A high-speed maglev track beam pre-camber and bending stiffness collaborative optimization design method

Abstract

This invention relates to the field of track engineering technology, and particularly to a method for the coordinated optimization design of precamber and bending stiffness of high-speed maglev track beams. The method includes: first, acquiring a dataset of high-speed maglev trains, constructing the vehicle-magnetic-track coupled dynamic relationship under moving loads, and extracting the suspension gap when the lead car and middle trains pass the track beam; using the maximum precamber and bending stiffness of the track beam as decision variables, constructing a multi-objective joint optimization model based on the principles of lead car gap balance, overall operational stability, and structural lightweighting, and setting a lower limit for stiffness, an upper limit for precamber, and resonance avoidance constraints; finally, using a multi-objective optimization algorithm incorporating non-dominated sorting to solve the model and generate a Pareto solution set, and selecting the optimal combination of precamber and bending stiffness. This invention achieves structural lightweighting of high-speed maglev track infrastructure while ensuring the overall levitation operational stability of multi-train formations.

Description

Technical Field

[0001] This invention belongs to the field of track engineering technology, specifically relating to a method for optimizing the structural parameters of a high-speed maglev track beam, and more particularly to a method for synergistic optimization of the pre-camber and bending stiffness of the track beam to balance the levitation stability of the train under high-speed operation and the lightweighting of the track infrastructure structure. Background Technology

[0002] When high-speed maglev trains pass through track beam sections, their operational stability is closely related to key structural parameters such as the track beam span and bending stiffness. Currently, the common approach is to significantly increase the bending stiffness of the track beam to compensate for the deflection caused by train loads, leading to a surge in construction costs and severely restricting the development of lightweight track infrastructure. To compensate for the deflection caused by train loads, pre-camber design has been introduced into the construction and installation of high-speed maglev track beams and functional components, aiming to bring the track to a near-zero deflection state when the train passes, thereby improving operational stability. However, this traditional pre-camber setting method causes an angular impact on the first train car during the train's entry into the track beam, resulting in severe fluctuations in the suspension gap of the lead car. Simply reducing the pre-camber will result in insufficient pre-camber compensation, causing the middle trains in multi-car formations to experience periodic deflection disturbances. Therefore, there is an urgent need for a multi-objective optimization method that can identify the fluctuation pattern of the suspension gap and balance train operational stability with lightweight track beam structure, in order to achieve synergistic optimization design of pre-camber and bending stiffness, improve the overall operational quality of the high-speed maglev system, and enhance structural lightweighting. Summary of the Invention

[0003] The purpose of this invention is to overcome the problems of unreasonable precamber setting and excessive redundancy in track beam stiffness design in existing technologies, and to provide a method for the coordinated optimization design of precamber and stiffness of high-speed maglev track beams. This method takes into account both the transient angle impact of the first train car and the downward deflection disturbance of the middle train car, and performs multi-objective coordinated optimization of the precamber and bending stiffness of the track beam to achieve control of suspension gap fluctuations and reasonable stiffness reduction under high-speed train loads, thereby improving the overall stability of multi-train operation and the lightweighting level of track infrastructure.

[0004] To achieve the above objectives, this invention provides a method for the coordinated optimization design of precamber and bending stiffness of high-speed maglev track beams. This method performs multi-objective coordinated optimization of the precamber and bending stiffness of the track beams to achieve structural lightweighting of the track infrastructure while ensuring the stable levitation operation of the high-speed maglev train. The method includes the following steps: First, acquiring a dataset of the high-speed maglev train; the dataset includes: the maximum operating speed, the span of the track beam, and the minimum bending stiffness and maximum precamber limits that satisfy the ultimate bearing capacity of the track beam structure; then, based on the dataset, constructing the vehicle-magnetic-track coupled dynamic relationship under the action of moving loads on the high-speed maglev train, and based on the dynamic relationship, obtaining the high-speed maglev train's passage through the track under different combinations of precamber and bending stiffness. The model analyzes the following parameters: the suspension gap during track entry, the maximum suspension gap of the head electromagnet when the lead car enters the track beam, and the maximum fluctuation of the suspension gap of the electromagnet when the middle train passes. Next, using the maximum pre-camber at mid-span of the track beam and the bending stiffness of the track beam as decision variables, a multi-objective joint optimization model is constructed based on the principles of balanced head car gap, priority of overall operational stability, and lightweight structure. The comprehensive constraints of this model include stiffness constraints, pre-camber constraints, and train resonance avoidance constraints. Finally, the multi-objective joint optimization model is solved to generate a non-dominated solution set that approximates the Pareto optimal front. This non-dominated solution set is then comprehensively evaluated to select the final optimal combination of pre-camber and bending stiffness design parameters, which will guide the design of the high-speed maglev track beam.

[0005] In some exemplary embodiments, obtaining the dataset of the high-speed maglev train includes: obtaining the operating parameters of the high-speed maglev train and the basic structural design data of the track beam to obtain the basic data of the train and construct the dataset of the train.

[0006] In some exemplary embodiments, the specific calculation method for the suspension gap of a high-speed maglev train passing over the track beam under different combinations of pre-camber and bending stiffness is as follows: The pre-camber value of the track beam functional component at any coordinate is defined according to the following formula: (1) In equation (1), z ( x i ) is the location x i The pre-arch value at the location, z max For the maximum pre-camber, L This refers to the span of the track beam.

[0007] Construct an analytical model of the suspension gap variation including pre-camber, and calculate the first... k An electromagnet in tChange in suspension gap at time: (2) In equation (2), Δ g k ( t ) is the first k The change in the levitation gap of each electromagnet, with positive values ​​indicating an increase in gap and negative values ​​indicating a decrease in gap; pre-camber displacement. z ( x k The direction upwards is positive; ω ( x k , t () represents dynamic deflection, with the downward direction being positive. x k = v ( t - t 0( k )) indicates the first k An electromagnet in t Location at any given moment v The train's operating speed; t 0( k () represents the initial moment when the electromagnet enters the beam.

[0008] Extract the suspension gap of the first train acting alone on the track beam stage, and define the maximum positive and negative suspension gap values ​​of the head electromagnet caused by the beam end angle impact as follows: , The maximum absolute value of the two is The suspension gap during the stage where multiple electromagnets subsequently enter the beam and the load accumulates, causing the beam to deflect downwards as a whole, is extracted. The maximum suspension gap of the central electromagnet is defined as... .

[0009] In some exemplary embodiments, the multi-objective joint optimization model has an objective function comprising three sub-objective functions, namely: The first sub-objective function, aimed at balancing the gap between the lead car and the track beam, is used to make the maximum amplitude of the positive and negative suspension gap of the lead car tend to be consistent, so as to smooth out the transient angle impact when the lead car enters the track beam and balance the deflection compensation. (3) In the formula, z max This represents the maximum pre-camber of the track beam. NO This refers to the bending stiffness of the track beam.

[0010] The second sub-objective function, prioritizing overall stability, is used to ensure that the periodic downward deflection disturbance experienced by the middle trains in a multi-car trainset is similar to that experienced by the end trains. (4) The third sub-objective function, aimed at achieving structural lightweighting, is used to promote lightweight design of the track beam structure to reduce the track beam construction cost. (5) In some exemplary embodiments, the comprehensive constraints are specifically manifested as a combination of the following mathematical boundaries and physical criteria: Stiffness lower limit constraint: NO > NO min ,in NO min To ensure that the cross-section of the track beam meets the lower limit of the bending stiffness allowed by the ultimate bearing capacity safety state of the structure; Upper limit constraint on pre-camber: z max ≤ z limit ,in z limit To meet the maximum pre-camber limit for the construction process and structural safety of high-speed maglev track beams and functional components; Vehicle resonance avoidance constraints: f req > v max / L ,in f req Let be the first-order vertical natural frequency of the track beam. v max For the maximum design speed, L The span of the track beam is used to avoid inducing track-vehicle coupling resonance when the train passes over the track beam; Overall stability constraints: ≤ The suspension gap fluctuation range of the middle train must not exceed that of the lead car to ensure the overall suspension stability of multi-train sets.

[0011] In some exemplary embodiments, a multi-objective optimization algorithm that incorporates non-dominated sorting and external archiving mechanisms is used to solve the multi-objective joint optimization model.

[0012] In some exemplary embodiments, the multi-objective optimization algorithm specifically employs a multi-objective sparrow search algorithm, and its solution and external archiving maintenance mechanism includes the following steps: The vector to be optimized [ z max , NO The position of each sparrow in the two-dimensional solution space is encoded using real numbers. Within the feasible region formed by the constraints, random initialization is performed, including... NA sparrow population of individuals is configured with a discoverer ratio of 20%, a joiner ratio of 70%, and a warning ratio of 10%, while creating a capacity of [missing information]. n Empty external archive; Call the analytical model of suspension gap change described in step B to calculate the objective function values ​​of each individual in the current population and evaluate its multi-objective fitness; In each iteration, based on the Pareto dominance relation, a sparsely distributed non-dominated solution is selected from the external archive according to the crowding distance as the optimal guide, and the spatial positions of the discoverer, joiner and warning are updated.

[0013] After the position is updated, the current generation population is merged with the original external archive, and the non-dominated sorting is re-executed to remove dominated inferior solutions. When the number of non-dominated solutions in the external archive exceeds the capacity, dynamic pruning is performed based on the crowding distance to retain solutions with more uniform boundary distribution until the maximum number of iterations is reached, and the final Pareto optimal solution set is output.

[0014] Extract the three sub-objective function values ​​corresponding to each non-dominated solution in the Pareto optimal solution set, construct a multi-objective decision matrix, and normalize the matrix to eliminate the influence of different physical dimensions; Identify the minimum value of each sub-objective in the normalized matrix and use it as the vector of the positive ideal optimal solution point. D + Identify the corresponding maxima and use them as the vector of negative ideal solutions. D - ; Using the Euclidean distance formula, the combined distance from each solution in the Pareto solution set to the positive ideal optimal solution point vector is calculated. d i + And the combined distance to the vector of the negative ideal solution point. d i - ; Calculate the relative proximity of each solution to the ideal optimal solution. C Select the relative proximity among all non-dominated solutions. C The largest individual entity corresponds to the optimal pre-camber amplitude and bending stiffness parameters of the track beam.

[0015] The technical solution provided by the embodiments of the present invention has at least the following advantages: 1. By taking into account the requirements of the uniformity of the suspension gap of the first train and the priority of overall stability, this invention optimizes the pre-camber of the track beam, which can effectively suppress the gap fluctuation during the process of the first train entering the track beam and fully compensate for the track beam deflection disturbance of the middle train, thus significantly improving the overall running stability of multi-train sets.

[0016] 2. This invention constructs a multi-objective optimization model with pre-camber and bending stiffness as joint decision variables. Under the premise of satisfying structural safety and other constraints, it achieves balanced control of the suspension gap fluctuation of the entire vehicle and reasonably reduces the bending stiffness of the track beam, thus achieving synergistic optimization of driving quality and structural lightweighting. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations do not constitute a limitation on the embodiments, and unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0018] Figure 1 is a flowchart illustrating the collaborative optimization design method for the pre-camber and bending stiffness of a high-speed maglev track beam provided by this invention.

[0019] Figure 2 is a schematic diagram of the process of the first high-speed maglev train passing through the track beam in an example of the present invention.

[0020] Figure 3 This is a graph showing the levitation gap of the head electromagnet during the process of the first high-speed maglev train passing the track beam in an example of the present invention.

[0021] Figure 4 This is a schematic diagram of the process of the high-speed maglev train passing through the track beam in an example of the present invention.

[0022] Figure 5 This is a graph showing the electromagnetic levitation gap during the process of the high-speed maglev train passing the track beam in the middle section of this invention. Detailed Implementation

[0023] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. This embodiment aims to provide an operable and detailed process for implementing the technical solution of the present invention, enabling those skilled in the art to implement the present invention accordingly.

[0024] See Figure 1 The technical solution adopted by the present invention to solve its technical problem includes the following steps: Step S1: Obtain the dataset of the high-speed maglev train; the dataset includes: the maximum operating speed, the span of the track beam, and the minimum bending stiffness and maximum precamber limit that meet the ultimate bearing capacity limit of the track beam structure.

[0025] Step S2: Based on the dataset, construct the vehicle-magnetic-track coupling dynamic relationship under the action of moving load of high-speed maglev train, and obtain the suspension gap when the high-speed maglev train passes through the track beam under different combinations of pre-camber and bending stiffness, the maximum value of the suspension gap of the head electromagnet when the head car enters the track beam, and the maximum fluctuation of the suspension gap of the electromagnet when the middle train passes through.

[0026] Step S3: Using the maximum pre-camber at mid-span of the track beam and the bending stiffness of the track beam as decision variables, and based on the multi-objective collaborative control principles of head car gap balance, overall operational stability priority, and structural lightweighting, a multi-objective joint optimization model is constructed. The comprehensive constraints of the model include stiffness constraints, pre-camber constraints, and train resonance avoidance constraints.

[0027] Step S4: Solve the multi-objective joint optimization model to generate a non-dominated solution set that approximates the Pareto optimal frontier, and comprehensively evaluate the non-dominated solution set to select the final optimal combination of precamber and bending stiffness design parameters to guide the design of high-speed maglev track beams.

[0028] Specifically, in step S1, by acquiring the operating parameters of the high-speed maglev train and the design data of the track beam, the basic data of the train are determined, namely the maximum operating speed of the train, the span of the track beam, and the minimum bending stiffness and maximum pre-camber limit that meet the ultimate bearing capacity limit state of the track beam structure, thus obtaining the train's dataset.

[0029] Furthermore, the aforementioned operating parameters and design data are specifically determined in conjunction with high-speed maglev transportation design standards and actual line conditions. For example, the span of the track beam is set to 24.768m, the maximum train operating speed is set to 600km / h, and the maximum mid-span deflection limit L / 4000 of a single span beam under the vertical static live load of the train is taken as the maximum pre-camber limit.

[0030] In step S2, based on operating parameters and basic data, the vehicle-magnetic-track coupled dynamic relationship under the action of moving load on the high-speed maglev train is constructed. Based on this dynamic relationship, the suspension gap of the high-speed maglev train passing over the track beam under different combinations of pre-camber and bending stiffness is obtained. The maximum value of the suspension gap of the head electromagnet when the lead car enters the track beam is extracted (e.g., ...). Figure 2 As shown), and the maximum fluctuation of the electromagnet's levitation gap when the central train passes (as shown). Figure 4 (as shown) Furthermore, the extraction and calculation of the suspension gap in step S2 are specifically achieved in the following way: (1) Define the pre-camber value of the track beam functional component at any coordinate according to the following formula: (1) In the formula, z ( x i ) is the location x i The pre-arch value at the location, z max For the maximum pre-camber, L This refers to the span of the track beam.

[0031] (2) Based on the Euler-Bernoulli beam theory, establish the dynamic equations of the track beam under moving loads, and calculate the first... k An electromagnet in t Change in suspension gap at time: (2) In the formula, Δ g k ( t ) is the first k The change in the levitation gap of each electromagnet, with positive values ​​indicating an increase in gap and negative values ​​indicating a decrease in gap; pre-camber displacement. z ( x k The direction upwards is positive; ω ( x k , t () represents dynamic deflection, with the downward direction being positive. x k = v ( t - t 0( k )) indicates the first k An electromagnet in t Location at any given moment v The train's operating speed; t 0( k () represents the initial moment when the electromagnet enters the beam.

[0032] (3) Extract the suspension gap of the first train acting alone on the track beam stage, and define the maximum positive and negative suspension gap of the head electromagnet caused by the beam end angle impact as respectively. , The maximum absolute value of the two is ,like Figure 3 As shown; the suspension gap is extracted during the stage when multiple electromagnets subsequently enter the beam and the load accumulates, causing the beam to deflect as a whole. The maximum suspension gap of the middle electromagnet is defined as... ,like Figure 5 As shown.

[0033] In step S3, the maximum precamber amplitude at mid-span of the track beam and the bending stiffness of the track beam are used as decision variables. Based on the multi-objective collaborative control principle of equal head car gap, priority of overall operation stability, and lightweight structure, a multi-objective joint optimization model is constructed. The comprehensive constraints of the model include stiffness constraints, precamber constraints, and train resonance avoidance constraints. Furthermore, the multi-objective joint optimization model described in step S3 is constructed in the following manner: (1) Construct an objective function composed of three sub-objective functions: The first sub-objective function, which aims to equalize the gap between the lead car and the track beam, is used to make the maximum amplitude of the positive and negative suspension gap of the lead car tend to be consistent, so as to smooth the transient angle impact when the lead car enters the track beam and equalize the deflection compensation. (3) In the formula, z max This represents the maximum pre-camber of the track beam. NO This refers to the bending stiffness of the track beam.

[0034] The second sub-objective function, prioritizing overall stability, is used to ensure that the periodic downward deflection disturbance experienced by the middle trains in a multi-car trainset is similar to that experienced by the end trains. (4) The third sub-objective function, aimed at structural lightweighting, is used to promote lightweight design of the track beam structure to reduce the construction cost of the track beam. (5) (2) Construct the following comprehensive constraint conditions combining boundary and physical criteria: Stiffness lower limit constraint: NO > NO min ,in NO min To ensure that the cross-section of the track beam meets the lower limit of the bending stiffness allowed under the structural ultimate bearing capacity safety state.

[0035] Upper limit constraint on pre-camber: z max ≤ z limit ,in z limit To meet the maximum pre-camber limit for the construction process and structural safety of high-speed maglev track beams and functional components.

[0036] Vehicle resonance avoidance constraints: f req > v max / L ,in f req Let be the first-order vertical natural frequency of the track beam. v max For the maximum design speed, L The span of the track beam is used to avoid inducing track-vehicle coupling resonance when the train passes over the track beam.

[0037] Overall stability constraints: ≤ The suspension gap fluctuation range of the middle train must not exceed that of the lead car to ensure the overall suspension stability of multi-train sets.

[0038] In step S4, a multi-objective optimization algorithm incorporating non-dominated sorting and external archiving mechanisms is used to solve the multi-objective joint optimization model, generating a non-dominated solution set that approximates the Pareto optimal front. The non-dominated solution set is then comprehensively evaluated to select the optimal combination of pre-camber and bending stiffness design parameters, which guides the design of the high-speed maglev track beam. Further, the specific solution and optimization process described in step S4 is implemented using a multi-objective sparrow search algorithm, including the following steps: (1) The vector to be optimized [ z max , NO The position of each sparrow in the two-dimensional solution space is encoded using real numbers. Within the feasible region formed by the constraints, random initialization is performed, including... N A sparrow population of individuals is defined with a discoverer ratio of 20%, a joiner ratio of 70%, and a warning ratio of 10%, while creating a capacity of [missing information]. n An empty external archive is used to store non-dominated solutions.

[0039] (2) Call the suspension gap change analysis model to calculate the three sub-objective function values ​​of each individual in the current population and evaluate its multi-objective fitness.

[0040] (3) In each iteration, based on the Pareto dominance relationship, the sparsely distributed non-dominated solutions are selected from the external archive according to the crowding distance as the optimal guides to update the spatial position of the population individuals.

[0041] For the discoverer, when no alarm threshold is triggered, it explores the global area, and its location update formula is: (6) In the formula, X h For individual location; h This represents the current iteration number; h max This represents the maximum number of iterations. α A random number between 0 and 1.

[0042] For newcomers, a local high-precision search is performed immediately following the current best discoverer, and the update formula is: (7) In the formula, It is the optimal position in the current population; A It is a 1×2 vector, where each element is randomly assigned 1 or -1, and A + =A T ( A A T ) -1 ; B 1× n vector.

[0043] For those who issue warnings, when they detect danger or fall into a local stagnation, they should move toward the global optimal position or implement a normally distributed random perturbation.

[0044] (4) After the position is updated, the current generation population is merged with the original external archive, and the non-dominated sorting judgment is re-executed to remove the dominated inferior solutions. When the number of non-dominated solutions in the external archive exceeds the capacity, dynamic pruning is performed based on the crowding distance to retain solutions with more uniform boundary distribution until the maximum number of iterations is reached, and the final Pareto optimal solution set is output.

[0045] (5) Optimize the Pareto solution set based on the TOPSIS method. Extract the three objective function values ​​of each non-dominated solution in the solution set to construct a decision matrix and perform normalization. Identify the minimum and maximum values ​​of each sub-objective in the normalized matrix, and construct the positive ideal optimal solution point vector respectively. D + with the negative ideal solution vector D - The Euclidean distance is used to calculate the distance to each solution. D + Comprehensive distance d i + And until D - Comprehensive distance d i - Then, the relative proximity is obtained. C .

[0046] (6) Select the relative proximity among all non-dominated solutions. C The largest individual, its corresponding [ z max , NO The optimal parameters are defined as follows. The results of the implementation examples show that, through joint optimization, the optimal parameter combination for the bending stiffness and pre-camber of the track beam is obtained. This scheme results in a near-uniform fluctuation in the maximum gap between the head and middle electromagnets, reducing the bending stiffness of the track beam while ensuring system stability, thus achieving collaborative optimization design.

[0047] Based on the above technical solutions, this invention provides a method for the coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams. This method is used to perform multi-objective coordinated optimization of the pre-camber and bending stiffness of the track beams, aiming to achieve structural lightweighting of the track infrastructure while ensuring the stable levitation operation of the high-speed maglev train. The method includes the following steps: First, acquiring a dataset of the high-speed maglev train; the dataset includes: the maximum operating speed, the span of the track beam, and the minimum bending stiffness and maximum pre-camber limits that satisfy the ultimate bearing capacity of the track beam structure; then, based on the dataset, constructing the vehicle-magnetic-track coupled dynamic relationship under the action of moving loads on the high-speed maglev train, and based on the dynamic relationship, obtaining the high-speed maglev train's passage through the track under different combinations of pre-camber and bending stiffness. The model analyzes the following parameters: the suspension gap during track entry, the maximum suspension gap of the head electromagnet when the lead car enters the track beam, and the maximum fluctuation of the suspension gap of the electromagnet when the middle train passes. Next, using the maximum pre-camber at mid-span of the track beam and the bending stiffness of the track beam as decision variables, a multi-objective joint optimization model is constructed based on the principles of balanced head car gap, priority of overall operational stability, and lightweight structure. The comprehensive constraints of this model include stiffness constraints, pre-camber constraints, and train resonance avoidance constraints. Finally, the multi-objective joint optimization model is solved to generate a non-dominated solution set that approximates the Pareto optimal front. This non-dominated solution set is then comprehensively evaluated to select the final optimal combination of pre-camber and bending stiffness design parameters, which will guide the design of the high-speed maglev track beam.

[0048] Those skilled in the art will understand that the above-described embodiments are specific examples of implementing this application, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of this application. Any person skilled in the art can make their own modifications and alterations without departing from the spirit and scope of this application; therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. A method for synergistic optimization design of precamber and bending stiffness of high-speed maglev track beams, characterized in that, The method for multi-objective collaborative optimization of the precamber and bending stiffness of track beams, in order to achieve structural lightweighting of track infrastructure while ensuring the stable levitation operation of high-speed maglev trains, includes the following steps: Obtain a dataset of high-speed maglev trains; the dataset includes: maximum operating speed, span of track beams, and minimum bending stiffness and maximum precamber limits that satisfy the ultimate bearing capacity of track beam structures; Based on the dataset, the vehicle-magnet-track coupling dynamic relationship under the action of moving load of high-speed maglev train is constructed, and based on the dynamic relationship, the suspension gap when the high-speed maglev train passes through the track beam under different combinations of pre-camber and bending stiffness, the maximum value of the suspension gap of the head electromagnet when the head car enters the track beam, and the maximum fluctuation of the suspension gap of the electromagnet when the middle train passes are obtained. Using the maximum precamber at mid-span of the track beam and the bending stiffness of the track beam as decision variables, a multi-objective joint optimization model is constructed based on the multi-objective collaborative control principles of head car gap balance, overall operational stability priority, and structural lightweighting. The comprehensive constraints of the model include stiffness constraints, precamber constraints, and train resonance avoidance constraints. The multi-objective joint optimization model is solved to generate a non-dominated solution set that approximates the Pareto optimal front. The non-dominated solution set is then comprehensively evaluated to select the final optimal combination of precamber and bending stiffness design parameters, which is used to guide the design of high-speed maglev track beams.

2. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 1, characterized in that, Obtain the dataset for high-speed maglev trains, including: The operating parameters of the high-speed maglev train and the basic structural design data of the track beam are obtained to obtain the basic data of the train and construct the train's dataset.

3. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 1, characterized in that, The specific calculation method for obtaining the suspension gap of a high-speed maglev train passing over the track beam under different combinations of pre-camber and bending stiffness is as follows: The pre-camber value of the track beam functional component at any coordinate is defined according to the following formula: (1) In equation (1), z ( x i ) is the location x i The pre-arch value at the location, z max For the maximum pre-camber, L For the span of the track beam; Construct an analytical model of the suspension gap variation including pre-camber, and calculate the first... k An electromagnet in t Change in suspension gap at time: (2) In equation (2), Δ g k ( t ) is the first k The change in the levitation gap of each electromagnet, with positive values ​​indicating an increase in gap and negative values ​​indicating a decrease in gap; pre-camber displacement. z ( x k The direction upwards is positive; ω ( x k , t () represents dynamic deflection, with the downward direction being positive; x k = v ( t - t 0( k )) indicates the first k An electromagnet in t Location at any given moment v The train's operating speed; t 0( k () represents the initial moment when the electromagnet enters the beam. Extract the suspension gap of the first train acting alone on the track beam stage, and define the maximum positive and negative suspension gap values ​​of the head electromagnet caused by the beam end angle impact as follows: , The maximum absolute value of the two is The suspension gap during the stage where multiple electromagnets subsequently enter the beam and the load accumulates, causing the beam to deflect downwards as a whole, is extracted. The maximum suspension gap of the central electromagnet is defined as... .

4. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 3, characterized in that, The multi-objective joint optimization model has an objective function comprising three sub-objective functions, namely: The first sub-objective function, aimed at balancing the gap between the lead car and the track beam, is used to make the maximum amplitude of the positive and negative suspension gap of the lead car tend to be consistent, so as to smooth out the transient angle impact when the lead car enters the track beam and balance the deflection compensation. (3) In the formula, z max This represents the maximum pre-camber of the track beam. EI The bending stiffness of the track beam; The second sub-objective function, prioritizing overall stability, is used to ensure that the periodic downward deflection disturbance experienced by the middle trains in a multi-car trainset is similar to that experienced by the end trains. (4) The third sub-objective function, aimed at achieving structural lightweighting, is used to promote lightweight design of the track beam structure to reduce the track beam construction cost. (5)。 5. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 1, characterized in that, The comprehensive constraints are specifically manifested as a combination of the following mathematical boundaries and physical criteria: Stiffness lower limit constraint: EI > EI min ,in EI min To ensure that the cross-section of the track beam meets the lower limit of the bending stiffness allowed by the ultimate bearing capacity safety state of the structure; Upper limit constraint on pre-camber: z max ≤ z limit ,in z limit To meet the maximum pre-camber limit for the construction process and structural safety of high-speed maglev track beams and functional components; Vehicle resonance avoidance constraints: f req > v max / L ,in f req Let be the first-order vertical natural frequency of the track beam. v max For the maximum design speed, L The span of the track beam is used to avoid inducing track-vehicle coupling resonance when the train passes over the track beam; Overall stability constraints: ≤ The suspension gap fluctuation range of the middle train must not exceed that of the lead car to ensure the overall suspension stability of multi-train sets.

6. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 1, characterized in that, A multi-objective optimization algorithm incorporating non-dominated sorting and external archiving mechanisms is used to solve the multi-objective joint optimization model.

7. The method for coordinated optimization design of pre-camber and bending stiffness of high-speed maglev track beams according to claim 1 or 6, characterized in that, The multi-objective optimization algorithm specifically adopts the multi-objective sparrow search algorithm, and its solution and external archiving maintenance mechanism includes the following steps: The vector to be optimized [ z max , EI The position of each sparrow in the two-dimensional solution space is encoded using real numbers. Within the feasible region formed by the constraints, random initialization is performed, including... N A sparrow population of individuals is configured with a discoverer ratio of 20%, a joiner ratio of 70%, and a warning ratio of 10%, while creating a capacity of [missing information]. n Empty external archive; The constructed analytical model of suspension gap change including pre-camber is invoked to calculate the objective function values ​​of each individual in the current population and evaluate its multi-objective fitness. In each iteration, based on the Pareto dominance relationship, a sparsely distributed non-dominated solution is selected from the external archive according to the crowding distance as the optimal guide, and the spatial positions of the discoverer, joiner and warning are updated. After the position is updated, the current generation population is merged with the original external archive, and the non-dominated sorting is re-executed to remove dominated inferior solutions. When the number of non-dominated solutions in the external archive exceeds the capacity, dynamic pruning is performed based on the crowding distance to retain solutions with more uniform boundary distribution until the maximum number of iterations is reached, and the final Pareto optimal solution set is output. Extract the three sub-objective function values ​​corresponding to each non-dominated solution in the Pareto optimal solution set, construct a multi-objective decision matrix, and normalize the matrix to eliminate the influence of different physical dimensions; Identify the minimum value of each sub-objective in the normalized matrix and use it as the vector of the positive ideal optimal solution point. D + Identify the corresponding maxima and use them as the vector of negative ideal solutions. D - ; Using the Euclidean distance formula, the combined distance from each solution in the Pareto solution set to the positive ideal optimal solution point vector is calculated. d i + And the combined distance to the vector of the negative ideal solution point. d i - ; Calculate the relative proximity of each solution to the ideal optimal solution. Ci Select the relative proximity among all non-dominated solutions. Ci The largest individual entity corresponds to the optimal pre-camber amplitude and bending stiffness parameters of the track beam.

Images