) is 3400kg / m 3 Under this condition, the vertical coupling dynamic model of vehicle-steel spring floating plate track is established, and the acceleration of the rail and the floating plate are obtained to be 6.6446m / s 2 , 2.9625m / s 2 , which is consistent with the actual value of 6.8252m / s 2 、3.52212m / s 2 The reductions were 2.65% and 15.9% respectively, indicating that the models established by the single factor method and the response surface optimization method are effective and feasible, which fully verifies the effectiveness of the steel spring floating plate track structural parameter design method proposed in this application in optimizing the dynamic characteristics of the steel spring floating plate track.

[0121] See also Figure 2 , which shows a structural block diagram of a steel spring floating plate track parameter design system based on response surface method in the present application.

[0122] like Figure 2 As shown, the steel spring floating plate track parameter design system 200 includes a construction module 210 , a fitting module 220 , a determination module 230 and a solution module 240 .

[0123] Among them, the construction module 210 is configured to construct a vertical coupling dynamic model of a vehicle-steel spring floating plate track; the fitting module 220 is configured to obtain at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamic model to obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value; the determination module 230 is configured to determine the response surface function between the objective function and the at least one parameter variable according to the response surface method; the solution module 240 is configured to solve the parameter variable value that makes the objective function optimal and meets the constraint requirements according to the response surface function.

[0124] It should be understood that Figure 2 Modules and references documented in Figure 1Therefore, the operations and features described above for the method and the corresponding technical effects are also applicable to Figure 2 The modules in it will not be described in detail here.

[0125] In some other embodiments, the embodiments of the present invention further provide a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor is caused to execute the steel spring floating plate track parameter design method based on the response surface method in any of the above method embodiments;

[0126] As an implementation mode, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are configured as follows:

[0127] Construct a vertical coupling dynamic model of vehicle-steel spring floating plate track;

[0128] Acquire at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamics model to obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value;

[0129] determining a response surface function between the objective function and the at least one parameter variable according to a response surface methodology;

[0130] According to the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the requirements of the constraint conditions are solved.

[0131] The computer-readable storage medium may include a program storage area and a data storage area, wherein the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the steel spring floating plate track parameter design system based on the response surface method, etc. In addition, the computer-readable storage medium may include a high-speed random access memory, and may also include a memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the steel spring floating plate track parameter design system based on the response surface method via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0132] Figure 3 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention, such as Figure 3As shown, the device includes: a processor 310 and a memory 320. The electronic device may also include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330 and the output device 340 may be connected via a bus or other means. Figure 3 The example of connecting through a bus is taken. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running the non-volatile software programs, instructions and modules stored in the memory 320, that is, the steel spring floating plate track parameter design method based on the response surface method of the above-mentioned method embodiment is realized. The input device 330 can receive input digital or character information, and generate key signal input related to user settings and function control of the steel spring floating plate track parameter design system based on the response surface method. The output device 340 may include display devices such as display screens.

[0133] The electronic device can execute the method provided by the embodiment of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the method provided by the embodiment of the present invention.

[0134] As an implementation mode, the electronic device is applied to a steel spring floating plate track parameter design system based on response surface method, and is used for a client, and includes: at least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can:

[0135] Construct a vertical coupling dynamic model of vehicle-steel spring floating plate track;

[0136] Acquire at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamics model to obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value;

[0137] determining a response surface function between the objective function and the at least one parameter variable according to a response surface methodology;

[0138] According to the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the requirements of the constraint conditions are solved.

[0139] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiment.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing track parameters of steel spring floating slabs based on response surface methodology, characterized in that: include: Construct a vertical coupling dynamic model of vehicle-steel spring floating plate track; Acquire at least one parameter variable, and input the at least one parameter variable into the vertical coupling dynamics model to obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value; determining a response surface function between the objective function and the at least one parameter variable according to a response surface methodology; According to the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the requirements of the constraint conditions are solved.

2. A method for designing track parameters of a steel spring floating plate based on response surface methodology according to claim 1, characterized in that: The vertical coupling dynamic model of the vehicle-steel spring floating plate track is constructed as follows: The vehicle-track coupling system is decomposed into a vehicle system and a steel spring floating plate track system, and the vehicle system and the steel spring floating plate track system are coupled vertically by the wheel-rail contact relationship, wherein the vehicle system includes a vehicle body, a secondary suspension system, a bogie, a primary suspension system and a wheelset from top to bottom, and the steel spring floating plate track system includes rails, fasteners, floating plates, steel springs and a foundation under the rail from top to bottom; The vehicle system takes into account the heave and nodding motion of the vehicle body, the heave and nodding motion of the front and rear frames, and the vertical vibration of the four wheel sets, a total of 10 degrees of freedom. The expression of the vibration differential equation of the vehicle system is: In the formula, [M v ]、[C v ]、[K v ] are the mass matrix, stiffness matrix and damping matrix of the vehicle system, {Z v } are the displacement vector, velocity vector and acceleration vector of the vehicle system respectively, {P v } is the generalized force vector of the vehicle system; The rail is regarded as a discrete point supported Euler beam, and the Ritz method is used to solve it. The canonical vibration mode coordinates of the rail are introduced to obtain the second-order ordinary differential equations of the vibration mode coordinates of the rail, which are expressed as follows: In the formula, is the vibration coordinate of the rail, p j (t) is the wheel-rail force of the jth wheelset, Z k (x i ) is the vibration mode of the sleeper support, Z k (x wj ) is the wheel vibration mode, E r ,I r are the elastic modulus and section inertia moment of the rail, m r , L r are the mass per unit length of the rail and the total length of the rail, k is a positive integer, π is the circumference of a circle, and q k (t) is the generalized coordinate of rail vibration, F rsi (t) is the support reaction force at the i-th fastener position, x i 、x wj are the coordinates of the ith fastener and the jth wheelset along the train, nr is the number of fasteners, and Nr is the rail modal order; The floating slab is regarded as a discrete point supported Euler beam, and the Ritz method is used to solve the vertical vibration differential equation of the track slab, which is expressed as: In the formula, E s ,I s are the elastic modulus and section inertia moment of the track plate, Z s (x, t) is the vibration displacement of the track plate, M s is the mass of the track slab, L s is the length of the track plate, C s , k s are the distributed damping and distributed stiffness of the filling layer under the track slab along the length direction, t is the train running time, x is the train running coordinate, x i is the coordinate of the ith fastener when running along the train; The Hertz nonlinear elastic contact model is applied to determine the vertical force between the wheel and the rail through the vertical elastic compression between the wheel and the rail. The vibration of the vehicle system and the vibration of the steel spring floating plate track system are coupled through the wheel-rail force to obtain the vibration model, which is expressed as follows: δZ(t)=Z wj (t)-Z r (x wj ,t)-Z0(t), G=3.86R -0.115 ×10 -8 , Where P(t) is the wheel-rail force, G is the wheel-rail contact constant, δZ(t) is the elastic compression between the wheel and rail, and Z wj (t) is the vertical displacement of the jth wheel at time t, Z r (x wj , t) is the vertical displacement of the rail under the jth wheel at time t, Z0(t) is the vertical irregularity of the track, and R is the wheel radius; For the vehicle-track coupled dynamic system, the explicit integration method is used to obtain the system dynamic response generated by the train operation through iterative calculation, and the time history curve of the train vibration load is determined. The expression is: {X n+1 }={X n }+{V n }Δt+(1 / 2+ψ){A} n Δt 2 -ψ{A} n-1 Δt 2 , {A n+1 }=[M] -1 ({{F} n+1 -[K] n+1 {X} n+1 -[C] n+1 {V} n+1 ), In the formula, ψ is the integration constant, Δt is the integration time step, {X n+1 } is the system displacement at time n+1, {X n } is the displacement of the system at time n, {V n } is the system speed at time n, {A} n is the system acceleration at time n, {A} n-1 is the system acceleration at time n-1, [M] is the system mass, {F} n+1 is the system force at time n+1, [K] n+1 is the system stiffness at time n+1, [C] n+1 The system damping at time n+1, the initial condition is {X}0={V}0={A}0=0.

3. The method for designing track parameters of a steel spring floating plate based on response surface methodology according to claim 1 is characterized in that: The expression of the objective function is: In the formula, y1 is the first objective function, y2 is the second objective function, α1 is the unknown coefficient of the constant term in the first objective function, α2 is the unknown coefficient of the constant term in the second objective function, and α ij is the unknown coefficient of the target term in the quadratic function, α i is the coefficient of the first-order term in the objective function, n is the number of parameter variables, x i is the i-th parameter variable, x j is the jth parameter variable.

4. The method for designing track parameters of a steel spring floating plate based on response surface methodology according to claim 1 is characterized in that: The expression of the response surface function is: Where y1 is the rail acceleration, y2 is the floating plate acceleration, x1 is the steel spring stiffness, x2 is the steel spring damping, x3 is the floating plate density, a is the design minimum value of the steel spring stiffness, b is the design maximum value of the steel spring stiffness, c is the design minimum value of the steel spring damping, d is the design maximum value of the steel spring damping, e is the design minimum value of the floating plate density, and f is the design maximum value of the floating plate density.

5. The method for designing track parameters of a steel spring floating plate based on response surface methodology according to claim 1 is characterized in that: The step of solving the parameter variables to obtain the optimal value of the objective function and meet the constraint requirements according to the response surface function includes: According to the response surface function, a constrained optimization problem solving method is used to obtain the values ​​of parameter variables that make the objective function optimal and meet the requirements of constraint conditions.

6. A steel spring floating plate track parameter design system based on response surface methodology, characterized in that: include: A construction module configured to construct a vertical coupled dynamic model of a vehicle-steel spring floating plate track; a fitting module configured to obtain at least one parameter variable, input the at least one parameter variable into the vertical coupling dynamics model, obtain a response value corresponding to the at least one parameter variable, and perform polynomial fitting regression on the at least one parameter variable and the response value to obtain an objective function of the response value; a determination module configured to determine a response surface function between the objective function and the at least one parameter variable according to a response surface method; The solution module is configured to solve, based on the response surface function, the parameter variable value that makes the objective function optimal and meets the constraint requirements.

7. An electronic device, characterized in that: include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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