Automatic optimization design method for super-large radius curve of operating railway line

Abstract

The invention discloses an automatic optimization design method for an ultra-large radius curve of an operating railway line. The method comprises the following steps: S1, carrying out local coordinate system mapping on measurement data of a long and large straight line segment; s2, under the local coordinate system, dividing the long and large straight line of the railway into a plurality of line segments through the break angle points to obtain a break angle point coordinate point set and a set of points in each line segment; establishing an objective function, a spacing constraint condition and a line constraint condition; s3, forming a population according to the coordinates of the break angle points; a penalty function is constructed based on the spacing constraint condition and the line constraint condition and used for constructing a correction target function, a fitness function is obtained, the population is optimized, and the local coordinate of the optimal break angle point serves as an optimal solution; and S4, according to the optimal solution, fitting a polyline and an ultra-large curve radius under a global coordinate system. According to the method, the position where the break angle needs to be added in the long and large straight line segment can be accurately found, the corresponding curve radius can be automatically matched, the efficiency is improved, and the uncertainty of a manual adjustment scheme is avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of railway operation and maintenance, and particularly relates to a method for automatically optimizing design of super-large radius curve of operating railway line. BACKGROUND

[0002] Since the rectification of the line during the long-time operation and maintenance of the operating railway is performed in view of the relative smoothness, the maintenance of the line alignment is not considered, so the long-time local smoothness rectification will lead to the problems of straight line not being straight and curve not being smooth in the line alignment of the operating railway. With the development of the absolute measurement technology in recent years, the absolute coordinates of the line can be measured by the track detector. According to the measured absolute coordinate data of the operating railway line, it is known that there are angle less than 2'' of the corner in the straight line section in the line with the length more than 5km, and there are multiple corners in the line with the length more than 10km. These corners cannot be fitted by the circular curve in the specification due to the small angle, and if the long and large straight line section is fitted and designed according to the single straight line by using the traditional design method, a large planar deviation will be generated, so the line alignment rectification will cause the intrusion of the catenary, bridge and platform along the line structure, and further affect the operation safety. Therefore, when the long and large straight line of the operating railway is designed, the actual line alignment should be fully considered, the corner position should be accurately found out, and the multiple straight lines should be fitted, and the super-large radius curve with more than 100,000 meters is used to connect the straight lines, but it is difficult to achieve by manual work. SUMMARY

[0003] In order to solve the problems in the background art and realize the accurate fitting of the long and large straight line, the present application provides a method for automatically optimizing design of super-large radius curve of operating railway line, which can accurately find out the number and position of the corner in the long and large straight line, and automatically adapt the super-large radius curve to realize the optimal fitting of the measured line alignment.

[0004] To this end, the present application adopts the following technical scheme:

[0005] 1. A method for automatically optimizing design of super-large radius curve of operating railway line, comprising the following steps:

[0006] S1. mapping the long and large straight line section measurement data of the operating railway line in the local coordinate system to obtain the coordinate point set in the local coordinate system ;

[0007] S2. in the local coordinate system, the long and large straight line of the railway is divided into multiple line sections by the corner points to obtain the corner point coordinate point set and the set of points in each line section; the sum of the squares of the distances from all points in the set of points in each line section to the corresponding line section is taken as the objective function; the corner point coordinate point set a distance constraint condition between adjacent corner points and a route constraint condition of the corner points in the set of points in the line segment; the corner points are end points of each line segment in the multi-segment line;

[0008] S3, encoding the corner point coordinates and forming a population for evolution; constructing a penalty function based on the distance constraint condition and the route constraint condition; constructing a modified objective function based on the penalty function and the objective function obtained in S2, and then obtaining an adaptive function for population evaluation, and optimizing the population through a roulette method, a crossover operation, a mutation operation and an iterative update, and taking the local coordinates of the optimal corner point obtained as an optimal solution;

[0009] S4, fitting the multi-segment line and the super-large curve radius in the global coordinate system:

[0010] According to the optimal solution obtained in S3, the slope of each line segment in the multi-segment line is calculated, and then the slope change value of adjacent line segments is calculated and the optimal corner point set is screened out; according to the optimal corner point set, the optimal fitting multi-segment line of the long straight line in the global coordinate system is obtained, and then the optimal radius of the circular curve at the corner point is calculated through the slope change value of adjacent line segments in the optimal fitting multi-segment line and the minimum circular curve length in the railway design specification.

[0011] The above step S1 includes the following steps:

[0012] S11, obtaining the measurement data of the long straight line segment, and sequentially sorting from small to large mileage to obtain the coordinate point set of the track plane in the global coordinate system , wherein, is the east coordinate of the plane coordinate point , and is the north coordinate of the plane coordinate point .

[0013] S12, performing straight line fitting on all points in the coordinate point set using the least square method to obtain a projection line;

[0014] S13, establishing a local coordinate system: in the track plane, taking the projection point of the first point in the coordinate point set on the projection line as the origin, taking the projection line as the X axis of the local coordinate system, and the direction points to the large mileage direction, and the Y axis direction is determined according to the right-hand rule;

[0015] S14, converting the points in the coordinate point set to the local coordinate system to obtain a coordinate point set , , wherein, is the total number of coordinate points, is the number of coordinate points, .

[0016] In step S2 above,

[0017] With coordinate point set middle and Using the x-coordinate as the boundary, insert A set of line segments connected end to end serves as a local coordinate point set. Fitting a polyline This yields the set of corner point coordinates in the local coordinate system, which includes the endpoints of each line segment in the fitted polyline as corner points. , ;in, The corner points are numbered. The total number of line segments. ; Corner point The coordinates; For decision variables, we have:

[0018] ;

[0019] In a polyline, the turning point The equation of the line segment originating from is:

[0020] ;

[0021] in, For the corner point The slope of the line segment starting from point A. For the corner point The intercept of the line segment originating from;

[0022] The coordinate point set is determined based on the x-coordinate of the corner point. The points in the middle are divided into A set, with the corner point The set of points inside the line segment originating from is ,in, , , For set The total number of local coordinate points in the middle. ;

[0023] The objective function is:

[0024] .

[0025] The spacing constraint in step S2 above is:

[0026] ;

[0027] The distance between adjacent bend points is in meters.

[0028] The line constraint condition in the above step S2 adopts an approximate algorithm, and the line constraint condition is:

[0029] ;

[0030] Wherein, is an upper limit value of the adjustment of the value, is a lower limit value of the adjustment of the value, and the and are determined according to actual conditions. The above step S3 includes the following steps:

[0031] S31, the coordinate point set of the corner points in the local coordinate system obtained in S21 is taken as an optimization variable, a random vector is generated by using real number coding, and a population containing

[0032] individuals is formed, wherein: ;

[0033] ;

[0034] Wherein, is the individual number in the initialized population, is the number of individuals in the population ; the interval is divided into by dividing the local coordinate point set , and is an integer; is a random vector value between ;

[0035] S32, a penalty function is constructed:

[0036] ;

[0037] Wherein, is a penalty coefficient corresponding to the constraint function ; is a penalty coefficient corresponding to the constraint function ;

[0038] A modified objective function is constructed:

[0039] ;

[0040] A fitness function is constructed:

[0041] ;​​

[0042] S33, roulette wheel method is used for genetic selection operation on the current population, specifically: for each individual in the population Calculate the fitness ; Calculate the cumulative probability of each individual , ; Generate a random number , select two individuals that meet As the excellent parent And ;

[0043] S34, based on the excellent parent, linear combination is used for cross operation on the population, and the cross offspring individual is obtained;

[0044] S35, each individual in the remaining population after removing the excellent parent is subjected to mutation operation, and the mutation offspring population is obtained;

[0045] S36, iterative update until the optimal individual .

[0046] The above step S36 is specifically:

[0047] The fitness of each individual is recalculated according to the fitness function constructed in S32 for the cross offspring individual and the mutation offspring population, and the current highest fitness is represented as , wherein Indicates the number of mutations;

[0048] If the number of mutations does not reach the maximum iteration number and the improvement rate is greater than 1%, the elite preservation strategy is used for iteration, and then S33-S36 is executed until the number of mutations exceeds 100 times or The improvement rate Is less than 1%, the iteration is stopped, and the individual with the highest fitness at this time is recorded as the optimal individual ; The improvement rate Is calculated by the following formula:

[0049] .

[0050] The above step S4 includes the following steps:

[0051] S41, according to the optimal individual obtained in S3, the slope of the corresponding line segment is calculated using the fold angle point coordinates , and the slope change value of the adjacent line segment is calculated by the following formula :

[0052] ;

[0053] Wherein, The number of the corner point in the optimal individual;

[0054] S42, screening the optimal corner point set according to the slope change value of adjacent line segments:

[0055] Calculate the screening criteria :

[0056] ;

[0057] Wherein, The minimum circular curve length is selected according to the railway line design specification, and the maximum circular curve radius According to the maximum limit value of the super large radius curve to be inserted in the actual situation, ;

[0058] If , the corner point corresponding to it is added to the optimal corner point set, if , the corner point corresponding to it is discarded, and finally the optimal corner point set containing +1 corner point is obtained ;

[0059] S43, fitting the long and large straight line segment of the operating railway line into the optimal fitting multi-segment line in the global coordinate system:

[0060] S44, calculating the optimal radius of the circular curve connecting the corner points between adjacent line segments in the optimal fitting multi-segment line, and completing the optimization of the long and large straight line segment.

[0061] In the above step S43, according to the method in step S22, the optimal corner point set in step S42 is divided into groups, and the coordinate point set of the track plane in the global coordinate system obtained by S11 is also divided into groups according to the corresponding grouping, and the least square method is used to fit each group of coordinate points in the global coordinate system after grouping, to obtain group line segments, which constitute the optimal fitting multi-segment line of the long and large straight line in the global coordinate system. In the above step S44, the slope change value between adjacent line segments in the optimal fitting multi-segment line in the global coordinate system is calculated by the method of S41 , and the optimal radius of the circular curve connecting the corner points between adjacent line segments is obtained by the following formula

[0062] :

[0063] ;

[0064] Wherein, ​​Optimal set of angle points Numbering of angle points.

[0065] Compared with the prior art, the present application has the following beneficial effects:

[0066] 1. The method of the present application realizes automatic optimization design, can accurately find the position where the angle needs to be added in the long and straight line section of the operating railway and automatically adapt the corresponding curve radius, effectively improves the design efficiency and avoids the uncertainty of manual line adjustment scheme design.

[0067] 2. The method of the present application takes the sum of mean square deviations of fitting line and actual track line as the optimization target, the fitting line has high fitting degree with the actual track line of the operating railway line, and the design scheme is more scientific and reasonable.

[0068] 3. The method of the present application can perform constraint optimization according to the adjustment limit value of special sections such as bridges, turnouts, catenary and clearance along the line, thereby avoiding the risk of limit invasion of the design scheme. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 Flowchart of the optimization design method of the present application;

[0070] Figure 2 Schematic diagram of the relationship between the global coordinate system and the local coordinate system in the method of the present application;

[0071] Figure 3 Schematic diagram of the multi-segment line optimization model in the local coordinate system in the method of the present application;

[0072] Figure 4 Flowchart of the genetic algorithm for solving the multi-segment line optimization model in the method of the present application;

[0073] Figure 5 Schematic diagram of the optimal fitting multi-segment line in the global coordinate system in the method of the present application;

[0074] Figure 6 Schematic diagram of the long and straight line section before optimization in the embodiment of the present application;

[0075] Figure 7 Schematic diagram of the long and straight line section after optimization inserted with super-large radius curve in the embodiment of the present application;

[0076] Figure 8 Graph of the change of the plane deviation amount with the mileage of the long and straight line section before and after optimization in the embodiment of the present application. DETAILED DESCRIPTION

[0077] The technical solutions of the present application are further described in detail below in combination with the drawings and embodiments.

[0078] As Figure 1 shown, the operation railway line super-large radius curve automatic optimization design method of the present application comprises the following steps:

[0079] S1, mapping the measurement data of the long and large straight line segment of the operation railway line to the local coordinate system, comprising:

[0080] S11, obtaining the measurement data of the long and large straight line segment:

[0081] The coordinate point set of the track plane of the long and large straight line segment on the operation railway line is measured by the track detector , wherein, , is the number of the plane coordinate point, is the total number of the plane coordinate point, and the coordinate point set is sorted in the order from small mileage to large mileage, wherein is the east coordinate of the plane coordinate point , is the north coordinate of the plane coordinate point .

[0082] S12, as shown, using the least square method to fit all points in the coordinate point set Figure 2 to obtain the projection line, and the angle between the projection line and the global coordinate system X axis (east coordinate axis) is .

[0083] S13, establishing a local coordinate system:

[0084] The local coordinate system takes the projection point of the starting point on the projection line obtained in S12 as the origin; the direction vector of the projection line direction is the X axis of the local coordinate system; the Y axis of the local coordinate system is perpendicular to the X axis of the local coordinate system, and the direction is determined according to the right-hand rule.

[0085] S14, coordinate conversion:

[0086] First, determine the transformation matrix of the global coordinate system and the local coordinate system, as shown in formula (1):

[0087] (1)

[0088] Convert the coordinates in the coordinate point set to the local coordinate system by formula (2) to obtain the coordinate point set in the local coordinate system:

[0089] (2) ​

[0090] S2, establish a multi-segment line optimization model under the local coordinate system:

[0091] S21, as shown in the local coordinate system, with the horizontal coordinates of the coordinate point set Figure 3 and , and , insert the line segment connected at the beginning and end as the fitting multi-segment line of the coordinate point set , the number of line segments in the fitting multi-segment line is related to the solving efficiency and the total length of the segment length, , get the coordinate point set of the corner point under the local coordinate system containing the end points of each line segment in the fitting multi-segment line as the corner point , , wherein represents the number of corner points, is the total number of line segments, is the coordinate of the corner point ; is a decision variable, as shown in the following formula:

[0092] (3)

[0093] The equation of the line segment in the multi-segment line starting from the corner point is:

[0094] (4)

[0095] wherein is the slope of the line segment starting from the corner point , is the intercept of the line segment starting from the corner point .

[0096] S22, according to the horizontal coordinates of the corner points, the points in the coordinate point set are divided into sets. The set of points in the line segment starting from the corner point is: , wherein , , is the total number of local coordinate points in the set ;

[0097] S23, determine the objective function:

[0098] The sum of the squares of the distances from all local coordinate points in the set to their corresponding line segments is the objective function : ​

[0099] (5)

[0100] S24, establish the spacing constraint condition:

[0101] In order to make the fitting multi-segment line adjacent to the corner point will not coincide, the corner point coordinate point set The coordinates of adjacent corner points should satisfy the following constraint relationship:

[0102] (6)

[0103] Wherein, The spacing constraint condition is that the spacing between adjacent corner points is in meters.

[0104] S25, establish the line constraint condition:

[0105] The set The coordinates of each point should also satisfy the requirements of bridge eccentricity, clearance, and contact net restriction. Using the approximate algorithm, the line constraint condition Is:

[0106] (7)

[0107] Wherein, The upper limit value of the adjustment value of , The lower limit value of the adjustment value of , And Determined according to the actual situation.

[0108] S3, solve the multi-segment line optimization model based on genetic algorithm, as Figure 4 Shown, as follows:

[0109] S31, the corner point coordinate point set In the local coordinate system obtained by S21 is taken as the optimization variable, real number coding is adopted, random vector generation is carried out, and a population containing Individuals Is formed, wherein:

[0110] (8)

[0111] Wherein, The individual number in the initial population is , the number of individuals in the population is set to , and the initial population is randomly generated, wherein each individual is a set of corner point coordinate points; divide the spacing The local coordinate point set Is divided into , which is an integer; for Random vector values ​​between.

[0112] S32, Constructing the fitness function includes the following steps:

[0113] S321, Construct the penalty function :

[0114] (9)

[0115] in, For the corresponding constraint function The penalty coefficient; For the corresponding constraint function The penalty coefficient. In one embodiment of the present invention, , .

[0116] S322, construct the modified objective function and fitness function, we have:

[0117] (10)

[0118] To accommodate the maximization characteristic of genetic algorithms, the fitness function is:

[0119] (11)

[0120] S33 employs a roulette wheel selection method for genetic selection, including:

[0121] S331, for each individual in the population Calculate fitness ,have:

[0122] (12)

[0123] S332, calculate the cumulative probability of each individual using the following formula:

[0124] (13)

[0125] in, .

[0126] S333, Generate random numbers Choose to satisfy Two individuals as excellent parents and This method ensures that individuals with higher fitness are selected with a greater probability, while maintaining population diversity.

[0127] S34 uses a linear combination to perform crossover operations on the population:

[0128] Through excellent parents and Generate crossover offspring individuals ,have:

[0129] (14)

[0130] in, For cross-rate random coefficients, This allows for a smooth integration of the characteristics of the two parent variables and provides better exploratory capabilities in representing continuous variables.

[0131] S35, perform mutation operation:

[0132] Eliminating outstanding parent generations and Perturb each individual in the remaining population (without crossover) to obtain a mutated offspring population. Specifically, the perturbation value is added to the original population. , , This is a regulatory factor, initially set to 1. This ensures population diversity while preventing premature convergence and local optima.

[0133] S36, iteratively update until the optimal individual is output:

[0134] The fitness of each individual is recalculated according to the fitness function constructed in S32 for the offspring produced after crossover and mutation, where the highest fitness is represented as... , Indicates the number of mutations.

[0135] If the number of mutations does not reach the maximum number of iterations and the improvement rate is greater than 1%, then the elite preservation strategy is used for iteration. The elite preservation strategy is as follows: select the 10 individuals with the highest fitness in the current population and save them directly to the next generation to preserve excellent genes. Then, merge the 10 saved individuals with 10 new individuals generated using the random vector generation method in S31 to generate a new population, in order to maintain the population. The scale. Then execute S33~S36 until the number of mutations exceeds 100 or improvement rate When the fitness rate is less than 1%, the iteration stops. The individual with the highest fitness at this point is the optimal solution, denoted as the optimal individual. .

[0136] In the middle, the improvement rate Calculated using the following formula:

[0137] (15)

[0138] S4, Fitting polylines and ultra-large curve radii in the global coordinate system:

[0139] S41, the optimal individual obtained from S3 The slope of the corresponding line segment is calculated using the coordinates of the corner points. Then, calculate the slope change of adjacent line segments using the following formula. :

[0140] (16)

[0141] in, for The numbering of the mid-angle point The unit is °.

[0142] S42, based on the slope change value of adjacent line segments Select the optimal set of corner points.

[0143] First, calculate the screening criteria. , The value is determined by the minimum circular curve length. and the maximum radius of the circular curve Confirmed, the calculation formula is as follows:

[0144] (17)

[0145] Among them, the minimum circular curve length The maximum radius of the circular curve was selected according to the "TB10098-2017 Railway Line Design Specification". Select the value based on the maximum limit of the extra-large radius curve that needs to be inserted in the actual situation. .

[0146] like Then the corresponding corner point Add to the optimal set of turning points, if Then discard the corresponding corner points to obtain the optimal set of corner points. The number of corner points is +1.

[0147] S43, in the global coordinate system, fit the long straight line to the optimal fitted polyline:

[0148] like Figure 5 As shown, following the method in step S22, based on the optimal set of turning points obtained in step S42... Set of local coordinate points Divided into Group, according to the corresponding group, the set of coordinate points of the orbital plane in the global coordinate system obtained by S11. Also divided into Grouping, the least squares method is used to fit the coordinates of each group in the global coordinate system after grouping, to obtain These line segments are the optimally fitted polylines for long straight lines in the global coordinate system.

[0149] S44, calculate the radius of the circular curve at each bend point:

[0150] The slope variation of adjacent segments in the best-fit polyline in the global coordinate system is calculated using formula (16). Then, the optimal radius of the circular curve connecting the bend points between adjacent line segments is obtained using the following formula. Finally, the optimization of the long straight line segment is completed:

[0151] (18)

[0152] in, For the optimal set of turning points Numbering of the mid-angle point.

[0153] Example

[0154] like Figure 6 As shown, the section of a certain conventional railway from K18+165 to K23+790 is a long straight section. There are 5625 coordinate points along the centerline of this straight section, forming a set of measurement points, i.e., a coordinate point set. .

[0155] First, based on the coordinate point set Using the coordinate data in the graph, the least squares method is used to fit the straight line segment to obtain its angle with the X-axis. for Calculate the projected coordinates of the point corresponding to the starting mileage DK18+165 on the fitted straight line, and use it as the origin. Finally, the transformation matrix is ​​calculated. :

[0156] .

[0157] Based on the transformation matrix Calculate the local coordinate point set in the local coordinate system corresponding to the point set. Eleven bend points were inserted into this section of the line, dividing the long straight section into 10 segments. Based on the railway's optimized design requirements, the horizontal deviation between the measured and fitted lines was controlled within the range of [-50mm, 50mm]. The railway's design speed is 120km / h, and according to the "TB10098-2017 Railway Line Design Specification," its minimum circular curve length is 80m, and its maximum circular curve radius... Select 500,000 m, the corresponding deflection angle When converted to an angle, it becomes 33″.

[0158] The final solution obtained by optimization using the method of this invention is as follows: Figure 7 As shown, three circular curves (circular curve radii rounded to the nearest ten thousand) are inserted into the long straight line segment within the range of K18+165-K23+790. The specific parameters are shown in Table 1.

[0159] Table 1

[0160]

[0161] Comparison of "plane deviation - mileage" before and after optimization Figure 8 As shown. Before optimization, the range of plane deviation was [-190.8mm, 227.7mm], and the standard deviation was 87.6mm; after optimization, the range of plane deviation was [-38.7mm, 33.8mm], and the standard deviation was 13.12mm.

[0162] As can be seen, the method of this invention enables the automatic insertion of ultra-large radius curves in long straight sections. The curve parameters meet the minimum curve length requirements in the specifications. The deviation of the center line of the measured long straight section is effectively reduced and can be controlled within the pre-set constraint range of [-50mm, 50mm]. The root mean square error is reduced from 87.6mm to 13.1mm.

[0163] This method enables the optimal design of ultra-large curves in long straight sections, avoiding the uncertainties of manual design. On the other hand, it controls the deviation within the constraint range according to the design requirements, effectively reducing the plane deviation, ensuring the clearance safety of the line, and facilitating the line maintenance and operation safety.

Claims

1. An automatic optimization design method for ultra-large radius curves on operating railway lines, characterized in that, Includes the following steps: S1. Map the measurement data of long straight sections of the operating railway line to a local coordinate system to obtain the set of coordinate points in the local coordinate system. ; S2, in the local coordinate system, the long straight railway line is divided into multiple line segments by several bend points, resulting in the set of coordinate points of the bend points. The set of points within each line segment; the objective function is the sum of the squares of the distances from each point within the set of points within all line segments to the corresponding line segment. Establish the coordinate set of the corner point The spacing constraints between adjacent corner points and the line constraints of corner points in the set of points within a line segment; the corner points are the endpoints of each line segment in a polyline; S3: Encode the coordinates of the corner points and form a population for evolution; construct a penalty function based on the spacing constraints and line constraints; construct a modified objective function based on the penalty function and the objective function obtained in S2, and then obtain a fitness function for population evaluation; then optimize the population through roulette wheel method, crossover operation, mutation operation and iterative update, and take the local coordinates of the optimal corner point as the optimal solution. S4, Fitting polylines and ultra-large curve radii in the global coordinate system: The slope of each segment in the polyline is calculated based on the optimal solution obtained from S3. Then, the slope change value of adjacent segments is calculated and the optimal set of turning points is selected. Based on the optimal set of turning points, the optimal fitting polyline of the long straight line in the global coordinate system is obtained. Then, the optimal radius of the circular curve at the turning point is calculated by the slope change value of adjacent segments in the optimal fitting polyline and the minimum circular curve length in the railway design specification.

2. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 1, characterized in that: S1 includes the following steps: S11: Obtain measurement data for the long straight section and sort it in order from small mileage to large mileage to obtain the coordinate point set of the track plane in the global coordinate system. ,in, plane coordinate points The eastern coordinates, plane coordinate points North coordinates; S12, the least squares method is used to process the coordinate point set. The projection line is obtained by fitting straight lines to all points within the area. S13, Establish a local coordinate system: In the orbital plane, using the set of coordinate points... The first point is projected onto the projection line as the origin. The projection line is used as the local coordinate system. The X-axis points in the direction of the large mileage, and the Y-axis direction is determined according to the right-hand rule. S14, the set of coordinate points The points in the coordinate system are transformed to the local coordinate system to obtain the coordinate point set. , ,in, This represents the total number of coordinate points. The coordinate point number, .

3. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 2, characterized in that: In S2, With coordinate point set middle and Using the x-coordinate as the boundary, insert A set of line segments connected end to end serves as a local coordinate point set. Fitting a polyline This yields the set of corner point coordinates in the local coordinate system, which includes the endpoints of each line segment in the fitted polyline as corner points. , ;in, The corner points are numbered. The total number of line segments. ; Corner point The coordinates; For decision variables, we have: ； In a polyline, the turning point The equation of the line segment originating from is: ； in, For the corner point The slope of the line segment starting from point A. For the corner point The intercept of the line segment originating from; The coordinate point set is determined based on the x-coordinate of the corner point. The points in the middle are divided into A set, with corner points The set of points inside the line segment originating from is ,in, , , For set The total number of local coordinate points in the middle. ; The objective function is: 。 4. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 3, characterized in that: The spacing constraint in S2 is: ； The distance between adjacent bend points is in meters.

5. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 4, characterized in that: The line constraints in S2 are obtained using an approximate algorithm. The line constraints are as follows: ； in, for The upper limit of the value adjustment, for The lower limit value of the value adjustment, the and Determined based on the actual situation.

6. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 5, characterized in that: S3 includes the following steps: S31, the set of coordinates of the corner points in the local coordinate system obtained in S21 As the variable to be optimized, real-number encoding is used to generate a random vector, forming a structure containing... individual The population, of which: ； in, To initialize the individual IDs in the population, Number of individuals in the population Evenly spaced intervals By using local coordinate point sets Divide into equal parts to obtain, , which is an integer; for Random vector values ​​between; S32, Construct the penalty function : ； in, For the corresponding constraint function The penalty coefficient; For the corresponding constraint function The penalty coefficient; Constructing the modified objective function : ； Constructing the fitness function : ； S33 employs a roulette wheel selection method to perform genetic selection on the current population, specifically: for each individual within the population... Calculate fitness ; Calculate the cumulative probability for each individual , Generate random numbers Choose to satisfy Two individuals as excellent parents and ; S34, Based on the excellent parent generation, a linear combination is used to perform a crossover operation on the population to obtain crossover offspring individuals; S35, perform mutation operation on each individual in the remaining population after removing the superior parents to obtain the mutated offspring population. S36, iterative update, until the optimal individual is output. .

7. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 6, characterized in that: S36 specifically refers to: The fitness of each individual is recalculated according to the fitness function constructed in S32 for the crossover offspring and the mutant offspring population. The current highest fitness is represented as... ,in Indicates the number of mutations; If the number of mutations has not reached the maximum number of iterations and the improvement rate is greater than 1%, then the elite retention strategy is used for iteration, and then S33~S36 are executed until the number of mutations exceeds 100 or improvement rate Iteration stops when the fitness rate is less than 1%, and the individual with the highest fitness at this point is designated as the optimal individual. ; Improvement rate Calculated using the following formula: 。 8. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 7, characterized in that, S4 includes the following steps: S41, based on the optimal individual obtained in S3, calculate the slope of its corresponding line segment using the coordinates of its turning points. Then, calculate the slope change of adjacent line segments using the following formula. : ； in, The number of the turning point in the optimal individual; S42, Select the optimal set of turning points based on the slope changes of adjacent line segments: Calculate screening criteria : ； in, The minimum circular curve length is selected according to railway line design specifications, and the maximum circular curve radius is... Select the value based on the maximum limit of the extra-large radius curve that needs to be inserted in the actual situation. ; like Then the corresponding corner point Add to the optimal set of turning points, if If the corner point is not found, then the corresponding corner point is discarded, and the final result is a result containing... The optimal set of +1 corner points ; S43, in the global coordinate system, fits the long straight segments of the operating railway line into the optimal fitted polyline: S44, calculate the optimal radius of the circular curve connecting the bend points between adjacent line segments in the best-fit polyline, and complete the optimization of long straight line segments.

9. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 8, characterized in that: In step S43, following the method in step S22, based on the optimal set of turning points in step S42... local coordinate point set Divided into Group, according to the corresponding group, the set of coordinate points of the orbital plane in the global coordinate system obtained by S11. Also divided into Grouping, the least squares method is used to fit the coordinates of each group in the global coordinate system after grouping, to obtain A set of line segments, which together form the optimal fit polyline for a long straight line in the global coordinate system.

10. The automatic optimization design method for ultra-large radius curves of operating railway lines according to claim 9, characterized in that: In step S44, the slope variation between adjacent segments in the best-fit polyline in the global coordinate system is calculated using the method in S41. The optimal radius of the circular curve connecting the bend points between adjacent line segments can be obtained using the following formula. : ； in, For the optimal set of turning points Numbering of the mid-angle point.

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