Steel spring floating slab track parameter design method and system based on response surface method

Abstract

The application discloses a steel spring floating slab track parameter design method and system based on a response surface method, and the method comprises the following steps: constructing a vertical coupling dynamic model of a vehicle-steel spring floating slab track; acquiring at least one parameter variable, 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 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 the response surface method; and solving the response surface function to obtain the value of the parameter variable which makes the target function optimal and meets the constraint condition requirement. The method realizes multi-objective optimization of various steel spring floating slab track structure dynamic characteristics such as rail acceleration and floating slab acceleration.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of urban rail parameter design, and particularly relates to a steel spring floating slab track parameter design method and system based on a response surface method. BACKGROUND

[0002] Because a subway line usually passes through a downtown area with a large number of people, a commercial center with dense buildings, a scenic area or a group of ancient buildings, a scientific research institute or a hospital with precision instruments, and an area with special regulations on vibration and noise, the buildings and people above the subway train will inevitably be affected by the ground or surface vibration and noise caused by the subway operation, and the people and instruments in the buildings will also be affected by the secondary vibration and secondary noise. Especially after the subway network is built, the vibration and noise generated by the subway operation will rise to become a public nuisance that cannot be ignored.

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

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

[0005] In a first aspect, the present application provides a steel spring floating slab track parameter design method based on a response surface method, comprising:

[0006] Constructing a vertical coupling dynamics model of a vehicle-steel spring floating slab track;

[0007] Obtaining at least one parameter variable and inputting 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 performing polynomial fitting regression on the at least one parameter variable and the response value to obtain a target function of the response value;

[0008] determine a response surface function between the target function and the at least one parameter variable according to the response surface method;

[0009] solving the value of the parameter variable which makes the target function optimal and meets the requirement of the constraint condition according to the response surface function.

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

[0011] a construction module configured to construct a vertical coupling dynamics model of a vehicle-steel spring floating slab track;

[0012] 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 a target function of the response value;

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

[0014] a solving module configured to solve the value of the parameter variable which makes the target function optimal and meets the requirement of the constraint condition according to the response surface function.

[0015] In a third aspect, an electronic device is provided, comprising 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 to enable the at least one processor to perform the steps of the steel spring floating slab track parameter design method based on the response surface method of any one of the embodiments of the present application.

[0016] In a fourth aspect, the present application further provides a computer readable storage medium having a computer program stored thereon, and the program instructions are executed by a processor to enable the processor to perform the steps of the steel spring floating slab track parameter design method based on the response surface method of any one of the embodiments of the present application.

[0017] The steel spring floating slab track parameter design method and system based on the response surface method of the present application are based on the response surface method, and realize multi-objective optimization of steel rail acceleration, floating slab acceleration and other steel spring floating slab track structure dynamic characteristics by adjusting steel spring stiffness, steel spring damping and floating slab density, thereby providing technical method support for urban rail transit dynamic characteristic analysis and vibration and noise reduction optimization design. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed in the embodiment description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort.

[0019] Figure 1 A flow chart of a steel spring floating slab track parameter design method based on a response surface method provided by an embodiment of the present application is shown in

[0020] Figure 2 A structural block diagram of a steel spring floating slab track parameter design system based on a response surface method provided by an embodiment of the present application is shown in

[0021] Figure 3 A structural schematic diagram of an electronic device provided by an embodiment of the present application is shown in DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort are within the protection scope of the present application.

[0023] Please refer to Figure 1 which shows a flow chart of a steel spring floating slab track parameter design method based on a response surface method.

[0024] As shown in Figure 1 , the steel spring floating slab track parameter design method based on a response surface method specifically includes the following steps:

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

[0026] In this step, the vehicle-track coupling system is decomposed into a vehicle system and a steel spring floating slab track system, and the vehicle system and the steel spring floating slab track system are coupled in the vertical direction by the wheel-rail contact relationship, wherein the vehicle system includes, from top to bottom, a vehicle body, a secondary suspension system, a bogie, a primary suspension system and a wheel set, and the steel spring floating slab track system includes, from top to bottom, a steel rail, a fastener, a floating slab, a steel spring and a track foundation.

[0027] The vehicle system considers 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, which are totally 10 degrees of freedom. The expression of the vehicle system vibration differential equation is:

[0028]

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

[0030] The rail is considered as a discrete-point supported Euler beam, and the Ritz method is used for solution. Introducing the normal mode coordinates of the rail, a system of second-order ordinary differential equations for the mode coordinates is obtained, expressed as follows:

[0031]

[0032] In the formula, p represents the rail vibration mode coordinates. j (t) represents the wheel-rail force of the j-th wheelset, Z k (x i Z represents the sleeper support vibration mode. k (x wj ) represents the wheel vibration mode, E r I r These are the elastic modulus and moment of inertia of the rail section, respectively, in meters. r L r These represent the mass per unit length of the rail and the total length of the rail, respectively, where k is a positive integer, π is pi, and q is the mass per unit length of the rail. k (t) is the generalized coordinate of rail vibration, F rsi (t) represents the support reaction force at the i-th fastener position, x i x wj Let be the coordinates of the i-th fastener and the j-th wheelset along the train's path, respectively; nr is the number of fasteners; and Nr is the rail mode order.

[0033] The floating slab is considered as a discrete-point supported Euler beam. Using the Ritz method, the differential equation for the vertical vibration of the track slab is obtained, expressed as:

[0034]

[0035] In the formula, E s I s These are the elastic modulus and moment of inertia of the track slab, respectively, Z. s (x, t) represents the vibration displacement of the track slab, M s For the mass of the track slab, L s C is the length of the track slab.s k s Here, represents the distributed damping and distributed stiffness of the underpass filling layer along its length, t represents the train travel time, and x represents the train's coordinate. i Let be the coordinates of the i-th fastener as the train travels;

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

[0037]

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

[0039] G = 3.86R -0.115× 10 -8 ,

[0040] In the formula, 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 is the wheel-rail contact constant. wj (t) represents the vertical displacement of the j-th wheel at time t, Z r (x wj Z0(t) represents the vertical displacement of the rail under the j-th wheel at time t, Z0(t) represents the vertical irregularity of the track, and R represents 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 train operation through iterative calculation, and the time history curve of the train vibration load is determined, with the expression as follows:

[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 are all integration constants, Δt is the integration time step, {X n+1} represents the system displacement at time n+1, {X n} represents the system displacement at time n, {V n Let {A} be the system velocity at time n. n Let {A} be the system acceleration at time n. n-1 Let {F} be the system acceleration at time n-1, [M] be the system mass, and {F} be the system acceleration at time n-1. n+1 Let [K] be the force acting on the system at time n+1. n+1 Let C be the system stiffness at time n+1. n+1 Let the system damping be at time n+1, and the initial conditions be {X}0={V}0={A}0=0.

[0046] Step S102: Obtain at least one parameter variable and input the at least one parameter variable into the vertically coupled dynamic model to obtain the response value corresponding to the at least one parameter variable. Perform polynomial fitting regression on the at least one parameter variable and the response value to obtain the objective function of the response value.

[0047] In this step, multiple single-factor variation tests were conducted on the steel spring floating slab track structure, using steel spring stiffness, steel spring damping, and floating slab density as influencing factors. Rail acceleration and floating slab acceleration were used as judgment criteria, and the influence of each factor on the dynamic characteristics of the steel spring floating slab track structure was obtained based on the single-factor tests. Based on the single-factor tests, steel spring stiffness, steel spring damping, and floating slab density were selected as the factors under investigation, and rail acceleration and floating slab acceleration were used as response values. A three-factor, two-level experimental design was used to experimentally design the parameters of the steel spring floating slab track structure. Polynomial fitting regression was performed on the experimental data in the experimental design to obtain the objective function of the response value.

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

[0049]

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

[0051] To determine the undetermined coefficients of the objective term in the quadratic function, m independent trials are required, where m ≥ k = (n+1)(n+2) / 2. Each trial yields m samples corresponding to the response values ​​y(i) (i = 0, 1, ..., m-1) of the objective function, depending on the values ​​of the design variables. By the least squares principle, we can derive:

[0052] β=(X T X) -1 X T y

[0053] In the formula, γ is the undetermined coefficient of the objective term, 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, The first variable value in the initial experiment. For the k-th variable value in the initial experiment, The first variable value in m-1 trials, Let the value of the k-th variable be from m-1 trials;

[0056]

[0057] In the formula, y (0) Let y be the initial objective function response value. (1) Let y be the response value of the objective function in the first experiment. (m-1) The objective function response value for the m-1th trial;

[0058]

[0059] In the formula, β0 is the initial target term undetermined coefficient, β1 is the target term undetermined coefficient, and β k-1 The coefficients of the m-1th degree objective term are undetermined.

[0060]

[0061] In the formula, x n-1 Let x be the value of the (n-1)th variable. n This is the value of the nth variable;

[0062]

[0063] In the formula, α (n-1)n The interaction coefficient between the (n-1)th 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 By finding y, the undetermined coefficients in the polynomial function can be obtained, thus yielding the fitted polynomial function.

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

[0066] In this step, based on the relevant requirements of the technical specifications for steel spring floating slab tracks and actual engineering values, the range and initial values ​​of the steel spring stiffness, steel spring damping, and floating slab density are determined. The expression for the response surface function is:

[0067]

[0068] In the formula, y1 is the rail acceleration, y2 is the floating slab acceleration, x1 is the steel spring stiffness, x2 is the steel spring damping, x3 is the floating slab density, a is the design minimum value of steel spring stiffness, b is the design maximum value of steel spring stiffness, c is the design minimum value of steel spring damping, d is the design maximum value of steel spring damping, e is the design minimum value of floating slab density, and f is the design maximum value of floating slab 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 requirement shall be set as the design objective.

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

[0072] The design requirements include rail acceleration and floating slab acceleration.

[0073] Step S104: Based on the response surface function, solve for the values ​​of the parameter variables that make the objective function optimal and meet the constraint requirements.

[0074] In this step, based on the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the constraint requirements are obtained by using the constrained optimization problem-solving method.

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

[0076] In one specific embodiment, a vertically coupled dynamic model of the vehicle-steel spring floating slab track is established, and the relevant vehicle and steel spring floating slab structural parameters are shown in Tables 1 and 2 below.

[0077] Table 1. Relevant parameters of Metro Type B trains

[0078]

[0079] Table 2. Relevant parameters of steel spring floating slab track structure

[0080]

[0081] Table 3 shows the parameter gradients for different steel spring stiffness, steel spring damping, and floating plate density, and the effects of each factor on the dynamic characteristics of the steel spring floating plate track structure are calculated.

[0082] Table 3 Gradient table of each parameter

[0083]

[0084] Results analysis:

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

[0086] From the time domain perspective, the rail acceleration fluctuates within the stiffness range of 5-20 kN / mm, and shows an overall decreasing trend. From the frequency domain perspective, the rail acceleration vibration level decreases with increasing stiffness within the range of 0-40 Hz, but the opposite trend occurs beyond 40 Hz.

[0087] 2) The effect of steel spring stiffness on the acceleration of the floating slab

[0088] From a time-domain perspective, the acceleration of the floating slab fluctuates within the stiffness range of 5-20 kN / mm, and shows an overall upward trend. From a frequency-domain perspective, the acceleration level of the floating slab decreases with increasing stiffness within the range of 0-40 Hz, but the opposite trend occurs beyond 40 Hz.

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

[0090] From a time-domain perspective, the rail acceleration is between 6.57 and 6.58 m / s². 2 The vibration level fluctuates within a certain range; from a frequency domain perspective, the rail acceleration vibration level decreases with increasing damping within the range of 8-40Hz, but the overall change is not significant.

[0091] 4) The effect of steel spring damping on the acceleration of the floating slab

[0092] From a time-domain perspective, the acceleration of the floating slab decreases as the damping increases; from a frequency-domain perspective, the acceleration of the floating slab decreases as the damping increases after 8 Hz.

[0093] 5) The effect of floating slab density on rail acceleration

[0094] From a time-domain perspective, the rail acceleration is between 2500-3200 kg / m. 3 Within a certain range, the magnitude increases, and beyond that range, it decreases; from a frequency domain perspective, the rail acceleration vibration level does not change much with density.

[0095] 6) The effect of floating slab density on floating slab acceleration

[0096] From a time-domain perspective, the acceleration of the floating slab decreases with increasing density; from a frequency-domain perspective, the acceleration level of the floating slab decreases with increasing density after 40Hz.

[0097] Response surface methodology:

[0098] Based on the single-factor experiments, steel spring stiffness (A), steel spring damping (B), and floating slab density (C) were selected as the factors to be investigated, and rail acceleration (y1) and floating slab acceleration (y2) were used as the response values. Using Design-Expert software and the Box-Benhnken method, a three-factor, three-level experimental design was used to optimize the structural parameters of the steel spring floating slab track. The experimental factors and level settings are shown in Table 4, and the response surface experimental design and results are shown in Table 5.

[0099] Table 4 Experimental Factors and Level Settings

[0100]

[0101] Table 5. Response Surface Experiment Design Scheme and Results

[0102]

[0103] Objective function establishment:

[0104] The experimental results were subjected to polynomial fitting regression using Design-Expert software, yielding quadratic polynomials for rail acceleration (y1) and floating slab acceleration (y2) relative to steel spring stiffness (A), steel spring damping (B), and floating slab density (C), respectively.

[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] Statistical analysis of regression models:

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

[0109] Table 6. Results of Variance Analysis of the Rail Acceleration Regression Model

[0110]

[0111] Table 7. Results of Variance Analysis for the Acceleration Regression Model of the Floating Board

[0112]

[0113] Table 6 shows the significance level of the regression model, P = 0.0002, indicating that the established regression model is significant; the coefficient of determination R... 2 = 0.9552, indicating that the model can explain 95.52% of the change in response value; R Adj 2 =0.9104, indicating that the regression equation fits well, demonstrating that the regression model established in this invention can well describe the relationship between each factor and the response value, fit the real experimental results, and can be used to guide the optimization of the structural parameters of the steel spring floating plate.

[0114] Table 7 shows the significance level of the regression model (P < 0.0001), indicating that the established regression model is significantly valid; the coefficient of determination R0 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 fits well, demonstrating that the regression model established in this invention can well describe the relationship between each factor and the response value, can fit the real experimental results, and can be used to guide the optimization of the structural parameters of the steel spring floating plate.

[0115] Establishment of the response surface function:

[0116] According to the technical specifications for steel spring floating slab tracks, the possible value ranges for A, B, and C are as follows:

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

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

[0119]

[0120] Analysis revealed that the optimal design parameters for the steel spring floating slab track structure are: steel spring stiffness (A) of 15 kN / mm, steel spring damping (B) of 100 kN*s / m, and floating slab density (C) of 3400 kg / m³. 3 Substituting these conditions into the vertically coupled dynamic model of the vehicle-steel spring floating slab track, the rail acceleration and the floating slab acceleration are obtained as 6.6446 m / s². 2 2.9625m / s 2 The actual value is 6.8252 m / s. 2 3.52212m / s 2 The reductions of 2.65% and 15.9% respectively indicate that the models established by the single-factor method and response surface methodology are effective and feasible. This fully verifies the effectiveness of the steel spring floating slab track structure parameter design method proposed in this application for optimizing the dynamic characteristics of the steel spring floating slab track.

[0121] Please see Figure 2 The diagram shows a structural block diagram of a steel spring floating slab track parameter design system based on the response surface methodology of this 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] The system includes: a construction module 210 configured to construct a vertically coupled dynamic model of a vehicle-steel spring floating slab track; a fitting module 220 configured to acquire at least one parameter variable, input the at least one parameter variable into the vertically coupled 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 for the response value; a determination module 230 configured to determine the response surface function between the objective function and the at least one parameter variable using the response surface method; and a solution module 240 configured to solve for the values ​​of the parameter variables that optimize the objective function and meet the constraint requirements based on the response surface function.

[0124] It should be understood that Figure 2 The modules and references described in the document Figure 1The steps described in the text correspond to those in the method described above. Therefore, the operations, features, and corresponding technical effects described above also apply to the method described in the text. Figure 2 The various modules in the document will not be described in detail here.

[0125] In other embodiments, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor performs the steel spring floating plate track parameter design method based on response surface methodology in any of the above method embodiments.

[0126] In one embodiment, the computer-readable storage medium of the present invention stores computer-executable instructions, which are configured as follows:

[0127] Construct a vertically coupled dynamic model of the vehicle and the steel spring floating slab track;

[0128] At least one parameter variable is obtained and input into the vertically coupled dynamic model to obtain the response value corresponding to the at least one parameter variable. A polynomial fitting regression is performed on the at least one parameter variable and the response value to obtain the objective function of the response value.

[0129] The response surface function between the objective function and the at least one parameter variable is determined using the response surface methodology.

[0130] Based on the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the constraints are obtained.

[0131] Computer-readable storage media may include a stored program area and a stored data area, wherein the stored program area may store an operating system and an application program required for at least one function; the stored data area may store data created by using the response surface methodology-based steel spring floating slab track parameter design system, etc. Furthermore, the computer-readable storage medium may include high-speed random access memory, and may also include memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include memory remotely located relative to a processor, which can be connected to the response surface methodology-based steel spring floating slab track parameter design system via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0132] Figure 3 This is a schematic diagram of the structure of the electronic device provided in the 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, memory 320, input device 330, and output device 340 can be connected via a bus or other means. Figure 3 Taking a bus connection as an example, memory 320 is the computer-readable storage medium described above. Processor 310 executes various server functions and data processing by running non-volatile software programs, instructions, and modules stored in memory 320, thereby implementing the steel spring floating slab track parameter design method based on response surface methodology described in the above embodiment. Input device 330 can receive input digital or character information and generate key signal inputs related to user settings and function control of the steel spring floating slab track parameter design system based on response surface methodology. Output device 340 may include a display screen or other display device.

[0133] The aforementioned electronic device can execute the method provided in the embodiments of the present invention, and has the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in the embodiments of the present invention.

[0134] In one implementation, the above-described electronic device is applied to a steel spring floating slab track parameter design system based on response surface methodology, for a client, and includes: 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, the instructions being executed by the at least one processor to enable the at least one processor to:

[0135] Construct a vertically coupled dynamic model of the vehicle and the steel spring floating slab track;

[0136] At least one parameter variable is obtained and input into the vertically coupled dynamic model to obtain the response value corresponding to the at least one parameter variable. A polynomial fitting regression is performed on the at least one parameter variable and the response value to obtain the objective function of the response value.

[0137] The response surface function between the objective function and the at least one parameter variable is determined using the response surface methodology.

[0138] Based on the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the constraints are obtained.

[0139] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing the parameters of a steel spring floating slab track based on response surface methodology, characterized in that, include: Construct a vertically coupled dynamic model of the vehicle and the steel spring floating slab track; At least one parameter variable is obtained and input into the vertically coupled dynamic model to obtain the response value corresponding to the at least one parameter variable. A polynomial fitting regression is then performed on the at least one parameter variable and the response value to obtain the objective function of the response value, wherein the expression of the objective function is: ， In the formula, Let the first objective function be... The second objective function is... The coefficients of the constant term in the first objective function are to be determined. The coefficients of the constant term in the second objective function are to be determined. Let be the undetermined coefficients of the objective term in the quadratic function. The coefficients of the linear term in the objective function are undetermined. The number of parameter variables. For the i-th parameter variable, Let j be the j-th parameter variable; The response surface function between the objective function and the at least one parameter variable is determined using the response surface methodology, wherein the expression of the response surface function is: ， In the formula, For rail acceleration, For the acceleration of the floating plate, For the stiffness of the steel spring, Steel spring damping, For the density of the floating plate, This represents the minimum design stiffness of the steel spring. This represents the design maximum value for the stiffness of the steel spring. This is the design minimum value for steel spring damping. This is the design maximum value for the steel spring damping. This is the design minimum for the density of the floating slab. This represents the maximum design density of the floating slab. Based on the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the constraints are obtained.

2. The method for designing parameters of a steel spring floating slab track based on response surface methodology according to claim 1, characterized in that, The vertically coupled dynamic model for constructing the vehicle-steel spring floating slab track includes: The vehicle-track coupling system is decomposed into a vehicle system and a steel spring floating slab track system. The vehicle system and the steel spring floating slab track system are coupled vertically by the wheel-rail contact relationship. The vehicle system, from top to bottom, includes the car body, secondary suspension system, bogie, primary suspension system and wheelset. The steel spring floating slab track system, from top to bottom, includes the rail, fastener, floating slab, steel spring and rail foundation. The vehicle system considers the heave and pitching motions of the vehicle body, the heave and pitching motions of the front and rear frames, and the vertical vibrations of the four wheelsets, totaling 10 degrees of freedom. The expression for the vibration differential equation of the vehicle system is as follows: ， In the formula, , , These are the mass matrix, stiffness matrix, and damping matrix of the vehicle system, respectively. , , These are the displacement vector, velocity vector, and acceleration vector of the vehicle system, respectively. This is the generalized force vector of the vehicle system; The rail is considered as a discrete-point supported Euler beam, and the Ritz method is used for solution. Introducing the normal mode coordinates of the rail, a system of second-order ordinary differential equations for the mode coordinates is obtained, expressed as follows: ， In the formula, For rail vibration mode coordinates, Let J be the wheel-rail force of the j-th wheelset. This is the vibration mode of the sleeper support. For wheel vibration mode, , These are the elastic modulus and moment of inertia of the rail section, respectively. , These are the mass per unit length of the rail and the total length of the rail, respectively. It is a positive integer. Pi For the generalized coordinates of rail vibration, For the support reaction force at the j-th fastener position, , Let be the coordinates of the i-th fastener and the j-th wheelset as they travel along the train's path. For the number of fasteners, The modal order of the rail; The floating slab is considered as a discrete-point supported Euler beam. Using the Ritz method, the differential equation for the vertical vibration of the track slab is obtained, expressed as: ， In the formula, , These are the elastic modulus and moment of inertia of the track slab, respectively. This represents the vibration displacement of the track slab. For the quality of the track slab, The length of the track slab, , These represent the distributed damping and distributed stiffness of the underfill layer along its length, respectively. For train travel time, For train running coordinates, Let be the coordinates of the i-th fastener as the train travels; Applying the Hertz nonlinear elastic contact model, the vertical force between the wheel and rail is determined by the vertical elastic compression between the wheel and rail. The vibration of the vehicle system and the steel spring floating slab track system are coupled through the wheel-rail force to obtain the vibration model, expressed as: ， ， ， In the formula, For wheel-rail force, The wheel-rail contact constant is... This refers to the elastic compression between the wheel and rail. Let be the vertical displacement of the j-th wheel at time t. Let be the vertical displacement of the rail under the j-th wheel at time t. The track is vertically uneven. The radius of the wheel; For the vehicle-track coupled dynamic system, the explicit integration method is used to obtain the system dynamic response generated by train operation through iterative calculation, and the time history curve of the train vibration load is determined, with the expression as follows: ， ， ， In the formula, , All are integration constants. For the integration time step, Let n be the system displacement at time n+1. Let n be the system displacement at time n. Let n be the system velocity at time n. Let n be the acceleration of the system at time n. Let n be the system acceleration at time n-1. For system quality, The force acting on the system at time n+1, Let n be the system stiffness at time n+1. The system damping at time n+1, with initial conditions as follows: .

3. The method for designing parameters of a steel spring floating slab track based on response surface methodology according to claim 1, characterized in that, The values ​​of the parameter variables obtained by solving based on the response surface function to make the objective function optimal and meet the constraint requirements include: Based on the response surface function, the values ​​of the parameter variables that make the objective function optimal and meet the constraint requirements are obtained by using the constrained optimization problem-solving method.

4. A parameter design system for a steel spring floating slab track based on response surface methodology, characterized in that, include: The module is configured to build a vertically coupled dynamic model of the vehicle-steel spring floating slab track; The fitting module is configured to acquire at least one parameter variable, input the at least one parameter variable into the vertically coupled dynamic model, obtain a response value corresponding to the at least one parameter variable, and perform a polynomial fitting regression on the at least one parameter variable and the response value to obtain the objective function of the response value, wherein the expression of the objective function is: ， In the formula, Let the first objective function be... The second objective function is... The coefficients of the constant term in the first objective function are to be determined. The coefficients of the constant term in the second objective function are to be determined. Let be the undetermined coefficients of the objective term in the quadratic function. The coefficients of the linear term in the objective function are undetermined. The number of parameter variables. For the i-th parameter variable, Let j be the j-th parameter variable; The module is configured to determine the response surface function between the objective function and the at least one parameter variable based on the response surface methodology, wherein the expression of the response surface function is: ， In the formula, For rail acceleration, For the acceleration of the floating plate, For the stiffness of the steel spring, Steel spring damping, For the density of the floating plate, This represents the minimum design stiffness of the steel spring. This represents the design maximum value for the stiffness of the steel spring. This is the design minimum value for steel spring damping. This is the design maximum value for the steel spring damping. This is the design minimum for the density of the floating slab. This represents the maximum design density of the floating slab. The solution module is configured to obtain the values ​​of the parameter variables that make the objective function optimal and meet the constraint requirements based on the response surface function.

5. 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 to enable the at least one processor to perform the method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method according to any one of claims 1 to 3.

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