0 Foreword Safety is the soul of high-speed trains, and is the most important prerequisite for the improvement of train speed. As the train speed increases, the aerodynamic problems of the train become more and more significant, which seriously affects the running safety and ride comfort of the train. In the strong cross wind environment, the aerodynamic forces and aerodynamic moments acting on the train increase sharply, which may cause an increase in the wheel load shedding rate, the derailment coefficient, the lateral force of the axle, etc., and the operational safety of the train is particularly prominent. Aiming at the aerodynamic characteristics of high-speed trains under strong cross wind conditions, domestic and foreign scholars have carried out a lot of research work. BAKER et al. use test methods and numerically oriented shapes. YU et al. carried out a comprehensive study on the flow field structure and aerodynamic load characteristics of the following vehicles with aerodynamic drag and wheel load shedding rate optimization method. KRANOVIC et al. studied the flow field characteristics and aerodynamic characteristics around the high-speed train under crosswind, and found that the numerical results agree well with the experimental results. Tian Hongqi found through research that the lateral wind makes the lateral force of the vehicle increase rapidly, and the side wall of the car body is designed as a drum-shaped wall, which can improve the lateral aerodynamic performance of the vehicle.

The development of these research efforts provides direction for improving the cross-wind aerodynamic performance of high-speed trains. In the windy areas along the railway, the reasonable construction of the windshield can significantly improve the cross-wind aerodynamic performance of the train. However, the construction of the windshield wall is huge and the cost is high. Therefore, it is necessary to find other methods to improve the cross-wind aerodynamic performance of the high-speed train. The streamlined head shape of high-speed trains has a great influence on the cross-wind aerodynamic performance of high-speed trains. By improving the streamlined head shape of high-speed trains, the cross-wind aerodynamic performance of high-speed trains can be improved. HEMIDA et al. studied the influence of the length and the side angle of the high-speed train on the flow field structure of the train. It was found that the flow field of the short nose head showed more obvious transient characteristics than the long nose type. And three-dimensional characteristics, and there are more vortex shedding near the nose. Feng Zhipeng studied the effects of streamlined head length, head control line shape and nose tip height on the aerodynamic performance of high-speed trains. CHELI et al. used a combination of wind tunnel test and Computational Fluid Dynamics (CFD) method to optimize the aerodynamic performance of Electric Multiple Units (EMU) 250 under crosswind, on train roof shape and nose shape. Improvements have been made to improve the shape of the train with better crosswind performance. In essence, the method adopted above is a preferred method, that is, various head type schemes are first developed, and then comparative selection is performed by wind tunnel test or CFD calculation.

This method relies more on engineering experience, and the final selected head shape is not necessarily optimal. To achieve a truly optimized head shape to overcome these shortcomings, a direct optimization approach must be employed. The direct optimization design is based on the premise of satisfying certain constraints, and uses mathematical methods to seek the largest or smallest possible (some lateral force minimization, minimum lift, etc.) for some design goals. Therefore, the high-speed train head design problem can be transformed into a multi-objective constrained optimization problem. In the direct optimization design of high-speed train head type, KWON et al studied the influence of nose shape on tunnel pressure wave, and optimized the nose shape of high-speed train based on response surface method. The analysis results show that the optimal design of the nose is adopted. The tunnel pressure wave strength can be well reduced. LEE et al studied the influence of the shape of the nose on the micro-pressure wave of the tunnel. By improving the support vector machine, an approximate optimization method for the shape of the nose was proposed. SUN et al. optimized the CRH3 nose shape and the height of the upper wall of the cab. Based on the three-dimensional parameterization method of local shape function, Yao Yibao established a parametric model of the shape of the high-speed train head and optimized the drag reduction for high-speed trains. Li Ming and others used Isight software to build a new head-type automatic optimization design platform for high-speed trains, and carried out multi-objective optimization design of high-speed trains. The head-type gas target with better comprehensive performance was given, and multi-objective optimization design for streamlined heads of high-speed trains was carried out. After optimization, the aerodynamic drag of the high-speed train can be reduced by up to 4.15%, and the wheel load shedding rate can be reduced by up to 1.72%. These direct optimization design work rarely involves the cross-wind aerodynamic performance of high-speed trains, and the existence of strong cross winds has deteriorated drastically. The aerodynamic performance of the train, therefore, is of great significance to improve the aerodynamic performance of the train. In this paper, the multi-objective aerodynamic optimization design of the streamlined head of high-speed trains will be carried out for the cross-wind aerodynamic performance of the train.

In this paper, a multi-objective optimization design method for streamlined heads of high-speed trains under crosswind is established. The lateral force and lift are used as the optimization design targets, and the high-speed train heads are automatically optimized. The optimization design process mainly involves the establishment of high-speed train three-dimensional parametric model, high-speed train aerodynamic calculation grid division, high-speed train aerodynamic numerical calculation, high-speed train vehicle dynamics calculation and multi-objective pneumatic optimization algorithm.

1 Multi-objective optimization basic concepts and solving methods 1.1 Multi-objective optimization The basic concept is to have a clear and clear understanding of multi-objective optimization problems, and briefly introduce some basic concepts in multi-objective optimization problems.

The multi-objective optimization problem can be described as the lower bound of the value of the xth i-th design variable; the upper limit of the value of the i-th design variable; the mth objective function of fm(x); the inequality constraint of g.(x); Hk(x) the kth equality constraint.

In the multi-objective optimization problem, the objective functions tend to conflict with each other, and it is generally impossible to achieve optimal solutions for multiple sub-goals. Otherwise, it is not a category of multi-objective optimization research. The French economist PARETO first studied the multi-objective optimization problem in the field of economics and proposed the concept of Pareto solution set.

If xeX (X is the feasible domain of the design variable), if and only if it does not represent the total number of sub-objects, and at least one of the strict inequalities holds, it is called a Pareto optimal solution for multi-objective optimization. The set of all Pareto optimal solutions is called the Pareto optimal solution set. The image of the Pareto optimal solution set in the objective function space is called the Pareto front.

Solving the multi-objective optimization problem is to find the Pareto optimal solution set, and then the decision maker determines a compromise solution based on the relevant information and requirements.

1.2 Multi-objective optimization algorithm The multi-objective optimization algorithm mainly includes normalization method and non-normalization method. The normalization method converts multiple targets into a single target by weighting, so that the single-objective optimization method can be used for solving. By setting different weights, a set of solutions can be obtained to approximate the Pareto optimal solution set. The normalization method is sensitive to the shape of the Pareto optimal frontier, cannot handle the concave portion of the Pareto front, and is less efficient to solve. The non-normalization method is an optimization technique that directly deals with multiple targets using the Pareto mechanism, so that the front edge of the solved set is as close as possible to the Pareto front, and the Pareto front is uniformly covered as much as possible. The representative method in the non-normalization method is a multi-objective genetic algorithm. In this paper, the multi-objective genetic algorithm NSGA- is used to solve the multi-objective optimization problem. NSGA- uses a non-inferior ranking with an elite strategy, using a simple crowding operator, without defining any parameters to maintain population diversity. In the process of evolution, the population corpse is first genetically manipulated, the population is obtained, and then the two groups are combined, and the non-inferior sorting and the crowding distance are sorted to form a new population, which is repeated until the end. The specific process of NSGA- is described below.

Randomly generate the initial population eight, the non-inferior ranking of the population, each individual is given the rank; then perform the binary tournament selection, crossover and mutation on the initial population, and obtain the new population 2, and the household 0. Form a new population brother = AU performs a non-inferior sorting of the population brothers, and obtains a non-inferior front-end eight, clever.

For all Fs, sort by crowding comparison operation, and select the best individual to form a population of eight +1. Perform copying, crossover and mutation on the population +1, forming the end if the termination condition is established; otherwise, / =+1. 2 Three-dimensional parametric model of high-speed trains Because of the high degree of symmetry of the streamlined heads of high-speed trains, only the left-hand (or right-hand) streamlined heads need to be parametrically modeled. According to the streamlined head shape of a high-speed train, 162 control points are established on the surface of the head, 12 spline curves are established from 162 control points, and 7 curved surfaces are created from 12 spline curves, thereby establishing a streamline type of the left half of the high-speed train. Head shape as shown. In order to facilitate the introduction of optimization design variables, 12 spline curves are numbered, respectively C1C12. For the streamlined head type of the left half of the high-speed train, five optimized design variables are extracted, corresponding to the longitudinal symmetry line C1 and the horizontal maximum outer contour line respectively. C3, vehicle bottom horizontal contour C4, middle auxiliary control line C7 and nose tip height. As the length of the streamline increases, the cross-wind aerodynamic performance of the high-speed train will be significantly improved. Therefore, the length of the streamline type is fixed, and the cross-wind aerodynamic performance of the high-speed train is improved by optimizing the outer shape of the streamlined head.

The changes in the positions of the vertices on the curves C1, C3 and C4 take a similar form. The vertical coordinates of the vertices on C1 change, and the lateral coordinates of the vertices on C3 and C4 change. When the coordinates change, the coordinate increments at the longitudinal midpoints of the curves C1, C3, and C4 are the largest (the coordinate increments are d, 3, 4), and the coordinates at the ends are unchanged, that is, the coordinate increment is equal to zero. For a point between the longitudinal midpoint and the end points, the coordinate increment value changes linearly. A schematic diagram of the deformation of C1 is given.

The deformation of the curve C7 is mainly the deformation of the curve concave and convex, and it is necessary to fix the end points of the control line at the same time, and at the same time, the change from the end point of the two ends to the midpoint of the control line is larger and larger, and the deformation is performed by the formula (2). 77, old (i') the value before the deformation; (0 after the deformation; iC7 control point number; dy7 design variables.

The line is concave inward, and when dy7<0, the curve is convex outward.

For the change of the tip height, it is only necessary to multiply the vertical coordinate of the curve C9 by a coefficient nr. When the coefficient n>1, the tip height becomes larger, and when the coefficient nr<1, the tip height becomes smaller.

It should be noted that when the above curves are deformed, other curves associated with them are correspondingly changed to ensure continuous smoothness of the curved surface, which will not be described in detail herein.

3 High-speed train aerodynamic model The calculation of the flow field around a high-speed train under crosswind can generally be performed using an incompressible steady flow. The turbulence model uses a standard turbulence model, and its governing equation can be expressed as P air density; u velocity vector; Flux; S source term; / diffusion coefficient.

The high-speed train model adopts the first car-middle car-tail car three-car group, and the streamlined head type adopts the three-dimensional parametric model established in the second part. The flow field calculation area and boundary settings are as shown, the top is set to a symmetrical boundary, the train surface is set to the wall boundary condition, the ground is set to slip the ground, and the slip speed is the train running speed to simulate the ground effect. When meshing, the high-speed train surface adopts a triangular mesh, the maximum mesh size is set to 100mm, the spatial mesh adopts a tetrahedral mesh, and the maximum mesh size is set to 4000mm. In the optimization process, the flow field is realized by using the ICEM script file. The calculation grid is automatically divided, and the Fluent script file is used to realize the automatic calculation of the flow field and the output of the high-speed train. The multi-objective genetic algorithm is used to achieve automatic updating of optimized design variables. The multi-objective optimization design flow of the streamlined head type of the high-speed train under the cross wind is as shown.

4 Analysis of calculation results 4.1 Optimization of cross-wind aerodynamic characteristics The train speed calculated in this paper is 300km/h, and the crosswind wind speed is 30m/s. The initial sampling point of the NSGA- algorithm is set to 12, and 25 generations of genetic calculations are performed. After completing 300 designs, the optimization of the streamlined head shape of the high-speed train was completed.

The overall variation curve of optimization design variables and optimization objectives in the optimization process is given, where a is the overall variation curve of the optimization design variable dz1, b is the overall variation curve of the optimization design variable dy7, and c is the overall variation curve of the optimization target side force. .

The middle five-pointed star "★" indicates the Pareto optimal solution obtained during the optimization process. It can be seen that by optimizing the sampling of the algorithm in the design space, the optimization design variables and the optimization target show convergence tendency. It should be noted that the variable dy7 in b converges to two different positions, because dy7 has the opposite effect on the two optimization targets, that is, dy7 causes another optimization target while improving one optimization target. deterioration. Through repeated iterative calculations, the multi-objective genetic algorithm finds the Pareto optimal design point and target value that minimizes the target value.

The correlation between the optimization goal and the optimization design variables is given in the optimization process. It can be seen from a that the optimized design variables dzi, d3, 〃r have a positive correlation with the lateral force within a certain range, and the optimized design variable d77 has a negative correlation with the lateral force within a certain range.

Therefore, reducing the optimized design variables dzi, d3, and increasing the optimal design variable can reduce the lateral force. It can be seen from b that the optimization design variables dzi, do 7, and have a positive correlation with lift within a certain range, and the optimization design variable 4 has a negative correlation with lift within a certain range, thus reducing the optimization design variable dzi, D7, call, increase the optimization design variable d74 can reduce the lift. In addition, it can be seen that the correlation between d77 and the two optimization targets is opposite, which is consistent with the law reflected by b.

In order to further study the relationship between optimization objectives and optimization design variables, based on the previous analysis, the optimization design variables d7 and 〃r are selected and the response objectives are analyzed. The three-dimensional response surface between the optimization target and the optimized design variable d7 is given, where a is the three-dimensional response surface between the lateral force and d7 and b, and b is the three-dimensional response surface between the lift and d7 and the call. It can be seen that there is not a purely linear relationship between the optimization target Fs and the optimization design variable d77, which is difficult to obtain in a general preferred design. The lateral force of the high-speed train under crosswind shows a decreasing trend with the increase and decrease of d7. The lift of the high-speed train under crosswind decreases with the decrease of d7 and the decrease of 〃r. The analysis results of the correlation diagram are consistent.

The convergence of the optimization target in the image space is given in the optimization design process. The curve of the "five-pointed star" "★" is the Pareto frontier of the multi-objective optimization of the streamlined head-type crosswind aerodynamic performance of the high-speed train. The dot "" indicates Side force and lift corresponding to the initial streamlined head shape. It can be seen that after multi-objective optimization design of the streamlined head type of high-speed train, the side force and lift of the high-speed train under the cross wind are improved, and the optimization achieves better results.

Through the multi-objective optimization design, a total of 12 Pareto optimal head shapes were obtained. Compared with the original head shape and lift, the side forces and lifts of the 12 Pareto optimal head models were significantly improved. It can be reduced by 4.16%, and can be reduced by at least 1.33%; the lift can be reduced by up to 19.60%, and the minimum can be reduced by 4.13%. 4.2 Basic aerodynamic performance analysis before and after optimization without wind According to the previous analysis, the multi-objective optimization design method established in this paper is adopted. It can effectively improve the cross-wind aerodynamic performance of high-speed trains. The optimized streamlined head type also has better basic aerodynamic performance in the windless environment, and further analysis is needed. This paper compares and analyzes the basic aerodynamic performance of high-speed trains in the windless environment before and after optimization. The basic aerodynamic performance of high-speed trains mainly refers to aerodynamic drag and aerodynamic lift. Aerodynamic drag directly affects energy consumption, and the smaller the aerodynamic drag, the less energy is consumed. The upward aerodynamic lift reduces the contact force of the vehicle, causing the train to “float” and easily cause the train to derail; the downward aerodynamic lift will increase the dynamic wheel weight of the train, making the train's impact on the rail intensified. That is, the smaller the aerodynamic drag of the high-speed train, the better, and the aerodynamic lift should be as close as possible to zero (the absolute value of the aerodynamic lift is as small as possible).

When calculating, the running speed of the train is 300km/h, and the optimized design variables are taken as the Pareto optimal solutions in the Pareto optimal solution set. Table 1 gives the absolute value of the aerodynamic drag and the absolute value of the aerodynamic lift in the absence of wind under each Pareto optimal solution, and the percentage of the aerodynamic drag and the absolute value of the aerodynamic lift relative to the original head type. For the original head train, the absolute values ​​of the aerodynamic drag and aerodynamic lift of the train without wind are 0=33.48kN, respectively. As can be seen from Table 1, the 12 Pareto optimal heads are compared with the aerodynamic drag of the original head. The aerodynamic drag is improved. Compared with the absolute value of the aerodynamic lift of the original head type, the absolute value of the aerodynamic lift of the four Pareto optimal head types deteriorates, and the absolute values ​​of the aerodynamic lift of the remaining eight Pareto optimal head types are improved. Therefore, in order to ensure that the basic aerodynamic performance of the high-speed train does not deteriorate, it is necessary to eliminate the four Pareto optimal head types that deteriorate the absolute value of the aerodynamic lift. At this time, there are a total of eight Pareto optimal head types. The aerodynamic performance of the eight Pareto optimal head models is analyzed. Compared with the original head shape, the lateral force under cross wind can be reduced by up to 3.06%, and the minimum can be reduced by 1.33%. The lift under cross wind can be reduced at most. 19.60%., at least 10.45%; the aerodynamic drag without wind can be reduced by up to 4.51%, and the minimum can be reduced by 2.93%; the aerodynamic lift without wind can reduce the aerodynamic drag and aerodynamics of the train when no wind is optimized in Table 1. Lift design variable dzi/mm design variable dy3/mm design variable variable 7 design variable called resistance F/kN resistance Fd reduction percentage lift absolute value 5 Conclusion In order to improve the cross-wind aerodynamic performance of high-speed trains, this paper uses direct optimization method to establish high speed A multi-objective optimization calculation model for the aerodynamic performance of cross-type cross winds of trains. By establishing a three-dimensional parametric model of streamlined head shape for high-speed trains, the script file is used to calculate the aerodynamic performance of cross-wind of high-speed trains, and the lateral force and lift are used as the optimization targets. The multi-objective genetic algorithm NSGA-high speed with global search capability is adopted. The train streamlined head type is designed for multi-objective automatic optimization. With this direct optimization method, the design cycle of the streamlined head type of the high-speed train can be greatly reduced, and the streamlined head type of the high-speed train with better aerodynamic performance can be obtained.

The optimization calculation results show that for the streamlined head shape studied in this paper, the optimization design variable heart 1, the 3, has a positive correlation with the lateral force within a certain range, and the optimized design variable 7 has a negative correlation with the lateral force within a certain range. Optimize the design variable heart 1, do 7, have a positive correlation with lift within a certain range, and optimize the design variable to have a negative correlation with lift within a certain range. Through the multi-objective optimization design, a total of 12 Pareto optimal head shapes are given, and the lateral forces and lifts of the 12 Pareto optimal head types are significantly improved. In order to ensure that the basic aerodynamic performance of the high-speed train does not deteriorate, eight Pareto optimal head types are finally given. Compared with the original head type, the Pareto optimal head type given in the paper can reduce the side force under cross wind by up to 3.06% and at least 1.33%; the lift under cross wind can be reduced by up to 19.60%, at least 10.45%; the aerodynamic drag without wind can be reduced by up to 4.51%, and the minimum can be reduced by 2.93%; the aerodynamic lift without wind can be reduced by up to 9.68%, at least

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Application of center drills
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