Railway line plane optimization method and device

Abstract

The invention provides a railway line plane optimization method and device, and relates to the technical field of railway track alignment. According to the method, various track line shapes are accurately distinguished through preliminary segmentation processing and secondary segmentation processing, on the basis, various track line shapes are respectively fitted in a data fitting mode, track lining quantity calculation is carried out, a plane optimization scheme of each track section is formed, and the track lining quantity is calculated. The automatic accurate division of the railway line and the automatic accurate calculation of the track lining quantity are realized, manual participation is not needed, and the accuracy and the efficiency of the correction and optimization of the railway line are improved.

Description

Technical Field

[0001] This invention relates to the field of railway track alignment technology, and in particular to a method and apparatus for railway line plan optimization. Background Technology

[0002] As a crucial component of the modern transportation system, the safe and efficient operation of railways has a significant impact on socio-economic development. However, due to the long-term effects of train loads, temperature variations, material fatigue, and environmental factors, railway lines may experience irregular deformations after a period of operation, such as track irregularities, gauge changes, and horizontal deviations. These deformations not only affect the smoothness of train operation and passenger comfort but may also lead to serious safety accidents such as derailments, threatening the safety and reliability of railway transportation.

[0003] To ensure the long-term stable operation of railway lines, railway authorities need to periodically perform horizontal alignment, which involves adjusting and optimizing the horizontal geometry of the railway lines. Traditional alignment methods mainly rely on manual measurement and experience-based judgment, resulting in low efficiency, poor accuracy, and high costs. With the increase in railway operating mileage and train speeds, traditional methods are no longer sufficient to meet the demands of modern railways for high precision, high efficiency, and high safety. Summary of the Invention

[0004] This invention provides a method and apparatus for railway line alignment optimization, which can solve the problems of poor accuracy and low efficiency of traditional railway line alignment methods, and improve the accuracy and efficiency of railway line alignment optimization.

[0005] In a first aspect, the present invention provides a method for optimizing the planar alignment of a railway track. The method includes: acquiring coordinate data of points on the railway track to be optimized; calculating the approximate curvature of each point based on the coordinate data; performing preliminary segmentation of the track alignment based on the approximate curvature to obtain track segments of various alignment types, including straight sections, circular curves, and transition curves; performing planar data fitting and secondary segmentation on each pair of track segments based on the coordinate data of each point and the fitting formulas for various alignment types to obtain the fitting equations and segmentation points of each track segment; and calculating the track realignment amount for each track segment based on the fitting equations and segmentation points to obtain a planar optimization scheme for each track segment, wherein the planar optimization scheme includes the track realignment amount at each point in each track segment.

[0006] In one possible implementation, the approximate curvature of each point is calculated based on the coordinate data of each point on the railway track to be optimized, including: for multiple consecutive points on the railway track to be optimized, the tangent slope of each point is calculated based on the coordinate data of the multiple consecutive points; and the approximate curvature of each point is calculated based on the tangent slope and the coordinate data of each point.

[0007] In one possible implementation, based on the approximate curvature of each point, the alignment of the railway track to be optimized is initially segmented to obtain track segments with various alignments, including: traversing all points of the railway track to be optimized; if the approximate curvature of multiple consecutive points is less than the threshold for a straight line segment, then the track segment containing these multiple consecutive points is determined as a straight line segment; if the approximate curvature of multiple consecutive points is greater than or equal to the threshold for a straight line segment and less than the threshold for a circular curve, then the track segment containing these multiple consecutive points is determined as a transition curve; if the approximate curvature of multiple consecutive points is greater than or equal to the threshold for a circular curve, then the track segment containing these multiple consecutive points is determined as a circular curve.

[0008] In one possible implementation, based on the coordinate data of each point and the fitting formulas for various line shapes, planar data fitting and secondary segmentation are performed on each pair of track segments to obtain the fitting equations and segmentation points of each track segment. This includes: Step 1, determining multiple segmentation points based on the various line shapes of the track segments obtained from the initial segmentation process; and setting these multiple segmentation points as initial segmentation points; Step 2, for any track segment whose line shape is a straight line or a circular curve, based on the coordinate data of each point in the track segment and the fitting formula for the corresponding line shape, data fitting is performed using the least squares method to obtain the fitting equation of the track segment and the fitting parameters of the fitting equation; wherein, the fitting parameters for a straight line segment include the slope and intercept; the fitting parameters for a circular curve include the radius and center of the circular curve; Step 3, based on the fitting equations of the track segments whose line shape is a straight line or a circular curve... The fitting equations and fitting parameters are combined, and an inverse algorithm is used to determine the fitting parameters of the transition curve. The fitting parameters of the transition curve include the transition curve offset, the transition curve turning angle, the circular curve inward shift, and the transition curve length. Step four: Based on the fitting equations of each track segment, the intersection points are calculated to determine the segmentation points, including straight-to-transition points, transition-to-straight points, transition-to-circular points, and circular-to-transition points. Step five: If the current iteration number is greater than the maximum iteration number, the iteration process is exited and step seven is executed; if the current iteration number is less than or equal to the maximum iteration number, step six is ​​executed. Step six: The distance difference between the coordinates of the segmentation points in the current iteration and the coordinates of the segmentation points in the previous iteration is calculated; if the distance difference is less than or equal to the distance threshold, step seven is executed; if the distance difference is greater than the distance threshold, steps two to six are repeated until the iteration process is exited. Step seven: The fitting equations and segmentation points of each track segment in the current iteration are output.

[0009] In one possible implementation, for any track segment whose alignment is a straight line or a circular curve, based on the coordinate data of each point in the track segment and the fitting formula for the corresponding alignment, the least squares method is used to fit the data to obtain the fitting equation of the track segment and the fitting parameters of the fitting equation. This includes: constructing a first function based on the coordinate data of each point in the track segment and the fitting formula for the corresponding alignment, with the sum of the squares of the distances from each point to the fitted line segment of the track segment as the dependent variable and the fitting parameters as the independent variables; solving for the fitting parameters of the fitting equation of the track segment based on the coordinate data of each point in the track segment, with the objective of minimizing the function value of the first function; and determining the fitting equation of the track segment based on the fitting parameters and the fitting formula.

[0010] Secondly, embodiments of the present invention provide a railway track planar optimization device, which includes: a communication module and a processing module. The communication module is used to acquire coordinate data of each point on the railway track to be optimized; the processing module is used to calculate the approximate curvature of each point based on the coordinate data of each point on the railway track to be optimized; based on the approximate curvature of each point, perform preliminary segmentation processing on the alignment of the railway track to be optimized to obtain track segments of various alignment types; the alignment types include straight segments, circular curves, and transition curves; based on the coordinate data of each point and the fitting formulas of various alignment types, perform planar data fitting and secondary segmentation processing on each pair of track segments to obtain the fitting equation of each track segment and the segmentation points of each track segment; based on the fitting equation and segmentation points of each track segment, calculate the track shifting amount for each track segment to obtain the planar optimization scheme for each track segment, the planar optimization scheme including the track shifting amount of each point in each track segment.

[0011] Thirdly, embodiments of the present invention provide an electronic device including a memory and a processor. The memory stores a computer program, and the processor is configured to call and run the computer program stored in the memory to perform the steps of the method as described in the first aspect and any possible implementation thereof.

[0012] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the method as described in the first aspect and any possible implementation thereof.

[0013] This invention provides a method and apparatus for railway line alignment optimization. Compared with traditional manual alignment methods, this invention can accurately distinguish various track alignments through preliminary segmentation and secondary segmentation. Based on this, a data fitting method is used to fit various track alignments separately and calculate the track shifting amount to form an alignment optimization scheme for each track segment. This achieves automatic and accurate division of railway lines and automatic and accurate calculation of track shifting amount without manual intervention, thus improving the accuracy and efficiency of railway line alignment optimization. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating a railway line plan optimization method provided in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of an orthogonal least squares fitting method provided in an embodiment of the present invention;

[0017] Figure 3 This is a schematic diagram of an independent coordinate system for a transition curve provided in an embodiment of the present invention;

[0018] Figure 4 This is a flowchart illustrating another railway line plan optimization method provided in an embodiment of the present invention;

[0019] Figure 5 This is a schematic diagram of the structure of a railway line plan optimization device provided in an embodiment of the present invention;

[0020] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0021] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0022] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner to facilitate understanding.

[0023] Furthermore, the terms "comprising" and "having," and any variations thereof, used in the description of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or modules is not limited to the steps or modules listed, but may optionally include other steps or modules not listed, or may optionally include other steps or modules inherent to such process, method, product, or device.

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0025] As described in the background section, current traditional railway line alignment methods suffer from technical problems such as poor accuracy and low efficiency.

[0026] To address the aforementioned technical problems, this invention establishes a precise mathematical model and combines it with advanced optimization algorithms to achieve intelligent optimization of the planar geometric parameters of railway lines, thereby improving the operational performance and safety of railway lines. Furthermore, by comprehensively considering factors such as train operation safety, passenger comfort, operating costs, and ease of maintenance, the long-term stability and economy of railway lines can be ensured. An exemplary technical solution adopted by this invention is shown below.

[0027] ① Define the basic components of the horizontal alignment of railway lines.

[0028] ② The fitting method for determining the railway horizontal alignment is orthogonal least squares fitting.

[0029] ③ The orthogonal least squares method is used to give the calculation formulas for the parameters when fitting line segments and circular curves.

[0030] ④ The parameter calculation formula for the transition curve fitting is determined by the inverse algorithm, and the coordinate calculation method of its global coordinate system is given.

[0031] ⑤ The fitting of railway tracks requires fitting both ③ and ④, therefore, it is necessary to first perform railway horizontal alignment segmentation.

[0032] ⑥ Preliminary segmentation yields the approximate ranges of straight line segments, circular curve segments, and transition curve segments.

[0033] ⑦ Further refine the segmentation by combining the iterative method of orthogonal least squares.

[0034] ⑧ After completing the planar line fitting based on the previous steps, it is necessary to determine whether the parameters such as the radius and length of the fitted curve and the length of the transition curve meet the specifications. If they do, the fitted line shape is the optimal line shape. If not, by solving the optimization model, it can be ensured that the designed curve not only meets the technical specifications but also achieves the minimum planar deviation value.

[0035] Based on the principle of orthogonal least squares, this invention derives the parameter calculation formulas for fitting straight line segments and circular curves, and then determines the fitting parameters of the transition curve through an inverse algorithm, and establishes a corresponding global coordinate system coordinate calculation method, thereby realizing accurate fitting and coordinate positioning of complex curves.

[0036] This invention is based on an iterative optimization method using orthogonal least squares. It improves the accuracy of curve fitting through a refined segmentation strategy, continuously optimizes the segmentation boundaries through iterative calculations to ensure the accuracy of the segmentation results, and accurately calculates the detailed coordinate values ​​of each boundary point in the global coordinate system.

[0037] After segmenting the planar alignment, this invention requires optimization of the alignment to minimize the overall planar deviation. The planar curve optimization problem is transformed into finding the optimal combination of curve parameters. The optimization model uses the minimization of the sum of squares of the planar deviations at measurement points as the objective function, and the radius of the circular curve and the lengths of the preceding and following transition curves as optimization variables. Furthermore, this invention considers the specified conditions and ranges for curve parameter values, as well as the adjustment limits for field control points, which constitute the constraints of the optimization problem. By solving this optimization model, it can be ensured that the designed curve both meets the technical specifications and achieves the minimum planar deviation.

[0038] This invention optimizes the planar geometric parameters of railway lines by establishing a mathematical model and selecting a suitable optimization algorithm, thereby improving the operational performance and safety of railways.

[0039] like Figure 1 As shown, this embodiment of the invention provides a method for railway line plan optimization. The method includes steps S101-S105.

[0040] S101. Obtain the coordinate data of each point on the railway track to be optimized.

[0041] For example, embodiments of the present invention can use an Amberg trolley to obtain the mileage and coordinate data of various points on the railway track to be optimized. The coordinate data may include two-dimensional planar coordinates, or it may also include three-dimensional coordinate data.

[0042] S102. Based on the coordinate data of each point on the railway track to be optimized, calculate the approximate curvature of each point.

[0043] As one possible implementation, step S102 can be specifically implemented as steps S1021-S1022.

[0044] S1021. For multiple consecutive points on the railway track to be optimized, calculate the tangent slope of each point based on the coordinate data of the multiple consecutive points.

[0045] S1022. Based on the tangent slope of each point and the coordinate data of each point, calculate the approximate curvature of each point.

[0046] S103. Based on the approximate curvature of each point, the alignment of the railway track to be optimized is initially segmented to obtain track segments with various alignments.

[0047] In this embodiment, the linear shape includes straight line segments, circular curves, and transition curves.

[0048] As one possible implementation, step S103 can be specifically implemented as steps S1031-S1033.

[0049] S1031. Traverse all points on the railway track to be optimized. If the approximate curvature of multiple consecutive points is less than the threshold of a straight line segment, then the track segment containing these multiple consecutive points is determined as a straight line segment.

[0050] S1032. If the approximate curvature of multiple consecutive points is greater than or equal to the threshold of a straight line segment and less than the threshold of a circular curve, then the track segment containing these multiple consecutive points is determined as a transition curve.

[0051] S1033. If the approximate curvature of multiple consecutive points is greater than or equal to the circular curve threshold, then the track segment containing these multiple consecutive points is determined as a circular curve.

[0052] S104. Based on the coordinate data of each point and the fitting formulas of various line shapes, perform planar data fitting and secondary segmentation on each pair of track segments to obtain the fitting equation of each track segment and the segmentation points of each track segment.

[0053] As one possible implementation, step S104 can be specifically implemented as steps one through seven.

[0054] Step 1: Based on the various linear track segments obtained from the preliminary segmentation process, determine multiple segmentation points; and set these multiple segmentation points as initial segmentation points.

[0055] Step 2: For any track segment whose alignment is a straight line or a circular curve, based on the coordinate data of each point in the track segment and the fitting formula of the corresponding alignment, the least squares method is used to fit the data to obtain the fitting equation of the track segment and the fitting parameters of the fitting equation of the track segment.

[0056] The fitting parameters for a straight line segment include the slope and intercept of the line; the fitting parameters for a circular curve include the radius and center of the circular curve.

[0057] For example, step two can be specifically implemented as steps A1-A3.

[0058] A1. Based on the coordinate data of each point in the track segment and the fitting formula of the corresponding line shape, construct the first function.

[0059] In some embodiments, the first function uses the sum of squares of the distances from each point to the fitted line segment of the track segment as the dependent variable and the fitting parameters as the independent variables.

[0060] A2. Based on the coordinate data of each point in the track segment, with the goal of minimizing the function value of the first function, the fitting parameters of the fitting equation for the track segment are obtained.

[0061] A3. Based on the fitting parameters and fitting formula of the fitting equation for this orbital segment, determine the fitting equation for this orbital segment.

[0062] For example, a straight line segment is the simplest line element in the horizontal alignment of a railway line. The least squares method is used to fit a straight line, based on the principle of minimizing the sum of the squared residuals of the orthogonal distances from each point to the fitted line, to solve for the unknown parameters in the equation of the straight line. Let the equation of the straight line in the railway alignment be as shown in formula (3-1).

[0063] Y i =f(X)=kX i +b(3-1)

[0064] Where k is the slope of the fitted line; b is the intercept of the fitted line; (X i ,Y i ) represents the plane coordinates of the i-th measuring point on the straight track segment.

[0065] Figure 2 This is a schematic diagram of orthogonal minimum fitting using a line segment as an example. In the diagram, v i Let X be a point with known coordinates, and its coordinates be (X, Y, Z). i Y i The distance from any known point to the fitted line. The sum of squares is shown in formula (3-2).

[0066] Among them, S i This represents the distance from the known location point to the fitted line.

[0067] The distance sum represented by equation (3-2) is a nonlinear equation, which is relatively complex to solve. In order to facilitate research and calculation, it is expanded and linearized using Taylor's formula, and the error equation of the formula with k and b as unknowns is shown in equation (3-3).

[0068]

[0069] in, δk is the square of the orthogonal distance residual from the i-th measurement point to the fitted line; δk and δb are the unknown parameters k. 0 and b 0 The correction value for the approximation; that is, the small adjustment amount that needs to be calculated through optimization. By adjusting δk and δb, the fitted line is made closer to the true distribution of the data points, thereby minimizing the orthogonal distance residual. For example, the correction value can be used to correct the truncation error of the Taylor expansion, and is generally used to supplement higher-order terms, k 0 and b 0 These are approximate values ​​for the unknown parameters k and b.

[0070] For ease of representation, equation (3-3) is transformed into matrix form, as shown in equation (3-4).

[0071] V=Bδx-L (3-4)

[0072] in:

[0073] by The objective function is to minimize the sum of the squares of the orthogonal distance residuals from each point on the track segment to the fitted line. Using the orthogonal least squares fitting principle, the fitting parameters are solved, and the solution is shown in equation (3-5).

[0074]

[0075] After calculating δk and δb from the above formula, the fitting parameters of the fitting equation of the track segment with a straight line shape, namely the optimal slope k and the optimal intercept b, can be calculated by formula (3-6) based on the principle of least squares.

[0076]

[0077] For example, a circular curve is a circular arc-shaped line element capable of changing the direction of a railway track, with a fixed radius of curvature. To perform least-squares fitting on the circular curve, let the equation of the circular curve in the railway alignment be as shown in (3-7). (X) m -X o ) 2 +(Y m -Yo ) 2 =R 2 (m=1,2,3…n)(3-7)

[0078] Among them, (X) m ,Y m (X) represents the plane coordinates of the m-th measurement point on the circular curve; o ,Y o ) represents the coordinates of the center of the circular curve; R represents the radius of the circular curve.

[0079] Based on equation (3-7), the distance from the m-th point on the circular curve to the circular curve can be expressed by equation (3-8):

[0080] Similar to the process of fitting a straight line, we now need to expand and linearize equation (3-8) according to the Taylor formula, which gives us the result based on the plane coordinates X of the center of the circle. o Y o The error equation obtained with the radius R of the circular curve as an unknown is shown in equation (3-9).

[0081]

[0082] Among them, Vs m The residual of the circular curve fitting result is the distance from the actual coordinates of the m-th point on the circular curve to the circular curve. R is an approximate value of the coordinates of the center of the circular curve; 0 ΔX and ΔY are approximate values ​​of the radius of the circular curve; ΔX and ΔY are corrections to the approximate coordinates of the center of the circular curve; ΔR is a correction to the approximate radius of the circular curve. Equation (3-9) can be rewritten in matrix form as shown in Equation (3-10).

[0083] V=BΔx-L(3-10)

[0084] in:

[0085] Based on the principle of least squares, The objective function is to minimize the sum of the distances from the actual coordinates of each point on the circular curve to the curve determined by the fitting equation of the circular curve. The solution for the center and radius of the circular curve is shown in equation (3-11).

[0086]

[0087] After calculating the correction values ​​for the approximate values ​​of the center and radius of the fitted circular curve, the parameters of the optimal fitted circular curve can be obtained through equation (3-12).

[0088]

[0089] Step 3: Based on the fitting equation and fitting parameters of the track segment whose linear shape is a straight line segment or a circular curve, the inverse algorithm is used to determine the fitting parameters of the transition curve. The fitting parameters of the transition curve include the transition curve offset, the transition curve turning angle, the circular curve inward displacement, and the transition curve length.

[0090] For example, in the fitting study of transition curves, if the method of fitting straight lines or circular curves is used to directly perform orthogonal least squares fitting, it often leads to ill-conditioned problems in the fitting, thus failing to accurately obtain the parametric equations of the transition curve. Therefore, by using the parameters of the straight lines and circular curves adjacent to the transition curve to inversely calculate the corresponding parameters of the transition curve, the coordinates of any point on the transition curve in the independent coordinate system of the transition curve can be obtained according to equation (3-13).

[0091]

[0092] Where, x i With y i L represents the coordinates of the i-th point on the transition curve in the independent coordinate system of the transition curve; i L is the length of the transition curve between the i-th point and the ZH point; s R is the total length of the transition curve; R is the radius of the circular curve.

[0093] It is important to note that the result obtained by equation (3-13) is not the result of the global coordinate system, but rather the result of the independent coordinate system of the transition curve. The independent coordinate system of the transition curve is established with the ZH point or HZ point as the origin, the tangent direction of the origin as the x-axis, and the direction perpendicular to the x-axis and pointing inwards towards the curve as the y-axis, as shown below. Figure 3 As shown.

[0094] according to Figure 3 From the geometric relationship shown, we can obtain formula (3-14).

[0095]

[0096] Where x0 and y0 are the coordinates of the intersection point (HY) of the transition curve and the circular curve; β is the turning angle of the corresponding curve of the transition curve; p is the inward displacement of the circular curve, that is, the inward displacement of the circular curve after the insertion of the transition curve; q is the length of the front and rear tangents of the circular curve; rad represents the unit of β, in radians.

[0097] According to equation (3-13), when i = 0, the point should be point ZH, at which point l0 = ls Substituting this into equation (3-13), we can obtain the calculation formulas for x0 and y0 as shown in equation (3-15).

[0098]

[0099] Substituting equation (3-15) into equation (3-13), we can obtain the formulas for calculating p and q, as shown in equation (3-16).

[0100]

[0101] To obtain the coordinates of any point on the transition curve, the length of the transition curve needs to be calculated. Using the least squares fitting principle, fitting parameters for the straight line and the circular curve, such as the slope, intercept, radius, and center of the circular curve, are obtained. Based on these fitting parameters, the inward displacement p can be calculated using formula (3-17).

[0102]

[0103] Where, x c y c x represents the coordinates of the intersection point of the transition curve and the circular curve; f y f Let be the coordinates of the intersection point of the center of the circle and the line. Substituting the calculated inward displacement p from equation (3-16) into equation (3-17), we obtain equation (3-18), which allows us to calculate l. s .

[0104] Substituting into formulas (3-13) and (3-15), the coordinates of any point on the transition curve in its independent coordinate system can be obtained.

[0105] To facilitate subsequent calculations and optimizations, the coordinates of the transition curve need to be transformed from independent coordinate systems to global coordinate systems. When calculating the initial transition curve, the ZH point is taken as the origin, and the formula for calculating the global coordinates of any point on the transition curve is shown in (3-19).

[0106]

[0107] Where, x ZH y ZH A represents the absolute coordinates of the starting point (ZH point) of the transition curve; i To soften the azimuth angle at the beginning of the curve; x i y i To provide the coordinates of any point on the curve in an independent coordinate system.

[0108] When calculating the transition curve, the HZ point is taken as the origin of the coordinate system. The formula for calculating the global coordinates of any point on the transition curve is shown in (3-20).

[0109]

[0110] Where, x HZ y HZ B represents the absolute coordinates of the endpoint (HZ point) of the transition curve; i To soften the azimuth angle at the end of the curve.

[0111] Step four: Based on the fitting equations of each track segment, calculate the intersection points and determine the segmentation points.

[0112] In some embodiments, the segmentation points include straight-to-gradient points, gradual straight-to-gradient points, gradual rounded points, and rounded-to-gradient points.

[0113] Step 5: If the current iteration count is greater than the maximum iteration count, exit the iteration process and proceed to Step 7; if the current iteration count is less than or equal to the maximum iteration count, proceed to Step 6.

[0114] Step 6: Calculate the distance difference between the coordinates of the segment point in the current iteration and the coordinates of the segment point in the previous iteration; if the distance difference is less than or equal to the distance threshold, proceed to Step 7; if the distance difference is greater than the distance threshold, repeat Steps 2 to 6 until the iteration process is exited.

[0115] Step 7: Output the fitting equations and segmentation points for each orbital segment in the current iteration process.

[0116] For example, in this invention, the initial segmentation of the line is based on the change in curvature. Therefore, the approximate curvature of the measured points is obtained using the 11-point method to observe the change in curvature. See steps S102-S103. After the initial segmentation is completed, an iterative method combining orthogonal least squares is used to further refine the segmentation. See step S104, a secondary segmentation process is performed.

[0117] The specific steps for precise horizontal segmentation of railway lines, i.e., secondary segmentation processing, are as follows.

[0118] ① Using the preliminary segmentation method in steps S102-S1031, the coordinates of the four main dividing points are obtained as the initial data for iteration. These are the initial segmentation points.

[0119] ② Perform orthogonal least squares fitting on the measuring points contained in the circular curve and the straight line to obtain the linear equations of the circular curve and the straight lines before and after it. See step 2.

[0120] ③ Based on the linear equations of the circular curve and the intersecting straight line, use equations (3-14)-(3-18), and equations (3-22) and (3-23) shown below, to calculate the coordinates of the intersection point of the curve, the inward displacement of the circular curve, the length of the transition curve, the turning angle of the transition curve, and other elements. See step three.

[0121]

[0122] Where k1 and k2 are the slopes of the front and rear clamping lines; b1 and b2 are the intercepts of the front and rear clamping lines, respectively; X JD and Y JD The coordinates of the intersection point of the tangents at the transition point and the transition point on the curve are given. α is the turning angle (or deflection angle) of the two straight lines, that is, the angle of change of direction of the two intersecting straight line segments at the intersection point (JD).

[0123]

[0124] in, R is the radius of the circular curve; L is the curve length; l1 and l2 are the lengths of the front and rear transition curves; T1 and T2 are the lengths of the front and rear tangents; E is the external distance; β is the tangent angle of the transition curve; p is the inward displacement; q is the tangent-perpendicular distance; p1 is the inward displacement of the first transition curve (entrance side); E1 is the external distance of the first transition curve (entrance side); E2 is the external distance of the second transition curve (exit side); and α is the turning angle (or deflection angle) of the two straight lines.

[0125] ④ Based on the coordinates of the intersection point, the length of the transition curve, and the linear equation of the straight line before and after it, obtain the coordinates of the straight-to-transition point and the transition-to-straight point.

[0126] ⑤ Calculate the coordinates of the transition point and the transition point based on the coordinates of the center of the circular curve and the turning angle of the transition curve.

[0127] ⑥ Compare the coordinates of the four key points obtained in the current iteration with the coordinates of the previous iteration. If this is the first iteration, the previous iteration is the initial segmentation point. Calculate the distance difference between the two. If the difference exceeds the set threshold ε, continue with steps ② to ⑤; if the difference is less than ε, it is considered that the required accuracy has been achieved, and the current result is taken as the final result of the iterative segmentation.

[0128] After the horizontal alignment is segmented, the alignment needs to be optimized to minimize the overall horizontal deviation (track alignment adjustment). This leads to the obtaining of the fitting equations and fitting parameters for each track segment, as well as the segmentation points.

[0129] S105. Based on the fitting equations and segmentation points of each track segment, the track adjustment amount is calculated for each track segment to obtain the planar optimization scheme for each track segment.

[0130] In this embodiment of the application, the planar optimization scheme includes the track shifting amount at each point in each track segment.

[0131] It should be noted that, due to the different fitting formulas or methods for straight lines, curves and transition curves in railway lines, the calculation methods for track shifting quantities for each track section are also different when calculating the level shifting quantity.

[0132] As one possible implementation, step S105 can be specifically implemented as steps S1051-S1058.

[0133] S1051. For track segments in each track section whose alignment is a straight line or a circular curve, calculate the track adjustment amount at each point based on the fitting equation of each track segment and the coordinate data of each point in each track segment.

[0134] S1052. Based on the value of the eccentricity at each point, determine the adjustment direction at each point.

[0135] S1053. Based on the track shift amount and adjustment direction at each point, determine the planar optimization scheme for each track segment.

[0136] For example, for a straight section of track, after segmenting the track, a fitting formula for the straight section, as shown in equation (3-24), can be obtained through fitting. The distance from the measured point to the straight line can be calculated using equations (3-1)-(3-6), thus yielding the planar adjustment Δ at the i-th point on the straight track segment. li .

[0137]

[0138] By substituting the X-coordinate of the straight line segment into the fitting formula for the straight line, and comparing the obtained theoretical Y-coordinate with the measured coordinate, the adjustment direction of the straight line segment can be determined.

[0139] For example, by fitting the circular curve segment, the fitting formula for the circular curve segment shown in equation (3-25) can be obtained. By calculating the difference between the distance from the measured point to the center point and the radius using equations (3-7)-(3-12), the planar adjustment Δ at the m-th point on the circular curve track segment can be obtained. mi .

[0140]

[0141] The direction of line adjustment can be determined by the sign of △mi. When △mi is positive, it means that the distance of the point from the center of the circle is greater than the radius, and the point should be adjusted towards the center of the circle; conversely, the point should be adjusted away from the center of the circle.

[0142] S1054. For any track segment whose linear shape is a transition curve, based on the coordinate data of each point in the track segment and the fitting equation of the track segment, determine the actual coordinates and theoretical coordinates of each point in the track segment.

[0143] S1055. Based on the theoretical coordinates of each point in the track segment and the fitting equation of the track segment, determine the theoretical coordinates of the adjacent points of each point.

[0144] S1056. Based on the actual and theoretical coordinates of each point, as well as the theoretical coordinates of the adjacent points of each point, determine the adjustment direction of each point.

[0145] For example, step S1056 can be specifically implemented as steps B1-B8.

[0146] B1. For any point, take the theoretical coordinates of the point above it as the starting point and the theoretical coordinates of the point as the ending point to determine the first vector.

[0147] B2. Using the theoretical coordinates of the point above this point as the starting point and the actual coordinates of this point as the ending point, determine the second vector.

[0148] B3. Using the theoretical coordinates of this point as the starting point and the theoretical coordinates of the next point as the ending point, determine the third vector.

[0149] B4. Perform a cross product of the first vector and the second vector to obtain the first cross product.

[0150] B5. Perform a cross product of the third vector and the second vector to obtain the second cross product.

[0151] B6. If the first cross product is positive and the second cross product is positive, then the measured point is located to the right of the theoretical linear direction of advancement, and the adjustment direction is to the left.

[0152] B7. If the first cross product is negative and the second cross product is negative, then the measured point is determined to be located to the left of the theoretical linear direction of advancement, and the adjustment direction is to the right.

[0153] B8. If the first cross product is zero and the second cross product is zero, then the point is determined to be on the theoretical line shape and no adjustment is needed.

[0154] The theoretical linear shape is the curve determined by the fitting equation of the trajectory segment whose linear shape is a transition curve.

[0155] S1057. Based on the actual and theoretical coordinates of each point, the adjustment direction of each point, and the fitting equation of the track segment, determine the slewing amount of each point.

[0156] S1058. Based on the track shift amount and adjustment direction at each point in the track segment, determine the planar optimization scheme for the track segment.

[0157] For example, for a transition curve, the difference between the theoretical coordinates and the actual measured coordinates at the same mileage point is the track leveling adjustment (track realignment) for that mileage point. The actual measured coordinate data mainly includes the mileage, the X-coordinate, and the Y-coordinate of that mileage. The theoretical coordinates of each measuring point on the transition curve are obtained through a transition curve fitting method. According to equation (3-26), the leveling adjustment Δ at the i-th point on the transition curve can be calculated. ci .

[0158]

[0159] Among them, (X) SJ Y SJ ) represents mileage L i Theoretical coordinates at (X) SC Y SC ) represents mileage L i The measured coordinates are shown. The sigh value represents the positional relationship between the measured point and the theoretical point. If the measured point is to the left of the theoretical point in the direction of travel, the sigh value is -1, and the track needs to be shifted to the right; if the measured point is to the right of the theoretical point in the direction of travel, the sigh value is -1, and the track needs to be shifted to the left.

[0160] The methods for determining which side of the linear shape the measured points on the transition curve lie on, as determined by the fitted equation, are mainly as follows:

[0161] Assume the mileage is L i The measured coordinates of the location are P(x1, y1), and the corresponding point on the theoretical scheme is D1(x2, y2). Two points before and after point D1 on the theoretical line are selected, assuming they are D0(x0, y0) and D2(x3, y3), respectively. This yields two vectors: D0D1(x2-x0, y2-y0) and D1D2(x3-x2, y3-y2). The cross product of vectors D0D1 and D0P(x1-x0, y1-y0) is calculated, where D0P is the vector from D0 to the measured point P. The cross product of vectors D1D2 and D0P is also calculated. The formula for calculating the cross product is shown in equation (3-27).

[0162] A×B=Ax·By-Ay·Bx(3-27)

[0163] Here, A is a two-dimensional vector with coordinates (Ax, Ay); similarly, B is also a two-dimensional vector with coordinates (Bx, By).

[0164] After obtaining the cross product result, determine the value of sign based on the following three cases.

[0165] ① If the cross product (D0D1,DP) is positive and the cross product (D1D2,DP) is also positive, then the measured point P is located to the right of the theoretical linear direction of advancement, and sigh = 1.

[0166] ② If the cross product (D0D1,DP) is negative and the cross product (D1D2,DP) is also negative, then the measured point P is located to the left of the theoretical linear direction of advancement, and sigh = -1.

[0167] ③ If both cross products are 0, then the measured point P lies on the theoretical line.

[0168] This invention provides a method for optimizing the horizontal alignment of railway lines. Through preliminary segmentation and secondary segmentation, various track alignments are accurately distinguished. Based on this, a data fitting method is used to fit each track alignment separately and calculate the track alignment amount to form a horizontal optimization scheme for each track segment. This method achieves automatic and accurate division of railway lines and automatic and accurate calculation of track alignment amount without manual intervention, thus improving the accuracy and efficiency of railway line alignment optimization.

[0169] Optionally, the railway line plan optimization method provided in this embodiment of the invention further includes steps S201-S203 before step S105.

[0170] S201. Based on the fitting parameters of each orbital segment and the preset standard threshold, determine whether the fitting equation of each orbital segment meets the standard requirements.

[0171] S202. For any track segment, if the fitting equation of the track segment meets the specification requirements, then the fitting equation of the track segment is determined to be the optimal linear equation, and the fitting equation of the track segment is kept unchanged.

[0172] S203. If the fitting equation of the track segment does not meet the specification requirements, the fitting equation of the track segment is optimized based on the preset specification threshold to obtain the optimal linear equation, and the optimal linear equation is determined as the fitting equation of the track segment.

[0173] For example, step S203 can be specifically implemented as steps S2031-S2033.

[0174] S2031. Based on the preset standard threshold and the fitting equation of each track segment, determine multiple parameter combinations.

[0175] In some embodiments, each parameter combination includes a set of fitting parameters for the fitting equations of each orbital segment.

[0176] S2032. Based on multiple parameter combinations, perform iterative calculations to obtain the parameter combination with the minimum overall track clearance.

[0177] S2033. Based on the parameter combination that minimizes the overall track alignment, determine the optimal alignment equation for each track segment.

[0178] This invention transforms the planar curve optimization problem into finding the optimal combination of curve parameters using the aforementioned method. The optimization model is shown in equation (3-28). The optimization model uses minimizing the sum of squared plane deviations at measurement points as the objective function, and the radius of the circular curve and the lengths of the preceding and following transition curves as optimization variables. Furthermore, the model considers the specified conditions and ranges for curve parameter values, as well as the adjustment limits for field control points; these constitute the constraints of the optimization problem. By solving this optimization model, it can be ensured that the designed curve both meets the technical specifications and achieves the minimum plane deviation value.

[0179]

[0180] Where, Δ i and Δ imax For the track adjustment amount and maximum allowable adjustment amount (mm) at the i-th measurement point; R0, l 10 and l 20 Let be the initial radius of the arc and the initial lengths (m) of the two preceding and following transition curves; ΔR, Δl1, and Δl2 are the step sizes (m) of the arc radius and the lengths (m) of the preceding and following transition curves during the iteration process; L R and L line L represents the length of the arc portion and the length of the straight portion (m); Rmin and L linemin This represents the minimum length (m) required for both the circular and straight sections. Δ i Let R be the track adjustment amount for the i-th measurement point, R be the optimized arc radius, l1 be the optimized length of the front transition curve, and l2 be the optimized length of the rear transition curve. min R is the minimum radius of the arc. max For the maximum radius of the arc, l min To minimize the length of the transition curve, l max is the maximum length of the transition curve, n is the number of measurement points on the transition curve, and N is the number of discrete points in the discrete point curvature calculation method.

[0181] In railway horizontal alignment, if a symmetrical transition curve is adopted, then L1 and L2 in equation (3-28) are equal, which can reduce one optimization parameter and improve computational efficiency. The steps for curve horizontal optimization based on equation (3-28) are as follows: Figure 4 As shown. The specific approach is as follows.

[0182] ① Fit circular curves, straight lines, and transition curves separately based on the three-dimensional coordinate data exported from the Amberg car, and calculate the fitting parameters, such as the length of the transition curve and the length of the curve.

[0183] ② Based on design specifications and specific site requirements, determine the limits for key parameters such as the radius of the circular curve, the length of the circular curve, the length of the clamping straight line, and the length of the transition curve. Simultaneously, set the search range and step size to provide the necessary input conditions for subsequent optimization algorithms.

[0184] ③ Given the curve parameter limits and search step size, the plane deviation of the track centerline and its sum of squares under different combinations of curve radii and transition curve lengths are calculated iteratively using an enumeration method. The goal is to find the parameter combination that minimizes the sum of squares of the track realignment amount while satisfying the track parameter requirements and control point adjustment constraints, so as to complete the optimized design of the plane alignment.

[0185] ④ If the initial optimization results fail to meet the constraints, expand the search range of the plane curve parameters and continue the search process until the optimal plane curve parameters that satisfy all constraints are found.

[0186] ⑤ Following the above method, optimize each of the plane curves along the entire line to determine the optimal plane shape for the entire line.

[0187] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0188] The following are device embodiments of the present invention. For details not described in detail, please refer to the corresponding method embodiments described above.

[0189] Figure 5 A schematic diagram of a railway line plan optimization device according to an embodiment of the present invention is shown. The optimization device 300 includes a communication module 301 and a processing module 302.

[0190] Communication module 301 is used to acquire coordinate data of various points on the railway track to be optimized;

[0191] The processing module 302 is used to calculate the approximate curvature of each point based on the coordinate data of each point on the railway track to be optimized; based on the approximate curvature of each point, perform preliminary segmentation processing on the alignment of the railway track to be optimized to obtain track segments of various alignment types; the alignment types include straight segments, circular curves, and transition curves; based on the coordinate data of each point and the fitting formulas of various alignment types, perform planar data fitting and secondary segmentation processing on each pair of track segments to obtain the fitting equation of each track segment and the segmentation points of each track segment; based on the fitting equation and segmentation points of each track segment, calculate the track shifting amount for each track segment to obtain the planar optimization scheme for each track segment, the planar optimization scheme including the track shifting amount at each point in each track segment.

[0192] Figure 6This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. For example... Figure 6 As shown, the electronic device 400 includes: a processor 401, a memory 402, and a computer program 403 stored in the memory 402 and executable on the processor 401. When the processor 401 executes the computer program 403, it implements the steps in the above-described method embodiments, for example... Figure 1 The steps S101-S105 are shown. Alternatively, when the processor 401 executes the computer program 403, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 5 The functions of the communication module 301 and the processing module 302 shown are illustrated.

[0193] For example, the computer program 403 can be divided into one or more modules / units, which are stored in the memory 402 and executed by the processor 401 to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 403 in the electronic device 400. For example, the computer program 403 can be divided into... Figure 5 The communication module 301 and the processing module 302 are shown.

[0194] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for optimizing the horizontal alignment of railway lines, characterized in that, include: Obtain the coordinate data of each point on the railway track to be optimized; Based on the coordinate data of each point on the railway track to be optimized, the approximate curvature of each point is calculated. Based on the approximate curvature at each point, the alignment of the railway track to be optimized is initially segmented to obtain track segments with various alignments; the alignments include straight segments, circular curves, and transition curves. Based on the coordinate data of each point and the fitting formulas of various linear shapes, planar data fitting and secondary segmentation are performed on each pair of track segments to obtain the fitting equation of each track segment and the segmentation points of each track segment. Based on the fitting equations and segmentation points of each track segment, the track alignment amount is calculated for each track segment to obtain the plane optimization scheme for each track segment. The plane optimization scheme includes the track alignment amount for each point in each track segment.

2. The railway line horizontal alignment optimization method according to claim 1, characterized in that, The process of calculating the approximate curvature of each point on the railway track to be optimized, based on the coordinate data of each point, includes: For multiple consecutive points on the railway track to be optimized, the tangent slope of each point is calculated based on the coordinate data of the multiple consecutive points; Based on the tangent slope and coordinate data of each point, the approximate curvature of each point is calculated.

3. The railway line horizontal alignment optimization method according to claim 1, characterized in that, Based on the approximate curvature at each point, the alignment of the railway track to be optimized is initially segmented to obtain track segments with various alignments, including: Traverse all points on the railway track to be optimized. If the approximate curvature of multiple consecutive points is less than the threshold for a straight line segment, then the track segment containing these multiple consecutive points is determined as a straight line segment. If the approximate curvature of multiple consecutive points is greater than or equal to the threshold of a straight line segment and less than the threshold of a circular curve, then the track segment containing these multiple consecutive points is determined as a transition curve. If the approximate curvature of multiple consecutive points is greater than or equal to the circular curve threshold, then the track segment containing these multiple consecutive points is determined to be a circular curve.

4. The railway line horizontal alignment optimization method according to claim 1, characterized in that, Based on the coordinate data of each point and the fitting formulas for various linear shapes, planar data fitting and secondary segmentation are performed on each pair of track segments to obtain the fitting equations for each track segment and the segmentation points for each track segment, including: Step 1: Based on the various linear track segments obtained from the preliminary segmentation process, determine multiple segmentation points; and set these multiple segmentation points as initial segmentation points. Step 2: For any track segment whose alignment is a straight line or a circular curve, based on the coordinate data of each point in the track segment and the fitting formula for the corresponding alignment, the least squares method is used to fit the data, obtaining the fitting equation of the track segment and the fitting parameters of the fitting equation; among them, the fitting parameters for the straight line segment include the slope and intercept of the straight line; the fitting parameters for the circular curve include the radius and center of the circular curve. Step 3: Based on the fitting equation and fitting parameters of the track segment whose linear shape is a straight line segment or a circular curve, the inverse algorithm is used to determine the fitting parameters of the transition curve. The fitting parameters of the transition curve include the transition curve offset, the transition curve turning angle, the circular curve inward displacement, and the transition curve length. Step 4: Based on the fitting equations of each track segment, calculate the intersection points and determine the segmentation points, which include straight-to-straight points, transition-to-straight points, transition-to-round points, and round-to-straight points. Step 5: If the current iteration count is greater than the maximum iteration count, exit the iteration process and proceed to Step 7; if the current iteration count is less than or equal to the maximum iteration count, proceed to Step 6. Step 6: Calculate the distance difference between the coordinates of the segment point in the current iteration and the coordinates of the segment point in the previous iteration; if the distance difference is less than or equal to the distance threshold, proceed to Step 7; if the distance difference is greater than the distance threshold, repeat Steps 2 to 6 until the iteration process is exited. Step 7: Output the fitting equations and segmentation points for each orbital segment in the current iteration process.

5. The railway line horizontal alignment optimization method according to claim 4, characterized in that, For any track segment whose alignment is a straight line or a circular curve, based on the coordinate data of each point in the track segment and the fitting formula for the corresponding alignment, the least squares method is used to perform data fitting to obtain the fitting equation of the track segment and the fitting parameters of the fitting equation, including: Based on the coordinate data of each point in the track segment and the fitting formula of the corresponding line shape of the track segment, a first function is constructed. The first function takes the sum of the squares of the distances from each point to the fitted line segment of the track segment as the dependent variable and the fitting parameters as the independent variables. Based on the coordinate data of each point in the track segment, with the goal of minimizing the function value of the first function, the fitting parameters of the fitting equation for the track segment are obtained. Based on the fitting parameters and fitting formula of the fitting equation for this orbital segment, the fitting equation for this orbital segment is determined.

6. The railway line horizontal alignment optimization method according to claim 1, characterized in that, Based on the fitting equations and segmentation points of each track segment, the track alignment amount is calculated for each track segment to obtain the plane optimization scheme for each track segment, including: For track segments with straight lines or circular curves, the track adjustment amount at each point is calculated based on the fitting equation of each track segment and the coordinate data of each point in each track segment. Based on the value of the track alignment at each point, determine the adjustment direction at each point; Based on the track shift amount and adjustment direction at each point, determine the planar optimization scheme for each track segment; For any track segment whose linear shape is a transition curve, the actual coordinates and theoretical coordinates of each point in the track segment are determined based on the coordinate data of each point in the track segment and the fitting equation of the track segment. Based on the theoretical coordinates of each point in the track segment and the fitting equation of the track segment, the theoretical coordinates of the adjacent points of each point are determined; Based on the actual and theoretical coordinates of each point, as well as the theoretical coordinates of each point's adjacent points, determine the adjustment direction for each point; Based on the actual and theoretical coordinates of each point, the adjustment direction of each point, and the fitting equation of the track segment, the slewing amount of each point is determined; Based on the track shift amount and adjustment direction at each point in the track segment, the planar optimization scheme for the track segment is determined.

7. The railway line horizontal alignment optimization method according to claim 6, characterized in that, The process of determining the adjustment direction for each point based on its actual and theoretical coordinates, as well as the theoretical coordinates of its adjacent points, includes: For any point, take the theoretical coordinates of the point above it as the starting point and the theoretical coordinates of the point as the ending point to determine the first vector; The second vector is determined by taking the theoretical coordinates of the point above it as the starting point and the actual coordinates of the point as the ending point. The third vector is determined by taking the theoretical coordinates of the point as the starting point and the theoretical coordinates of the next point as the ending point. The first cross product is obtained by cross-product of the first vector and the second vector; The cross product of the third vector and the second vector is obtained as the second cross product; If the first cross product is positive and the second cross product is positive, then the measured point is determined to be located to the right of the theoretical linear direction of advancement, and the adjustment direction is to the left. If the first cross product is negative and the second cross product is negative, then the measured point is determined to be located to the left of the theoretical linear direction of advancement, and the adjustment direction is to the right. If the first cross product is zero and the second cross product is zero, then the point is determined to be on the theoretical line shape and no adjustment is needed. The theoretical linear shape is the curve determined by the fitting equation of the trajectory segment whose linear shape is a transition curve.

8. The railway line horizontal alignment optimization method according to any one of claims 1 to 7, characterized in that, Before calculating the track alignment amount for each track segment based on the fitting equations and segmentation points of each track segment to obtain the plane optimization scheme for each track segment, the following steps are also included: Based on the fitting parameters of each orbital segment and the preset standard threshold, determine whether the fitting equation of each orbital segment meets the standard requirements. For any track segment, if the fitting equation of the track segment meets the specification requirements, then the fitting equation of the track segment is determined to be the optimal linear equation, and the fitting equation of the track segment is kept unchanged. If the fitting equation for a track segment does not meet the specification requirements, the fitting equation for the track segment is optimized based on a preset specification threshold to obtain the optimal linear equation, and the optimal linear equation is determined as the fitting equation for the track segment.

9. The railway line horizontal alignment optimization method according to claim 8, characterized in that, The process of optimizing the fitting equation for the orbital segment based on a preset standard threshold to obtain the optimal linear equation includes: Based on the preset standard threshold and the fitting equations of each orbital segment, multiple parameter combinations are determined. Each parameter combination includes a set of fitting parameters of the fitting equations of each orbital segment. Based on multiple parameter combinations, iterative calculations are performed to obtain the parameter combination that minimizes the overall lane shifting amount; The optimal alignment equation for each track segment is determined based on the parameter combination that minimizes the overall track alignment amount.

10. A railway line plan optimization device, characterized in that, include: The communication module is used to acquire the coordinate data of various points on the railway track to be optimized; The processing module is used to calculate the approximate curvature of each point based on the coordinate data of each point on the railway track to be optimized; Based on the approximate curvature of each point, the alignment of the railway track to be optimized is initially segmented to obtain track segments with various alignments, including straight sections, circular curves, and transition curves. Based on the coordinate data of each point and the fitting formulas for various alignments, planar data fitting and secondary segmentation are performed on each pair of track segments to obtain the fitting equations and segmentation points of each track segment. Based on the fitting equations and segmentation points of each track segment, the track shifting amount is calculated for each track segment to obtain the planar optimization scheme for each track segment, which includes the track shifting amount at each point in each track segment.

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